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An experimental investigation of the aerodynamic interaction of yacht sails

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Title:
An experimental investigation of the aerodynamic interaction of yacht sails
Creator:
Ladesic, James G., 1946-
Publication Date:
Language:
English
Physical Description:
xv, 141 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Boats ( jstor )
Planforms ( jstor )
Sails ( jstor )
Sloops ( jstor )
Turbulence ( jstor )
Velocity ( jstor )
Wind tunnel models ( jstor )
Wind tunnels ( jstor )
Wind velocity ( jstor )
Yachts ( jstor )
Sails -- Aerodynamics ( lcsh )
Yachting ( lcsh )
Yachts ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1983.
Bibliography:
Includes bibliographical references (leaves 137-139).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by James G. Ladesic.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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000365837 ( ALEPH )
ACA4659 ( NOTIS )
09902929 ( OCLC )

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AN EXPERIMENTAL INVESTIGATION OF THE
AERODYNAMIC INTERACTION OF YACHT SAILS












BY

JAMES G. LADESIC


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1983


























Copyright 1983
by
James G. Ladesic
















To Marlene, my loving wife,
for all, the time and things in life
she sacrificed .











ACKNOWLEDGEMENTS


I extend my heartfelt thanks to all those who

supported and assisted in the work represented by this

dissertation: to Embry-Riddle Aeronautical University

for the use of their facilities during the test phase;

to Dr. Howard D. Curtis, my department chairman at

Embry-Riddle, for his considerate support during this

lengthy activity; to Mr. Glen P. Greiner, Associate

Instructor, for his assistance early on in the equipment

development phase, especially for his help with the

planetary boundary layer synthesis; to Mr. Don Bouvier

for his expert help with advice on hardware fabrication;

to Professor Charles N. Eastlake for his insight on wind

tunnel testing techniques and to all of my student

assistants for their aid during the data collection

phase. Finally, I extend special thanks to my committee

chairman, Dr. Richard K. Irey, of University of Florida.

His love for sailing and his insistence on excellence has

left me with a lasting impression which I shall demon-

strate in all my future work.











TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS..................................... iv

LIST OF TABLES........................................ vii

LIST OF FIGURES ............................... ....... viii

KEY TO SYMBOLS.................................... .... x

ABSTRACT............................................. xiv

CHAPTER


INTRODUCTION AND GENERAL EXPERIMENTAL
APPROACH................................. ...

Introduction. ................................
Experimental Motivation......................
Experimental Method.........................

EXPERIMENTAL SIMILITUDE FOR THE SAILING
YACHT.......................................

General Problem of Complete Yacht
Similitude................................
Sail Test Similitude........................

YACHT AERODYNAMIC FORCES AND THEIR
MEASUREMENT.................................

Resolution of Aerodynamic Forces and
Moments ..................................
Common Measurement Methods..................

OTHER EQUIPMENT AND APPARATUS...............

The Wind Tunnel..............................
Data Collection and Reduction...............

SYNTHESIS OF THE ONSET VELOCITY PROFILE.....

Motivation and Basic Approach...............
The Model Atmospheric PBL and Scale
Effects. .................................
Profile Synthesis............................

v


ONE


TWO







THREE







FOUR




FIVE







Page

SIX YACHT MODEL DESIGN.......................... 35

Planform Geometry........................... 35
Model Geometry and Trim Adjustments........ 42
Sail Construction.......................... 45
Sail Trim, Setting and Measurements........ 48

SEVEN COMMON EXPERIMENTAL PROCEDURE.............. 50

Sail Trim Pre-test ......................... 50
Wind Tunnel Test............................ 51

EIGHT MODEL CONFIGURATION TEST RESULTS........... 54

The Finn-Type Sail Test.................... 54
Variable Jibsail Hoist Series.............. 66
High Aspect Ratio Series................... 67

NINE EXPERIMENTAL AND THEORETICAL COMPARISONS... 82

The Influence of the Simulated Planetary
Boundary Layer.......................... 82
Comparisons of Potential Flow Models
and Wind Tunnel Results................. 84

TEN CONCLUSIONS AND RECOMMENDATIONS............ 95

Wind Tunnel Test Conclusions............... 95
Recommendations............................ 96

APPENDICES

A SAIL TWIST AS RELATED TO THE APPARENT WIND
AND THE INDUCED FLOW FIELD................. 98

B AERODYNAMIC FORCES AND THE CENTER OF EFFORT 104

C AERODYNAMIC FORCE MEASUREMENT.............. 110

D WIND TUNNEL DATA REDUCTION COMPUTER PROGRAM
"BOAT" ................ ...................... 121

E BOUNDARY LAYER SYNTHESIS................... 126

F CENTER OF EFFORT BY DIRECT INTEGRATION..... 133

LIST OF REFERENCES...................................... 137

BIOGRAPHICAL SKETCH..................................... 140












LIST OF TABLES


Table Page

3-1 Experimental Force and Moment Coefficient
Maximum Uncertainties...................... 22

4-1 Typical Output Format from "BOAT"........... 28

6-1 Planform Geometries....................... 40

7-1 Mean Sail Shape and Trim Parameters........ 52

9-1 Rig Configuration Test and Theoretical
Results.................................... 88

9-2 Finn-Type Sail Results from Experiment and
Theory ...................... ................. 90

9-3 Masthead Sloop (Tl5MH1) for Various 8,
Experiment vs. Theory...................... 91


vii










LIST OF FIGURES


Figure Page

2-1 Coordinate Systems and Basic Dimensions... 10

4-1 ERAU Subsonic Wind Tunnel General
Arrangement............................... 24

6-1 Sail Geometry Nomenclature................ 36

6-2 Lift Coefficient vs. Angle of Attack for a
Thin, Single Cambered Section as Measured
by Milgram (ref. CR1767) for Three
Reynolds Numbers and as Predicted by Thin
Airfoil Theory............................ 41

6-3 Wind Tunnel Yacht Model Configurations.... 43

6-4 Sail Surface Description................. 47

6-5 Typical Sail Camber Lines, Draft and Twist
Measurement Locations..................... 49

8-1 Finn Sail Yarn Observations............... 57

8-2 Finn Sail Upwash Observation.............. 57

8-3 Effect of the Planetary Boundary Layer on
Sail Test Data........................... 59

8-4 Finn Moment Coefficients with and without
the Planetary Boundary Layer.............. 61

8-5 Finn Sail Center of Effort Location....... 64

8-6 Masthead Sloop Test Results.............. 68

8-7 Masthead Sloop Polars..................... 69

8-8 Test Results, 7/8 Sloop................... 70

8-9 Polars, 7/8 Sloop.......................... 71

8-10 Test Results, 3/4 Sloop................... 72

8-11 Polars, 3/4 Sloop.......................... 73

8-12 Test Results, 1/2 Sloop.................... 74
viii







Figure Page

8-13 Polars, 1/2 Sloop........................... 75

8-14 Catboat Test Results....................... 76

8-15 Catboat Polars.............................. 77

8-16 Masthead Sloop, High Aspect Ratio Main and
Jib, Test Results........................... 78

8-17 Masthead Sloop, High Aspect Ratio Main and
Jib, Polars................................. 79

8-18 Masthead Sloop, High Aspect Ratio Jib and
Standard Main, Test Results................ 80

8-19 Masthead Sloop, High Aspect Ratio Jib,
Polars..................................... 81

9-1 Masthead Sloop Theoretical C C CFWD and
C /C vs. Test Results............. ...... 85
y x
9-2 Masthead Sloop Theoretical Polar vs. Test
Polars..................................... 86

9-3 L/D Ratios From Theory and Test. .......... 93

A-1 Typical Wind Triangle for the Sailing Yacht 99

C-l Six-component Floating Beam Force Balance
In Schematic.... ......................... 115

E-l Correlation of Screen Impedance with the
Resultant Downstream Velocity Distribution. 127

E-2 Yarn Spacing and the Resultant Flow
Impedance Distribution..................... 127

E-3 Dimensionless Velocity Ratios (Measured and
Desired) and Turbulence Intensity
Distributions (10T) ........................ 131











KEY TO SYMBOLS


AA BB numerical solutions to the Glauert and image
n n integral equations

A.. direction cosine coefficient matrix

A Fourier coefficients
n
AR aspect ratio

BAD boom above deck distance

B.. general constant coefficient matrix
13
C force or moment coefficient

CpF planform chord length

E mainsail foot length

F() generalized force vector

F( magnitude of the force vector components

FBA free board area

FRF fractional rig factor

H height of the mast above the water plane

I jib span

I(z) flow impedance distribution function

J fore-triangle base length

K von Karman's constant

K. any generalized constant
1
L/D lift to drag ratio

LOA length overall

LP luff perpendicular

Lt non-dimensional turbulence scale parameter







M( generalized moment vector

M() magnitudes of the moment vector components

OR overlap ratio

P mainsail span

PBL planetary boundary layer

R. force balance strain gauge resistance reading

R Reynolds number

SA total planform sail area

T. local applied sail traction
1
UA apparent wind speed

UB boat speed

UT true wind speed

U (z) true wind velocity profile

U30 apparent/true wind speed at 30 feet

W() uncertainty weighting factor

x' yacht rig parameter group

a,b general constants

c chord length, straight line distance from
luff to leech

d depth of draft (%)

e exponential base

e. 3-space unit vectors
1
F. force vector

h reference distance from water plane to the
force balance

1H geometric scale factor

n reference length of the force balance







s surface area

u* friction velocity

u'v' Reynolds stress

u', v' turbulent fluctuating velocities

w uncertainty

w(z) downwash velocity

x sail shape and trim parameter group
s
x,y,z orthogonal coordinate system

a angle of attack

8 apparent wind angle

Y true wind angle

6 sail trim angle

Eijk permutation symbol

Si position vector

C() magnitude of the position vector components

A leeway angle

A sail geometry polar coordinate

v kinematic viscosity

p density

T shear stress

6 heel angle

turbulence scale correlation coefficient

sail twist

R Prandtl mixing length


xii








Subscripts

A,B,C,...

F

HL

J

M

MOD

PF

PROT

i,j,k,l...

x,y,z

mx,my,mz


force balance channel indicators

fore-triangle

heel

jibsail

mainsail

model

planform

prototype

coordinate indices or counters

3-space reference coordinates

moment subscripts


xiii












Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


AN EXPERIMENTAL INVESTIGATION OF THE
AERODYNAMIC INTERACTION OF YACHT SAILS

By

James G. Ladesic

Chairman: Dr. Richard K. Irey
Major Department: Mechanical Engineering

Steady flow wind tunnel test results of sail planforms

and rig configurations for typical sloops and catboats are

presented. Tests were conducted in the subsonic wind

tunnel at Embry-Riddle Aeronautical University, Daytona

Beach, Florida, from September, 1981, through August, 1982.

Force and moment data were collected using a special pur-

pose six-component force balance. Test generated force and

moment coefficient uncertainties are reported for all tests

with a maximum uncertainty for lift as 4.3%, for drag as

6.0% and for the moments as 6.1%. Test results are given

for the entire yacht. Estimates of the forces and moments

attributable to the sails alone are calculated by subtract-

ing data of hull and rig tested without sails from the

total rig data.

The one-design Finn dinghy planform was used to assess

the effect of onset velocity profile distribution. A


xiv







logarithmic distribution of velocity, modeled after the

planetary boundary layer (PBL) typical over water, decreased

the net lift and drag coefficients approximately 28% com-

pared with those determined for a uniform onset velocity

distribution. The net sail force center with the PBL was

30% farther above the water plane than that with a uniform

onset flow.

The sloop configuration was used to assess the effect

of jib hoist. Results are compared to theoretically derived

lift and drag coefficients. Good agreement was obtained for

lift at attack angles less than 350, the stall angle. Theore-

tical drag estimates are underpredicted but agree in trend.

Drive force coefficients from the tests have been found to

be more realistic relative to current sailing wisdom and

suggest that the omission of pressure, viscous,and boundary

layer interference drag in the analytical models is significant.

Further experimental research is needed to assess the

effects of Reynolds number. Force center movement relative

to sail trim, especially for the close reach and beat, also

requires further investigation. Continued effort towards

empirical stall prediction is called for. Finally, full or

fractional size on-the-water tests are suggested to advance

both sail and yacht design.


xv












CHAPTER ONE
INTRODUCTION AND GENERAL
EXPERIMENTAL APPROACH


Introduction

Sail design and fabrication have relied heavily on the

talent of the naval architect and sailmaker (1). Effective

sail production has been the result of an individual sail-

maker's intuitive understanding of fluid dynamics, his knowl-

edge of prevailing weather conditions for the locality of in-

tended use and his adroitness in developing complicated three-

dimensional surfaces from two-dimensional patterns (2). In

recent times, state-of-the-art sailmaking has gone through a

renaissance with the application of mathematics and digital

computers to the geometric aspect of this transformation task

(3). As a result, the accuracy and speed of sail shape develop-

ment has been significantly improved allowing the sailmaker to

market his products as "computer designed". The computer has

also been applied to the more complex task of sail aerodynamics

with limited success.

Computer-aided applications of lifting line and vortex

lattice flow models provide a theoretical link between desired

pressure distributions and the related surface geometry (4, 5,

6, 7). Recent computerized application of the vortex lattice

approach by Register (7) has extended this model in two re-

spects: it includes a logarithmic non-uniform onset velocity

1








patterned after that expected over open water; in addition,

no linearizing assumptions are made with respect to sail

shape or wake geometry. The latter is particularly signifi-

cant with respect to modelling the strongly interacting sails

of the sloop rig.

While application of the potential flow concept shows

great promise, it must be understood that such analyses are

applicable only for angles of attack less than that of the

sail stall point. Superficially this encompasses the beat,

close reach and beam reach headings. However even at these

headings performance is determined by the ability to maintain

maximum sail lift without incurring large scale separation.

As such, identification of the stall point and determination

of lift and drag coefficients in the vicinity of the stall

point are a necessary part of a comprehensive sail study. In

this range potential flow theory does not provide useful infor-

mation. Furthermore, applications of lifting line and vortex

lattice theories to the sail have in some instances predicted

results that are contrary to accepted sailing beliefs. As a

result, controversy shrouds the credibility, practicality and

usefulness of predictions made by these analytical methods

for sails.


Experimental Motivation

Motivation for research is usually coupled with national

security and/or commercial enterprise. Admittedly, sail

research has almost no application to the former and the

association with the latter is on a rather small financial








scale. As such, experimental efforts have been infrequent.

What has been done has often been the guarded property of

the designer, naval architect or sailmaker. In the public

domain one rarely finds reference to specific documentation.

The most dedicated group for altruistic experimental

sail research has been that of Marchaj (8) and Tanner (9)

at the University of Southampton. Much of this work has

been undertaken in a large low-speed wind tunnel using fabric

model sails. No apparent attempt has been made to develop an

onset velocity gradient and tests have been run at Reynolds

numbers based primarily on distortion and shape control

rather than model similitude. The results reported are

significant from a qualitative point of view. However, they

have limited quantitative applicability because experimental

uncertainties are unreported. Many of the tests are performed

for specific yacht or planform configurations and thus are

not applicable to a wide range of yachts or configurations in

general.

Milgram (10, 11) has provided general, normalized, two-

dimensional sail coefficients with and without mast effects

at appropriate Reynolds numbers. (His experimental uncertainty

is also unreported.) Methods for applying such two-dimensional

sail data to a three-dimensional sail configuration for forces

and moments are, at present, unclear in that no corrections for

such factors as aspect ratio and sail geometry variations are

provided. Milgram proposes a scheme for estimating three-

dimensional pressure and viscous drag effects from two-

dimensional data but admits the need for experimental








verification of the method. Such techniques do exist for air-

foil sections and wings (12) but whether they apply directly

to the sailboat has not been established. In short, experi-

mental sail characteristics that can be readily employed to

verify analytical results are necessary to further the advance-

ment of sail aerodynamic research.

One fact agreed upon by both proponents and opponents of

the analytical approach is the need for experimental research.

Such research would not only quantify the performance of the

sails tested, they would also complement the theoretical efforts

by validating their range of applicability. For the sloop

rigged vessel (jib and mainsail), the aerodynamic interaction

associated with the close proximity of the headsail and main-

sail has not been fully explored. Specifically, how performance

is affected by the amount of jibsail overlap and the percentage

of jib hoist has not been reported. Nor has the effect of

non-uniform onset velocity. These topics are principal ob-

jectives of this research. How this experimental information

compares with analytical results is also of keen interest.


Experimental Method

Measurements are made in a low-speed subsonic wind tunnel

into which a flow impedance distribution can be introduced to

model the nonlinear onset velocity profile at a scale compat-

ible with the yacht model. All sails are cylindrical surfaces.

Such shapes are easy to characterize geometrically, but they

do not match the shapes offered by present day sailmaking








technology. Sails are constructed from aluminum sheets which

are cut and rolled to shape. Once fastened to the yacht

model's standing rigging, the built-in shapes are maintained

throughout the tests. Yacht rig configurations tested fall

into three categories: a cat rigged, Finn-type sail which is

tested without a hull model in order to assess the influence

that onset velocity profile has on the sail force magnitude

and its location relative to the water reference plane; a

variable hoist series, hull present, in which the headsail

hoist is decreased at a constant main sail size; and a rig

aspect ratio series, hull present, for the masthead sloop.

Tests are conducted at velocities that model a 4 to 6 kt

true wind speed at the masthead. All data are corrected for

wall effects, solid blocking and wake blocking. Each datum

point displayed is presented with its estimated experimental

uncertainty. Some salient aspects of sail testing and theo-

retical extension into very low Reynolds number regimes are

discussed.

In the present effort, three-dimensional sails are em-

ployed to assess the effects of trim and rig under steady flow

conditions. These trends are compared to the vortex lattice

analysis completed by Register for identical configurations

and trim and to the vortex line model developed earlier by

Milgram for similar rig configurations and trim.












CHAPTER TWO
EXPERIMENTAL SIMILITUDE FOR
THE SAILING YACHT


General Problem of Complete Yacht Similitude

Experimental efforts in yacht testing are classically

divided at the air-water interface. That is the hydro-

dynamics of the hull are evaluated independently of the aero-

dynamics of the sails. This division is convenient in that

it permits a reduction in the number of parameters required

for model similarity but it cannot assess interactive effects

that are a consequence of the air-water interface. As such,

hull hydrodynamic results must be partnered with sail aero-

dynamic results on the basis of assumed interface conditions.

It has not been practical to attain complete experimental

similitude in either sail aerodynamics or hull hydrodynamics

(13, 14). It is standard practice for these methods to de-

part from strict compliance with similarity laws. For con-

venience the inference is often made that sail theory is

an extension of the body of literature developed for aircraft

wings. As such, differences in the governing parameters are

sometimes assumed trivial and design parameters are deduced

from existing airfoil data, such as that collected in Abbott

and von Doenhoff (12). However, applications of such data

even to the single cambered, flexible sail must be done with








caution as significant differences between the two exist.

As differentiated from the rigid aircraft wing, cloth

sails are normally highly loaded and generally have large

geometrical twist. In addition, the criterion for optimum

sail performance must be related to the projections of

lift and drag to the vessel's center line that resolve into

the driving force; whereas wing optimum performance is

governed primarily by lift alone. Also, the sail is sub-

ject to a non-uniform onset velocity resulting from the

atmospheric boundary layer; while in contrast, the air-

craft wing moves through an air mass that is to the first

order stationary. As a consequence of these effects, the

variation of lift with attack angle cannot be considered a

constant for sails, whereas this is a typical assumption

in wing design. In addition, tests for aircraft are usually

conducted at Reynolds numbers much larger than those en-

countered on yacht sails. These differences clearly justify

a treatise on sail test similitude based on the pertinent

variables and conditions that are unique to the sailing

yacht.

For the work presented herein, the hydrodynamic effects

of the hull are ignored. The scaled true wind magnitude is

determined by the available wind tunnel capacity for the

model size selected, with the profile impedance screen in

place. This wind speed is equivalent (based on Reynolds

number) to prototype on-the-water wind speed of 4 to 6 kt.








As such, heel effects for the yacht being modeled can be

ignored and an assumption of no wave-air interaction is

reasonable. Thus, it is not necessary to model motions

that would result from a wind driven sea state.

A major discrepancy between this work and on the water

conditions is that the onset flow has zero twist which, in

turn, implies the assumption of zero boat speed. This limi-

tation is a practical necessity in wind tunnel testing. To

model the effect of boat speed, one could either move the

model at constant speed in a direction oblique to the tunnel

flow during data collection or modify the wind tunnel air-

flow in both direction and magnitude with the yacht model

stationary. Either procedure could simulate the vectorial

addition of boat speed and true wind speed. The former would

require a suitably wide tunnel test section and would intro-

duce uncertainties associated with model inertial response.

The latter concept would complicate the synthesis of the onset

velocity profile. For present purposes, the added complexity

of either procedure is unwarranted in terms of what it would

contribute to the results. Therefore, the distortion of re-

sults that are a consequence of zero boat speed are accepted.

The effect of this distortion on the overall test results is

assessed in Appendix A; it is shown to be small.

Finally, the apparent heading (B-X) of a yacht sailing

to weather is different from the true heading measured re-

lative to the apparent wind by the angle X. This small dif-

ference is measured from the yacht center line and is referred








to as the leeway angle. This angle is the effective angle

of incidence for the keel. While X is small (on the order

of 4 degrees), it is necessary for the development of the

keel reaction to the sail-produced heel force. Consequently,

the desired component resolution of the aerodynamic sail

forces are taken parallel and perpendicular to a plane

passed vertically through the yacht and rotated X from the

yacht center line. Since the hydrodynamic properties of the

hull and keel are unknown and, therefore, ignored in the pre-

sent work, the aerodynamic sail forces are resolved parallel

and perpendicular to the boat center line. This is equiva-

lent to assuming A = 0. It is seen from Figure 2-1 that this

assumption will slightly decrease the component of lift and

increase the component of drag in the selected driving force

direction and is therefore conservative with respect to the

net predicted driving force.


Sail Test Similitude

Dimensionless variables can be formulated by applica-

tion of Buckingham's Pi Theorem (15). This is the approach

adopted here. For the sailing yacht, forces and moments of

interest are resolved with respect to the wind tunnel flow

direction. Figure 2-1 illustrates the Cartesian coordinate

frame selected for this purpose. From the assumption that

X = 0, the force coefficient is then defined functionally as


F UT(z) UB UT UC --
2__ CF[ X',xS Lt,lH
2 CF[,e, U (z ) U U V 'S t H
pUA(SA) UT(MAX A UA
(2-la)










Lift
C






Boat ]
Heading? _


CIIL


e"x

Drag ea(
Cx



Mi Boat Center
mz Line



Note: Force coefficients shown are
resolved about an arbtirary
point.


Masthead Level


FIGURE 2-1 Coordinate System And Basic Dimensions







Where the non-dimensional arguments of this function are

defined as


8 = heading angle from the apparent wind to the
boat center line

8 = heel angle

U (z)/U (zMAX) = onset velocity profile normalized
for zM at the masthead
MAX

U /UA = boat to apparent wind speed ratio

UT/UA = true to apparent wind speed ratio
UAc/v = inertial to viscous force ratio (Reynolds
number, Re)

X' = rig parameters such as (cat, sloop, cutter, or
ketch), vertical or raked masts), (standing rig-
ging area to sail area), (free board area to sail
area), (rig aspect ratio H2/2SA), (etc.)
I
x = sail shape and trim parameters such as draft,
draft position, foot curve, roach curve, sail
dimension ratios (I/P, J/E ,.. ), trim angles
(6M,6 ), twist parameters (J ,4M), etc.

Lt = dimensionless scale of turbulent

1H = the geometric scale factor.


It is evident from Figure 2-1 that a smaller yacht "sees"

a lower portion of the profile shown. Thus, scale similarity

is dependent on the mast height (H) relative to the onset

velocity function U(z). Writing the relation between homo-

logous model (MOD) and prototype (PROT) dimensions defines

the geometric scale factor or


1 PROT
H HMOD








Application of the conditions of negligible leeway, zero

heel, and zero boat speed yields

U UT
6=0, = 0 and 1
A A


For the test results reported, the same sloop hull model with

standing rigging is used except for those in which the sail

is tested without a hull model. Therefore, in comparing one

set of test results with another among the rig parameter

variable group (X') the most significant variables are the

rig aspect ratio (H /2SA) and freeboard to sail area ratio

(FBA/SA). Only these will be reported.

Of all the sail shape and trim parameters (xs) only
s
those that are related to the overall planform shape and

the sail trim adjustments furnished on the yacht model are

reported. Sail parameters such as the foot and roach curves

are proportional for each model and therefore are not listed.

Similarly, the draft positions for cylindrical sails are

constant and are located at the 50% chord point. As such,

they are not parametrically varied and, therefore, are not

reported. The sail shape and trim parameter group can then

be written as


xs = xs'(I/P, P/E, J/E 6, 6M' J' M' dj, dM)


and equation 2-la becomes


2 FBA -
C = C (8, R H /2SA, SA ', Lt' 1 ) (2-1b)
F F eS s t H








Free stream turbulence is known to effect both laminar

to turbulent transition and separation of the boundary layer

attached to a lifting surface. Increased free stream turbu-

lence normally results in increased drag and decreased lift.

This phenomenon is an interactive one, it is thought to be a

function of the scale of the free stream turbulence relative

to the scale of the lifting surface turbulent shear layer

(16, 17). Specifically, evidence suggests that if the free

stream scale is large relative to that of the shear layer,

the interaction is negligible. Referring to yacht sails,

the free turbulence scale of the majority of the atmosphere

is large; however, the scale of the lower regions of the air-

water interface boundary layer is small. The actual and

tunnel simulated velocity profiles are of classical logarith-

mic form. The portion of that boundary layer normally inci-

dent on the sails is generally within the "overlap layer"

(18). In this region the scale of turbulence is proportional

to elevation, z.

Investigation within the atmospheric boundary layer over

open water by Ruggles (19) and later Groscup (20)included

measurements of the Reynolds stress. Groscup (20)gives a

value for the planetary boundary layer Reyonolds stress per

unit density of 0.328 ft2/s2 at a height near that of the

prototype yacht midchord. This Reynolds stress was measured

in a true wind velocity of 4 to 8 kt at a 30 ft elevation.

This is compatible with the conditions of interest here. To

compare this to the sail boundary layer, assume it to the that




14



of an equivalent flat plate so that a convenient length

scale for comparison is the Prandtl mixing length ().

Then using the one seventh power velocity distribution

for the sail boundary layer, one can estimate that the max-

imum mixing length for the sails is about 0.2 in. at the

trailing edge. A similar mixing length calculation, made

for the planetary boundary layer, incorporating the measured

Reynolds stress provided by Groscup gives a mixing length

of about 30 in. Defining the prototype dimensionless para-

meter (Lt) for turbulence scale as


PBL
Lt (2-2)
SAIL


gives for the velocity range of interest here Lt = 150.

This suggests two orders of magnitude difference between

the two scales. The preceding estimates refer to actual

sailing conditions of a prototype yacht. If this were also

the case for the model sail in the simulated wind tunnel

boundary layer, then Lt could be eliminated from the perti-

nent governing parameters.

Turbulent intensity rather than Reynolds stress was

experimentally measured in the wind tunnel. Thus to eval-

uate the same ratio, the Reynolds stress must be inferred

from the turbulence intensity measurement. The correlation

coefficient is defined by


u'v'
u = (2-3)
rrsrr








As suggested by Schlichting (16), it is taken as 0.45 in

the overlap layer, and the lateral perturbation velocity

v' is assumed directly proportional to u consistent

with the experiments performed by Reichardt (16). Given a

measurement of 4 for the mean velocity profile, one can

evaluate the Reynolds stress using equation 2-3 with the

above assumption and approximate the mixing length as



(BL)m = u'v (2-4)
PBL m ;u/az

where au/3z can be found directly from the measured mean

velocity profile at an appropriate height (z), taken here

as the height of the planform geometric chord. Equation

2-4 gives a model mixing length (PBL)m of about 2.0 in.

at U30 = 80 ft/s. The sail model shear layer is considered

in the same manner as the prototype; this yields a sail

model mixing length ( SAIL)m of 0.02 in. The dimensionless

turbulence scale for the model (Lt)m is thus estimated to

be about 100. This is sufficient to allow turbulent inter-

actions to be ignored. As a result, equation 2-1b simpli-

fies to


H FBA
C = C (H, R H', 1 ) (2-5)
F F e' 2SA' SA x 1H)


The three-dimensional moments may also be written in

coefficient form similar to equation 2-la or







2
M = C (8, Re, A A x' 1H) (2-6)
PU2 SA Cp m 2SA 'SA s H
pU SA C
A PF


where CpF is the planform geometric chord. The moment co-

efficients represented by equation 2-6 are subject to the

same dimensionless groups as those of equation 2-5.

For the experiments reported here, UA is taken as the

wind speed measured at the masthead of the model and the

three principal force coefficients (reference Figure 2-1)

are


*C -- drag, parallel to and positive in the
direction of the apparent wind

*C -- lift, perpendicular to the apparent
Y wind and to the mast

*C -- heave, parallel to the mast and
z mutually perpendicular to C and C
x y


The corresponding moments C C and C represent moments
mx my mz
about the same xyz coordinate system. Referring once more

to Figure 2-1, the forward and side (heel) force coefficients

relative to the boat center line are then defined respec-

tively (for X=0) as



CFWD = C sin (8) C cos (8) (2-7a-)
FWD = x

CHL = C cos (8) = C sin (8) (2-7b)



Equations 2-7 will be used in later discussions regarding

potential yacht performance.








Finally, only one size yacht model is correct rela-

tive to the fixed onset velocity distribution [UMOD(2)]

used here. However, slight extensions of the scale

factor (1H) may be assumed without appreciable error. For

example, to represent a 30 ft prototype mast height while

maintaining the same velocity distribution, the scale fac-

tor would increase to approximately 13. Conversely, for a

26 ft prototype mast height, 1H becomes approximately 11.

Corresponding to these stretched scale factors, the esti-

mated error in the net forces is 2.0% of the nominal 28

ft prediction. The uncertainty in predicted force center

is 0.7%, while the moment uncertainty is 5.3%. The dif-

ference in average velocity that the sails would see is 1.0%.

All of these percentages are within the estimated experi-

mental uncertainty of the tests conducted. Accordingly,

the test results presented here may be considered applicable

within reported uncertainty to sailboats from 18 to approxi-

mately 26 ft LOA as a function of their mast height off the

water.












CHAPTER THREE
YACHT AERODYNAMIC FORCES
AND THEIR MEASUREMENT


Resolution of Aerodynamic Forces and Moments

In steady flow, the net aerodynamic forces and moments

experienced by the sails, rigging and above water hull of

the sailing yacht are reacted by hydrodynamic forces on the

keel, rudder and hull underbody surfaces. These aerodynamic

forces and moments are transmitted to the sails, rigging

and above water hull via nearfield airflow pressure distri-

butions and viscous boundary layer shear stresses on every

free surface exposed to the flow. From the equations for

static equilibrium three components of force and three com-

ponents of moment are needed to define the net reaction of

all the applied aerodynamic loads. Therefore, the direct

measurement of orthogonal force and moment triples at any

preselected location, on or off the yacht, would yield the

net aerodynamic reactions.

In order to assess the contribution that the aerodynamic

forces make towards the balance and stability of a yacht it

is necessary to know both the magnitude and the location of

these forces. For this purpose, the center of effort is

commonly defined as a point in space where the applied aero-

dynamic forces may be resolved so that the net aerodynamic








moment about this point is zero. Appendix B discusses, in

detail, resolution of the sail aerodynamic loads and the ex-

perimental determination of the yacht's center of effort.

In general, it is demonstrated in Appendix B that direct

measurement of forces and moments relative to an arbitrary

global origin will not uniquely yield the center of effort

location. As such, the center of effort must be known a

priori or must be estimated from some physical constraints

of the experiment.


Common Measurement Methods

The measurement of forces and moments resulting from flow

about the sailing yacht model may be accomplished by any of

three different methods:


1) Measure the pressure distribution over the
free surfaces (Equation B-2) and sum the
measurements as a function of area (Equation
B-3);

2) Survey the upstream and downstream flow for
momentum difference and evaluate the stream-
wise static pressure distribution upstream
and downstream of the model (valid for steady
flow only);

3) Measure the three orthogonal components of
force and moment via a force transducer or
balance directly.


Pope and Harper (21) discuss each of these methods in

detail relative to wind tunnel tests of aircraft. They indi-

cate that three forces (lift, drag and yaw) and their companion

moments completely describe the local spectrum of interest for

aircraft. Symmetry and aircraft design experience indicate








that the point of resolution for these forces and moments

is normally considered to be known a priori. These restric-

tions admit a unique solution for the aircraft. However, as

discussed in Appendix B, this is not the case for the sailing

yacht.

Most sails, including those tested, are thin. As a result

surface orifices for pressure measurement are impractical. Wake

survey methods are of use but require the measurement of both

static and dynamic pressure at each survey point. Hence, the

accuracy of any calculated force from such a survey is a func-

tion of the number of survey points selected. In order to

reduce the number of measurements, it is common practice to

measure only stagnation pressure at each of the survey points

and to measure the static pressure at the wind tunnel wall.

It is then assumed that this static pressure is uniform across

the section of the tunnel where the measurements are made. This

assumption is valid providing the distance downstream from the

model is sufficiently far to allow static pressure recovery.

Unfortunately, this is not often possible due to changes in

wind tunnel geometry downstream of the test section. These

can cause appreciable wall effect losses that must be accounted

for with the consequence of an increase in the level of exper-

imental uncertainty. Direct measurement with a force balance

is the simplest and most straightforward method of attaining

net force and moment data. However, as discussed above, spe-

cific details as to local force and moment distribution are not

possible.








In the present work, a six-component force balance has

been used to measure the aerodynamic response of various model

sailing yacht rig configurations. A general discussion on

six-component force balances is given in Appendix C with de-

tails of the six-component floating beam balance used here.

The net maximum uncertainty for each force and moment coeffi-

cient range discussed in Appendix C is calculated employing

the methods of Holman (22) and is given in Table 3-1. In addi-

tion to these direct measurements, the static pressure through

the wind tunnel test section was surveyed both upstream and

downstream of the model to establish correction parameters for

solid blocking and horizontal bouyancy.









TABLE 3-1
Experimental Force and
Moment Coefficient
Maximum Uncertainties


Coefficient Cx

Range 0.0 to 0.2 0.2 to 0.4 0.4 to 1.0
Uncertainty 4.3% 3.9% 3.1%


Coefficient Cy

Range 0.0 to 0.5 0.5 to 1.0 1.0 to 1.-5
Uncertainty 6.0% 4.9% 3.8%


Coefficient Cz

Range -0.4 to -0.2 -0.2 to -0.1 -0.1 to 0.0
Uncertainty 2.0% 2.1% 2.2%


Coefficient Cmx

Range -3.0 to -2.0 -2.0 to -1.0 -1.0 to 0.0
Uncertainty 4.8% 5.8% 5.9%


Coefficient Cmy

Range 0.0'to 0.2 0.2 to 0.5 0.5 to 1.5
Uncertainty 6.1% 5.8% 4.6%


Coefficient Cmz

Range -0.2 to 0.2 0.2 to 0.4 0.4 to 0.6
Uncertainty 3.1% 2.6% 2.1%












CHAPTER FOUR
EQUIPMENT AND APPARATUS


The Wind Tunnel

The most essential piece of equipment used for the tests

reported herein is the subsonic wind tunnel at Embry-Riddle

Aeronautical University, Daytona Beach, Florida. This wind

tunnel is a closed circuit, vertical, single return design

which has an enclosed, low-speed and high-speed test section.

Flow is produced by a 6-blade, fixed pitch, laminated wood

propeller, 56 in. in diameter, that is driven by a 385

horsepower, 8-cylinder internal combustion engine. Speed

control is provided by throttle and a 3-speed fluid drive

transmission. Figure 4-1 illustrates the overall dimensions,

general arrangement and location of the main features of

interest.

The operational range of the tunnel is from 0 to 190

ft/s, 0 to 96 ft/s in the low-speed and 0 to 190 ft/s in the

high-speed test sections. The low-speed test section is

octagonal, 36 in. high by 52 in. wide, with a cross-sectional
2
area of 11.5 ft To permit easy access to the model area

and force balance, the entire low-speed section is mounted

on a wheeled frame and can be removed from the tunnel proper.

The six-component floating beam balance was installed on the

under side of this test section, external to the tunnel




















































I M



>o
0 -
coq
a)O
Q)OlE)


I -~ --







interior. The rectangular high-speed test section is 24 in.
2
wide by 36 in. high with an area of 5.96 ft2. Considering

the effects of solid blocking together with the size of model

needed for reasonable scale similitude, the low-speed test

section allows the most flexibility and was used for all the

results presented.

The low-speed test section was designed with 1/2 degree

diverging walls to maintain a constant streamwise static pres-

sure through the section as the wall boundary layer thickens

in the streamwise direction. For the range of velocities of

concern here, the turbulence intensity of the mean flow is

less than 0.004 and is considered well within acceptable limits

for low-speed testing. The velocity distribution through the

test section is uniform to within 1%. This, of course, was

intentionally modified along with the turbulence intensity to

produce the model velocity profile discussed in the next

chapter.


Data Collection and Reduction

The experimental data presented were collected with the

six-component floating beam force balance discussed in Chapter

Three via a ten-channel Baldwin-Lima-Hamilton (BLH) Model 225

Switching and Balancing Unit and interpreted with a BLH Model

120C Strain Indicator. Each of the flexural elements of the

force balance was fitted with a matched pair of Micro-

Measurement EA-06-250BG-120 precision 120R gauges which were

wired as two arms of a four-arm Wheatstone bridge circuit on








the Model 225 Switching and Balancing Unit for each of the

six channels monitored. The remaining bridge circuit was com-

pleted using two precision 1200 "dummy" resistors. Strains

were read directly from the Model 120C Strain Indicator in

microinches per inch, pin./in. The backup and calibration

check unit used for the BLH system was a Vishay Instruments

BAM-1 Bridge Amplifier and Meter. System calibration checks

were made monthly to ensure that experimental accuracy was

maintained.

Flow air temperature was measured upstream of the low-

speed test section at the inlet contraction cone by a mercury

bulb thermometer probe connected to an external dial-type

indicator which reads to 10F precision. Flow velocities

were inferred from direct measurement of the local static and

dynamic pressure with a common Pitot-static tube and a 50 in.

water manometer. A Thermonetic Corporation HWA-101 hot wire

anemometer was used for backup and to augment velocity survey

measurements.

The force balance calibration equations were incorporated

into a Fortran computer program along with all the pertinent

flow relations for Reynolds number, yacht rig configuration

sail area calculation, wind tunnel solid blocking and hori-

zontal buoyancy corrections. The strain gauge resistance data

for all six strain channels at each heading angle tested were

loaded to a computer disc file. In addition, flow air tempera-

ture, the static and dynamic pressure at the masthead and the




27



rig configuration geometry were stored in this file. All

of this information was subsequently processed through the

Fortran program BOAT (a listing BOAT is given in Appendix D)

on a Hewlett Packard HP-1000 mini-computer. A sample of the

typical output information is shown in Table 4-1. The xyz-

coordinate system is global; x being in the flow direction and

z vertical while the boat coordinates of "Drive", "Heel" and

"Vertical" are those as illustrated in Figure 2-1.







TABLE 4-1
Typical Output Format
From "BOAT"
RU,BOAT
INPUT NAME OF FILE RUN DATA IS STORED IN
(UP TO SIX CHARACTERS,FIRST CHARACTER START IN COLUMN 1,
JUSTIFIED LEFT, INCLUDE TRAILING BLANKS, IF ANY)
T15MH1


WIND TUNNEL DATA REDUCTION PROGRAM





SAIL BOAT DATA INPUT


INPUT SAIL DIMENSIONS (for model) I J
25 8 22.5 9


P E (inches)


INPUT PERCENT OVERLAP, FRACTIONAL RIG FACTOR
1.5 ,1




WIND TUNNEL EXPERIMENT, DATA REDUCTION OUTPUT

TEST MODEL : SAIL BOAT

7/12/82 STD 150 SLP, W/PBL, FLOOR SEALED, STD ASPECT RATIO.


SAIL DIMENSIONS :
I = 25.00
E 9.00


8.00


P 22.50


SAIL AREA (ACTUAL) = 1.82ft**2
SAIL AREA (100 Z F.T.) = 1.40
PERCENT OVERLAP = 1.50
FRACTIONAL RIG FACTOR = 1.00


J =






TABLE 4-1 -continued


SAIL ANGLES(DEG),VELOCITY(FPS),REYNOLDS NUMBER, DYNAMIC FORCE


Delta Delta
jib main


12.0
12.0
12.0
12.0
12.0
12.0
12.0
12.0


0.'0
0.0
0.0
0,
0.0
0.0
0.0
0.0


VELOCITY

'78.41
79.36
80.06
81.35
81.50
82.01
82.34
82.71


REYNOLDS
NUMBER

402566.
407417.
411020.
417675.
418426.
421015.
422739.
424646.


FORCE AND MOMENT COEFFICIENTS RELATIVE TO


COURSE
ANGLE

8.0
15.0
20.0
25.0
30.0
35.0
40.0
46.0


Cx

.2607
.2727
.3207
.3542
.4592
.5641
.7103
.9575


Cy
.3778
.6533
.8607
1.1499
1.3206
1.4165
1.4891
1.4652


Cz

-.0427
-.0773
-.1086
-.1402
-.1672
-.1878
-.2095
-.2202


Cmx

-.0800
-.3655
-.6114
-.7936
-.9597
-1.1360
-1.0961
-1.1495


THE WIND

Cmy

.0569
.0698
.0727'
.1124
.1241
.1755
.2723
.4645


FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE BOAT


COURSE
ANGLE
8.0
15.0
20.0
25.0
30.0
35.0
40.0
46.0


DRIVE
COEF.

-.2056
-.0943
-.0070
.1649
.2626
.3503
.4130
.3887


HEEL
COEF.
.4104
.7016
.9185
1.1918
1.3733
1.4840
1.5973
1.7066


VERT.
COEF.

-.0427
-.0773
-.1086
-.1402
-.1672
-.1878
-.2095
-.2202


HEEL
MOMENT
COEF.
.0871
.3711
.5994
.7668
.8932
1.0313
1.0148
1.1327


PITCH
MOMENT
COEF.
.0675
.1620
.2774
.4373
.5873
.7953
.9132
1.1495


COURSE
ANGLE

8.0
15.0
20.0
25.0
30.0
35.0
40.0
46.0


DYNAMIC
FORCE

12.50
12.78
13.01
13.44
13.46
13.58
13.69
13.81


Cmz

.0769
.0538
.0206
-.0032
-.0430
-.0571
-.0408
-.0164


YAW
MOMENT
COEF.
.0769
.0538
.0206
-.0032
-.0430
-.0571
-.0408
-.0164











CHAPTER FIVE
SYNTHESIS OF THE ONSET
VELOCITY PROFILE


Motivation and Basic Approach

The sailing yacht is subject to a non-uniform onset

velocity resulting from the vector addition of the atmos-

pheric planetary boundary layer (PBL) and the yacht's for-

ward velocity. This summation produces what is termed the

yacht's apparent wind. The magnitude of this apparent wind

varies as a function of vertical height while its direction

tends to rotate aft from the deck to the masthead of the

yacht. Proper modeling of this boundary layer with respect

to a sail rig configuration is essential for achieving scale

similitude. Previous tests of sails and rig configurations

(8, 9, 10, 11, 13) both two- and three-dimensional, have

not used such an onset velocity. As such, conclusions re-

garding lift, drag and center of pressure could be signi-

ficantly different than with non-uniform onset.

Modeling both the variation and direction in the wind

tunnel is difficult. Modeling only magnitude variation with

respect to one geometric axis is commonplace. Well developed

methods for modifying a wind tunnel velocity profile exist

(23, 24, 25). When the size of a particular wind tunnel is

fixed in shape upstream of the test section, methods which

develop a desired velocity distribution by artificial fetch








(roughness pegs, counter jets or, simply, the length of

upstream convergent section) must be discarded. A more

direct approach in such cases is to progressively impede

the flow in the geometric direction of the desired velocity

variation. That is if


U = U(z) (5-1)


the direction of impedance (I) would also be


I = I(z) (5-2)


This simple approach implies that a desired distribution

could be synthesized by physically obstructing the flow up-

stream of the test section. In principle this is correct.

However, the level of turbulence introduced into the flow

due to the upstream obstruction(s) must be within some pre-

determined limits. Similarly, the pressure drop across the

obstruction equates to an overall reduction in tunnel operat-

ing efficiency. With these considerations in mind, a direct

impedance scheme can be planned to provide a desired velocity

distribution and a reasonable turbulence intensity in the

wind tunnel test section.


The Model Atmospheric PBL and Scale Effects

The measurement and formulation of the atmospheric

boundary layer above the ocean has been the topic of numer-

ous research efforts (19, 20, 26, 27). For modeling such

a boundary layer in the wind tunnel with respect to the








sailing yacht, only the first 100 ft, measured from the

water surface, is of interest. In this first 100 ft, often

referred to as the surface layer, the characteristics of

the actual PBL that are of significance towards such test-

ing, for steady flow, are as follows:


*The wind direction is essentially constant and
Coriolis effects may be ignored.

*The long duration vertical velocity distribution
is logarithmic in form to within a 95% certainty.

*The scale of turbulence in the PBL is large re-
lative to that of the sail boundary layer (this
is verified in Chapter Two).

*Vertical variation of stresses and other fluxes
can be neglected.

*The friction velocity (u*) can be assumed a
linear function of the wind speed rate of shear
and is defined as


u* =


where Tw is the shear stress at the boundary
(water plane) and p is the local flow density.


Neglecting convective terms, the generally agreed-upon form

of the long duration, stable surface layer PBL is


U(z) = ln( ) (5-3)
K z


where z = vertical distance above the water plane

U(z) = velocity at height z

K = von Karman Constant taken to equal 0.42

z = roughness length







From this form Kerwin (28) has developed a useful average

wind gradient formula applicable to the sailing yacht in

terms of the wind velocity at a height of 10(m) above the

water surface [U10] and the vertical position (z) for any

profile velocity as


U(z) = 0.1086 UI0 ln[304.8z(m)] (5-4)


Since equation 5-4 was that adopted by Register in his vortex

lattice scheme, it will similarly be the profile shape syn-

thesized in the wind tunnel.

As mentioned in Chapter Two, similarity requires that

a specific size yacht be determined for test that simultan-

eously sizes an explicit portion of the PBL which must be

synthesized. Converting equation 5-4 to scale (1H = 12)

yields


U(z) = 0.1086 lnz(in.) + 0.4918 (5-5)
U30


where z is measured above the wind tunnel floor. Equation

5-5 is considered the desired shape of the scale velocity

profile to be synthesized in the wind tunnel.


Profile Synthesis

The details of the direct impedance method used to syn-

thesize the velocity profile described by equation 5-5 are

given in Appendix E. The profile obtained by this method




34


fits the desired profile to a confidence of 96.5% using a

least squares logarithmic curve fitting scheme on the

measured velocity values. The turbulence intensity dis-

tribution through this synthesized profile has also been

measured and it has been found to be in reasonable agree-

ment with classical turbulent boundary layer measurements.












CHAPTER SIX
YACHT MODEL DESIGN


Planform Geometry

As discussed previously, the overall model dimensions

were selected as a function of the wind tunnel test section

size relative to the type of yacht data desired. Consis-

tent with popular sailcraft nomenclature, the primary

geometric dimensions of the sail planform are I, J, P, and

E as illustrated in Figure 2-1. The right triangle formed

by the horizontal "J" and vertical "I" dimensions is termed

the sail platform "fore-triangle". The vertices of any

foresail and the edges between these vertices are shown in

Figure 6-1. The luff perpendicular (LP) is drawn from the

luff to the clew as shown. Foresails or headsails which

exceed the fore-triangle area are named or "rated" as a

percent of "J". Ergo the 150% genoa headsail is a sail

with LP=1.5J. The region of the sail area which extends

beyond the J dimension is termed the "overlap". For the

research reported here, it is convenient to define the

overlap ratio (OR) factor where


LP
OR = L
-Y



Similarly, sloop rigs which have fore-triangles that do

not extend to the vessel masthead are termed "fractional

35
























Luff


Clew


Foot


FIGURE 6-1 Sail Geometry Nomenclature.


C- -l








rigs". To classify these geometries, one can define a

fractional rig factor (FRF)


(I)
FRF =
(P+BAD)


where (P+BAD) is the distance from the yacht deck to the

masthead and for convenience is set equal to H.

The foresail triangular area (SAF) can then be written

as


SAF =(I 2+ 2(OR)(J)


The mainsail dimensions are designated P and E, Its triangu-

lar area (SAM) is


SAM =PE.


The rig planform area used for all of the force and moment

coefficients is the sum of the foresail and mainsail area


SA = SAF + SAM


This area is slightly smaller than the actual sail area due

to the curvature or "roach" of each sail's trailing edge.

It is common practice to omit this area when defining sail

area.

Rig aspect ratio is another quantity of interest and

is somewhat more arbitrary in definition. The classical

definition of aspect ratio used in the sailing community is







defined by the particular sail being referenced. The main-

sail aspect ratio is taken as


AR ME


while the fore-triangle aspect ratio is

I
AR
J J


For the present work, it is desirable to use an aspect ratio

that adequately represents the entire rig configuration re-

flecting both mainsail and jibsail aspect ratios. For this

purpose, a rig aspect ratio is defined here (for H=P+BAD) as


(H)
AR =
2SA


It is believed that this definition is compatible with the

classical individual sail aspect ratio definitions while

satisfying the need for a single representative value for

the rig.

The mean planform chord length is taken to be


1 SAF SAM SAM
PF 2 P ]Jib PF P Main


Test Reynolds numbers for each wind tunnel test run are cal-

culated using this chord length. It is reasoned that CpF

represents a realistic average length for the evaluation of

the flow related viscous forces as opposed to other charac-

teristic lengths which could be offered. This is thought







to be significant when comparing such test results to

other wind tunnel data, either sail or airfoil, where the

Reynolds number characteristic length can easily be

ascertained.

Table 6-1 lists the planform geometry of the rigs

investigated. Comparing the mean planform chords for the

different configurations permits an interpretation of the

similitude scaling problems discussed in Chapter Two.

Indeed, if the mean planform chord provides a representa-

tive flow Reynolds number and if the effect of Reynolds

number variation on the aerodynamic performance of a rig

is strong, then results for the catboat (CPF = 4.6 in.)

compared with those of a sloop (Cp = 5.3 in.) for the

same wind velocity at the masthead, could be quite differ-

ent than at the same Reynolds number. This observation

would, in effect, make the Reynolds number a significant

design parameter and somewhat removes the regime-like con-

clusions often made for wing and airfoil theory.

There is strong evidence that both of the premises

offered above are valid. For Reynolds numbers less than 10 ,

the viscous flow effects are strong and the amount of sur-

face area exposed to the flow is increasingly important;

that is, the force coefficients produced by a thin single

cambered surface in the flow are non-linear and vary with

samll changes in Reynolds number. Figure 6-2, reproduced

here from NASA CR1767 (10), is an illustration of this


















* k

,-v ,-i


0000 00 O O O
( e N C N (N (N (N (N (N



C C C) C) C C C) CD
00 on V) u?) Ln ur t n



NO NO NO O








*. .
o o o co m o o
O L CO CO C) L LA
C O r-4i O in in
CN C14 1N C4


Cd
O -4 )
0 -< 14 < F<:


-" (d -. .-H r(d *--

1 a -
0-i U) E r- "r C- mS tr)

) > I I I I 4 I 0
0) C 1O C -4
a 4 04 ,i o 0 ra Q4 F:
C O O O O O O
r- 0 0 0 0 0 0
n cr O O O O -p O 0.
-H H- -4 -4 ,--I .-1 rd ,-- -'- -I -
I' ) U) U) LA LA) P-)


r--
0



(0 C
.-l (


O7 0) 0
. 4- U


0
U


- 4-4 r-4 -4 (N

UEmm-rd C4
U S N Cn) ,-m U z
o Ln Ln Ln LLn LAn
O r ,--4 ,-4 ,- 0 -
H EH l H EH l H


U)

i-4
.,-I
4J

I E
ED 0

C)



4-4

Cd
-4
(^


(U

0)

u

Q)

-l





4J











O
U)




4,













mo
0
















HO
1a






O







U
0

















CO
C4












O)
.C0







-A















O -



*.4 4
S0n














-a,
.U

















0 4)
U) a)









4U4
a)



Q)

P C
0 -r)


Q) 4a
C o 0



44-1 C4


Z*l


a _________________________




41








2.8
I .. ....".. ..













S -20% Change in CL for

0- .8", ARe= 53.0x105

S.. Re 6 x 105 -
I- 0
o I


tx Io.e 3 1 __ x05




Re = 1.2 x106

-0.4 .


-0.8

-24 -20 -16 -12 -8 -4 0 4 8 12 16 20

Angle of Attack (degrees)

FIGURE 6-2 Lift Coefficient vs. Angle of Attack for a Thin,
Single Cambered Section as Measured by Milgram
(ref. CR1767) for Three Reynolds Numbers and as
Predicted by Thin Airfoil Theory.








effect. For the sailor though, the point of interest is

normally the rig performance at a given wind speed. Thus,

increasing or decreasing the Reynolds number can play an

important role as a practical performance parameter.

For the results presented here, comparisons are made

for the same masthead velocity on each of the rigs tested.

Each will, therefore, be at a different Reynolds number as

a function of CPF.


Model Geometry and Trim Adjustments

The geometric scale factor (1H) is taken as 12 to per-

mit a model size that is within acceptable limits relative

to wind tunnel test section blocking requirements. This

size also provides a fair representation of actual sailboats

ranging from 18 to 25 ft LOA for the wind velocity profile

being simulated. A scale mast height above the water sur-

face of 28 ft is chosen to allow a reasonable fit with the

planform geometries previously defined. Figure 6-3 gives

the overall model and standing rigging dimensions. The

different planform geometries are also shown for clarity.

Deck size is arbitrary and is selected to permit a

reasonable arrangement of sail trim control and adjustment

devices. The standing rigging acts as the structural sup-

port for the sail and consists of upper shrouds and a

backstay. The upper shrouds are adjustable to maintain the

mast perpendicular to the deck in the athwart-ship direction

and to control the shroud tension. Backstay tension is also











































04 0 I
O 0
r t rP f1
o P,
SIN0 0
H '- 0







0 0N Q *
Zd N H
0:
Nd( r
a, k6
Wc3 kco 05
S
C's C'S


o 0
0 0
CM
Nu


S0)

*-H
ghO


43




























o



o-H

0
00)






*H







r l
S*a







0


U ->
*H












00
P *H


.0)


ADo $-


94-3
Y
3o )
ry a0
<;v







adjustable and can be used to bend the mast in the fore

and aft plane. The mast is rigidly fastened to the deck

to prevent its base from rotating about the athwart-ship

axis. No forestay is used. Instead, the metal fore-sail

head is attached directly to the mast by a threaded

fastener and the tack is connected to a through-deck adjust-

ment screw. Tensioning the luff via this screw controls the

fore and aft position of the masthead and opposes the back-

stay. In contrast to cloth sails, an increase in luff ten-

sions on the metal sail does not move the sail draft forward

and only the lower one-third to one-half of the sail draft

is adjustable by means of sheet trim and clew downhaul.

Upper section headsail draft is rolled into the sail prior

to installation on the model and can only be altered by re-

rolling. Headsail sheet trim is achieved by means of a

threaded rod adjustment device that is fastened to the deck.

When the length of the rod is reduced, it draws the sail

clew aft. This decreases the trim angle and flattens the

lower portion of the sail. Headsail leech downhaul is

attained using a second device fastened directly to the

sail clew and to the model deck. Therefore,the clew vertical

position can be changed, secured and maintained throughout

testing.

The mainsail boom is equipped with a traveler/downhaul

that permits the trim angle and sail twist to be controlled

adequately. A downhaul adjustment permits the leech tension








to be eased or tightened as needed. Finally, a mainsail

clew may be trimmed independent of the trim angle or leech

tension.


Sail Construction

All the sails are made of 2024-T3 aluminum sheet,

0.020 in. thick, cut to the planform described above. Each

sail is then rolled parallel to its luff to produce a cylin-

drical surface such that any camber line drawn perpendicular

to the sail luff is a circular arc or constant radius of

curvature. The LP, the longest such camber line, and the

sail draft depth (d) as a proportion of straight line chord

lenght are used to define a characteristic radius of curva-

ture or

2 -1
LP 1-4(d)
r = P [ARCCOS( )] (6-1)
2 1+4(d)



For the headsail, (I2 +J2 ) is taken as the cardinal surface

ruling. Then the total surface is easily defined in cylin-

drical coordinates by equation 6-1 for the intervals

2
0 < A < 2 ARCCOS[ 4(d)]
1+4 (d)


and (6-2)


S(1 r) < z,' < (I2+2 z (1- r
F LP F LP
O O







where


z' =-J [
F 2+1
zo (I/J) +1



Figure 6-4 illustrates the coordinate system and the

surface bounds. The z' coordinate system is rotated and

translated relative to the previously described global

coordinates. z' and z' are foot and leech bounds respec-
F L
tively. Equations 6-1 and 6-2 in the defined intervals of

A and z' describe the cylindrical headsail in terms of its

rated dimensions. Similar intervals can be written for the

mainsail in terms of its P, E dimensions and the d proportion.

With the geometry of the sail defined as indicated, it

is clear that the deepest draft point of each sail is located

at 50% chord. While this is farther aft than suggested by

current sailing wisdom for the headsail, it is approximately

correct for the mainsail. This divergence from current sail

set philosophy is considered acceptable for the comparisons

made here, since it is consistently applied throughout all

of the rig configurations tested and is similarly employed

for the vortex lattice models discussed later. Certainly,

such comparisons should establish performance trends and

it seems probable that these trends should be preserved as

the deepest sail draft point is moved moderately further

forward.










4


2) 1/2


C


FIGURE 6-4 Sail Surface Description.







Sail Trim, Setting and Measurements

The model deck is equipped with two protractor scales;

one to measure the headsail trim angle (6 ) and one to mea-

sure the mainsail trim angle (6 ) relative to the boat cen-

terline. The trim angle is defined as the angle between the

boat centerline and a line drawn from tack to clew along the

foot of the sail in question. Each sail has camber lines

drawn at selected z-locations as shown in Figure 6-5. Once

the sail is fitted to the model, a sail "set" may be de-

scribed by measuring the leech position of each camber line

relative to the vertical plane that contains the foot trim

angle line, thus yielding the sail twist. The draft position

and depth of draft are measured directly from a line drawn

from the camber line luff the camber line leech. In total,

these measurements provide a mapping of sail shape which

characterizes a particular set.

Finally, each sail is equipped with tufts along both

the luff and leech on both windward and leeward sides. By

direct visual observation of tuft motion, any sail set may

be assessed for attached or separated flow. This visual

observation is useful prior to test data collection to

ensure that reasonable trim has been attained and that no

large scale flow separation exists over the planform.










Mainsail
Twist


1 M3= 210

2 = 160
M2


>M = 70



,- = 00


Headsail
Tvsist


240


3

-2


22.50


24.0

20.0

16.0

12.0


-, = 210


8.0

4.0


0o


o
12


Mainsail
Chords


2.4

3.7


5.1



6.3


Model Deck Level


FIGURE 6-5 Typical Sail Camber Lines, Draft and
Twist Measurement Locations.
(Dimensions shown are in inches.)











CHAPTER SEVEN
COMMON EXPERIMENTAL PROCEDURE


Sail Trim Pre-Test

Prior to each configuration test, the model was placed

in the wind tunnel with an approximate sail set and trim.

A first order approximation of trim was established at pre-

selected trim angles for the jib and main with draft and

twist selections estimated from sailing experience and

judgement. An observation test run was then conducted to

assess the twist and draft set. The sails were inspected

for windward or leeward separation. For this purpose, a

large mirror was installed on the far wall of the wind tun-

nel test section; this allowed simultaneous observation of

both sides of the sails. If flow separation was noted from

the motion of the sail tufts, appropriate trim adjustments

were made. Such adjustments were analogous to their counter-

parts of the full scale yacht, each adjustment having the

corresponding effect. For example, if large separation was

noted aloft on the leeward side of the jib, a correction was

to ease the leech downhaul which induced increased sail twist.

This is analogous to moving the jib sheet fairlead aft on a

full scale sailboat which relaxes leech tension and increases

twist on the upper portions of the sail.








With the wind tunnel operating at approximately the

speed of the intended test, the model was slowly rotated

through a range of heading angles from approximately 100 to

450. Leading edge and trailing edge separation points were

noted using the tufts as indicators as a function of B and

a few strain gauge resistances were recorded at the maximum

y-force point. Small adjustments were then made to the trim

to maximize the lift force as indicated by a maximum resis-

tance reading. The model was rechecked for leading and

trailing edge separation heading angles. Finally, the wind

tunnel was shut down, the model removed and sail trim measure-

ments were recorded (reference Table 7-1).


Wind Tunnel Test

The model was reinstalled in the wind tunnel and the

force balance was nulled on each of the six channels with

the model set at a heading angle of B=100. The model was ro-

tated through 450 to indicate if any weight balancing was

necessary to maintain each of the six channel null points.

Variations in resistances that correspond to more than 5pin.

were corrected by the addition or removal of weights from the

model. The correct model center of gravity having been

determined relative to the force balance, the wind tunnel was

started and brought up to test speed. Raw test data were

recorded manually for each channel at each heading angle and

checked for repeatability in an up-down reading sequence. Head-

ing angles were indexed in approximately 50 increments from

10 to 45











S dP dP oP dP dP dP dP dP
I--l (N (CN r-I r- i







04 0 0 0 0 0 0 0 0
I rJ. ( 0 ,-q m u, tD (N lq









0 0 0 0 0 0 0 0
'0 0 0 0 0 0 0 0 0





dP dP ctP cdP d dP dP
I c o o r r-i r- C o o








0 0 0 0 0 0
Ft& o o o0 co 0 o
| Loooooo Z
1 Z r-A '-i (N rrl







.t o o o o o 0 o o
'0 a. (N M zN (I N m DN tN













44 E E- H E4 E4 E-4
0
- -I l I-I l





U


E


'r.



I 1

M (0 (


E- 4




'U
a








During each test, the static and dynamic pressure of the flow

at the calibration point (3.00 in. above the model masthead)

were noted along with the airflow temperature. At the end of

each test, the force balance was checked for zero return. Any

zero drift error found was investigated. If the error was in

excess of Spin., that set of test data was discarded. For such

cases, the same configuration was rerun.

Each configuration test required approximately two hours

of wind tunnel run time. After each run, a calibration check

was made on the force balance and the calibration equations

were adjusted accordingly.












CHAPTER EIGHT
MODEL CONFIGURATION TEST RESULTS


The Finn-Type Sail Test

The Finn is a simple, one-design catboat rigged, sail-

ing dinghy which offers an easily modeled sail planform

(reference Table 6-1). Marchaj (8) has used a one-seventh

scale (1 H=7) fabric scale model of the Finn sail to experi-

mentally investigate the effects of boom vang tension and

resulting sail sha: on the total sail lift and drag coef-

ficients. His test results were achieved under uniform

onset flow conditions and they are reported at scale Reynolds

numbers that are in the range reasonable for similitude.

In the present work, a geometric scale factor of 1 =9

yields a Finn model of appropriate size to fit the wind tun-

nel test section without severe blocking. This model was

constructed absent of a hull and deck to permit an accurate

determination of the sail force center both with and without

a simulated non-uniform onset velocity. The non-uniform

velocity profile that was used in these tests is described

in Chapter Five and,; thus, is slightly distorted relative

to the portion of the true PBL that the full-size prototype

Finn sail would actually "see". This distortion, however,

is believed to be unimportant for the comparisons presented.








The sail planform is given in Table 6-1, Configuration

Code TOOCB1. The sail model was rolled to a cylindrical

shape parallel to the luff and fastened to a cylindrical

shape parallel to the luff and fastened to a mast/boom

assembly. The mast/boom assembly was stiffened using a

small spreader and shroud combination. This stiffening

was necessary since the mast section modulus must be small

in order to conform to the prototype mast. Its contribu-

tion to the resultant drag has been verified by measuring

the drag of bare poles (mast and boom alone). This test

indicated that the mast drag contribution was negligible.

Camber lines at 4 in. intervals starting at the boom were

used to define draft and twist. Since this model had no

hull or deck, the adjustments of the sloop model tests were

not available and the sail set capability was correspond-

ingly limited. Angles of attack measured between the boom

and the wind tunnel center line were used in place of head-

ing angles. Partial sail twist control was realized by using

a boom topping lift and vang but at a slight drag increase.

At large angles of attack, the stress on the sail was

observed to be sufficient to slightly alter the initial sail

twist. Naturally, the effect increased with increasing flow

velocity. The same effects would occur on the prototype Finn

but vang, sheet and mast bend have not been modeled propor-

tionately for the wind tunnel test. Therefore, at large

flow velocities (Reynolds numbers) there would be some de-

parture from geometric similitude.







Direct flow observations on the windward side of the

sail were of particular interest both with and without the

PBL velocity profile. Figure 8-1 illustrates a side view

of the model and the positions long yarn tufts assumed

when placed in a 40 ft/s flow with the sail model at an

angle of attack of 250. Using the camber lines for approxi-

mate measurement, a yarn tuft was estimated to be near the

windward side of the sail pressure center if it was not

deflected up or down relative to the horizontal plane. This

observations was made with the non-uniform logarithmic ve-

locity profile in the tunnel and tuft #2, approximately 0.36

H above the floor, was estimated to be at the windward side

center of pressure. Similar observations of the leeward

side of the sail were not as informative because of large

random yarn motion.

As expected, two strong votices were seen; one near the

masthead and one near the boom. A top view of the leeward

side, Figure 8-2, reveals the strong upwash which was ob-

served upstream of the leading edge and smooth flow to about

the 3/4 chord point where turbulence and the shed trailing

edge vortex displaced the yarn. Near the 0.36 H height noted,

an upwash angle of approximately 100 at the sail leading edge

was measured relative to the wind tunnel centerline. This

angle appeared to vary along the leading edge as a function

of vertical position.







z(in.)

30
Tuft
#6

#15 20

#4

#3

#2 o. -- 10


#1 \

SWind Tunnel
Floor

FIGURE 8-1 Finn Sail Yarn Observations.
Observed yarn motion for the Finn
sail at an attack angle of 25, V=40 ft/s,
without the simulated PBL.


Wind Tunnel Center
iLine


10 (Approx.)


Edge
FIGURE 8-2 Finn Sail Upwash Observation.
Position assumed by a long yarn on the
leeward side of the sail as viewed from above.


Flow








While the above observations come as no surprise, they

do provide insight and evidence in support of concepts

suggested later in this work. For instance, the strong

upwash noted is in agreement with the arguments offered in

Appendix A for quantifying the magnitude of relative wind

twist that results solely from the sail circulation and is

almost independent of boat speed.

The results of the force balance data collected for the

Finn sail, both with and without the simulated PBL onset

velocity profile, are given in Figure 8-3 as lift (Cx) and

drag (C ) coefficients along with the lift to drag ratio

(C /Cx) plotted against the attack angle. Selected data

points from Marchaj's work are superposed for comparison

and are seen to be in fair agreement considering the large

differences in models used (metal to fabric) and the unre-

ported uncertainty of the earlier work. The second stall

or "bump" seen in both C -plots at approximately 30 attack

angle for uniform and logarithmic onset velocities is thought

to be a result of sail trim changes caused by the pressure

distributions in these high loading conditions. Both tests

were conducted for a velocity of 80 ft/s at the model mast-

head and a Reynolds number of 3 x 10 The simulated PBL

had the effect of decreasing the lift and drag values over

those measured for uniform flow at the same attack angle.

As a point of interest, the negative vertical force

coefficient is also plotted in Figure 8-4 for the case with









LEGEND
SWith PBL
Without PBL -- -
- Marchaj's Data ----
o0 Cx
0 Cy
V Cy/Cx




/




+#x
4


/ A/
I,^


;--
-n- 0-
-r8'


I I I I i I i1
10 20 30 40 50
HEADING ANGLE(Degrees)

FIGURE 8-3 Effect of the Planetary Boundary Layer on
Sail Test Data. Finn sail for Re= 1.8 x 105
vs. Marchaj's data for Re= 2.2 x 105.


I


SAIL SHAPE AND TRIM


6J = N/A

Pj = N/A

dj = N/A


6M= 00

M1= 320
aM= 11%


3.5




3.0





2.5


1.5




1.0




0.5


``H--n







the simulated PBL. Because of mast and sail deflection

under load, a small projection of sail area can be ob-

tained in the xy-plane. The centroid of this projected

area is not necessarily the same as the planform centroid.

The negative vertical force.related to this coefficient

(C ) can be thought of as the net reaction of the span-
z
wise flow momentum on this projected area. This inter-

pretation is supported by the yarn observations made

earlier and would also be true for the prototype Finn.

The x and y moment coefficients are shown in Figure

8-4. While the overall trends of the coefficients are

preserved, the net effect of the non-uniform onset velocity

is seen to reduce the values of C and C.
mx my
In an attempt to resolve the sail force center, it is

conservative to assume that each of the forces represented

by the coefficients Cx, C and Cz are concentrated at dif-

ferent x, y, z locations or



Fx = x(xl y1, z)

F = Fy(X2' 2' z2)



and


Fz = Fz(x3' y3' Z3)










LEGEND
With PBL
Without PBL ---
0 -Cmx
O C
my
-C
z


Y


SAIL SHAPE AND TRIM


6J = N/A


6M =


(j = N/A M= 32


dj = N/A


dM= 11/o


k6'


--- *
I' I I- ~ '


/ '1


I I


10 20 30 40 50
HEADING ANGLE(Degrees)
FIGURE 8-4 Finn Moment Coefficients With and Without
the Planetary Boundary Layer.


3.5





3.0






2.5


1.5





1.0





0.5







If the vertical force is taken as the vertical component

of the total lift vector, where the total lift vector is

normal to the sail surface at its center of pressure, one

obtains


x2 = x3 and y2 = y3 0 (8-1)


The resultant moments of the three forces in coefficient

form can be written as



Cmz = (CyX2 + CxY1)/CPF

Cmx = (Cy2 + Czy3)/CPF (8-2)

Cy =(Cxz + Cx)/CPF



Applying the conditions of equation 8-1 to equation 8-2 gives

C C
S=mx PF 8-3)
2 C
y

From the plots in Figure 8-3 it is noted that


C > C
y x

It is logical to assume yl < x2, therefore, the z-moment

coefficient can be approximated as


Cmz Cy X2/CPF








Solving for x2 yields

C C
mz PF
x2 C (8-4)
y


Using equations 8-1, 8-2 and 8-4 the vertical height to the

x-force location can be approximated as

C
mz
Cm-C ( )
my z C (
z, = --- (8-5)
x


It is clear that the uncertainty of z2 is less than that of

z1 which, in turn, is greater than the uncertainty of any

one of the contributing coefficients. The uncertainty of

z2 is calculated as 7.87% while z1 is estimated at 11.09%.

Using these uncertainties to generate weighting factors W1

and W2, a sensible vertical distance to the force center

is defined as

2 2
z(nominal) = 1 + (W22(8-6)
1 2


Where W1 = 9.02 and W2 = 12.71 based on the above uncer-

tainties. Since the plane of the projected sail planform

rotates relative to the x,y,z-coordinated system, the hori-

zontal distance from the mast to the force center is a

function of x,y and the attack angle. Figure 8-5 shows

the force center locations as calculated by equations 8-4

and corrected for the attack angle.












1.13-
ll-





0.93 -








-0.73-


0





4- 1

0
h-H


(d






0.13


Wind Tunnel Floor Ratio of Foot to Boom Length
S/ 7 ///////////////// /////////////////////////777


FIGURE 8-5


Finn Sail Center of Effort Location.
Center of effort locations at various attack
angles with and without the simulated PBL.
Note: Because the PBL is distorted slightly
for the model used the effect on the c.e.
translation as shown is less than it would be
for a correctly scaled PBL.


For:
P = 24.8 and E = 15.3
Center of Effort:

(z/P) = 0.46 Without PBL
(z/P) = 0.52 With PBL


1.0-






0.8-




r-)





0
4-P





0
o.6-










0
*d






0.2-


PBL







The concentration of points around the planform cen-

troid for the uniform velocity is logical and suggests an

analytical check using a direct integration scheme. Such

a scheme is presented in Appendix D for both with and

without the modeled PBL. Without the planetary boundary

layer model the calculated center of effort is shown to

be 0.39 H, which is identical to the planform area centroid

and agrees with the location indicated in Figure 8-5 for

attack angles of 250 to 35. With the non-uniform onset

velocity the method requires an approximate model for the

lift coefficient variation as a function of span position.

Approximating polynomials are selected for this purpose to

allow a convenient form for integration by parts. For the

selected precision the results are nearly invarient with

the assumed lift coefficient models and the net center of

effort is shown to be0.48 H. This value is also in close

agreement with the measured value as indicated by Figure 8-5.

Finally, the Finn model was used in an effort to assess

the effect of Reynold's number on C values at or near stall.

At an angle of attack of 300, three tests were conducted cor-

responding to Reynolds numbers of 2.3 x 10 2.9 x 10 and
5
3.3 x 10 The C values obtained show no variation beyond

that of the expected uncertainty, see Table 3-1. The same

results were found for C and C values. Therefore within
x mx
the range of Reynold's numbers investigated, this parameter's

effect is negligible.







Variable Jibsail Hoist Series

Employing the full yacht model described in Chapter Six,

a variable headsail hoist series of tests was conducted. The

results of this series were intended to be compared with

theoretically derived lift and drag coefficients. For this

purpose, the yacht model was fitted with a mainsail (P =

22.50 in. and E = 9.00 in.), common to all tests. A series

of jibsails, all of the same aspect ratio but with various

hoists, was fitted to the model and tested as described in

Chapter Seven. Tests start with the masthead sloop as an

arbitrary upper limit on headsail size with the catboat, no

headsail, as a lower limit. Table 6-1 lists the planform

geometries for the configurations tested. The configuration

code of interest are


T15MH1 -- Full hoist masthead sloop

T15781 -- 7/8 hoist headsail sloop

T15341 -- 3/4 hoist headsail sloop

T15121 -- 1/2 hoist headsail sloop

TOSCB1 -- catboat (no headsail)


A general "bareboat" test was made to determine the lift,

drag and vertical force of the hull and standing rigging.

This force data has been reduced to coefficient form using

the area of each respective configuration and they have been

subtracted from the total configuration coefficients to give

an estimate of the force and moment contribution made by the








sails alone. Since drag associated with boundary layer

interactions between the sails and rigging are present in

the full configuration tests, such estimates for the sails

alone are considered to be conservative.

Figure 8-6 through 8-15 give the results of these

tests. In each case, both the "complete rig" and the "sails

alone" data are displayed. As such, it is evident that the

hull and rigging not only contribute to drag but to lift as

well. Therefore, conclusions directed towards over-all on-

the-water boat performance could be misleading, if only the

aerodynamics of the sail were considered. [The same obser-

vation was made earlier by Marchaj (8).] On a macro scale

the maximum value of the lift coefficient appears to in-

crease monotonically as the jib hoist is decreased. This

is seen to be true for both the complete rig and the sails

alone. However, the drag is also seen to increase porpor-

tionately, somewhat offsetting the useful component of lift.

This will be discussed in greater detail in Chapter Nine.


High Aspect Ratio Series

A 150% masthead sloop configuration is chosen to assess

the effects that different rig aspect ratios have on the

resultant sail forces and moments. Configuration Reference

codes T15MJ2 and T15MJ3, given in Table 6-1, were tested

for comparison with the standard sloop T15MH1. The results

of these tests are given in Figures 8-16 through 8-19 and

are discussed in the next chapter.










LEGEND
-Sails Alone -
Complete Rig---
Cx
O Cy

V Cy/Cx

A CFWD


SAIL SHAPE AND TRIM


6M= 0

TM= 300

dM= 120/


I --



8 ...A-~1 _-


i i


FIGURE 8-6


I I a I a


10 20 30 40 50
HEADING ANGLE(Degrees)

Masthead Sloop Test Results. R = 280,000.,
FBA/SA = 0.23 (T15IH1) e


3.5





3.0






2.5


[-



U2.
L.
0
u-


1.5





1.0





0.5


I I I I






















2.0 Cy vs.C

OC vs.C
OCFWDVS' CHL


5



U *

1.0 -





0.5





0.5 1.0 5 2.0
Cx or CHL

FIGURE 8-7 Masthead Sloop Polars. Re= 280,000.,
FBA/SA = 0.23 (T15MH1)









LEGEND
-Sails Alone--
Complete Rig---
D Cx
0 Cy

V Cy/Cx
A CFWD


SAIL SHAPE AND TRIM

6J =12 6M. 0

jJ =18 M= 31


dM= 12~/


6A


SI I ,


FIGURE 8-8


I I I I I I


10 20 30 40
HEADING ANGLE(Degrees)
7/8 Sloop Test Results. Re= 240,000.,
FBA/SA = 0.27 (T15781)


3.5





3.0





2.5


1.5





1.0





0.5


1






















2.0 C vs.C
y x

OC vs.C
OCFWDV. CE


1.5





1.0





0.51r
0.5 El





I I '-^J5-1- 14
0.5 1.0 1. 2.0
Cx or CHL
FIGURE 8-9 7/8 Sloop Polars. Re= 240,000. ,
FBA/SA = 0.27 (T15781)










LEGEND
-Sails Alone
Complete Rig---
Cx
0 Cy
V Cy/Cx

A CFWD


SAIL SHAPE AND TRIM


6J =12 6M= 0

=J =20 #M =35

j =1 1% dM= 11%


- -a


I I I Li --I- _


10 20 30 40
HEADING ANGLE(Degrees)
FIGURE 8-10 3/4 Sloop Test Results. Re= 210,000.
FBA/SA = 0.32 (T15341)


3.5





3.0






2.5


1.5





1.0





0.5


I
I I I I ~h'


I I I I I




















2.0 OC vs .Cx

." OC vs.C
OFWDS CH:

1.5 -1-



o"U .1
1.0




0.5 -






Cx or CHL
x HL
FIGURE 8-11 3/4 Sloop Polars. Re= 210,000. ,
FBA/SA = 0.32 (T15341)









LEGEND
-Sails Alone -
Complete Rig---

- x C
D Cx
O Cy

V Cy/Cx
A CFWD


SAIL SHAPE AND TRIM


6j .12

ij =18

'a =11%


6M= 0

Mi= 350

dM= 1 2%


LI f i I -


10 20 30 40
HEADING ANGLE(Degrees)
FIGURE 8-12 1/2 Sloop Test Results. Re= 90,000. ,
FBA/SA = 0.43 (T15121)


3.5





3.0





2.5


1.5





1.0





0.5


!


I


I I

















LEGEND

Sails Alone-
Complete Rig---
2.0 OC yVs.Cx












*I
0 CFWDVS. CHL


.1.5 /


U .!

1.0




I
0.5





0.5 1.0 1.5 2.0
C or C,
x HL
FIGURE 8-13 1/2 Sloop Polars. Re= 90,000. ,
FBA/SA = 0.43 (T15121)








LEGEND
-Sails Alone--
Complete Rig---
- D Cx
O Cx
0 Cy
v VC
A CFWD


SAIL SHAPE AND TRIM


6J = N/A


dj = N/A


0
6M = 0

aM 360

dM= 13/o


S
A I,


I I i I


20
HEADING


30
ANGLE(Degrees)


FIGURE 8-14 Catboat (with hull) Test Results. R = 90,000.
FBA/SA = 0.60 (TOSCB1)


3.5





3.0





2.5


1.5





1.0





0.5


i I iI i I Iieel























2.0 -C vs.C


/ OCFWD VSCHL


1.5 -
S4 /
0 /


1.0
I




0.5




I I I I I
0.5 1.0 1.5 2.0
C or CHL
x HL
FIGURE 8-15 Catboat Polars (with hull).
Re= 90,000. FBA/SA = 0.60 (TOSCBI)











3.5


3.0 i


/ V \

2.5 \


o \
TT
t/ \
"2.0 0




I -A
I / rQ
1.5





/ k/
1.0 7




0.5





10 20 30 40 50
HEADING ANGLE(Degrees)
FIGURE 8-16 Masthead Sloop, High Aspect Ratio Main and
Jib. R = 260,000. FBA/SA = 0.32 (T15MJ2)
























2.0 C vs.C
y x

O CFWVS. CHL









O
J1.0 4






I
I !



0.5 -






0.5 1.0 1.5 2.0
C or CHL

FIGURE 8-17 Masthead Sloop, High Aspect Ratio
Main and Jib, Polars. Re= 260,000.
FBA/SA = 0.32 (T15MJ2)







LEGEND
-Sails Alone -
Complete Rig---
D Cx
- O C
O Cy
V Cy/Cx

A CFWD


SAIL SHAPE AND TRIM


6J = 120 6= 0

j 14 M = 24

dj =10% dM= 11%


1A- -A- -A


L 1 I I


10

FIGURE 8-18


20
HEADING
Masthead
Standard
(T1 5MJ3)


I I I I I


S 30 40 50
ANGLE(Degrees)
Sloop, High Aspect Ratio Jib and
Main. Re= 270,000. FBA/SA = 0.28


3.5





3.0





2.5


1.5





1.0


0.5


1


I I I I h I I I I I























2.0 DC Cvs.Cx
y x

0 CL FWD VS'CHL


>1.5

0 ^




I
1.0I




El
0.5 -





0.5 1.0 1.5 2.0
C or CHL
x HL
FIGURE 8-19 Masthead Sloop, High Aspect Ratio Jib,
Polars. Re= 270,000. FBA/SA = 0.28 (T15MJ3)











CHAPTER NINE
EXPERIMENTAL AND THEORETICAL
COMPARISONS


The Influence of the Simulated Planetary Boundary Layer

Wind tunnel tests of yacht models made with and with-

out a simulated PBL indicate that the influence of the PBL

is significant, accounting for reductions on the order of

28% in the lift and drag coefficients relative to those

without the PBL for the same trim and attack angles. In

addition, the effective force center with the PBL is 30%

farther above the deck than with no PBL model while yield-

ing approximately the same moment coefficients about the

water plane. This is important in that test work which

does not model the PBL properly will tend to over predict

yacht potential performance relative to lift and drag for

the same vessel heel limitations. The assessment of the

PBL onset profile by direct integration suggests that

tests conducted with a uniform onset velocity model can be

analytically corrected for any given onset velocity profile

providing a functional formulation of that profile is

possible and that some knowledge of the lift coefficient

variation with height is available. Such a correction

scheme could allow the test results of one model configura-

tion to be applied to any size prototype independent of








similitude requirements for the PBL with all such require-

ments evaluated by analysis.

The direct impedance method offered for onset velocity

profile synthesis is effective and practical, giving reason-

able control over the velocity distribution and the turbulence

in the wind tunnel test section. As pointed out earlier,

the scale of turbulence for the test must be large relative

to the turbulence scale of the sail model viscous shear

layer. The evaluation provided here indicates that a rea-

sonable PBL model should have approximately two orders of

magnitude difference between these turbulence scales. For

the prototype yacht, it can then be concluded that the scale

of turbulence in the over-the-water PBL is insignificant and

can be ignored relative to the sail aerodynamic performance.

A review of previous two and three-dimensional sail

test data (8, 9, 10, 11, 13, 29) for lift and drag reveals

a sensitivity to Reynolds number. This indicates a further

complexity in a complete treatise on sail aerodynamics. Re-

call that in subsonic airfoil theory where the Reynolds

numbers are large the viscous properties of flow may be

neglected in the determination of lift and have only limited

impact on drag. In contrast, experimental evidence for sails

suggests that both lift and drag are strongly affected by

their much lower Reynolds numbers at all angles of attack.

It is speculated here that this Reynolds number sensitivity








is closely related to boundary layer stability. Specifically,

the sharp edges of the single camber sail are simultaneously

subject to an adverse pressure gradient and a fairly large

free stream turbulence intensity; both of these effects could

cause boundary layer instability. More research dealing with

flow separation on sails at Reynolds numbers of 5 x 105 and

less is needed.


Comparison of Potential Flow Models and Wind Tunnel Results

A potential flow analysis of the sail rig configurations

described in Chapter Six has been made employing Register's

SAIL-3 computer program. SAIL-3 produces numerical solutions

to the classical potential flow problem of the Neumann ex-

terior type by means of a discrete vortex lattice distribution.

Register has shown SAIL-3 to be convergent to the exact solu-

tion of the governing equations in terms of detailed wake

geometries as well as force coefficients with upper bound

uncertainties for lift coefficients of 6% and 17% for drag

coefficients for the specific sail discretization reported.

This same discretization is used here. Therefore, the same

uncertainty estimates are applicable. Rig configuration

T15MH1 has been evaluated using SAIL-3. The results are

given in Figure 9-1. Upon comparing these calculated results

with the wind tunnel test results for the "sails alone" (see

Figure 8-6) remarkable agreement is observed in lift up to

the region of sail stall (8=350). In this same region, the

drag coefficient values are seen to be under predicted. This

is to be expected with an inviscid solution.












3.5





3.0





2.5


Y


SAIL SHAPE AND TRIM


6j =12

~j =16


6M= 0

-Mi= 30


LEGEND
-Sails Alone (Theory)
Complete Rig-- -(Test)
O Cx
OCY
V C /Cx
A CFWD A
/
/


-/


V






/
/,'
I
I
I







II

/4


(Test)


EI__~---EJ


I I A-


I I I I I I


10 20 30 40 50
HEADING ANGLE(Degrees)


FIGURE 9-1


Masthead Sloop Theoretical Cx, C CFWD, and
C Cx vs. Test Results.
(ref. T1511I1)


Uj =121% dM= 12%


z

"2.

u
0
u.,


1.5





1.0





0.5




Full Text

PAGE 1

AN EXPERIMENTAL INVESTIGATION OF THE AERODYNAMIC INTERACTION OF YACHT SAILS BY JAMES G. LADESIC A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1983

PAGE 2

..._ ... Copyright 1983 by James G. Ladesic

PAGE 3

To Marlene, my loving wife for all the time and things in life she sacrificed.

PAGE 4

ACKNOWLEDGEMENTS I extend my heartfelt thanks to all those who supported and assisted in the work represented by this dissertation: to Embry-Riddle Aeronautical University for the use of their facilities during the test phase; to Dr. Howard D. Curtis, my department chairman at Embry-Riddle, for his considerate support during tDis lengthy activity; to Mr. Glen P. Greiner, Associate I n s t ructor, for his assistance early on in the equipment development phase, especially for his help with the planetary boundary layer synthesis; to Mr. Don Bouvier for his expert help with advice on hardware fabrication; to Professor Charles N. Eastlake for his insight on wind tunnel testing techniques and to all of my student assistants for their aid during the data collection phase. Finally, I extend special thanks to my committee chairman, Dr. Richard K. Ire y of University of Florida. His love for sailing and his insistence on e x cellence has left me with a l a sting impression which I shall demon strate in all my future work. iv

PAGE 5

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS. . . . . . . . . . . . . . . . . . . iv LIST OF TABLES ....................................... vii LI ST OF FIGURES ............................ ......... vi ii KEY TO SYMBOLS. . . . . . . . . . . . . . . . . . . . X ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . xiv CHAPTER ONE INTRODUCTION AND GENERAL EXPERIMENTAL APPROACH. . . . . . . . . . . . . . . . . . 1 Introduction. . . . . . . . . . . . . . . . 1 Experimental Motivation ..................... 2 Experimental Method ......................... 4 TWO EXPERIMENTAL SIMILITUDE FOR THE SAILING YACHT....................................... 6 General Problem of Complete Yacht Similitude............................... 6 Sail Test Similitude ........................ 9 THREE YACHT AERODYNAMIC FORCES AND THEIR MEASUREMENT . . . . . . . . . . . . . . . . 18 Resolution of Aerodynamic Forces and Moments .................................. 18 Common Measurement Methods .................. 19 FOUR OTHER EQUIPMENT AND APPARATUS ............... 23 The Wind Tunnel. . . . . . . . . . . . . . . 2 3 Data Collection and Reduction ............... 25 FIVE SYNTHESIS OF THE ONSET VELOCITY PROFILE ..... 30 Motivation and Basic Approach ............... 30 The Model Atmospheric PBL and Scale Effects .................................. 31 Profile Synthesis ........................... 33 V

PAGE 6

SIX SEVEN EIGHT NINE TEN APPENDICES A Page YACHT MODEL DESIGN ......................... 35 Planform Geometry .......................... 35 Model Geometry and Trim Adjustments ........ 42 Sail Construction .......................... 45 Sail Trim, Setting and Measurements ........ 48 COMMON EXPERIMENTAL PROCEDURE .............. 50 Sail Trim Pre-test ......................... 50 Wind Tunnel Test. . . . . . . . . . . . . . 51 MODEL CONFIGURATION TEST RESULTS ........... 54 The Finn-Type Sail Test .................... 54 Variable Jibsail Hoist Series .............. 66 High Aspect Ratio Series ................... 67 EXPERIMENTAL AND THEORETICAL COMPARISONS ... 82 The Influence of the Simulated Planetary Boundary Layer. . . . . . . . . . . . . 8 2 Comparisons of Potential Flow Models and Wind Tunnel Results ................. 84 CONCLUSIONS AND RECOMMENDATIONS ........... 95 Wind Tunnel Test Conclusions ............... 95 Recommendations............................ 96 SAIL TWIST AS RELATED TO THE APPARENT WIND AND THE INDUCED FLOW FIELD ................ 98 B AERODYNAMIC FORCES AND THE CENTER OF EFFORT 104 C AERODYNAMIC FORCE MEASUREMENT .............. 110 D WIND TUNNEL DATA REDUCTION COMPUTER PROGRAM "B OA T" ..................................... 121 E BOUNDARY LAYER SYNTHESIS ................... 126 F CENTER OF EFFORT BY DIRECT INTEGRATION ..... 133 LIST OF REFERENCES . . . . . . . . . . . . . . . . . 13 7 BIOGRAPHICAL SKETCH. . . . . . . . . . . . . . . . . 14 0 vi

PAGE 7

LIST OF TABLES Table Page 3-1 Experimental Force and Moment Coefficient Maximum Uncertain ties. . . . . . . . . . . 2 2 4-1 Typical Output Format from "BOAT".......... 28 6-1 Planform Geometries ..................... 40 7-1 Mean Sail Shape and Trim Parameters 52 9-1 Rig Configuration Test and Theoretical Results .................................... 88 9-2 Finn-Type Sail Results from Experiment and Theor y . . . . . . . . . . . . . 9 O 9-3 Masthead Sloop (TlSMHl) for Various B, Experiment vs. Theory ..................... 91 vii

PAGE 8

LIST OF FIGURES Figure Page 2-1 Coordinate Systems and Basic Dimensions ... 10 4-1 ERAU Subsonic Wind Tunnel General 6-1 6-2 6-3 6-4 6-5 8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 8-10 8-11 8-12 Arrangement............................... 24 Sail Geometry Nomenclature ............... 36 Lift Coefficient vs. Angle of Attack for a Thin, Single Cambered Section as Measured by Milgram (ref. CR1767) for Three Reynolds Numbers and as Predisted by Thin Airfoil Theory ............................ 41 Wind T~nnel Yacht Model Configurations .... 43 Sail Surfac e Description ................. 47 Typical Sail Camber Lines, Draft and Twist Measurement Locations. . . . . . . . . . . 4 9 Finn Sail Yarn Observations ............... 57 Finn Sail Upwash Observation .............. 57 Effect of the Planetary Boundary Layer on Sail Test Data............................ 59 Finn Moment Coefficients with and without the Planetary Boundary Layer ............. 61 Finn Sail Center of Effort Location ....... 64 Masthead Sloop Test Results ............... 68 Masthead Sloop Polars .................... 69 Test Results, 7/8 Sloop ................... 70 Polars, 7/8 Sloop ......................... 71 Test Results, 3/4 Sloop ................... 72 Polars, 3/4 Sloop......................... 73 Test Results, 1/2 Sloop .................. 74 viii

PAGE 9

Figure 8-13 8-14 8-15 8-16 8-17 8-18 8-19 Page Polars, 1/2 Sloop .......................... 75 Catboat Test Results ....................... 76 Catboat Polars............................. 77 Masthead Sloop, High Aspect Ratio Main and Jib, Test Results. . . . . . . . . . . . . 7 8 Masthead Sloop, High Aspect Ratio Main and Jib, Polars................................ 79 Masthead Sloop, High Aspect Ratio Jib and Standard Main, Test Results ................ 80 Masthead Sloop, High Aspect Ratio Jib, Polars. . . . . . . . . . . . . . . . . . . 81 9-1 Masthead Sloop Theoretical ex, Cy, CFWD and C JC vs. Test Results ..................... 85 y X 9-2 Masthead Sloop Theoretical Polar vs. Test Polars. . . . . . . . . . . . . . . . . . . 86 9-3 L/D Ratios From Theory and Test ........... 93 A-1 Typical Wind Triangle for the Sailing Yacht 99 C-1 Six-component Floating Beam Force Balance In Schematic ............................... 115 E-1 Correlation of Screen Impedance with the Resultant Downstream Velocity Distribution. 127 E-2 Yarn Spacing and the Resultant Flow Impedance Distribution ..................... 127 E-3 Dimension l ess Velocity Ratios (Measured and Desired) and Turbulence Intensity Distributions (lOT) ....... ................ 131 ix

PAGE 10

AA n A . 1J A n AR BAD B . 1J c() CPF E F () F () FBA FRF H I I ( z) J K K 1 L/D LOA LP Lt BB n KEY TO SYMBOLS numerical solutions to the Glauert and image integral equations direction cosine coefficient matrix Fourier coefficients aspect ratio boom above deck distance general constant coefficient matrix force or moment coefficient planform chord length mainsail foot length generalized force vector magnitude of the force vector components free board area fractional rig factor height of the mast above the water plane jib span flow impedance distribution function fore-triangle base length von Karman's constant any generalized constant lift to drag ratio length overall luff perpendicular non-dimensional turbulence scale parameter X

PAGE 11

p PBL R. l. R e SA T. l. UA UB UT UT(z) u30 w () x' a,b C d e e. l. F l. h n generalized moment vector magnitudes of the moment vector components overlap ratio mainsail span planetary boundary layer force balance strain gauge resistance reading Reynolds number total planform sail area local applied sail traction apparent wind speed boat speed true wind speed true wind velocity profile apparent/tre wind speed at 30 feet uncertainty weighting factor yacht rig parameter group general constants chord length, straight line distance from luff to leech depth of draft (%) exponential base 3-space unit vectors force vector reference distance from water plane to the force balance geometric scale factor reference length of the force balance xi

PAGE 12

s u* u'v' U I I VI w w ( z) X I s x,y,z a y 6 A \) p T e


PAGE 13

Subscripts A,B,C, F HL J M MOD PF PROT i,j,k,l ... x,y,z rnx,my,mz force balance channel indicators fore-triangle heel jibsail mainsail model planform prototype coordinate indices or counters 3-space reference coordinates moment subscripts xiii

PAGE 14

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN EXPERIMENTAL INVESTIGATION OF THE AERODYNAMIC INTERACTION OF YACHT SAILS By James G. Ladesic Chairman: Dr. Richard K. Irey Major Department: Mechanical Engineering Steady flow wind tunnel test results of sail planforms and rig configurations for typical sloops and catboats are presented. Tests were conducted in the subsonic wind tunnel at Embry-Riddle Aeronautical University, Daytona Beach, Florida, from September, 1981, through August, 1982. Force and moment data were collected using a special pur pose six-component force balance. Test generated force and moment coefficient uncertainties are reported for all tests with a maximum uncertainty for lift as .3%, for drag as .0% and for the moments as .1%. Test results are given for the entire yacht. Estimates of the forces and moments a t tributable to the sails alone are calculated by subtract ing data of hull and rig tested without sails from the total rig data. The one-design Finn dinghy planform was used to assess the effect of onset velocity profile d istribution. A xiv

PAGE 15

logarithmic distribution of velocity, modeled after the planetary boundary layer (PBL) typical over water, decreased the net lift and drag coefficients approximately 28 % com pared with those determined for a uniform onset velocity distrib u tion. The net sail force center with the PBL was 30 % farther above the water plane than that with a uniform onset flow. The sloop configuration was used to assess the effect of jib hoist. Results are compared to theoretically derived lift and drag coefficients. Good agreement was obtained for lift at attack angles less than 35, the stall angle. Theore tical drag estimates are underpredicted but agree in trend. Drive force coeffici ent s from the tests have been found to be more realistic relative to current sailing wisdom and suggest that the omission of pressure, viscous,and boundary layer interference drag in the analytical models is significant. Further experimental research is ne e ded to assess the effects of Reynolds number. Force cent e r movement relative to sail trim, especially for the close reach and beat, also requir es further investigation. Continued effort towards em pirical stall prediction is called for. Finally, full or fractio nal size on-th e-wa ter t es ts are suggested to advance both sail and yacht design. xv

PAGE 16

Introduction CHAPTER ONE INTRODUCTION AND GENERAL EXPERIMENTAL APPROACH Sail design and fabrication have relied heavily on the talent of the naval architect and sailmaker (1}. Effective sail production has been the result of an individual sail mak e r's intuitive understanding of fluid dynamics, his knowl edge of prevailing weather conditions for the locality of in tended use and his adroitness in developing complicated three dimensional surfaces from two-dimensional patterns (2). In recent times, state-of-the-art sailmaking has gone through a renaissance with the application of mathematics and digital computers to the geometric aspect of this transformation task (3). As a result, the accuracy and speed of sail shape develop ment has been significantly improved allowing the sailmaker to market his products as "computer designed". The computer has also been applied to the more comple x task of sail aerodynamics with limited success. Computer-aided applications of lifting line and vortex lattice flow models provide a theoretical link between desired pr e ssure distributions and the related surface geometry (4, 5, 6, 7). Recent computerized application of the vortex lattice approach by Register (7) has extended this model in two respects: it includes a logarithmic non-uniform onset velocity 1

PAGE 17

patterned after that expected o v er open water; in addition, no l ine ari z ing assumptio ns are made with respect to sail shap e or wake geometry. The latter is particularly signifi cant with respect to modelling the strongly interacting sails of the sloop rig. While application o f the potential flow concept shows great promise, it must be understood that such analyses are applicab le only for angle s of att ack less than that of the sail stall point. Superficially t hi s encompasses the beat, close reach and beam reach headings. However even at these hea dings performance is determined by the ability to maintain ma x imum sail lift without incurring large scale separation. As such, identification of the stall point and determination 2 of lift and drag coeffici en ts in the vicinity of the st a ll point are a necessary part of a comprehensive sail study. In this range potential flo w theory does not provide useful infor mation. Furthermore, applications of lifting line and vortex lattice the o ries to the s ai l have in some instances pre di cted results that are contrar y to acc epte d sailing beliefs. As a result, controversy shroud s the credibility, practicality and u sefulness of predictions mad e by these analytical methods for sails. Ex perime ntal Motivation Motivation for res earch is u sua lly coupled with n atio n al security and/or c o mmercial enterp r ise Admittedly, a il research has almost no __ application to th e former and the association with the latt er is on a rather small financial

PAGE 18

scale. As such, experimental efforts have been infrequent. What has been done has often been the guarded property of the designer, naval architect or sailmaker. In the public domain one rarely finds reference to specific documentation. The most dedicated group for altruistic experimental sail research has been that of Marchaj (8) and Tanner (9) at the University of Southampton. Much of this work has 3 been undertaken in a large low-speed wind tunnel using fabric model sails. No apparent attempt has been made to develop an onset velocity gradient and tests have been run at Reynolds numbers based primarily on distortion and shape control rather than model similitude. The results reported are significant from a qualitative point of view. However, they have limited quantitative applicability because experimental uncertainties are unreported. Many of the tests are performed for specific yacht or planform configurations and thus are not applicable to a wide ra~ge of yachts or configurations in gener a l. Milgram (10, 11) has provided general, normalized, two dimensional sail coefficients with and without mast effects at appropriate Reynolds numbers. (His experimental uncertainty is also unreported.) Methods for applying such two-dimensional sail data to a three-dimensional sail configuration for forces and moments are, at present, unclear in that no corrections for such factors as aspect ratio and sail geometry variations are provided. Milgram proposes a scheme for estimating three dimensional pressure and viscous drag effects from two dimensional data but admits the need for experimental

PAGE 19

4 verification of the method. Such techniques do exist for air foil sections and wings (12) but whether they apply directly to the sailboat has not been established. In short, experi mental sail char acteristics that can be readiiy employed to verify analytical results are necessary to further the advance ment of sail aerodynamic research. One fact agreed upon by both proponents and opponents of the analytical approach is the need for experimental research. Such research wou l d not only quantify the performance of the sails tested, they would also complement the theoretical efforts by validating their range of applicability. For the sloop rigged vessel (jib and mainsail), the aerodynamic interaction associated with the close proximity of the headsail and main sail has not been fully explored. Specifically, how performance is affected by the amount of jibsail overlap and the percentage of jib hoist has not been reported. Nor has the effect of non-uniform o nset velocity. These topics are principal ob jectives of this research. How this experimenta l information compares with analytical results is also of keen interest. Exp e rim e ntal M et hod Measurements are m ade in a low-s pee d subsonic wind tunnel into which a flow impedance distribution can be introduc ed to mod e l th e nonlin ea r onset velocity profile at a scal e compat ibl e with the yacht m o d e l. All sails are cylindrical surfaces. Such shapes ar e e asy to characterize g e om e trically, but th ey do not match th e shap es offered by pres e nt day sailmaking

PAGE 20

technology. Sails are constructed from aluminum sheets which are cut and rolled to shape. Once fastened to the yacht model's standing rigging, the built-in shapes are maintained throughout the tests. Yacht rig configurations tested fall into three categories: a cat rigged, Finn-type sail which is tested without a hull model in order to assess the influence that onset velocity profile has on the sail force magnitude and its location relative to the water reference plane; a variable hoist series, hull present, in which the headsail hoist is decreased at a constant main sail size; and a rig aspect ratio series, hull pres e nt, for the masthead sloop. Tests are conducted at velocities that model a 4 to 6 kt true wind speed at the masthead. All data are corrected for wall effects, solid blocking and wake blocking. Each datum point displayed is presented with its estimated experimental uncertainty. Some sali e nt aspects of sail testing and theo retical extension into v e ry low Reynolds number regimes are discussed. 5 In the pres e nt e f f or t three-dimensional sails are em plo y ed to assess th e effe cts of trim and rig under stead y flow conditi o ns. Th e s e tr e n ds ar e compar e d to th e vort ex lattic e analysi s complet e d b y Reg ist e r for id e ntical confi g urations and t r im and to th e vo rt ex lin e mod e l dev e lop e d e a r li e r b y Mil g ra rn f or sim i lar ri g configuration s and trim.

PAGE 21

CHAPTER TWO EXPERIMENTAL SIMILITUDE FOR THE SAILING YACHT General Problem of Complete Yacht Similitude Experimental efforts in yacht testing are classically divided at the air-water interface. That is the hydro dynamics of the hull are evaluated independently of the aero dynamics of the sails. This division is convenient in that it permits a reduction in the number of parameters required for model similarity but it cannot assess interactive effects that are a consequence of the air-water interface. As such, hull hydrodynamic results must be partnered with sail aero dynamic res u lts on the basis of assumed interface conditions. It has not been practical to attain complete experimental similitude in either sail aerodynamics or hull hydrodynamics (13, 14). It is standard practice for these methods to depart from strict compliance with similarity laws. For con v e nience the inference is often made that sail theory is an e x tension of the body of literatur e developed for aircraft wings. As such, differences in the governing param e ters are sometimes assum e d trivial and design parameters are deduced from existing airfoil data, such as that collected in Abbott and von Doenhoff (12). However, applications of such data even to the single camb e red, flexible sail must be done with 6

PAGE 22

caution as significant differences between the two exist. As differentiated from the rigid aircraft wing, cloth sails are normally highly loaded and generally have large geometrical twist. In addition, the criterion for optimum sail performance must be related to the projections of lift and drag to the vessel's center line that resolve into the driving force; whereas wing optimum performance is governed primarily by lift alone. Also, the sail is sub ject to a non-uniform onset velocity resulting from the atmospheric boundar y layer; while in contrast, the air craft wing moves through an air mass that is to the first order stationary. As a consequence of these effects, the variation of lift with attack angle cannot be considered a constant for sails, whereas this is a typical assumption 7 in wing design. In addition, tests for aircraft are usually conducted at Reynolds numbers much larger than those en countered on yacht sails. These differences clearly justify a treatise on sail test similitude based on the pertinent variables and conditions that are unique to the sailing yacht. For th e wor k p res e nted h e rein, the h y drodynamic effects of the hull are i g nored. The scaled true wind magnitud e is determin ed by th e available wind tunnel capacity for th e model size s e lect e d, with the profile impedance screen in place. This wind speed is equivalent (based on Reynolds number) to prototyp e on-the-water wind speed of 4 to 6 kt.

PAGE 23

As such, heel effects for the yacht being modeled can be ignored and an assumption of no wave-air interaction is reasonable. Thus, it is not necessary to model motions that would result from a wind driven sea state. 8 A major discrepancy between this work and on the water conditions is that the onset flow has zero twist which, in turn, implies the assumption of zero boat speed. This limi tation is a practical necessity in wind tunnel testing. To model the effect of boat speed, one could either move the model at constant speed in a direction oblique to the tunnel flow during data collection or modify the wind tunnel air flow in both direction and magnitude with the yacht model stationary. addition of Either procedure could simulate the vectorial boat speed and true wind speed. The former would require a suitably wide tunnel test section and would intro duce uncertainties associated with model inertial response. The latter concept would complicate the synthesis of the onset velocity profile. For present purposes, the added complexity of either procedure is unwarranted in terms of what it would contribute to the results. Therefore, the distortion of re sults that are a consequence of zero boat speed are accepted. The effect of this distortion on the overall test results is assessed in Appendi x A; it is shown to be small. Finally, the apparent heading ( 8 \ ) of a yacht sailing to weather is different from the true heading measured re lative to the apparent wind by the angle\. This small dif ference is measured from the yacht center line and is referred

PAGE 24

9 to as the leeway angle. This angl~ is the effective angle of incidence for the keel. While A is small (on the order of 4 degrees), it is necessary for the development of the keel reaction to the sail-produced heel force. Consequently, the desired component resolution of the aerodynamic sail forces are taken parallel and perpendicular to a plane passed vertically through the yacht and rotated A from the yacht center line. Since the hydrodynamic properties of the hull and keel are unknown and, therefore, ignored in the pre sent work, the aerodynamic sail forces are resolved parallel and perpendicular to the boat center line. This is equiva lent to assuming A= 0. It is seen from Figure 2-1 that this assumption will slightly decrease the component of lift and increase the component of drag in the selected driving force direction and is therefore conservative with respect to the net predicted driving force. Sail Test Similitude Dimensionless variables can be formulated by applica tion of Buckingham's Pi Theorem (15). This is the approach adopted here. For the sailing yacht, forces and moments of interest are res olved with respect to the wind tunnel flow direction. Figur e 2-1 illustrates the Cartesian coordinate fram e selected for this purpose. From the assumption that A = 0, the force coefficient is then defined functionally as F (2-la)

PAGE 25

10 >. Boa t f Headi= n_.g.........._ __ -J + B oat Cente r Line 8 Onset Velocity Profile Note: Force coefficients shown are resolved about an arbtirary point. z J \ \ Fo t ELOA Masthead Level p I H FIGURE 2-1 Coordinate System And Basic Dimensions

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Where the non-dimensional arguments of this function are defined as B = heading angle from the apparent wind to the boat center line 8 = heel angle UT(z)/UT(zMAX) = onset velocity profile normalized for zMAX at the masthead UB/UA = boat to apparent wind speed ratio UT/UA = true to apparent wind speed ratio UAc/v = inertial to viscous force ratio (Reynolds number, Re) X' = rig parameters such as (cat, sloop, cutter, or ketch), vertical or raked masts), (standing rig ging area to sail area), (free board area to sail area), (rig aspect ratio H2/2SA), (etc.) = sail shape and trim parameters such as draft, draft position, foot curve, roach curve, sail dimension ratios (I/P, J/E ) trim angles (oM,oJ), twist parameters (J,M), etc. Lt= dimensionless scale of turbulent lH = the geometric scale factor. 11 It is evident from Figure 2-1 that a smaller yacht "sees" a lower portion of the profile shown. Thus, scale similarity is dependent on the mast height (H) relative to the onset velocity function U(z). Writing the relation between homo logous model (MOD) and prototype (PROT) dimensions defines the geometric scale factor or

PAGE 27

Application of the conditions of negligible leeway, zero heel, and zero boat speed yields = 1 12 For the test results reported, the same sloop hull model with standing rigging is used except for those in which the sail is tested without a hull model. Therefore, in comparing one set of test results with another among the rig parameter variable group (X') the most significant variables are the rig aspect ratio (H 2 /2SA) and freeboard to sail area ratio (FBA/SA). Only these will be reported. Of all the sail shape and trim parameters (x~) only s those that are related to the overall planform shape and the sail trim adjustments furnished on the yacht model are reported. Sail parameters such as the foot and roach curves are proportional for each model and therefore are not listed. Similarly, the draft positions for cylindrical sails are constant and are located at the 50 % chord point. As such, they are not parametrically varied and, therefore, are not reported. The sail shap e and trim param e ter group can then be writt e n as and equation 2-la becomes I X s (2-lb)

PAGE 28

13 Free stream turbulen9e is known to effect both laminar to turbulent transition and separation of the boundry layer attached to a lifting surface. Increased free stream turbu; lence normally results in increased drag and decreased lift. This phenomenon is an interactive one, it is thought to be a function of the scale of the free stream turbulence relative to the scale of the lifting surface turbulent shear layer (16, 17). Specifically, evidence suggests that if the free stream scale is large relative to that of the shear layer, the interaction is negligible. Referring to yacht sails, the free turbulence scale of the majority of the atmosphere is large; however, the scale of the lower regions of the air water interface boundary layer is small. The actual and tunnel simulated velocity profiles are of classical logarith mic form. The portion of that boundary layer normally inci dent on the sails is generally within the "overlap layer" (18). In this region the scale of turbulence is proportional to elevation, z. Investigation within the atmospheric boundary layer over open water by Ruggles (19) and later Groscup (20) included measurements of the Reynolds stress. Groscup (20) gives a value for the planetary boundary la ye r Reyonolds stress per 2 2 unit density of 0.328 ft /s at a height near that of the prototype yacht midchord. This Reynolds stress was measured in a true wind velocity of 4 to 8 kt at a 30 ft elevation~ This is compatible with the conditions of interest here. To compare this to the sail boundary layer, assume it to the that

PAGE 29

of an equivalent flat plate so that a convenient length scale for comparison is the Prandtl mixing length ( ). Then using the one seventh power velocity distribution 14 for the sail boundary layer, one can estimate that the max imum mixing length for the sails is about 0.2 in. at the trailing edge. A similar mixing length calculation, ; m ad e for the planetary boundary layer, incorporating the measured Reynolds stress provided by Groscup gives a mixing length of about 30 in. Defining the prototype dimensionless para meter (Lt) for turbulence scale as PBL SAIL ( 2-2) gives for the velocity range of interest here Lt= 150. This suggests two orders of magnitude difference between the two scales. The preceding estimates refer to actual sailing conditions of a prototype yacht. If this were also the case for th e model sail in the simulated wind tunnel boundary layer, then Lt could be eliminat e d from the perti nent governing p ara me ters. Turbule n t i nt e nsity rat he r th a n Re ynolds stress was e x perimenta l ly m ea sure d in the wind tunn e l. Thus to eval uate th e sam e ratio, th e R e ynolds str e ss must b e inferred from the turbulence int e nsity measurement. The correlation coefficient is defined by = ( 2-3)

PAGE 30

As suggested by Schlichting (1 6 ), it is taken as 0.45 in the overlap layer, and the lateral perturbation velocity 15 v' 2 is assumed directly proportional to~ u' 2 consistent with the experiments performed by Reichardt (16). Given a measurement of~ for the mean velocity profile, on e can evaluate the Reynolds stress using equation 2-3 with the above assumption and approximate the mixing length as u'v' (tPBL)m = 3u/ (2-4) where au/az can be found directly from the measured mean velocity profile at an appropriate height (z), taken here as the height of the planform geometric chord. Equation 2-4 gives a model mixing length (tPBL)m of about 2.0 in. at u 30 = 80 ft/s. The sail model shear layer is considered in the same manner as the prototype; this yields a sail model mixing length (tSAIL)m of 0.02 in. The dimensionless turbulence scale for the model (Lt)m is thus estimated to be about 100. This is sufficient to allow turbulent inter actions to be ignored. As a result, equation 2-lb simpli fies to x' s' ( 2-5) The three-dimensional moments may also be written in coefficient form similar to equation 2-la or

PAGE 31

M ( 2-6) where CPF is the planform geometric chord. The moment co efficients represented by equation 2-6 are subject to the same dimensionless groups as those of equation 2-5. For the experiments reported here, UA is taken as the wind speed measured at the masthead of the model and the three principal force coefficients (reference Figure 2-1) are C X C y C z drag, parallel to and positive in the direction of the apparent wind lift, perpendicular to the apparent wind and to the mast heave, parallel to the mast and mutually perpendicular to C and C X y 16 The corresponding moments C C and C represent moments mx my mz about the same xyz coordinate system. Referring once more to Figure 2-1, the forward and side (heel) force c o efficients relative to the boat center line are then defined respec tively (for A=O) as = C sin y ( B) C cos X (B) = c cos (S) = C sin (S) y X (2-7a ) (2-7b) Equations 2-7 will be used in later discussions regarding potential yacht performance.

PAGE 32

Finally, only one size yacht model is correct rela tive to the fixed onset velocity distribution [UMOD(z)] used here. However, slight extensions of the scale factor (lH) may be assumed without appreciable error. For example, to represent a 30 ft prototype mast height while maintaining the same velocity distribution, the scale factor would increase to approximately 13. Conversely, for a 26 ft prototype mast height, lH becomes approximately 11. Corresponding to these stretched scale factors, the esti mated error in the net forces is .0% of the nominal 28 ft prediction. The uncertainty in predicted force center 17 is .7%, while the moment uncertainty is .3%. The dif ference in average velocity that the sails would see is .0%. All of these percentages are within the estimated experi mental uncertainty of the tests conducted. Accordingly, the test results presented here may be considered applicable within reported uncertainty to sailboats from 18 to approxi mately 26 ft LOA as a function of their mast height off the water.

PAGE 33

CHAPTER THREE YACHT AERODYNAMIC FORCES AND THEIR MEASUREMENT Resolution of Aerodynamic Forces and Moments In steady flow, the net aerodynamic forces and moments experienced by the sails, rigging and above water hull of the sailing yacht are reacted by hydrodynamic forces on the keel, rudder and hull underbody surfaces. These aerodynamic forces and moments are transmitted to the sails, rigging and above water hull via nearfield airflow pressure distri butions and viscous boundary layer shear stresses on every free surface exposed to the flow. From the equations for static equilibrium three components of force and three com ponents of moment are needed to define the net reaction of all the applied aerodynamic loads. Therefore, the direct measurement of orthogonal force and moment triples at any preselected location, on or off the yacht, would yield the net aerodynamic reactions. In order to assess the contribution that the aerodynamic forces make towards the balance and stability of a yacht it is necessary to know both the magnitude and the location of these forces. For this purpose, the center of effort is commonly defined as a point in space where the applied aero dynamic forces may be resolved so that the net aerodynamic 18

PAGE 34

moment about this point is zero. Appendix B discusses, in detail, resolution of the sail aerodynamic loads and the ex perimental determination of the yacht's center of effort. In general, it is demonstrated in Appendix B that direct measurement of forces and moments relative to an arbitrary global origin will not uniquely yield the center of effort location. As such, the center of effort must be known a priori or must be estimated from some physical constraints of the experiment. Common Measurement Methods 19 The measurement of forces and moments resulting from flow about the sailing yacht model may be accomplished by any of three different methods: 1) Measure the pressure distribution over the free surfaces (Equation B-2) and sum the measurements as a function of area (Equation B-3) ; 2) Survey the upstream and downstream flow for momentum difference and evaluate the stream wise static pressure distribution upstream and downstream of the model (valid for steady flow only); 3) Measure the three orthogonal components of force and moment via a force transducer or balance directly. Pope and Harper (21) discuss each of th e se methods in detail relative to wind tunnel tests of aircraft. They indi cate that three forces (lift, drag and yaw) and their companion moments completely describe the local spectrum of interest for aircraft. Symmetry and aircraft design experience indicate

PAGE 35

20 that the point of resolution for these forces and moments is normally considered to be known a priori. These restrictions admit a unique solution for the aircraft. However, as discussed in Appendix B, this is not the case for the sailing yacht. Most sails, including those tested, are thin. As a result surface orifices for pressure measurement are impractical. Wake survey methods are of use but require the measurement of both static and dynamic pressure at each survey point. Hence, the accuracy of any calculated force from such a survey is a func tion of the number of survey points selected. In order to reduce the number of measurements, it is common practice to measure only stagnation pressure at each of the survey points and to measure the static pressure at the wind tunnel wall. It is then assumed that this static pressure is uniform across the section of the tunnel where the measurements are made. This assumption is valid providing the distance downstream from the model is sufficiently far to allow static pressure recovery. Unfortunately, this is not often possible due to changes in wind tunnel geometry downstream of the test section. These can cause appreciable wall effect losses that must be accounted for with the consequence of an increase in the level of experim e ntal uncertainty. Dir e ct measurement with a force balance is the simplest and most straightforward method of attaining net force and moment data. However, as discussed above, specific details as to local force and moment distribution are not possible.

PAGE 36

21 In the present work, a six-component force balance has been used to measure the aerodynamic response of various model sailing yacht rig configurations. A general discussion on six-component force balances is given in Appendix C with de tails of the six-component floating beam balance used here. The net maximum uncertainty for each force and moment coeffi cient range discussed in Appendix C is calculated employing the methods of Holman (22) and is given in Table 3-1. In addi tion to these direct measurements, the static pressure through the wind tunnel test section was surveyed both upstream and downstream of the model to establish correction parameters for solid blocking and horizontal bouyancy.

PAGE 37

Coefficient Range Uncertainty Coefficient Range Uncertainty Coefficient Range Uncertainty Coefficient Range Uncertainty Coefficient Range Uncertainty Coefficient Range Uncertainty TABLE 3-1 Experimental Force and Moment Coefficient Maximum Uncertainties Cx 0.0 to 0.2 0.2 to 0.4 .3% .9 % Cy 0.0 to 0.5 0.5 to 1.0 .0% .9% Cz -0.4 to -0.2 -0.2 to -0.1 .0% .1% Crnx -3.0 to -2.0 -2.0 to -1.0 .8 % .8% Cmy 0. 0 to 0.2 0.2 to 0.5 .1% .8 % Cmz -0.2 to 0.2 0.2 to 0.4 .1 % .6 % 22 0.4 to 1.0 .1 % 1.0 to 1.-5 .8% -0.1 to 0.0 .2% -1.0 to 0.0 .9 % 0.5 to 1.5 .6 % 0.4 to 0.6 .1%

PAGE 38

The Wind Tunnel CHAPTER FOUR EQUIPMENT AND APPARATUS The most essential piece of equipment used for the tests reported herein is the subsonic wind tunnel at Embry-Riddle Aeronautical University, Daytona Beach, Florida. This wind tunnel is a closed circuit, vertical, single return design which has an enclosed, low-speed and high-speed test section. Flow is produced by a 6-blade, fixed pitch, laminated wood propeller 56 in. in diameter, that is driven by a 385 horsepower, 8-cylinder internal combustion engine. Speed control is provided by throttle and a 3-speed fluid drive transmission. Figure 4-1 illustrates the overall dimensions, general arrangement and location of the main features of interest. The operational range of the tunnel is from Oto 190 ft/s, 0 to 96 ft/sin the low-s peed and Oto 190 ft/sin the high-speed test sections. The low-speed test section is octagonal, 36 in. high by 52 in. wide, with a cross-sectional 2 area of 11.5 ft. To permit easy access to the model area and force balance, the entire low-speed section is mounted on a wheeled frame and can be removed from the tunnel proper. The six -com ponent floating beam balance was installed on the under side of this test section, external to the tunnel 23

PAGE 39

~-------------44 .0 ft \ :\ / ~ ' I "' : ~ -, \\ \ '\ \ .'\. . \ \ \ \ ' ', '," / ',' !' ,~;\ . [;( \~ \ \\ I \ '',\\I 0 ~"-'\ / ~' \ ', '', -Flo\'! Straightene r Velocity Profile Screen Removable Low Speed Test Section TS 0 TS 68 Floating Beam Balance Turning -J Vanes FIGURE 4-1 ERAU Subsonic Wind Tunnel General Arrangement. I\.) .i,.

PAGE 40

25 interior. The rectangular high-speed test section is 24 in. wide by 36 in. high with an area of 5.96 ft 2 Considering the effects of solid blocking together with the size of model needed for reasonable scale similitude, the low-speed test section allows the most flexibility and was used for all the results presented. The low-speed test section was designed with 1/2 degree diverging walls to maintain a constant strearnwise static pres sure through the section as the wall boundary layer thickens in the strearnwise direction. For the range of velocities of concern here, the turbulence intensity of the mean flow is less than 0.004 and is considered well within acceptable limits for low-speed testing. The velocity distribution through the test section is uniform to within %. This, of course, was intentionally modified along with the turbulence intensity to produce the model velocity profile discussed in the next chapter. Data Collection and Reduction The experimental data presented were collected with the six-component floating beam force balance discussed in Chapter Three via a ten-channel Baldwin-Lima-Hamilton (BLH) M od e l 225 Switching and Balancing Unit and int e rpreted with a BLH Model 120C Strain Indicator. Each of the flexural elements of the force balance was fitted with a matched pair of Micro Measurement EA-06-250BG-120 precision 120 n gauges which were wired as two arms of a four-arm Wheatstone bridge circuit on

PAGE 41

26 the Model 225 Switching and Balancing Unit for each of the six channels monitored. The remaining bridge circuit was completed using two precision 120St "dummy" resistors. Strains were read directly from the Model 120C Strain Indicator in microinches per inch, in./in. The backup and calibration check unit used for the BLH system was a Vishay Instruments BAM-1 Bridge Amplifier and Meter. System calibration checks were made monthly to ensure that experimental accuracy was maintained. Flow air temperature was measured upstream of the low speed test section at the inlet co~~raction cone by a mercury bulb thermometer probe connected to an external dial-type indicator which reads to precision. Flow velocities were inferred from direct measurement of the local static and dynamic pressure with a common Pitot-static tube and a 50 in. water manometer. A Thermonetic Corporation HWA-101 hot wire anemometer was used for backup and to augment velocity survey measurem e nts. The force balance calibration equations were incorporated into a Fortran computer program along with all the pertinent flow relations for Reynolds numb er yacht rig c0nfiguration sail area calculation, wind tunnel solid blocking and horizontal bu oyancy corrections Th e strain gau ge resistanc e data for all six strain channels at ea ch heading angl e test ed were load e d to a computer disc file. In addition, flow air temp e ra ture, the static and qynamic pressure at the masthead and the

PAGE 42

27 rig configuration geometry were stored in this file. All of this information was subsequently processed through the Fortran program BOAT (a listing BOAT is given in Appendix D) on a Hewlett Packard HP-100~ mini-computer. A sample of the typical output information is shown in Table 4-1. The xyz coordinate system is global; x being in the flow direction and z vertical while the boat coordinates of "Drive", "Heel" and "Vertical" are those as illustrated in Figure 2-1.

PAGE 43

TABLE 4-1 Typical Output Format From "BOAT" RU,BOAT 1 INPUT NAME OF FILE RUN DATA IS STORED IN (UP TO SIX CHARACTERS,FIRST CHARACTER START IH COLUMN 1, JUSTIFIED LEFT, INCLUDE TRAILING BLANKS, IF AHY) T15MH1 WIND TUNNEL DATA REDUCTION PROGRBM SAIL BOAT DATA INPUT INPUT SAIL DIMENSIONS (for model) I J P E Cinches) 25 8 22.5 9 INPUT PERCENT OVERLAP, FRACTIONAL RIG FACTOR 1 5 I 1 WINO TUNNEL EXPERIMENT, DATA REDUCTION OUTPUT TEST MODEL : SAIL BOAT 28 7/12/82 STD 150 SLP, W/PBL, FLOOR SEALED, STD ASPECT RATIO. SAIL DIMENSIONS I= 25.00 J = 8.00 p C 22.50 E 9.00 SAIL AREA (ACTUAL) = 1.82ft**2 SAIL AREA (100 Z F.T.) = 1.~0 PERCENT OVERLAP= 1.50 FRACTIONAL RIG FACTOR= 1.00

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29 TABLE 4-1 -continued SAIL ANGLESCOEG),VELOCITYCFPS),REYNOLO~ NUMBER, DYNAMIC FORCE COU R SE Delta Delta REYNOLDS DYNAMIC ANGLE jib main VELOCITY NUMBER FORCE 8.0 12. 0 0 .o '78. 41 402566. 12.50 15.0 12 0 0.0 79.36 407417. 12.78 20.0 12.0 0.0 80.06 411020. 13.01 25.0 1 2 0 0 .-0 81 35 417675. 13.44 30 0 12.0 o b 81 50 418426. 13.46 35 0 12. 0 0.0 82.01 421015. 13.58 40.0 1 2 0 0. o 82.34 422739. 13.69 46.0 1 2 0 0.0 82.71 424646. 13. 81 FORCE ANO MOMENT COEFFICIENTS RELATIVE TO THE WINO COURSE ANGLE Cx Cy Cz Cmx Cmy Cmz 8.0 .2607 .3778 -.0427 -.0800 .0569 .0769 15 0 .2727 .6533 -.0773 -.3655 .0698 .0538 20.0 .3207 .8607 1086 -.6114 0727'" .0206 25.0 ~3542 1.1499 1402 -.7936 .1124 -.0032 30.0 .4592 1.3206 1672 -.9597 1241 -.0430 35.0 .5641 1 4165 1878 -1.1360 1755 -.0571 40.0 .7103 1 4 891 -.2095 -1.0961 .2723 -.0408 46.0 .9575 1 4652 -.2202 -1.1495 .4645 -.0164 FORCE ANO MOMENT COEFFICIENTS RELATIVE TO THE BOAT HEEL PITCH YAW COU RSE DRIVE HEEL VERT. MOME N T MOME N T MOMEt'lT ANGLE C OEF C O EF COEF. COEF. COEF. COEF. 8 0 ,.,oc5 L 1 4 1 0 4 -.0427 .0 8 71 .0 6 75 .0 769 1 5 0 0943 .701 6 077 3 .3711 1620 0 538 20.0 0070 9 1 85 1 086 .5 994 .2 77 4 .0 206 2S.O 1 649 1.1 9 1 8 -.14 02 .7 668 .4 3 7 3 -. 0032 3 0. 0 2 626 1. 3 7 3 3 167 2 .89 32 .5 8 73 -.0 43 0 3:, 0 .3503 1 4 84 0 1878 1.0 3 1 3 .7953 -.0571 40.0 4130 1 5973 -.20 9 5 1.0 1 4 8 .913 2 -.0 4 0 8 46.0 3 88 7 1.706 6 -.2202 1.1327 1. 14 9 5 -.016 4

PAGE 45

CHAPTER FIVE SYNTHESIS OF THE ONSET VELOCITY PROFILE Motivation and Basic Approach The sailing yacht is subject to a non-uniform onset velocity resulting from the vector addition of the atmos pheric planetary boundary layer (PBL) and the yacht's for ward velocity. This summation produces what is termed the yacht's apparent wind. The magnitude of this apparent wind varies as a function of vertical height while its direction tends to rotate aft from the deck to the masthead of the yacht. Proper modeling of this boundary layer with respect to a sail rig configuration is essential for achieving scale similitude. Previous tests of sails and rig configurations (8, 9, 10, 11, 13) both twoand three-dimensional, have not used such an onset velocity. As such, conclusions re garding lift, drag and center of pressure could be signi ficantly different than with non-uniform onset. Modeling both the variation and direction in the wind tunnel is difficult. Modeling only magnitude variation with respect to one geometric axis is commonplace. Well developed methods for modifying a wind tunnel velocity profile exist (23, 24, 25). When the size of a particular wind tunnel is fixed in shape upstream of the test section, methods which develop a desired velocity distribution by artificial fetch 30

PAGE 46

31 (roughness pegs, counter jets or, simply, the length of upstream convergent section) must be discarded. A more direct approach in such cases is to progressively impede the flow in the geometric direction of the desired velocity variation. That is if U = U(z) (5-1) the direction of impedance (I) would also be I= I(z) (5-2) This simple approach implies that a desired distribution could be synthesized by physically obstructing the flow up stream of the test section. In principle this is correct. However, the level of turbulence introduced into the flow due to the upstream obstruction(s) must be within some pre determin~d limits. Similarly, the pressure drop across the obstruction equates to an overall reduction in tunnel operat ing efficiency. Wi t h these considerations in mind, a direct impedance sch eme can be planned to provide a desired velocity distribution and a reasonable turbulence intensity in the wind tunnel te s t section. The Model Atmospheric PBL and Scale Effects The measurement and formulation of the atmospheric bou nda ry layer above the ocean has been the topic of numer ous research efforts (19, 20, 26, 27). For modeling such a boundary layer in the wind tunnel with respect to the

PAGE 47

32 sailing yacht, only the first 100 ft, measured from the water surface, is of interest. In this first 100 ft, often referred to as the surface layer, the characteristics of the actual PBL that are of significance towards such test ing, for ste a dy flow, are as follows: The wind d i rection is essentially constant and Coriolis effects may be ignored. The long d u ration vertical velocity distribution is logarithm ic in form to within a 95% certainty. The scale of turbulence in the PBL is large re lative to that of the sail boundary layer (this is verified in Chapter Two). Vertical variation of stresses and other fluxes can be negl e cted. The friction velocity (u*) can be assumed a linear function of the wind speed rate of shear and is defined as u* = where Tw is the shear stress at the boundary (water plane) and p is the local flow density. N eg lecting conv e ctiv e terms, the generally agreed-upon form o f the long duration, stable surface layer PBL is where U(z) = u* K z ln(-) z 0 (5-3) z = vertical distance above the water plane U(z) = velocity at height z K = von Karman Constant taken to equal 0.42 z = roughn e ss length 0

PAGE 48

From this form Kerwin (28) has developed a useful average wind gradient formula applicable to the sailing yacht in terms of the wind velocity at a height of l0(m) above the water surface [u 10 J and the vertical position (z) for any profile velocity as U(z) = 0.1086 u 10 ln[304.8z(m)J (5-4) 33 Since equation 5-4 was that adopted by Register in his vortex lattice scheme, it will similarly be the profile shape syn thesized in the wind tunnel. As mentioned in Chapter Two, similarity requires that a specific size yacht be determined for test that simultan eously sizes an explicit portion of the PBL which must be synthesized. Converting equation 5-4 to scale (lH = 12) yields U(z) = 0.1086 lnz(in.) + 0.4918 0 30 ( 5-5) where z is measured above the wind tunnel floor. Equation 5-5 is considered the desired shape of the scale velocity profile to be synthesized in the wind tunnel. Profile Synthesis The details of the direct impedance method used to syn thesize the velocity profile described by equation 5-5 are given in Appendix E. The profile obtained by this method

PAGE 49

fits the desired profile to a confidence of 96.5% using a least squares logarithmic curve fitting scheme on the measured velocity values. The turbulence intensity dis tribution through this synthesized profile has also been measured and it has been fo~nd to be in reasonable agree ment with classical turbulent boundary layer measurements. 34

PAGE 50

Planform Geometry CHAPTER SIX YACHT MODEL DESIGN As discussed previously, the overall model dimensions were selected as a function of the wind tunnel test section size relative to the type of yacht data desired. Consis tent with popular sailcraft nomenclature, the primary geometric dimensions of the sail planform are I, J, P, and E as illustrated in Figure 2-1. The right triangle formed by the horizontal "J" and vertical "I" dimensions is termed the sail planform "fore-triangle". The vertices of any foresail and the edges between these vertices are shown in Figure 6-1. The luff perpendicular (LP) is drawn from the luff to the clew as shown. Foresails or headsails which exceed the fore-triangle area are named or "rated'' as a percent of "J". Ergo the 150% genoa headsail is a sail with LP=l.SJ. The region of the sail area which extends beyond the J dimension is termed the "overlap". For the research reported here, it is convenient to define th e overlap ratio (OR) factor where OR= LP J Similarly, sloop rigs which have fore-triangles that do not extend to the vessel masthead are termed "fractional 35

PAGE 51

36 Head Luff I Clew Fo ot FIGURE 6-1 Sai l Ge o metry Nome ncl a ture.

PAGE 52

rigs". To classify these geometries, one can define a fractional rig factor (FRF) FRF = (I) (P+BAD) where (P+BAD) is the distance from the yacht deck to the masthead and for convenience is set equal to H. 37 The foresail triangular area (SAF) can then be written as The mainsail dimensions are designated P and E, Its triangu lar area (S) is The rig planform area used for all of the force and moment coefficients is the sum of the foresail and mainsail area SA= SAF + S~ This area is slightly smaller than the actual sail area due to the curvature or "roach" of each sail's tr a iling edge. I t is common practic e to omit this ar e a when de f ining sail ar ea Rig aspect ratio is another quantity of interest and is somewhat more arbitrary in definition. The classical definition of aspect ratio used in the sailing community is

PAGE 53

38 defined by the particular sail being referenced. The main sail aspect ratio is taken as p A= E while the fore-triangle aspect ratio is I ARJ = J For the present work, it is desirable to use an aspect ratio that adequately represents the entire rig configuration re flecting both mainsail and jibsail aspect ratios. For this purpose, a rig aspect ratio is defined here (for H=P+BAD) as AR = (H) 2 2SA It is believed that this definition is compatible with the classical individual sail aspect ratio definitions while satisfying the need for a single representative value for the rig. The mean planform chord length is taken to be SA.M [-] p Main Test Reynolds numbers for each wind tunnel test run are calculated using this chord length. It is reasoned that CPF represents a realistic average length for the evaluation of the flow related viscous forces as opposed to other charac teristic lengths which could be offered. This is thought

PAGE 54

to be significant when comparing such test results to other wind tunnel data, either sail or airfoil, where the Reynolds number characteristic length can easily be ascertained. Table 6-1 lists the planform geometry of the rigs investigated. Comparing the mean planform chords for the different configurations permits an interpretation of the similitude scaling problems discussed in Chapter Two. Indeed, if the mean planform chord provides a representa tive flow Reynol d s number and if the effect of Reynolds number variation on the aerody n amic performance of a rig is strong, then results for the catboat (CPF = 4.6 in.) compared with those of a sloop (CPF = 5.3 in.) for the same wind velocity at the masthead, could be quite differ ent than at the same Reynolds number. This observation would, in effect, make the Reynolds number a significant design parameter and somewhat removes the regime-like con clusions often made for wing and airfoil theory. There is strong evidence that both of the premises 39 offered above are valid. 6 For Reynolds numbers less than 10 the viscous flow effects are strong and the amount of sur face area exposed to the flow is increasingly important; that is, th e force coefficients produced by a thin single cambered surface in the flow are non-linear and vary with ~amll changes in Reynolds number. Figure 6-2, reproduced here from NASA CR1767 (10), is an illustration of this

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Configuration Reference Code* T00CBl Tl5MH1 Tl5781 Tl5341 Tl5121 TOSCBl Tl5MJ2 Tl5MJ3 TABLE 6-1 Planform Geometries Rig Description Finn-Type Sail Sloop Masthead Sloop 7/8 Sloop 3/4 Sloop 1/2 Catboat Sloop High AR Jib and Main Sloop High AR Jib Alone FRF 0.0 1.00 0.875 0.750 0.500 0.0 1.00 1.00 I 0.0 25.00 21.88 18.75 12.50 0.0 25.00 25.00 NOTE: Dimensions shown are in inches 0.016 in. Planform Nomenclature J p E o.o I 24.80 I 15.30 8.oo I 22.50 I 9.oo 7.oo I 22.50 I 9.00 6.oo I 22.50 I 9.oo 4.oo I 22.50 I 9.oo o.o I 22.50 I 9.oo 6.oo I 22.50 I 6.43 6.00 I 22.50 I 9.oo PO 0.0 1.52 1.52 1.52 1.52 0.0 1.52 1.52 *Configuration Ref e rence Codes are used throughout this work to cross reference test information. 0

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f,z w u IJ.. IJ.. w 0 u f,IJ.. ....J z 0 f,u w V, 41 2 S r ----+ ~= 1 ~ ] l '' t ---+----+2 0 +--+--.--+--l -+---+---4 1.6 I l -1 I -t -i -t 20% Change in CL for 0 8 I f' 0 4 0 I 0 4 -24 -+--4--1----. .., .,___.__ ___..,~, ___ _,,... .6. Re= 3. 0 x 1 0 5 -12 -8 -4 0 Re = 1 2 x tQ6 I 4 8 A n gle of Att a c k ( deg r ees ) 12 16 20 FIGUR E 62 Lift Coefficient v s A n gle of At t a ck for a Thin, S ingle Cambered Se ction as Measured by Milgrrun (r ef CR1767) for Three Reynolds N umbers o.n d as P redicted by Thin Airfoil Theory.

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effect. For the sailor though, the point of interest is normally the rig performance at a given wind speed. Thus, increasing or decreasing the Reynolds number can play an important role as a practical performance parameter. For the results presented here, comparisons are made for the same masthead velocity on each of the rigs tested. Each will, therefore, be at a different Reynolds number as a function of CPF" Model Geometry and Trim Adjustments 42 The geometric scale factor (lH) is taken as 12 to per mit a model size that is within acceptable limits relative to wind tunnel test section blocking requirements. This size also provides a fair representation of actual sailboats ranging from 18 to 25 ft LOA for the wind velocity profile being simulated. A scale mast height above the water sur face of 28 ft is chosen to allow a reasonable fit with the planform geometries previously defined. Figure 6-3 gives the overall model and standing rigging dimensions. The different planform geometries are also shown for clarity. Deck size is arbitrary and is selected to permit a reasonable arrangement of sail trim control and adjustment devices. The standing rigging acts as the structural sup port for the sail and consists of upper shrouds and a backstay. The upper shrouds are adjustable to maintain the mast perpendicular to the deck in the athwart-ship direction and to control the shroud tension. Backstay tension is also

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I I 2 5.0 3 .0 Mas t, 3 / 8 in. Dia. Sp re ade rs 1/ 8 in. Dia. 8.0 4.5 Std. Sloop 7/8 Sloop 3/4 Sloop S hrou ds 1 / 32 i,n. Dia. Aluminum S h ee t i--10.0 -23 .0 I I Mai n Trim D eck(3/4 in. plywood) High AR Main Ba ckstay 1/1} l // /lll/1/I/IIII _j__ I ) ) y' W / 3/ 'funnel 77 l I/II/Ill/I// r71/I/III//I/I/// / T Floor 3 /16 in. Li Clearance FIGURE 6-3 V/i nd Tunnel Yacht Model Configuration s (A ll d imensions given are in inche s ) w

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adjustable and can be used to bend the mast in the fore and aft plane. The mast is rigidly fastened to the deck to prevent its base from rotating about the athwart-ship axis. No forestay is used. Instead, the metal fore-sail head is attached directly to the mast by a threaded 44 fastener and the tack is connected to a through-deck adjust ment screw. Tensioning the luff via this screw controls the fore and aft position of the masthead and opposes the back stay. In contrast to cloth sails, an increase in luff ten sions on the metal sail does not move the sail draft forward and only the lower one-third to one-half of the sail draft is adjustable by means of sheet trim and clew downhaul. Upper section headsail draft is rolled into the sail prior to installation on the model and can only be altered by re rolling. Headsail sheet trim is achieved by means of a threaded rod adjustment device that is fastened to the deck. When the length of the rod is reduced, it draws the sail clew aft. This decreases the trim angle and flattens the lower portion of the sail. Headsail le ech downhaul is attained using a second device fastened directly to the sail clew and to the model deck. Therefore,the clew vertical posi tio n can be changed, secured and maintained throughout testing. The mainsail boom i~ equipped with a traveler/downnaul that permits the trim angle and sail twist to be controlled adequately. A downhaul adjustment permits the leech tension

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to be eased or tightened as needed. Finally, a mainsail clew may be trimmed independent of the trim angle or leech tension. Sail Construction All the sails are made of 2024-T3 aluminum sheet, 45 0.020 in. thick, cut to the planform described above. Each sail is then rolled parallel to its luff to produce a cylin drical surface such that any camber line drawn perpendicular to the sail luff is a circular arc or constant radius of curvature. The LP, the longest such camber line, and the sail draft depth (d) as a proportion of straight line chord lenght are used to define a characteristic radius of curva ture or r = 2 -1 LP [ARCCOS(l-4(d) )] 2 1+4(d) 2 (6-1) For the headsail, (I 2 +J 2 is taken as the cardinal surface ruling Then the total surface is easily defined in cylin drical coordinates by equation 6-1 for the intervals and 2 0 < A < 2 ARCCOS[l4 (d) ] 1+4(d) 2 (6-2)

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where Z I = -J [ 1 ] F o (I/J) 2 +1 Figure 6-4 illustrates the coordinate system and the surface bounds. The z' coordinate system is rotated and translated relative to the previously described global coordinates. z~ and z~ are foot and leech bounds respec tively. Equations 6-1 and 6-2 in the defined intervals of 46 A and z' describe the cylindrical headsail in terms of its rated dimensions. Similar intervals can be written for the mainsail in terms of its P, E dimensions and the d proportion. With the geometry of the sail defined as indicated, it is clear that the deepest draft point of each sail is located at 50% chord. While this is farther aft than suggested by current sailing wisdom for the headsail, it is approximately correct for the mainsail. This divergence from current sail set philosophy is considered acceptable for the comparisons made here, since it is consistently applied throughout all of the rig configurations tested and is similarly employed for the vortex lattice models discussed later. Certainly, such comparisons should establish performance trends and it seems probable that these trends should be preserved as the deepest sail draft point is moved moderately further forward.

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I Zr, cd ~ C FIGUR t 6 4 Sai l S ur f a c e Des c r ip ti o n z 47

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48 Sail Trim, Setting and Measurements The model deck is equipped with two protractor scales; one to measure the headsail trim angle (oJ) and one to mea sure the mainsail trim angle (oM) relative to the boat cen terline. The trim angle is defined as the angle between the boat centerline and a line drawn from tack to clew along the foot of the sail in question. Each sail has camber lines drawn at selected z-locations as shown in Figure 6-5. Once the sail is fitted to the model, a sail "set'' may be de scribed by measuring the leech position of each camber line relative to the vertical plane that contains the foot trim angle line, thus yielding the sail twist. The draft position and depth of draft are measured directly from a line drawn from the camber line luff the camber line leech. In total, these measurements provide a mapping of sail shape which characterizes a particular set. Finally, each sail is equipped with tufts along both the luff and leech on both windward and leeward sides. By direct visual observation of tuft motion, any sail set may be assessed for attached or separated flow. This visual observation is useful prior to test data collection to ensure that reasonable trim has been attained and that no large scale flow separation exists over the planforrn.

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Headsail Twist 24.0 J = 24 20.0 3 Mainsail Twist ~1 = 7 0 00 M = 0 Mainsail Chords 2.4 49 = 22 .5 16.0 3.7 J2 J = 2 1 1 0 J = 0 1 2 1 2 .0 5. 1 8 .0 4.0 6 3 ,,,,,,, Model De ck Level FIGURE 6 5 Typical Sail Camber Lines Draft and T\'Iist Meas ur eme nt Location s ( Dimen s ion s shovm are in inch es .)

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CHAPTER SEVEN COMMON EXPERIMENTAL PROCEDURE Sail Trim Pre-Test Prior to each configuration test, the model was placed in the wind tunnel with an approximate sail set and trim. A first order approximation of trim was established at pre selected trim angles for the jib and main with draft and twist selections estimated from sailing experience and judgement. An observation test run was then conducted to assess the twist and draft set. The sails were inspected for windward or leeward separation. For this purpose, a large mirror was installed on the far wall of the wind tun nel test section; this allowed simultaneous observation of both sides of the sails. If flow separation was noted from the motion of the sail tufts, appropriate trim adjustments were made. Such adjustments w e re analogous to their counter parts of the full scale yacht, each adjustment having the corr e sponding e ffect. For example, if large separation was not e d aloft on the l ee ward sid e of th e jib, a correction wa s to e as e the l ee ch downhaul which induced increased sail twist. This is analo g ous to moving th e jib sheet fairlead a f t on a full scale sailboat which r e lax e s leech tension and increas e s twist on the upper portions of the sail. 50

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With the wind tunnel operati~g at approximately the speed of the intended test, the model was slowly rotated through a range of heading angles from approximately 10 to 45. Leading edge and trailing edge separation points were noted using the tufts as indicators as a function of Band a few strain gauge resistances were recorded at the maximum y-force point. Small adjustments were then made to the trim 51 to maximize the lift force as indicated by a maximum resis tance reading. The model was rechecked for leading and trailing edge separation heading angles. Finally, the wind tunnel was shut down, the model removed and sail trim measure ments were recorded (reference Table 7-1). Wind Tunnel Test The model was reinstalled in the wind tunnel and the force balance was nulled on each of the si x channels with the model set at a heading angle of B=l0. The model was ro tated through 45 to indicate if any weight balancing was necessar y to maintain each of the six channel null points. Variations in resistances that correspond to more than 5in. were corrected by th e a ddition or removal of weights from the model. The cor r ect model center of gravity having been determine d rel a tive to the force balance, the wind tunnel was started and brought up to test speed. Raw test data were r e corded manually for each channel at each heading angl e and checked for repeatability in an up-down reading sequence. Head ing angles were index~d in approximately 5 increments from 10 to 4

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Configuration Reference oJ Code T00CBl N/A TlSMHl 12 Tl5781 12 Tl5341 12 Tl5121 12 T0SCBl N/A Tl5MJ2 12 Tl5MJ3 12 TABLE 7-1 Mean Sail Shape and Trim Parameters (Per~ipan) dJ N/A N/A 16 12% 18 10% 20 11% 18 11% N/A N/A 14 10% 14 10% oM (Per ~pan) oo 32 oo 30 oo 31 oo 33 oo 35 oo 36 oo 22 oo 24 dM 11% 12% 12% 11% 12% 13% 7% 11% (J1 N

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53 During each test, the static and dynamic pressure of the flow at the calibration point (3.00 in. above the model masthead) were noted along with the airflow temperature. At the end of each test, the force balance was checked for zero return. Any zero drift error found was investigated. If the error was in excess of Sin., that set of test data was discarded. For such cases, the same configuration was rerun. Each configuration test required approximately two hours of wind tunnel run time. After each run, a calibration check was made on the force balance and the calibration equations were adjusted accordingly.

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CHAPTER EIGHT MODEL CONFIGURATION TEST RESULTS The Finn Type Sail Test The Finn is a simple, one-design catboat rigged, sail ing dinghy which offers an easily modeled sail planform (reference Table 6-1). Marchaj (8) has used a one-seventh scale (1H=7) fabric scale model of the Finn sail to experi mentally investigate the effects of boom vang tension and resulting sail sha : on the total sail lift and drag coef ficients. His test results were achieved under uniform onset flow conditions and they are reported at scale Reynolds numbers that are in the range reasonable for similitude. In the present work, a geometric scale factor of 1H=9 yields a Finn model of appropriate size to fit the wind tun nel test section without severe blocking. This model was constructed absent of a hull and deck to permit an accurate determination of the sail force center both with and without a simulated non-uniform onset velocity. The non-uniform velocity profile that was used in these tests is described in Chapter E iv e and, ; thus, is slightly distorted relative to the portion of the tru e PBL that the full-siz e prototype Finn sail would actually ''see''. This distortion however, is believed to be unimportant for the comparisons presented. 54

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55 The sail planform is given in Table 6-1, Configuration Code TOOCBl. The sail model was rolled to a cylindrical shape parallel to the luff and fastened to a cylindrical shape parallel to the luff and fastened to a mast/boom assembly. The mast/boom assembly was stiffened using a small spreader and shroud combination. This stiffening was necessary since the mast section modulus must be small in order to conform to the prototype mast. Its contribu tion to the resultant drag has been verified by measuring the drag of bare poles (mast and boom alone). This test indicated that the mast drag contribution was negligible. Camber lines at 4 in. intervals starting at the boom were used to define draft and twist. Since this model had no hull or deck, the adjustments of the sloop model tests were not available and the sail set capability was correspond ingly limited. Angles of attack measured between the boom and the wind tunnel center line were used in place of head ing angles. Partial sail twist control was realized by using a boom topping lift and vang but at a slight drag increase. At large angles of attack, the stress on the sail was observed to be sufficient to slightly alter the initial sail twist. Naturally, the effect increased with increasing flow velocity. The same effects would occur on the prototype Finn but vang, sheet and mast bend have not been modeled propor tionately for the wind tunnel test. Therefore, at large flow velocities (Reynolds numbers) there would be some de parture from geometric similitude.

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Direct flow observations on the windward side of the sail were of particular interest both with and without the PBL velocity profile. Figure 8-1 illustrates a side view of the model and the positions long yarn tufts assumed 56 when placed in a 40 ft/s flow with the sail model at an angle of attack of 25. Using the camber lines for approxi mate measurement, a yarn tuft was estimated to be near the windward side of the sail pressure center if it was not deflected up or down relative to the horizontal plane. This observations was made with the non-uniform logarithmic ve locity profile in the tunnel and tuft #2, approximately 0.36 H above the floor, was estimated to be at the windward side center of pressure. Similar observations of the leeward side of the sail were not as informative because of large random yarn motion. As expected, two strong votices were seen; one near the masthead and one near the boom. A top view of the leeward side, Figure 8-2, reveals the strong upwash which was ob served upstream of the leading edge and smooth flow to about the 3/4 chord point where turbulence and the shed trailing edge vortex displaced the yarn. Near the 0.36 H height noted, an upwash angle of approximately 10 at the sail leading edge was measured relative to the wind tunnel centerline. This angle appeared to vary along the leading edge as a function of vertical position.

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Tuft #6 #5 #2 #1 z( in.) 30 20 10 57 Wi nd Tunnel c:-:11 7 7 7 7 7 7 7 7 7 @-.. ~,_::)Ir-~.,..-:......,....""'---,---'-~~r_.-'---r-'---,--'-~~r__,r-<. Flo or FIGURE 8-1 Finn Sail Yarn Observations. ----Observed yarn motion for the Finn sail at an attack angle of 25, V=40 ft/s, without the simulated PBL. Tunnel Center ---~ L ine 0 10 (A pp ro x .) --J!o:td L. ~.:Z.lle Sail Trailing.:z. 12 Edge FIGURE 8-2 Finn Sail Upv 1ash Obse rv a tion. Position ass umm ed by a lon g yarn on the lee\'tar d side of th e sai l as vic, ,ed from above

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58 While the above observations come as no surprise, they do provide insight and evidence in support of concepts suggested later in this work. For instance, the strong upwash noted is in agreement with the arguments offered in Appendix A for quantifying the magnitude of relative wind twist that results solely from the sail circulation and is almost independent of boat speed. The results of the force balance data collected for the Finn sail, both with and without the simulated PBL onset velocity profile, are given in Figure 8-3 as lift (C) and X drag (Cy) coefficients along with the lift to drag ratio (C /C) plotted against the attack angle. Selected data y X points from Marchaj's work are superposed for comparison and are seen to be in fair agreement considering the large differences in models used (metal to fabric) and the unre ported uncertainty of the earlier work. The second stall or "bump" seen in both C -plots at approximately 30 attack y angle for uniform and logarithmic onset velocities is thought to be a result of sail trim changes caused by the pressure distributions in these high loading conditions. Both tests were conducted for a velocity of 80 ft/sat the model masts head and a Reynolds number of 3 x 10 The simulated PBL had the effect of decreasing the lift and drag values over those measured for uniform flow at the same attack angle. As a point of interest, the negative vertical force coefficient is also plotted in Figure 8-4 for the case with

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3 5 3 0 2 5 1. 5 1. 0 0 5 LEGEND SAIL SHAPE AND TRIM Wit h PB L W i t ho ut PBL Mar c ha j I s Da t a 6-----~ D C X O Cy v CY / ex / / \ 1/ V l \ 't \ 0 J = N / A 1J = N / A dJ = N / A _;JGr-0 ~ l"."I / / ---G---~ --~ ,, 0 ~/ 10 20 30 40 HEADING ANGLE(Degrees) 0 ~M = 32 dM= 11 % so 59 F I GUR E 8 3 Eff e ct of the Pla n eta r y Bo un da ry La y e r o n Sa il Te s t Da t a F i n n c a il fo r Re= 1. 8 x 1 05 v s M n rch o j s da t a fo r R e = 2 2 x 1 0 5

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the simulated PBL. Because of mast and sail deflection under load, a small projection of sail area can be ob tained in the xy-plane. The centroid of this projected area is not necessarily the same as the planfo~m centroid. The negative vertical force related to this coefficient (C) can be thought of as the net reaction of the spanz wise flow momentum on this projected area. This interpretation is supported by the yarn observations made earlier and would also be true for the prototype Finn. 60 The x and y moment coefficients are shown in Figure 8-4. While the overall trends of the coefficients are preserved, the net effect of the non-uniform onset velocity is seen to reduce the values of C and C mx my In an attempt to resolve the sail force center, it is conservative to assume that each of the forces represented by the coefficients C, C, and C are concentrated at difx y z ferent x, y, z locations or and

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3.5 3 0 2.5 ti) .... z w M u ~2. 0 (.I. (.I. w 0 u 1.5 1. 0 0 S LEGEND SAIL SHAPE AND TRIM With PBL Without PBL OJ = N / A 6M = 0 0 o-c mx 1J = N / A 0 ~M = 32 0 C my dJ = N / A dM= 11 % -c z .. _:I(_ -) ..... -r .._ ----=--~ --;4 ~--:::~ ~:::..::-'.t :4 10 20 30 40 so HEADING ANGLE(Degrees) FIGURE 8 -4 Fi nn M o m e nt Coef f i c ie nt s With a n d W ith o ut th e Pla n eta r y Bo un da ry Laye r. 61

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62 If the vertical force is taken as the vertica l component: of the total lift vector, where the total lift vector is normal to the sail surface at its center of pressure, one obtains and 0 (8-1) The resultant moments of the three forces in coefficient form can be w r itten as C rnx = (Cyx2 + Cxyl)/CPF = (Cyz2 + Czy3)/CPF Cmy = (Cxzl + Czx3)/CPF C mz ( 8-2) Applying the con d itions of equation 8-1 to equation 8-2 gives (8-3) From the plots in Figure 8-3 it is noted that C > C y X It is logical to assum e y 1 x 2 therefore, the z-moment coefficient c a n b e appro x imat e d as C mz

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63 Solving for x 2 yields (8-4) Using equations 8-1, 8-2 and 8-4 the vertical height to the x-force location can be approximated as C C -c ( mz) my z C C X (8-5) It is clear that the uncertainty of z 2 is less than that of z 1 which, in turn, is greater than the uncertainty of any one of the contributing coefficients. The uncertainty of z 2 is calculated as .87% while z 1 is estimated at .09%. Using these uncertainties to generate weighting factors w 1 and w 2 a sensible vertical distance to the force center is defined as z(nominal) = (8-6) Where w 1 = 9.02 and w 2 = 12.71 based on the above uncer tainties. Since the plane of the projected sail planform rotates relative to the x,y,z-coordinated system, the hori zontal distance from the mast to the force center is a function of x,y and the attack angle. Figure 8-5 shows the force center locations as calculated by equations 8-4 and corrected for the attack angle.

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+' 1. 13 0.93 ~0.73 Q) H Ct-i Ct-i ::s H 0 +> o. 53 +> bD n Q) :::r:: 0.13 0 +' +' z t ~0.4n Q) :::r:: Ct-i 0 0 n +> ro P'.io.2 I 0 I 0 2 Fo r: P = 24 8 and E = 15.3 Center of Eff ort: ( z / P ) = o 46 \ 1 /i thout PBL ( z/P) = 0 52 W ith PBL A tt a c k A n g les 0 30 35 0} 25 0 V/i th 20 PBL 2 5 \ 'Ji thout PBL 30 I o 6 35 ,,-20 I 0 8 I 1. 0 \'/i nd Tunnel Floo r R a t io of Foo t to B oom Le ngth r1111 FIGURE 8 5 Fi nn Sa il Cent e r of Effo rt Location Cen t e r of effo r t lo c a tion s a t v a r ious a tt a ck a n gles \'Ji th an d vii th o ut th e sim ul a t ed PBL No t e : Be c a u se t he PBL is d i s tort ed s li g htly for t he model u sed th e effect on th e c.e. tr ansla tion a s chorm is less than i t vJOul d be fo r a corr e ctly s cale d PBL 64

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The concentration of points around the planform cen troid for the uniform velocity is logical and suggests an analytical check using a direct integration scheme. Such a scheme is presented in Appendix D for both with and without the modeled PBL. Without the planetary boundary layer model the calculated center of effort is shown to 65 be 0.39 H, which is identical to the planform area centroid and agrees with the location indicated in Figure 8-5 for attack angles of 25 to 35. With the non-uniform onset velocity the method requires an approximate model for the lift coefficient variation as a function of span position. Approximating polynomials are selected for this purpose to allow a convenient form for integration by parts. For the selected precision the results are nearly invarient with the assumed lift coefficient models and the net center of effort is shown to be0.48 H. This value is also in close agreement with the measured value as indicated by Figure 8-5. Finally, the Finn model was used in an effort to assess the effect of Reynold's number on C values at or near stall. y At an angle of attack of 30, three tests were conducted cor5 5 responding to Reynolds numbers of 2.3 x 10 2.9 x 10 and 5 3.3 X 10 The C values obtained show no variation beyond y that of the expected uncertainty, see Table 3-1. The same results were found for C and C values. Therefore within X rnx the range of Reynold's numbers investigated, this parameter's effect is negligible.

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66 Variable Jibsail Hoist Series Employing the full yacht model described in Chapter Six, a variable headsail hoist series of tests was conducted. The results of this series were intended to be compared with theoretically derived lift and drag coefficients. For this purpose, the yacht model was fitted with a mainsail (P = 22.50 in. and E = 9.00 in.), common to all tests. A series of jibsails, all of the same aspect ratio but with various hoists, was fitted to the model and tested as described in Chapter Seven. Tests start with the masthead sloop as an arbitrary upper limit on headsail size with the catboat, no headsail, as a lower limit. Table 6-1 lists the planform geometries for the configurations tested. The configuration code of interest are TlSMHl Full hoist masthead sloop Tl5781 7/8 hoist headsail sloop Tl5341 3/4 hoist headsail sloop Tl5121 1/2 hoist headsail sloop TOSCBl catboat (no headsail) A general "bareboat" test was made to determine the lift, drag and vertical force of the hull and standing rigging. This force data has been reduced to coefficient form using the area of each respective configuration and they have been subtracted from the total configuration coefficients to give an estimate of the fprce and moment contribution made by the

PAGE 82

sails alone. Since drag associated with boundary layer interactions between the sails and rigging are present in the full configuration tests, such estimates for the sails alone are considered to be conservative. 67 Figure 8-6 through 8-15 give the results of these tests. In each case, both the "complete rig" and the "sails alone" data are displayed. As such, it is evident that the hull and rigging not only contribute to drag but to lift as well. Therefore, conclusions directed towards over-all on the-water boat performance could be misleading, if only the aerodynamics of the sail were considered. [The same obser vation was made earlier by Marchaj (8) .] On a macro scale the maximum value of the lift coefficient appears to in crease monotonically as the jib hoist is decreased. This is seen to be true for both the complete rig and the sails alone. However, the drag is also seen to increase porpor tionately, somewhat offsetting the useful component of lift. This will be discussed in greater detail in Chapter Nine. High Aspect Ratio Series A 150 % masthead sloop configuration is chosen to assess the effects that different rig aspect ratios have on the resultant sail forces and moments. Configuration Reference codes Tl5MJ2 and Tl5MJ3, given in Table 6-1, were tested for comparison with the standard sloop Tl5MH1. The results of these tests are given in Figures 8-16 through 8-19 and are discussed in the next chapter.

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LEGEND SAIL SHAPE AND TRIM Sails Alone Complete Rig3. 5 Cx 0 Cy 3.0 2.5 1.5 1. 0 0.5 V Cy/Cx A CFWD T I OJ =1 2 o 60 4>J = 1 dJ = 1 c1 /o \ \ \ \ \ \ J __ ? -: / / 6M =0 0 0 h-1 = 30 dM= 1 c1 /o 10 20 30 40 so HEADING ANGLE(Degrees) FIGURE 8 -6 Masthead Sloop Test Results. R = 280 ~ 000 ., F I3 A/ SA = 0 23 ( T 1 5MH 1 ) e 68

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1-4 : 0 >t u 2.0 1.0 o.s 69 LEGEND Sails AloneComplete Rig--0 Cyvs.Cx 0 CFWD vs. CHL o.s ex or c 8 L FIGUR E 8 7 M as thead Sloop P o la r s Re = 280 000 ., FBA/SA = 0 23 (T 1 5MH 1)

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3.5 3.0 2.5 V) f-, z 1,1,1 M u 1-42. 0 ""U.l 0 u 1.5 1. 0 0.5 LEGEND Sails Alone Complete Rig--Cx 0 Cy V Cy/ Cx A CfWD I I ft t I I ,, 10 20 30 SAIL SHAPE 6J =12 0 ~J =18 dJ =10 % 40 HEADING ANGLE(Degrees) AND TRIM 6M = 0 0 h1= 31 dM= 12% so FIGURE 8-8 7/8 Sloop Test Result s Re= 240,000., FBA/SA = 0. 2 7 (T15781) 70

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2.0 1.0 o.s o.s LEGEND Sails AloneComplete Rig 0 Cyvs~Cx 0 CFWD vs. CHL ex or CHL FIGURE 8 9 7/8 Sloop Pota r s Re= 2 40, 00 0. FB A/ SA = 0 2 7 (T15 78 1) 71

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3.5 3.0 2.5 1.5 1.0 0.5 LEGEND SAIL SHAPE AND TRIM Sails Alone 0 0 Complete Rig--OJ = 1 2 OM= 0 J Cx ~J = 20 ~M = 3 5 0 0 Cy dJ = 11 %
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2.0 c141.s H 0 >, u 1.0 o.s /~ --? r I o.s LEGEND Sails AloneComplete Rig 0 CFWD vs. CHL ex or cHL FIGURE 8 -11 3/ 4 Sloop Po l a r s Re= 2 1 0 000 F~A / SA = 0 32 ( T 15 3 41) 73

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LEGEND Sails Alone Complete RigSAIL SHAPE 6J :1 2 0 AND TRIM 6M = 0 0 3. 5 Cx 0 Cy 80 4'J =1 h1 = 35 3.0 2.5 ti) z LIJ M u ..... 2. 0 (.I.. (.I.. LIJ 0 u 1. 5 l 0 0 5 V Cy/Cx A CFWD dJ =11 % dM= 10 20 30 40 so HEADING ANGLE(Degrees) FIGURE 8-12 1/ 2 Sloop Test Results. Re= 90 ,000. F BA/ SA = O.43 ( T 151 21) 1 2/4 74

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2.0 LEGEND Sails AloneComplete Rig Cy vs.ex Ur,.. l. 5 ~-f 0 :>, u 1.0 o.s I I I 0 o.s ex or CHL FIGURE 8-13 1/ 2 Sloop Polars. Re= 90 ,000. FBA/SA 0.43 (T151 21 ) 75

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3.5 3.0 2.5 ti) Ez w 1--4 u 1--42 0 u.. u.. w 0 u 1.5 1. 0 0.5 76 LEGEND SAIL SHAPE AND TRIM Sails Alone 0 Complete Rig6J = N/ A 6M = 0 D Cx 0 1J = N /A ~M= 36 0 Cy dJ = N / A dM= 1 3% V Cy/Cx A CFWD 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 8 -14 C a tbo a t ( wi th hu l l) T es t R es ult s R e = 90 000 F BA / SA = 0.60 (TOSC B 1)

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2.0 Ura. l. 5 $-4 0 >, u 1.0 o.s I I 0 o s LEGEND Sails AloneComplete Rig--cyvs .ex ex or CHL FIGURE 8 -1 5 Catboat Polars ( with hu~~J. Re= 90 000. F BA /SA = 0.60 (T OS CBl) 77

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ti) E:z i.lJ 3.5 3.0 2.5 1--4 u .... 2.0 I&. ti.. l,1l 0 u 1.5 1. 0 0.5 78 LEGEND SAIL SHAPE AND TRIM Sails Alone -\ Complete Rig6J = 12 0 0 6M = 0 Cx 0 0 4>J = 14 4>M = 22 0 Cy V Cy/Cx dJ = 10 % dM= 7 % ,v7-\ A CFWD /'l \ \ I I 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 8-16 Masthead Sloop, High Aspect Ratio M ai n a n d Jib. Re= 260,000. F B A/SA = 0. 32 (Tl5MJ 2 )

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'-4 0 >, u 2.0 1.0 o.s I $ I ch I I I I 6 0.5 LEGEND Sails AloneComplete Rig C Cyvs.Cx 0 CFWD vs. CHL ex or CHL FI G UR E 8-17 Mas th ead S loo p Hi g h A spe ct R a tio M ain a n d Jib Pol a r s R e= 260 00 0 F B A/ S A = 0 3 2 (T 1 5MJ 2 ) 79

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V) z UJ .... LEGEND Sails Alone Complete Rig--3.5 Cx 0 Cy 3.0 2.5 v cyfcx A Cpwn SAIL SHAPE AND TRIM 0 4>J = 14 0 h1 = 2 4 dJ = 10 % dM= 11 % u .... 2. 0 "1.. "1.. UJ 0 u 1. 5 1.0 0.5 10 20 30 40 50 HEADING ANGLE(Degrees) FIGURE 8 -1 8 Mas t head Sloop High Aspect Ratio Jib and S t anda r d Mai n. R e= 270 000 FBA / SA = 0 28 ( T 1 5MJ3 ) 80

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2.0 tr i. 5 ~ 0 >, u 1 0 o.s I 0 I I I o.s LEGEND Sails AloneComplete Rig 8 1 FIGURE 8 -1 9 Masthead Sloop High Aspect Ratio Jib Polars Re= 270 000 FBA/SA = 0 28 ( T 1 5MJ3)

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CHAPTER NINE EXPERIMENTAL AND THEORETICAL COMPARISONS The Influence of the Simulated Planetary Boundary Layer Wind tunnel tests of yacht models made with and with out a simulated PBL indicate that the influence of the PBL is significant, accounting for reductions on the order of 28% in the lift and drag coefficients relative to those without the PBL for the same trim and attack angles. In addition, the effective force center with the PBL is 30% farther above the deck than with no PBL model while yield ing approximately the same moment coefficients about the water plane. This is important in that test work which does not model the PBL properly will tend to over predict yacht potential performance relative to lift and drag for the same vessel heel limitations. The assessment of the PBL onset profile by direct integration suggests that tests conducted with a uniform onset velocity model can be analytically corrected for any given onset ve l ocity profile providing a functional formulation of that profile is possible and that some knowledge of the lift coefficient variation with height is available. Such a correction scheme could allow the test results of one model configura tion to be applied to any size prototype independent of 82

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similitude requirements for the PBL with all such require ments evaluated by analysis. 83 The direct impedance method offered for onset velocity profile synthesis is effective and practical, giving reason able control over the velocity distribution and the turbulence in the wind tunnel test section. As pointed out earlier, the scale of turbulence for the test must be large relative to the turbulence scale of the sail model viscous shear layer The evaluation provided here indicates that area sonable PBL model should have approximately two orders of magnitude difference between these turbulence scales. For the prototype yacht, it can then be concluded that the scale of turbulence in the over-the-water PBL is insignificant and can be ignored relative to the sail aerodynamic performance. A review of previous two and three-dimensional sail test data (8, 9, 10, 11, 13, 29) for lift and drag reveals a sensitivity to Reynolds number. This indicates a further complexity in a complete treatise on sail aerodynamics. Re call that in subsonic airfoil theory where the Reynolds numbers are large the viscous properties of flow may be neglected in the determination of lift and have only limited impact on drag. In contrast, experimental evidence for sails suggests that both lift and drag are strongly affected by their much lower Reynolds numbers at all angles of attack. It is speculated here that this Reyn o lds number sensitivity

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84 is closely related to boundary layer stability. Specifically, the sharp edges of the single camber sail are simultaneously subject to an adverse pressure gradient and a fairly large free stream turbulence intensity; both of these effects could cause boundary layer instability. More research dealing with 5 flow separation on sails at Reynolds numbers of 5 x 10 and less is needed. Comparison of Pdtential Flow Models and Wind Tunnel Results A potential flow analysis of the sail rig configurations described in Chapter Six has been made employing Register's SAIL-3 computer program. SAIL-3 produces numerical solutions to the classical potential flow problem of the Neumann ex terior type by means of a discrete vortex lattice distribution. Register has shown SAIL-3 to be convergent to the exact solu tion of the governing equations in terms of detailed wake geometries as well as force coefficients with upper bound uncertainties for lift coefficients of % and % for drag coefficients for the specific sail discretization reported. This same discretization is used here. Therefore, the same uncertainty estimates are applicable. Rig configuration Tl5MH1 has been evaluated using SAIL-3. The results are given in Figure 9-1. Upon comparing these calculated results with the wind tunnel test results for the "sails alone" (see Figure 8-6) remarkable agreement is observed in lift up to the region of sail stall (8=35). In this same region, the drag coefficient values are seen to be under predicted. This is to be expected with an inviscid solution.

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3.5 3.0 2.5 V) E:z LU .... u ~2. 0 u.. 0. IJJ 0 u 1.5 1.0 0.5 LEGEND SAIL SHAPE Sails Alone -(Theory) Complete Rig(Test) 6J = 120 0 Cx O Cy J V Cy/Cx A CFWD 0 ~J =16 dJ =1 ZJ/4 I \ I \ I A' \ \ T / I I 'l I I I I I f / t /~/, / / ,,,,_ / I I ,' <-f Lift ,,,,pl Sails Alo ne y,,, (T es t) I / /~ / / /. d .,,, -0-0' [:}---EJ' .,,, ,,, .,,lY 10 20 30 HEADING ANGLE(Degrees) 40 AND TRIM 0 6M = 0 0 ~M = 30 I dM~ 1 ZJ/4 so FIGUR E 9 -1 Masthead S loop Theoretical Cx' Cy' CFWD' and C /C x vs. Test Results. ( re f T 1 5t 1II 1 ) 85

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. 2.0 J ,1.s H 0 >, u 1.0 o.s I I lil I I 0 I I I El t ~,~-4--~ I I LEGEND Theory,Sails AloneTe s t,Complete R i g---Ocyvs.Cx G----1 t-f)~ 1---, ',--, ,, l-;{)-1 .,, ,,,. o.s FIGUR E 9 2 Mas t head Sloop Theo r e t ical Pola r s vs Tes t P ol a r s (r ef T 1 _5MH 1) 86

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In that light, the results appear to agree in trend. The following configuration comparisons are limited to a single heading. This permits comparison of the present experimental values with the theory of Register (7) but also with that of Milgram (30). Table 9-1 gives a compari son of each configuration code listed in Table 6-1 all at 87 a heading angle of 27, a jib trim angle of 12 and a main sail trim angle of approximately 0. These trim selections are matched with the calculations reported by Milgram and Register. Test values are selected from the appropriate test results of Chapter Eight for a heading angle of 27 (Figure 8-6 through 8-19). It should be noted that the values indicated as SAIL-3 have been calculated for condi tions that model the wind tunnel test conditions. That is, the rig dimensions and sail twist were set equal to those of the test prototype and the SAIL-3 boat speed was set equal to zero. Hence, SAIL-3 provides a theoretical analog of the wind tunnel test prototype. Milgram systematically analyzes sail force coefficients (30) for two distinct sailing conditions which are termed the "high lift" and "reduced lift" conditions. The high lift condition corresponds to a sail lift distribution optimized for maximum drive force coefficients. This is analogous to the light wind sailing state that is simulated in the wind tunnel tests. Therefore, these results have been selected for comparison with the test values, Table 9-1. Milgram's coefficients, however, relfect a boat speed equal to 60% of

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TABLE 9-1 Rig Configuration Test and Theoretical Results Aspect Ratio Rig Ratios Sails Alone Complete Descr i pt i on R i g Main Jib 1/P J / E C C CFWD CHL C/Cx C C y X y X H 2 /2 S A P/E 1/J I (I) 1. J 4 2 50 3 13 1. J l 0.89 1. 04 0 18 0.46 1.01 S 62 ''"""' i ,,, I. S O 2 50 3 00 10 0. 89 l. 2S 0 26 0.4S 1. 24 4. 7 3 Sloop ( 3 ) J.50 2 50 3 00 1.10 Q.. 89 l. 25 0 22 0 51 l. 21 5 83 TIS~Hl ( 4 ) J. 1 4 2 5 0 3 13 1.11 0.89 1.15 0.32 0 20 1.33 3 56 1. 24 0.40 r I. 40 2 50 3 13 0 97 0 78 0 95 0 15 0.24 0 91 6.40 7/8 (2) J.82 3 00 2 78 1.02 1.10 1. 24 0.26 0.32 1.22 4 80 Sloop (3 ) I. 82 3 00 2 87 l. 02 1.10 1 24 0.21 0 36 1.20 S.96 TIS781 (4) J. 40 2 50 3 13 0.97 0 78 1.16 0.35 0 12 1.18 3 31 l. 30 0 41 r 1. 63 2 50 3.13 0 83 0 67 0.91 0 13 0.29 0.87 6 8S 3 / 4 (2 ) 2 04 3.00 2 63 0 96 1.10 l. 24 0.26 0.33 1.22 4.68 Sloop ( 3 ) 2 04 3 00 2 63 0.96 1.10 1. 24 0 .0 2 0.37 1. 20 s. 77 Tl5341 ( 4 ) I. 63 2 50 3.13 0. 83 0.67 1. 02 0.41 0 10 1.10 2 .49 l. IS 0 50 r 2 21 2 50 3 13 0 56 0 44 0 91 0 14 0.24 0.78 5.86 1 / 2 ( 2) 2 58 3 00 2 25 0 82 1.10 1.24 0.28 0.32 1. 23 4 49 Sloop (3 ) 2 58 3 00 2 25 0 82 1.10 1. 24 0 22 0 36 l. 20 5.54 Tl 5 1 2 1 ( 4 ) 2 2 1 2 50 3 13 O S6 0 44 1.18 0.46 0 12 1.35 2 57 l. 34 0 5 7 r 2 50 2 50 1. 44 0.21 0 46 1. 37 6. 77 Catboat ( 2 ) 2 50 2 50 1.42 0 22 0 4S 1.35 6.56 TOSCBI (3 ) 2 50 2 SO N/A N/A N/A 1. 42 0.21 0 51 9 S7 1. 33 ( 4 ) 2. 50 2 50 1. 48 0.S3 0.20 2.00 2 97 1. 72 0 70 High AR(!) I. 65 3 50 2 78 1.11 0 9S 1. 03 0.13 0 3S 0 97 8.14 J&M Masthead ( 2 ) 1. 67 3 50 2 75 1.10 1.41 1.23 0.2S 0 34 1.21 4 92 Sloop ( 3) I. 67 3 50 2.75 1. 10 l. 41 1.03 0.20 0 38 1.19 6 13 TISI-U 2 (4) I. 65 3. 5 0 2 78 1.11 2 95 1. 1S 0.37 0.20 1.2S 3 11 1..28 0 4 7 H i gh AR ( I ) I. 44 2 5 0 2 78 1.11 0 67 1. 09 0.18 0. 34 I.OS 6 19 J i b Ma s the~d (2) I. 4 4 2 50 2 75 I. 10 1.01 1. 24 0 28 0 32 1. 23 4 50 Sloop ( 3 ) I 44 2 50 2 .7 5 1. 10 1.01 1. 24 0 23 0 36 1. 21 5 47 TIS~ U3 ( 4 ) 1. 44 2 50 2 78 1. 11 0 6 7 1. 2 5 0 45 0. 20 1. 38 2 78 I. 38 0 5 0 Le g end : (1 ) Sail-3 results. (2) M i l g ra m 's results with a pressure and viscous drag estimat e ( 3) M i l g r a m's r es ults without the pr e ssure and viscous drag estimat e. (4) W i nd tunnel test results. 88 Rig L /D 3 10 3 17 2 30 2 35 2 46 2 72 2 .7 6

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89 the apparent wind speed. There are also minor differences in rig dimensions, as noted. Nevertheless, comparison re mains of interest. To facilitate this co~parison, when necessary, Milgram's results have been interpolated or extra polated from neighboring cases to rig dimensions that are equivalent to those of the the wind tunnel tests. Additional comparisons between theory and test results are shown in Tables 9-2 and 9~3. These compare the test results for the Finn model to a SAIL-3 analysis of a similar configuration and extrapolated catboat data from Milgram. In this case, comparison of the heights to the force center is possible, Table 9-2. These heights have been normalized using the hoist of the mainsail (P). It is evident that agreement between methods is good. Next consider the drag coefficients. SAIL-3 only models induced drag. Milgram's vortex line model similarly yields only induced drag but his report also includes an independent estimate of viscous and pressure drag for the sail and mast. Comparing the drag coefficient entries of Table 9-2, it is clear that the addition of a pressure and viscous drag estimate to the potential flow prediction of induced drag gives drag coefficients close to the test re sults. It is also clear from the listed lift coefficients that Milgram has made no adjustment to the calculated lift as a consequence of the estimated pressure and viscous drag.

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TEST (T00CB5) SAIL-3 (After Register) MILGRAM (With Viscous and Pressure Drag Extrapolated) MILGRAM (No Viscous and Pressure Drag Extrapolated) 8>.. = 27 TABLE 9-2 Finn-Type Sail Results From Experiment and Theory* Coefficients C ex CFWD Lilt Draq Forward 1.050 0.280 0.230 1.258 0.232 0.424 1.405 0.271 0.410 1.405 0.208 0.450 CHL Heel 1.130 1.196 1.372 1.350 z/p Side Force 0.52 0.518 0.522 0.529 \0 0

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B 25 27 30 NOTE: ( 1) ( 2) ( 3) TABLE 9-3 Masthead Sloop (Tl5MH1) For Various B Experiment vs. Theory Source of Data Coefficient CV ( 1) SAIL-3 0.96 (2) MILGRAM 1.20 (3) TEST 1.05 (1) SAIL-3 1.05 (2) MILGRAM 1.25 ( 3) TEST 1.14 ( 1) SAIL-3 1.16 (2) MILGRAM 1.27 ( 3) TEST 1.22 ASPECT RATIOS MAIN JIB 2.50 3.13 3.00 3.00 2.50 3.13 C X 0.14 0.25 0.30 0.18 0.26 0.32 0.23 0.26 0.38 \D t-'

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92 The need for such an adjustment can be illustrated consider ing the experimental values for lift and drag coefficients, Table 9-1. These data verify that when headsail size is reduced, the effect of viscous and pressure drag from mast and sail become increasingly important. This is well illus trated by the lift to drag ratio (L/D). This parameter is representative of potential rig performance. Figure 9-3 pre sents a plot of this ratio as a function of the ratio of jib hoist to mainsail luff (I/P). Appropriate values of I/P and L/D are selected from Table 9-1. As noted in Chapter Eight, sail only results obtained by subtracting bareboat from complete rig measurements in clude the changes in lift and drag associated with the boundary layer interaction of the mast and sail Therefore, the lift to drag ratio for these sail-only results provide insight as to the magnitude of the performance reduction that results from such boundary layer interaction. Figure 9-3 shows that the difference between the L/D calculated by Milgram with the viscous and pressure drag estimates and that given by the wind tunnel test decreases as I/P increases. This suggests that the mast is relatively more important with respect to the performance potential of the catboat than that of the masthead sloop. It is apparent that the inclusion of viscous and pressure drag in the potential flow analysis produces a trend in calculated L/D that more closely follows the wind tunnel test data. Without the inclusion of a drag model, potential flow theory (indicated by SAIL-3) and the

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L/D 10 8 6 4 DRAG {S) INCLUDED Induced 6. Induced Pressure, V iscous o Induced Pressure, Viscous and Interference {Sails Alone) 0 All {Hull and Rig) Mi l grarn* '-./ SAIL-3 f;:r-l::,.--6 .....5 Milgram -5 Test {Sails Alone) 2 ~~============teic:=======-e --._s-Test (Hull and Rig) 0.5 1.0 1.5 I/P FIGURE 9 3 L/ D Ratios From Theory and Test. Comparison of wi n d tunnel test da t a w ith potential flo w theoretical p re d iction s \.D w

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94 Milgram curve uncorrected is substantially above the data. The smallest value of L/D from test results occurs in the 3/4-fractional sloop. This minimum is thought to be caused by a combination of mast effect and the interactive headsail/ mainsail induced flow. However, it should be noted that the magnitude of this minimum is only slightly less than the difference in measurement uncertainty. A relative maximum appears for the 7/8-fractional sloop. The differential between this maximum and the aforementioned maximum is greater than the measurement uncertainty.

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CHAPTER TEN CONCLUSION AND RECOMMENDATIONS Wind Tunnel Test Conclusion? The test results are sensitive to rig configuration and trim conditions. Experimentally predicted performance potentials agree with current sailing wisdom. The experi mental uncertainties for the results presented are of the same order as those provided by the latest numerical tech niques for potential flow models. Comparison between the test results and the numerical potential flow models shows reasonable to good agreement for lift below rig stall. Above the stall point, the lift predicted by potential flow is incorrect. This affirms that stall inferrence is necessary to extend the analytical tools for a complete evaluation of yacht aerodynamic per formance. Moreover, the important drive component of the total aerodynamic force produced by the sail(s) is given by the difference in the projections of lift and drag as indicated by equation 2-7. Therefore, a realistic drag value that includes viscous, pressure and parasite drag must be used to accurately predict rig aerodynamic performance potential. Since potential flow, by definition, includes only induced drag, an empirically based extension appears in order. Milgram's addition of these drag compo nents is sensible an~ apparently, of the correct magnitude 95

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as the corrected predictions show good agreement with test. However, the effect of local separation, especially the three-dimensional local separation in the region of the mast of the lift produced by the sails, is of great significance. 96 In two-dimensional water tunnel tests, Milgram (11) found that th e addition of the mast to the sail model in creased the pressure and viscous drag to the order of that expected for the induced drag in a typical three-dimensional sail. For the sharp leading edge sail, experiment and theory have shown that the maximum pressure coefficient is developed near the leading edge. The inclusion of a mast, at the lead ing edge increases form and viscous drag. As a consequence, it also decreases the net lift. Thus, calculated lift to drag ratios and driving force coefficients that do not ac count for the mast effect on lift and drag will tend to over estimate performance. Further, the overestimation of per formance w~ll be greater for single sail catboats than for 1 sloops. Recommendations Having summarized what has been investigated, t he following param eters have not yet been adequately defin ed 1 s1oops generally have a sharp leading edge on their head sails and the mast is well aft in the induced flow field. As a result, the pressure distribution obtained on th e headsail is nearly that predicted by a no ~ast theory and this dominates the net aerodynamic force produced by the entire yacht rig. Conversely, the single sail of the cat boat has the mast as its leading edge and is adversely affected by the mast/sail boundary lay er interference.

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97 The movement of the sail force center as a function of heading angle, especially on the sloop rig, is in order to give a better understanding of yacht hull/sail force balance. Further investigation into the variation of sail force co efficients with Reynolds is also needed. Sensible stall inferrence schemes for lift are needed to advance potential flow models of sailing yachts. In addition, empirically based estimates of viscous, pressure and interference drag must be included to make such models more realistic for yacht performance predictions. Finally, future research should be focused towards comparing theoretical and wind tunnel test results with full scale yacht tests. Many of today's theoretical and empirical yacht sail investigations conclude with a direct application to a full size yacht. Unfortunately, the actual on-the-water performance of such an application is often inadequately measured to be useful as a check against theory and test. Such data would be invaluable towards advancing the complete understanding of sailing yacht aerodynamics.

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APPENDIX A SAIL TWIST AS RELATED TO THE APPARENT WIND AND THE INDUCED FLOW FIELD The vector addition of the local true wind velocity and the boat velocity results in a change of apparent wind direction as a function of vertical position. The angular magnitude of this change from the deck of the boat to the masthead, for conditions analogous to those being simulated here, may be assessed as shown below. The law of cosines may be applied to the relationship between the true wind speed UT(z), boat speed UB, and the true wind angle, y, to determine the apparent windspeed UA. (A-1) Similarly the apparent wind angle, B, may be defined using the law of sines as sin (180-y)] (A-2) These relationships describe the wind triangle for the sail ing yacht (see Figure A-1). For this triangle it is conven ient to parametrically define boat speed as directly propor tional to the true wind speed at the masthead or (A-3) 98

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FIGURE A-1 Typical Wind Triangle for the Sailing Yacht 99

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where K is the constant of proportionality. From Chapter 0 Five the true wind speed at any height, z, may also be characterized in terms of the masthead wind speed as (A-4) where A and Bare constants (see Appendix D). Substituting equations A-3 and A-4 into equations A-1 and A-2 and combining gives the apparent wind angle as a function of z alone for any selected K and y as 0 B = arcsin K 0 [ ( l + A ln ( z) + B sin 2 + 2 K A ln~z) + B cosy)] (A-5) 100 For the present analysis consider UT(H) to be u 30 {the wind speed at 30 ft), A= 0.1086, B = 0.4918 and K = 0.6 {after 0 Milgram). As a specific example let y = 45 and then B can be calculated for the heights z 1 = 3 ft and z 2 = 30 ft; roughly the scale distance from the water to the yacht deck and from the water to the mast head respectively. Substitut ing into equation A-5 the change in the apparent wind angle is calculated as (A-6) From equation A-6 for z 2 !z 1 = 10, ~B from the deck to the masthead is calculated to be 7. This change may be consi dered distributed over the span as an amount of "twist" in

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101 the onset velocity profile. Comparing this typical wind twist to the twist of a well trimmed sail, one finds a dif ference on the order of 10. That is, conventional sail trim (1, 2, 8) would call for a sail twist of approximately 20 for the conditions sighted. Obviously this twist would be excessive if it were to account for the wind/boat velocity addition alone. As per the flow observations discussed in Chapter Eight, a large induced upwash deflection of the wind field was observed at the sail leading edge. Good sail trim, in the form of a vertical distribution of twist, would require that the slope of the sail at the leading edge be parallel to the direction of the near field induced flow. That is proper trim avoids luff or stall at the leading edge. Register (7) noted a need for a large amount of sail twist in order to maintain sensible pressure coefficients as predicted by his vortex lattice method. He found that twist of the order of 30 per span was required. This is in agreement with reasonable sail trim wisdom and in contrast to the 7 apparent wind twist calculated above. Assuming that the induced field upwash angle is of the same magnitude as that of the induced downwash angle, one may provide a closure for this discussion. Adapting the method of Milgram (5), the local flow induced downwash angle ( a. ) can be approximate in terms of the local induced down1 wash velocity w(z) and the freestream velocity UT(z) as a. = 1 (A-5)

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102 With a linear approximation of the onset velocity profile, Milgram has shown that the induced downwash velocity may be described in terms of Fourier coefficients and the wind velocity at the sail mid-span as where k w(z) = -U 0 m~l nAn(AAn BB ) n u 0 A n AA and BB n n = wind velocity at the sail mid span = Fourier coefficients = numerical solution points of the Glauert integral and the image sail integral respectively. From Milgram's solution the values of AA and BB fork= 3 n n gives a representative downwash velocity at the boom and at the masthead, respectively, of -0.189 U 0 -1.096 U 0 (A-6) The freestream velocity at these same locations may be ap proximated using Milgram's linear model and u 0 u 0 (A-7) Selecting U = 6 ft/s as representative of the test condi o tions of interest, equations A-6 and A-7 can be evaluated

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103 and substituted into equation A-5. The difference of the resulting induced attack angle from the boom to the masthead thus found is approximately 20. Conclusion For the work reported here the similarity distortion of zero boat speed equates to a reduced sail twist on the order of 7 over that of the prototype. Roughly a 20% reduction in sail twist. (This twist is in good agreement with that which was determined during the observation tests as described in Chapter Eight). The significance of this twist reduction is that the forward components of lift will be slightly reduced while the aft component of drag is slightly increased over the entire sail planform. Both effects are thought to be conservative relative the net driving force and the potential yacht performance predictions that are suggested.

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APPENDIX B AERODYNAMIC FORCES AND THE CENTER OF EFFORT The sail is conveniently described in terms of curvi linear surface coordinates defined by the surface unit normal vector (e 1 ) and the unit tangent vectors (e 2 e 3 ) of two orthogonal surface parameter curves. Every point thus defined also has a description in a predetermined global cartesian coordinate system denoted by the position vector~-. The net result of all the applied aerodynamic 1 loads per unit area at any such surface point can therefore be considered as an applied surface traction (T) described in the surface coordinates as a vector The corresponding elemental differential surface area vec tor (ds.) at this location has a magnitude (ds) defined as J ds = e.ds J J such that the differential force applied to this elemental surface can be written df = T ds; j = l, 2, 3 J J (B-1) 104

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Equation B-1 represents a vector described in local coordinates. Let A .. be the direction cosines between the 1] locale-coordinates and a global coordinate system. Then 105 A . is a function of the surface parameters and the differen1J tial force in the global coordinates becomes df. = A . T. ds; i = 1, 2, 3 1 1J J (B-2) and the total force applied over all of the free surfaces is given in global form as i = f = Jfs A .. T ds; j 1 1] J 1, 2, 3 = 1, 2, 3 (B-3) The moment about the global origin resulting from the applied local surface traction at s is defined as the 1 vector product of the position vector and the element force df .. It is convenient to introduce the permutation symbol 1 ijk such that: ijk = 0 if i, j k do not form a permutation of 1,2,3. ijk = +l if i, j k form an even permutation. ijk = -1 if i' j k form an odd permutation. The global differential moment due to the local applied stress vector can then be written as dM. = c:: .. ks,dfk 1 1J J

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From equation B-2 dM. i 106 (B-4) The total global moment vector can then be obtained by inte grating equation B-4 over all the free surfaces exposed to air flow or (B-5) Equations B-3 and B-5 demonstrate that three components of force and three components of moment define the net reaction of all the applied aerodynamic loads with respect to a pre selected global origin. As such, the direct measurement of orthogonal force and moment triples at any preselected loca tion, on or off the yacht, would give the net aerodynamic reactions. It is frequently desirable, for measurement purposes, to define the global origin on a body immersed in a flow so that equation B-5 is identically zero. (The center of pressure of a two-dimensional airfoil for example). Early in the development of classical airfoil theory it was recognized that such a point shifted locations as the attack angle was varied. Subsequently, for symmetric models, a second point (the aerodynamic center [a.c.]) was defined about which the pitching moment coefficient remained constant with changes in the angle of attack. When testing an unsymmetric three dimensional model such as the sailing yacht, insight to a

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107 similar aerodynamic center or "center of effort" cannot be obtained, in general, by measurement of orthogonal force and moment triples alone. As oroof, let F. be a force vector .. l. applied at a location in space denoted by the position vector z:;~ such that: l. M = E .. kz:;~Fk l. l.J J From equation B-5 then For static equilibrium = f. l. (B-6) Equation B-6 may be expanded to yield a set of simultaneous scalar equations in M, ~, and F of the form Ml = F3Z2 F2~3 M2 = -F ~* + Flz:;3 (B-7) 3 1 M3 = F2~i Fl"2 N ow, consider the vector equation M = B . z:;. l. l.J J (B-8) where the coefficient matrix B .. is singular skew-symmetric l.J which, by definition, has no inverse and is subject to the following conditions:

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and B .. = -B .. ; i#j lJ Jl B .. = 0; i=j lJ 108 Expanding equation B-8 into its component form, applying the above conditions and multiplying out the right hand side yields three simultaneous scalar equations of the form Ml = B12Z2 B31Z3 M2 = -B12Zi + B23Z3 (B-9) M3 = B31Zi B23Z2 By comparison, equation B-9 is seen to be identical to equation B-7 for (B-10) Therefore, equations B-7 may be thought of as a vector equation of the form M. = F . r;~ 1 lJ J (B-11) where the numerical subscripts on the matrix F .. are related lJ to the Fk as indicated by equation B-10. The desired solutions are the components values of r;~ or 1

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-1 = [F . ] M. lJ J (B-12) The solution indicated in equation B-12 exists if and only if the inverse of F . exists. But, for equation B-11 lJ 109 to represent the moment corn~onents of equation B-7, F . must lJ be singular skew-symmetric. As such, equation B-11 does not have a unique solution and the definition of a ''force center" is arbitrary with the measurement of only three forces and three moments. Conversely, the equations for static equil ibrium allow only three orthogonal force and moment triples to be uniquely defined. If one of the position vector cornponents s~ is known from symmetry or can be estimated from 1 some physical constraint of the experiment, a unique solution of equation B-11 results. For the simplest case where a sail alone is tested, absent of hull and major portions of the rigging, a reasonable center of effort can be found by designing the test model so as to eliminate sj, (s 3 =0), in equation B-7 allowing position vector components si and ~ 2 to be determined. Even this method is approximate, owing to the fact that portions of the model structure like the mast and boom contribute drag and diminish lift, separating the effective lift center from the drag center relative to the global reference frame.

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APPENDIX C AERODYNAMIC FORCE MEASUREMENT Six-component Force Balance The most appropriate approach to aerodynamic force and moment measurement is dependent upon the type of experiment proposed. As such, the requirements for the force measure ment mechanism or "force balance" vary with application and are discussed in detail by Pope and Harper (21). As suggested in the previous appendix, the most general applied force/moment combination requires a measurement of six independent quantities. A six-component force balance is necessary for such measurements. Such balances can be of varied designs; individual balances should be developed to be effective relative to their intended use. A typical six component or six-channel force balance in the most general case would display cross coupling on all six channels. Consequently, the calibration procedure for such a balance would be quite complex and time consuming to implement. Each single-channel reading would reflect all three force and moment components due to this coupling. The general form of the relationships for any one channel reading is i = 1, 2, j = 1, 2, 110 6 . 6 (C-1)

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where R is the net reading (load cell output, electrical 1. 111 resistance, force, etc.) for any one channel in terms of the y actual applied calibration load or moment on any one eJ channel and the cross coupling influence coefficients aR./ 1. ae. of all six channels. The calibration equations for any J net, single-channel, reaction is then obtained by inverting equation C-1 or r eJ R. 1. (C-2) Equation C-2 implies that each calibration equation is formed by making six separate calibration runs, one for each channel, and recording all six channel reactions for each applied known load. All of the data thus acquired is then assembled to form the influence coefficient matrix and in verted to yield the final calibration equations. The ex perimental uncertainty (w ) of any y reaction is therefore, yej eJ dependent on all six R. channel readings and each of their 1. respective individual uncertainties. Employing the methods discussed by Holman (22) and assuming a uniform odds distri bution, the single channel uncertainty, w is then given ye1. in terms of the individual reading uncertainties, wRk as (C-3) If the coupling effects are strong and the uncertainty of all the readings are approximately the same, the final net

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reaction uncertainty is then determined by any one typical channel uncertainty as (C-4) ay el For the worst case, all the a_ are considered of equal magnitude and equation C-4 reduces to In this case, the required precision for any one channel reading can be predetermined as a function of the final desired outcome uncertainty. This outcome can be improved 112 by decreasing (elimination is the optimum) the cross coupling terms of equation C-3 and/or by reducing the reading un certai~ty, wR. The pyramidal balance is classically offered as a means ay whereby all of the 0 ~ 1 coupling terms of equation C-4 approach zero except for i=k. Accordingly, the pyramidal balance pro vides one independent reaction reading for each applied force or moment. [Reference (21) presents a discussion on the design and function of the pyramidal force balance.] This is accomplished through precise machining and alignment of the components to establish a balance focal point that serves as the balance global origin. Such machining and alignment can only be achieved with great care and, as a consequence, at considerable cost. If the model to be tested is symmetric about one plane (such as the airplane

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with respect to the fuselage) and it is mounted on the bal ance so that this plane passes through the balance focus, all the forces and moments measured are uniquely positioned with respect to the global origin. For the sailboat model however, there is no such symmetry plane. As a result, at leastaportion of the advantage of such a balance is lost; however, the unique correspondence of one balance reaction reading to each one applied load or moment remains an at tractive balance feature. As suggested above, one of the controlling parameters for experimental measurements is the acceptable level of uncertainty. If more than one channel reading is required 113 to establish a net reaction at a balance point, the uncer tainty of that reading is increased since the net uncertainty can be assessed at the outset, then the design requirements for individual channels may be defined by a relation similar to equation C-1. The present effort is not funded by outside sources. It is therefore, limited with respect to the capital acquisi tion of equipment. All of the hardware and materials that are used herein are provided by Embry-Riddle Aeronautical University or at the author's personal expense in the spirit of altruistic sail research. A typical commercially avail able, si x -component pyramidal force balance, such as Aerolab Supply Company's Model PD-3-6, is beyond the available re sources for this effort. Consequently, a six-component

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floating beam balance has been designed, constructed, and is employed as the data acquisition tool. Six-component Floating Beam Balance 114 The design specification for the beam balance was to provide six force component measurements within an accept able, predetermined, level of uncertainty without incurring exhorbitant costs or requiring exotic manufacturing techniques. To this end, each of six channels is reduced to a simple cantilever beam fitted with electrical resistance strain gauges. The beam cross sections are sized as a func tion of the largest anticipated loads so as to remain within the small strain assumptions of beam theory. Primary forces F and F are determined from the sum of two forces and the X y inclusion of a z-moment coupling coefficient. The principle moments, M and M, are then obtained from the forces, F X y X and F, and their relative position to a preselected global y origin. This origin is arbitrary and for this exercise is selected as the intersection of the balance vertical axis and the wind tunnel test section floor. The vertical z-axis force and moment are measured directly. Figure C-1 schema tically depicts this balance concept. The floating beam establishes the vertical z-axis and is connected to orthogonal pairs of cantilever beams at A, C and B, E through ball end connecting rods. Vertical displacement of the floating beam is prevented by way of a cable held taut from (A) to (B) and fixed through the end of a fifth cantilever beam (H)

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z, ( 3) t x, ( 1) ,... Flow h Fe Cable n -Linear Sh a ft Br g s. (Two Plc s ) F d FIGUR E C-1 Six Compon e nt Fl oa ting Beam Force Balance In Sch e m a tic. 115

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116 which measures F directly. The moment about "z" is reacted z at F by a sixth beam. The subsequent force calibration equation takes the form (C-5) where CA, CB, etc. are calibration coefficients determined by application of known loads to each of the independent channels. Rearranging equation C-5 for the individual flexural element contributions gives F == FA + FB y F == FC + FB X F == CHRS z The principle moments are then functions of the known dis tances (hand n) and the measured forces or (C-6)

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117 Problems one would normally encounter with change in the model angle of attack or heading angle are avoided because the z-a x is rotation does not effect "x" or "y"; that is both x" and "y" are oriented with respect to wind tunnel flow direction independent of the heading angle. It is the head ing angle that is varied throughout the testing. This is done manually while the wind tunnel is operating. The balance design allows the model to be rotated relative to the balance and then locked in place at a specific heading. Any small change in this angle due to displacements can be corrected by small angular ~isplacements of the model rela tive to the wind tunnel floor (the x-y reference frame). The experimental uncertainty for measurements made with this floating beam balance are assessed using equation C-5 and C-6 plus observing uncertainties from tests, manufac turer's calibration uncertainties for the instruments used and the calibration loading apparatus employed. The calibration loads that were used are measure weights, accurate to 0.10 g. The loads were applied via cables ov er ball bearing pulleys. The pulley hysteresis and "stiction" w e re measured at .2 % of the applied load. Any single strain gauge channel could be statically read to an accuracy o f .2 % of the scale of interest. The net accuracy of a calibration coefficient over a range of chan nel reading s for all six channels used is adequately r e pre sented by an uncertainty of .1%. The useful output un certainty of the balance for any one force or force

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118 coefficient is seen, from equation C-5, to be dependent on as many as four such calibration coefficients. In addition, the output load (FA, FB, Fe, etc.) also contains from one to three separate channel readings with a larger uncertainty than for the static case due to vibrations, wind tunnel tur bulence and model response to these excitations. For any such measured force, the principal quantity of interest is the force coefficient CF defined as F qA (C-7) The uncertainty of q, the dynamic pressure, is dependent upon a water manometer reading, .010 in. of H 2 0, and a temperature reading, F. The area factor, A, is depen dent upon actual model measurements. All model dimensions are accurate to within 0.032 in. The net uncertainty of a force coefficient due to dynamic pressure and area measure ments is calculated to be .15%. Each channel resistance, R 1 through R 6 was assessed using the common uncertainties indicated above the equations C-5, C-6 and C-7. A uniform odds distribution was assumed and channel reading fluctuation histories were compiled from all of the test runs made. The experimental uncertainty for each channel was then statistically assembled over a range of coefficient values as a local mean of all the un certainties in that range. This approach allowed the appli cation of small uncertainties to the output readings near

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119 stall when the model is highly loaded and the fluctuations in readings were small relative to the magnitude of the reading. Conversely, for zero loads or light loads, the reading uncertainties were larger and were reflected as such. It is the high loading cases which are of primary interest for the sailboat. From all the above considera tions, the net uncertainty for each force coefficient range is reported in Chapter Three, Table 3-1.

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APPENDIX D WIND TUNNEL DATA REDUCTION COMPUTER PROGRAM "BOAT"

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F Tt-J4X ,L 1-FILES (0,1) PROGRAM BOPT WIND TUNNEL TEST DATA REDUCTION PHASE ( note The main program is written ta be general 111i th the only arrays and/or variables being stored in COMMON that are applicable to any type of model that can be b~sted in the wind tunnel. The subrcuti~es are seared towaras sailbcat analysis. PART OF 121 ) C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C i.iI~D TLJNNEL. / DATA AQUISITION UNIT/ HP1000L PROJECT J. LADESIC ORIGINIALLY WRITTEN 26 MARCH 1982 MODIFIED 8 APRIL 1982 12 APRIL 1982 15 APRIL 1982 21 MAY 1982 9 MAY 1982 15 JUN 1982 COMMON NR,ANGLE(30l,V(30),REC30),CXC30),CYC30),CZC30), I CMX(30) ,CMY(30) ,CMZ(30) ,QAC30) REAL M2,JS,IS,EPSLN,AM,82M,CM,EM,R6F INTEGER FNAME(3),DESC(30) DIMENSION CDRC30) ,CHL(30) ,CVT(30) ,CMHLC30) ,CMPTC30) ,CMYW(30) / 8J(30) ,BM(30) DATA VK/.C00157/ C C COMMON data table C NR Number of wind turi 1 runs for C model being teste d C ANGLEj: Ansle model is ~09nted relative to wind, C can be X Y rla~e or X Z pl~ne C Vj : P.irspeed C CX1,CYj, C CZ j : Force co e ff i c i en ts X Y 2 C coordinate system C CMXj,CMYj, C CMZj Moment coefficients X Y Z C coordinate system C REj : Reynolds number C QAj : Dynamic force C WRITE ( 1 ,5)

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, C C 5 FORMAT (" INPUT NAME OF FILE RUN DATA IS STORED IN" / 122 / "CUP TO SIX CHARACTERS,FIRST CHARACTER START IN COLUMN 1," I I JUSTIFIED LEFT, INCLUDE TRAILING BLANKS, IF ANY}") READ (1,6) CFNAMECI) ,I=1,3) 6 FORMAT (3A2) OPEN CUNIT=6,IOSTAT=IERR,ERR~S98,FILE=FNAME,STATUS='OLD') GOTO 50 998 WRITE (1,55) CFNAMECI) ,I=l ,3) ,IERR 55 FORMAT (" ERROR ON OPENING DATA FILE ",3A2 I I "ERROR 11 ",I4) GOTO 9g9 50 !~RITE (1,7) 7 FORMAT(/// SX,'.'WIND TUNNEL DATA REDUCTION PROGRAM") READ (5,10) NR,CDESC(I),I=1,30) 10 FORMAT (I4,30A2) WRITE (1, 15) 15 FORMAT (////) ICNTRL=2 CALL SINPT (IS,JS,P,ES,PC,FRF,AR,CHORD,SA,ARTD) C CKINEMATIC VISCOSITY CORRECTED FOR TEMP AS 1.083VKCSTD>=VK C C C CONST=CHORD/(1.083VK.) DD 1 J=1,NR EPSLN=O.O READ (6,20) ANGLE CJ), T ,PS,PT ,R1 ,R2,R3,R4,RS,R6,BJ(J) ,BM(J) 20 FORMAT (F5.1,FS.0,2F7 .2,6F7 .0,2FS.1). A=((R1-4000)/(12.11))+((4000-R6)/307.656) 8=((4000-R3)/(8.11))+((4000-R6)/1589.35) C=((R2-4000)/(83.3333))+((4000-R6)/300.0) E=((4000-R4)/(87.500))+((4000-R6)/40S0.0) MZ=(4000-R6)/56.8627 H=((R5+(.276R1)-5104)/161.8) QA(J)=(A8SCPT-PS)/12.).4SA EPSLN=1+.027CSA+.45)SINCANGLECJ)/S7.3) QA(J)=(EPSLN)QA(J) IF (QA(J)) 100,200,100 100 CX(J) =-C C+E)/QA(J) CY(J) =-(A+B )/QP.(J) CZ(J)=H/QA(J) CMXCJ) = ((-4.525A)-(16.053))/(Q~(J)CHORD) CMY(J) = -((-4.525C)-(16.053f))/(QA(J)CHORD) CMZCJ)=MZ/(QACJ)CHORD) GOTO 300 200 CX(J)=O. CYC..1) = 0. CZ(J)=O. CMX(J)=O. CMYCJ)=O. CMZCJ)=O. 300 V(J)=2.905SQRTCABSCPS-PT)T) V(J)=EPSLNV(J) RE(J)=V(J)CONST 1 CONTINUE CALL SCOEF (CDR,CHL,CVT,CMHL,CMPT,CMYW) CALL SBOUT (IS,JS,P,ES,PO,FRF ,AR,CHORD,SA,ARTD,CDR,CHL,CVT,

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C C C C C C C C C C C C C C C C C C ( C C C C C C C C C C C C C C C C C I CMHL,CMPl ,CMYW,BJ,EM,DESC) CLOSE (UNI1=5) 999 SlOP END SUBROUlINE SJNPl (I,J,P,E,PO,FRF,PR,CHORD,SA,ARTD) Sailboat INPuT Accept sail dimensions data from (Pl, ccmpute sail area (actual), ~ail area (100 'l. F .T.), mean aerodynamic chord, aspect ratio ( note subroutine is designed for sailboat applications, however subroutine can serve as a model for aircraft/ missle / rocket type applications ) SUBROUTINE WRillEN 12 APRIL 1982 MODIFIED 9 MAY 1982 10 INCLUDE THE CATBOAT COMMON NR,ANGLEC30),VC30),REC30),CXC30),CYC30),CZC30), / CMXC30) ,CMYC30) ,CMZC30) ,QAC30) REAL I,J,JSTAR data table I,J,P,E . CHORD SA . ARTD AR PO FRF Sail(s} Dimensions Mean Aerodynamic Chord of sail(s) Total (Actual) Sail Area Area of Sail(s) as projected to a plane parrallel to longitudinal axis Aspect Ratio of sail(s) Percent Overlap Fractional Rig Factor WR I l E ( 1 5 ) 5 FORMAT (I 5X,"5AIL BOAT DAlA INPUT"// 123 I" INPUl SAIL DIMENSIONS (for model) I J P E (inches)" REP.D Cl,) I,J,P,E WRITE (1, 10) 10 FORMAl (/ INPUT PERCENT OVERLAP, FRACTIONAL RIG FACTOR") READ Cl,) PO,FRF IF CFRF) 30,50,30 30 JSlAR SQRTCCP0)/((1 ./CJ))-(CP0)-1.)/CI))) H = I/FRF SA a C.SJSTARI+ .SEP)/144. ARlD"' (.SJI + .SEP)/144. GOTO 60 SO ARTD = .SEP/144. H=P SA=ARTD

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. ' C C C C C C C C C C C C C C C C C C C C C C C C c C C C C C C 60 AR= H/(SA~4.) CHORD= SA./H RETURN ENO SUBROUTINE (CDR,CHL,CVT,CMHL,CMPT CM Y W ) SUBROUTINE Sailboat COEFficients 1 24 Computes coefficients when rotating win d t unnel X Y a x is to DRIVE ATHWARTSHIP axis SUBROUTINE WRITTEN 12 APRIL 1982 MODIFIED (none) data table (DR, CHL, CVT : force coefficients CMHL, CMPT, CMYW : moment ccefficients COMMON NR,ANGLEC30),VC30),REC30),CX(30),CY(30),CZC30), / CMX(30) ,CMY(30) ,CMZ(30) ,QA(30) DIMENSION CDR(30),CHL(30),CVT(30),CMHL(30),CMPT(30),CMYM(30) DD 1 J .. 1 NR CDR(J) = CY(J)SIN(ANGLE(J)/57.3)-CX(J)COS(ANGLE(J)/57.3) CHLCJ) CY(J)COSCANGLECJ)/57.3)+CX(J)SIHCAHGLE(J)/57.3) CV TC J) CZ CJ) CMHLCJ) CMY(J)SINCANGLECJ)/57.3)-CMX(J)COSCAHGLECJ)/57.3 CMPT(J) CMYCJ)COSCAHGLE(J)/57.3)-CMXCJ)SIHCAHGLE(J)/57.3 CMYW(J) C CMZ(J) 1 CONTINUE RETURN END SUBROUTINE SBOUT
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C C C C C C 125 / CMX(30) ,CMY(30) ,CM2(30) ,QA(30) REAL I J DIMENSION CDR(30),CHL(30),CVT(30),CMHL(30),CMPTC30),CMYW(30) / BJC30),8MC30),IDESC30) WRITE (1,5) CIDES(K),K=1,30),I,J,P,E S FORMAT (///// SX,"WIND TUNNEL EXPERIMENT, DATA REDUCTION 11 /"OUTPU1 11 // 11 TEST MOD~L : SAIL BOAT"// 1X,30A2 /// I" SP.IL DIMENSIONS :" I I= ",F7.2,7X,"J = ",F7.2,7X, /"P = 11 ,F7.2,7X, 11 E = ",F7.2 ) ~RI1E (1 ,10) AR,CHORD,SA,ARTD,PO,FRF 10 FORMAT CSX," ASPECT RATIO= ",F7.2 / "ME~1N AERODYNAMIC", /"CHORD= ",F7. 2," in."/ SX, 11 SAIL AREA (ACTUAL)= ",F7.2,"f I I 5X,"SAIL AREA (100 1/. F.T.) = 11 ,F?.2 / SX,"PERC~NT /,F7 2 I SX,"FRACTIONAL RIG FACTOR= 11 ,F?.2) WRITE (1,15) 15 FORMAT(/// 11 SAIL ANGLESCDEG),VELOCITYCFPS),REYNOLDS NUMBER /"DYNAMIC FORCE(qSA}LB)" // / "COURSE 11 ,1X,2(3X,"Delta"),18X,"REYNOLDS 11 I 6X, "DYNAMIC" / 11 ANGLE" ,6X /"jib" ,SX, "main ,4X, "VELOCITY" ,6X, "NUMBER" ~8X, "FORCE" / ) DO 1 K "' 1 ,NR WRI lE (1,20) ANGLE CK) ,BJCK) ,BMCK) ,V(K) ,RECK) ,QA(K) 20 FORMAT (1X,FS.1,SX,FS.1,3X,FS.1,4X,F7.2,7X,F8.0,SX,F7.2) 1 CONTINUE WRITE (1,25) 25 FORMAT(///" FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE / "W IND / / 11 CO UR SE 11 / 11 ANGLE 11 6 X C x 11 7 X .... C y 7 X 11 C z 7 X /"Cmx",6X,"Cmy",6X,"Cmz" /) DO 2 K 1 ,NR WRITE (1,30) ANGLE CK) ,CXCK) ,CYCK) ,CZ(K) ,CMX(K) ,CMY(K) ,CMZCK) 30 FORMAT (1X,FS.1,6(2X,F7.4)) 2 CONTINUE WRITE (1,35) 35 FORMAT (///"FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE /"BOAT" // 37X, "HEEL" ,5X, "PITCH" ,5X, "YAW" ) WRITE (1 ,40) 40 FORMAT c II 4X, "DR IVE", ~x, "HEEL", sx, "VERT.", / 3(3X,"MOMENT") / '' ANGLE",1X,6(4X,"COEF.") /) DD 3 K = 1 ,NR WRITE (1,30) ANGLE(K) ,CDRCK) ,CHLCK) ,CVTCK) ,CMHLCK) ,CMPTCK), / CMYWCK) 3 CONTINUE RETURN END

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APPENDIX E BOUNDARY LAYER SYNTHESIS Local velocity impedance was achieved by positioning a partial wire cloth upstream of the test section and weav ing 4-ply acrylic yarn (0.06 in. diameter) at various heights until the desired profile was developed. An initial experi ment was conducted to measure the impedance of the screen/ frame assembly alone. With the wind tunnel running at 0(30) = 85 ft/s, the profile was surveyed both vertically and horizontally. The horizontal survey was used to ascertain latteral uniformity. A second similar experiment was then made with 0.06 in. diameter yarns woven at arbitrary loca tions paralle to the tunnel floor. A correlation was made between these two experiments for 6z yarn spacing and the resultant change in velocity = [Qitl ] 0 30 screen -[U(z) ] 0 30 screen/yarn measured in the test section (TS-0) for the same relative height (Figure E-1). From the initial arbitrary yarn placement and experiments mentioned above, a discrete empirical predictor was developed by least square curve fit to the formula. 126

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126 TS-(-52) 52 Impedance Screen TS-0 z T Position W here .6.( U( z)/U 30 ) is Measured 127 I FIGURE E-1 Correlatio~ of Screen Impedance With The Resultant Downstream Velocity Distribution. l z(in.) J--1}---Desired Profile Spacing / I f ( z), Screen with arbitrary / yarn spacing. g(z), Screen / alone. _i_ /II 6~T -----;1 .f:J: T // / I/ I .f\_,,%'_ I J V. U( z)/U30 6/U( z)/u 30 ) ---.-1 r1 TS-(52) TS-0 FIGURE E-2 Yarn Spacing A nd The Resultant Flow Impedance Dis tribution.

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bl'.\ [U(z)l = ae k u30 (E-1) 128 where "a" and "b" are constants determined by the fitting procedure. Figure E-2 illustrates the effect of yarn spac ing on the velocity profile which data are fed into the predictor algorithm. With the desired profile known a priori the determination of the required solidity distribution for the required screen can be predicted from the empirical algorithm. For practical reasons, the screen was placed in the tun nel between 45 in. and 55 in. upstream of the test section zero position. This allowed easy removal of the one-piece screen assembly when the wind tunnel was required for other test purposes. For sailing yacht wind tunnel testing the vertical velocity distribution, U(z), relative to the model is considered to be of principal importance and rela tive scale of turbulence to be of a lesser concern. As such, the initial screen size selected as as: 1/4 X 1/4 X 0.025 in. wire cloth set 52 in. upstream of the test section zero posi tion (TS-0). The effect on local turbulence at TS-0 was therefore minimal and the local turbulence was thought to be an exclusive function of the yarns. The scale of the turbulence thus generated was determined as indicated in Chapter Two to be at least an order of magnitude larger than that anticipated in the sail model turbulent shear layer and, as such, did not effect the drag properties of this shear layer.

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129 Final form of the velocity profile could then be synthesized using the difference between the velocity dis tribution caused by the screen alone and the desired velocity distribution from Chapter Five given by equation 5-5. The screen velocity profile was piece-wise curve fitted to a correlation coefficient of 0.99 minimum. This profile may be described as gl (z), 0 < z < al I g ( z) = I I l. I gn ( z) a -1 < z < a n n where i = 1, 2, 3, ... n and g (z) is an admissible function meeting the correlation n requirement over (a 1) < z < a. The required profile is n n known from equation 5-5 and may be written as f ( z) t) ( z) = 0 30 = A ln(z) + B where A= 0.1086, B = 0.4918, z(in.) is the vertical height above the tunnel floor, u 30 is the velocity at z = 30 in., and U(z) is the velocity at any z. The required local kth impedance is th e n a function of the velocity difference at

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... 130 in which form equation E-1 becomes () b[g.(zk) f(zk)] uk z = a e 1 Taking b. 1 (z) = a, initiates the marching scheme. Successive values of the independent variable were determined by the regression from In an efrort to ensure smoothness of profile in the vicinity of the piece-wise continuity points (g 's) the l. marching was slightly over extended. Any significant differences in spacing prediction in these areas were then averaged. The above technique is an excellent way of determining a solidity distribution for a pre-defined velocity profile. In application it has been found to be satisfactory. Only slight modifications were necessary in the final yarn spacing near the top and bottom of the wire cloth screen. Figure E-3 shows the resultant profiles obtained at two different tunnel speeds. The average confidence of fit was 96.5% using a least squares logarithmic curve fit for each. A vertical turbulence survey of the profile appears reasonable and is also shown in Figure E-3. This turbulence is measured using a 5.0 inch diameter sphere by the method of Dryden and Kuethe (31). The sphere

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131 Measured U(z);u 30 O-OU =7Sft/s 30 30 0U = 86 f t/s 30 I ,.---. I s:: I .-l + ...__,, P:. 0 0 ....:1 t z z :::> 8 20 A ,, z 1 ~ i::,::i ::c: t-{i)t 8 ,, i::,::i i > 0 (::Q 8 JI ::c: c., t H 10 i::,::i ::c: 101 u' 2 l0T = u3o // 0 , ,' H J r.::i > ~esired ,:,Y ~~ ; 0.2 0.4 0.6 0.8 LO U (z) ;u 30 or l0T FIGUR E E 3 D im e n s ionl e s s V e locity R a tio s (Me as ured an d Des ired) and Turbulence Intensity D i s tribution ( 10T).

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132 is modified to read the pressure difference from the front to the rear of the sphere. Pressure readings are converted to electrical signals through two Validyne P300 D/A pres sure transducers and are connected directly to a HP7046A x-y plotter. By varying the tunnel speed from low to high, a direct plot of pressure difference on the sphere versus dyna mic pressure was obtained. The critical drag point indicat ing transition to a turbulent boundary layer was taken as 6P = l.22q The sphere's Reynolds number at this point was an indication of the stream local turbulence intensity. Positioning the sphere at 5.0 in. vertical increments leads to the plot shown. The bands at each datum point on the curve indicate the uncertainty of the reading. Comparing Figure E-3 with the classical turbulent boundary layer for flow over a flat plate shows reasonable agreement.

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APPENDIX F CENTER OF EFFORT BY DIRECT INTEGRATION As discussed in Chapter Eight, the concentration of points around the planform centroid suggests an analytical check using a direct integration scheme for both cases of the Finn sail tested; with and without a simulated PBL. The following analysis is presented in support of the con clusions made in Chapter Eight. For the Finn sail planform, define the force center vertical distance as z = JH z dL 0 where z equals the distance from the wind tunnel floor, dL is the differential lift force component in the hori zontal plane at z. Then let wh e r e dL = q(z) CL(z)C(z)dz q(z) equals the local dynamic pressure, CL(z) is the local section lift coefficient, and C(z) is the chord length at z 133

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Then z = H J O z Q ( z) CL ( z) C ( z) dz H f Q(z) CL(z) C(z) dz 0 (F-1) The local length of chord is adequately represented by the linear model of the form where K 1 and K 2 are constants determined from the sail planform. For the uniform velocity, dynamic pressure is independent of z. Therefore, H z = f O z CL ( z ) ( Kl z + K 2 ) dz H Jo CL(z) (K 1 z + K 2 ) dz (F-2) 134 It is now a matter of selecting a sensible relation ship for lift coefficient. As a first approximation CL can be considered a constant and independent of z. This is com parable to assuming each accurate section of the sail has the same lift characteristics at any one given angle of attack. Further, this approximation infers that the sail twist is matched to the vertical apparent wind twist such that the angle of attack is independent of z. In this approximation, equation F-2 identically yields the planform area centroid height of z = 0.394 in. This value is plotted in Figure 8-5 and is seen to be in good agreement with the measurements

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135 made for attack angles from 25 to 35. Recalling the 0.36 H vertical height noted in the tuft observation experi ment, it appears that the windward/leeward centers of pres sure are most likely different, the latter being well above the former, and resolve to 0.39 H. For the nonuniform onset velocity, equation F-1 with uniform flow density reduces to z = (F-3) where A and Bare constants of the onset velocity distribution. It is now necessary to select an appropriate functional form for the spanwise lift coefficient. As a first approximation this function is assumed propor tional to the actual sail twist. This leads to a transcen dental cosine function which overly complicates the integra tion of equation F-3. Approximating this cosine function as a polynomial allows equation F-3 to be integrated by parts, the zeroth degree polynomial being identical to a constant coefficient of lift as in the uniform flow case. For in terest, both first and second degree approximating poly nomials are calculated and applied to equation F-3 with the following results:

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Approximating Polynomial Height to Force z/H Degree Center, z (in) 0 13.35 0.48 1 13.55 0.48 2 13.56 0.48 Comparing these theoretical values to the measured values given in Figure 8-5 shows reasonable agreement and adds credibility to the measured values. 136 In order to verify and check the overall procedure and apparatus, the magnitude of the x, y, z forces were calcu lated for the 30 angle of attack force coefficient deter mined by test with the simulated PBL. Using an adjustable stanch ion in place of the sail model, dead loads of the same magnitude (.0%) as those calculated for the 30 angle of attack were statically applied at the estimated force center indicated in Figure 8-5. The resistances thus pro duced in the six force balance strain guage channels agreed with the original dynamic strain readings obtained during the wind tunnel test to within % While large, these values of uncertainty are considered reasonable because of the duplication of uncertainty through the calibration coefficients. The calculations made here add further credi bility to the correctness of the estimated force center.

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LIST OF REFERENCES (1) Ross, w., Sail Power, Alfred A. Knopf, New York, 1976. (2) Haarstick, S.~ ''Principles of Sail Design," Proceedings of the Third Chesapeake Symposiwn, Annapolis, Maryland, January, 1977. (3) Rosenberg, R.M., "On Sail Building and Differential Geometry of Sails," Proceedings of the Ninth AIAA Symposium on the Aero/Hydronautics of Sailing, Vol. 24, February 24, 1979. (4) Milgram, J .H., "The Design and Construction of Yacht Sails," Master's Thesis, Massachusetts Institute of Technology, Cambridge, 1961. (5) Milgram, J .H., "The Analytical Desig r of Yacht Sails," Proceedings of the SNAME Annual M eeting, New York, November 13, 1968. (6) Thrasher, D.F., Mook, D.T., Nayfeh, A.H., "A Computer Based Method for Analyzing the Flow Over Yacht Sails," Engineering Science and Mechanics Depart ment, Virginia Polytechnic University, 1978. (7) Register, D.S., "A Computer Based Analysis of Steady Flow Over Interacting Yacht Sails," Doctor's Dissertation, University of Florida, Gainesville, 19 81. (8) Marchaj, C.A., Aero-Hydrodynamics of Sailing, Dodd, Mead & Company, New York, 1979. (9) Tanner, T., "The Analysis of Wind Tunnel Sail Test Data," SUYR Technical Note NO. 503, Southampton University, England, July, 1968. (10) Milgram, J.H., "Section Data for Thin, H~ghly Cambered Airfoils in I n co m pressible Flow," NASA CR1767, National Technical Information Service, Springfield, Virginia, 1971. (11) Milgram, J.H., "Effects of Masts on the Aerodynamics of Sail Sections," Marine Technology, Vol. 15, No. 1, Pp. 35-42, January, 1978. (12) Abbott, I.H., Von Doenhoff, A.E., Theory of Wing Sections, Dover Publications, Inc., New York, 1959. 137

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(13) Telionis, D.P., Zivic, E.L., "On a New Method for Testing Sails," The Naval Architect, Vol. 5, Pg. 164-65, 1976. (14) Millward, A., "Comment on a N~w Method for Testing Sails," The Naval Architect, Vol. 5, Pg. 115, 1976. (15) Baker, W.E., Westine, P.S., Dodge, F.T., Similarity Methods in Engineering Dynamics, McGraw-Hill Book Company, New York, 1968. (16) Schlichting, Hermann, Boundary-Layer Theory, Sixth Edition, McGraw-Hill Book Company, New York, 1968. ( 17) Raghunathan, S. McAdam, R. J. W., "Free Stream Turbulence and Attached Subsonic Turbulent Boundary Layers," AIAA-82-0029, 20th Aerospace Sciences Meeting, Orlando, Florida, 1982. (18) White, F.M., Viscous Fluid Flow, McGraw-Hill Book Company, New York, 1974. (19) Ruggles, K.W., "Observations of the Wind Field in the First Ten Meters of the Atmosphere Above the Ocean," Doctor's Dissertation, Massachusetts Institute of Technology, Cambridge, 1969. (20) Groscup, W.D., "Oberservations of the Mean Wind Profile Over the Open Ocean," Master's Thesis, Massachu setts Institute of Technology, Cambri~ge, 1971. (21) Pope, A., Harper, J.J., Low-Speed Wind Tunnel Testing, John Wiley & Sons, New York, 1966. (22) Holman, J.P., Experimental Methods for Engineers, Third Edition, McGraw-Hill Book Company, New York, 1978. 138 (23) Nagib, H.M., Morkovin, M.V., Yung, J.T., "On Modeling of Atmospheric Surface Layers by the Counter Jet Technique," AIAA Journal, Vol. 14, No. 2, Pp. 185190, February, 1976. (24) Cook, N.J., "A Boundary Layer Wind Tunnel for Building Aerodynamics," Building Research Establishment, Application Services Division, BRE, Watford, England, 1975. (25) Raine, J.K., "Simulation of a Neutrally Stable R ural Atmospheric Boundary Layer in a Wind Tunnel," Fifth Australasian Conference on Hydraulics and Fluid Mechanics, Christchurch, New Zealand, December, 1974.

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(26) Ruggles, K.W., "The Vertical Mean Wind Profile Over the Ocean for Light to Moderate Winds," Journal of Applied Meterorology, Vol. 9, No. 3, Pp. 389395, June, 1979. (27) Wippermann, F., The Planetary Boundary-Layer of the Atmosphere, Deutscher Wetterdienst, Offenbach, a.M., 1973. 139 (28) Kerwin, J.E., "A Velocity Prediction Program for Ocean Racing Yachts, Revised," H. irving Pratt Ocean Race Handicapping Project, OSP No. 81535, Massachusetts Institute of Technology, Cambridge, 1978. ( 29) Robert, J. Newman, B G. "Lift and Drag of a Sail Airfoil~" Wind En g.i eering, Vol. 3, No. 1, Pp. 1-22, 1979. (30) Milgram, Jerome H., "Sail Force Coefficients for Systematic Rig Variations," Research Report R-10, Society of Naval Architects and Marine Engineers, New York, September, 1971. (31) Dryden, H.L., Kuethe, A.M., "Effects of Turbulence in Wind Tunnel Measurements," NACA Report No. 342, 16th Annual NACA Report, U.S. Government Printing Office, Washington, D.C., 1931.

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BIOGRAPHICAL SKETCH James G. Ladesic was born July 10, 1946, in Pittsburgh, Pennsylvania. He attended Hampton High School In Allison Park, Pennsylvania and graduated June 1964. His under graduate studies were completed August 1967, in aeronautical engineering at Embry-Riddle Aeronautical University (ERAU), Daytona Beach, Florida. After spending four years in the aerospac e industry in mechanical design and research/develop ment activities, Jim entered graduate school at the Florida Technological University in Orlando (now the University of Centra1 Florida) A Master of Engineering degree was con fered August 1973 in engineering mechanics. During graduate studies Jim began teachi ng undergraduate engineering mathe matics at ERAU and remained in academia until June 1978. During this same period, practically all of his free time was devoted to the design, fabrication, and development of ultralight aircraft and to sailing research. Jim began graduate studies toward a Ph.D. in mechanical engineering at the University of Florida in 1976 and con tinued through 1977. This effort was interrupted by a four year return to engineering practice where he functioned in design, development, and mechanical vibration analysis. In 1981, he rejoined ERAU's faculty as an Associate Professor of Engineering and continued his pursuit of the Ph.D. 140

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141 Upon graduation, Jim wishes to continue working in both the academicandindustrial environments. He is a licensed engineer in the State of Florida and is president of Associated Engineering Techn6logies, Inc., a small but hopeful firm consulting in the applied engineering sciences.

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this stu dy and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and qu a lity, as a disse rtat ion for the degree o f Doctor of Philosophy. Richard L Fearn Professo r of Engineering Sciences I certify that I have read this s t udy a nd t ha t in my opinion it conforms to acceptable st andards of scholarly presentation and is fully adequa t e, in scope and quality, as a disser t ation for the degree of Docto r of Philosophy. Elmer C. Hansen Assistant Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Docto r of Philosophy Calvin C Oliver Professor of Mechanical Engineering

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. erc,<;e 9 / ~1A' ? L George N'/. Sandor Research Professor of Mechanical Engineering This dissertation was submitted to the G r aduate Faculty of the College of Engineering and to the Graduate Council, and was accepted as partia l fulfillment of the r equirements for the de gr ee of Doctor of Philosophy. January, 1983 Dean, Colle g e of Engineering Dean for Graduate Studies and Research

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UNIVERS I TY OF FLORIDA I I I II II I II I I ll I l l ll l ll l l lll I I l ll l ll l l ll ll l l llll 11 111111 11 111111 1 3 1262 08554 0903


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