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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.
Resource Identifier:
029291302 ( 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

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.
IV

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iv
LIST OF TABLES vii
LIST OF FIGURES viii
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 2 3
The Wind Tunnel 23
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
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 8 2
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
vi

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 9 0
9-3 Masthead Sloop (T15MH1) for Various g,
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 , C and
C /C vs. Test Results *...Y 85
Y x
9-2 Masthead Sloop Theoretical Polar vs. Test
Polars 86
9-3 L/D Ratios From Theory and Test. ¡ 93
A-l Typical Wind Triangle for the Sailing Yacht 99
C—1 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
IX

KEY TO SYMBOLS
AA , BB
n n
A. .
ID
n
AR
BAD
B. .
ID
0
'PF
0
0
FBA
FRF
H
I
I (z)
J
K
K .
l
L/D
LOA
LP
L,
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 Harman’s constant
any generalized constant
lift to drag ratio
length overall
luff perpendicular
non-dimensional turbulence scale parameter
x

M
M
0
0
OR
p
PBL
R.
l
e
SA
T.
l
U,
U
B
U„
UT(Z)
U
30
W
0
x'
a, b
c
d
e
e .
i
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/true 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

s
surface area
u*
ÃœW1"
U ' , V '
w
W (z)
X '
s
x,y, z
a
B
Y
6
X
A
v
P
T
0
$>
H
friction velocity
Reynolds stress
turbulent fluctuating velocities
uncertainty
downwash velocity
sail shape and trim parameter group
orthogonal coordinate system
angle of attack
apparent wind angle
true wind angle
sail trim angle
permutation symbol
position vector
magnitude of the position vector components
leeway angle
sail geometry polar coordinate
kinematic viscosity
density
shear stress
heel angle
turbulence scale correlation coefficient
sail twist
Prandtl mixing length
xii

Subscripts
A, B , C , . . .
force balance channel indicators
F
fore-triangle
HL
heel
J
jibsail
M
mainsail
MOD
model
PF
planform
PROT
prototype
i/j/K/1.••
coordinate indices or counters
x,y, z
3-space reference coordinates
mx, my, mz
moment subscripts
Xlll

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 35°, 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

2
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

3
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

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 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

5
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
6

7
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.

8
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 (8-A) 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

9
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 X = 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
hpU^(SA)
F
U
U
A
B
U
U
A
T
V
X',xs ,Lt,1H]
(2-la)

10

11
Where the non-dimensional arguments of this function are
defined as
6 = heading angle from the apparent wind to the
boat center line
0 = heel angle
UT(z)/U = onset velocity profile normalized
for at the masthead
MAX
U /U = boat to apparent wind speed ratio
n> A
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
xs = sail shape and trim parameters such as draft,
draft position, foot curve, roach curve, sail
dimension ratios (I/P, J/E ), trim angles
(¿M'Sj)' twist parameters (<}>j,M), etc.
L = dimensionless scale of turbulent
1„ = the geometric scale factor.
n
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
, HPROT

12
Application of the conditions of negligible leeway, zero
heel, and zero boat speed yields
UB °T
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
2
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 (x^) only
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
x
s
»
x ' (I/P, P/E, J/E, 6 ,
s u
M
and equation 2-la becomes
CF =
Cf(B, Re,
H /2SA,
FBA -
SA ' X s
Lt' 1H)
(2-lb)

13
Free stream turbulence 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 layer 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

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 (L^) for turbulence scale as
L
t
L„t
PBL
£
SAIL
(2-2)
gives for the velocity range of interest here = 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 L 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
(2-3)

15
As suggested by Schlichting (16), it is taken as 0.45 in
the overlap layer, and the lateral perturbation velocity
J 2 J 2
J v' is assumed directly proportional to i u' , consistent
with the experiments performed by Reichardt (16). Given a
measurement of $ 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
U
PBL^m
u1 v1
du/dz
(2-4)
where 8u/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 (of about 2.0 in.
at U^q = 80 ft/s. The sail model shear layer is considered
in the same manner as the prototype; this yields a sail
model mixing length (£_.._,.) of 0.02 in. The dimensionless
SAIL m
turbulence scale for the model (L^) is thus estimated to
t m
be about 100. This is sufficient to allow turbulent inter¬
actions to be ignored. As a result, equation 2-lb simpli¬
fies to
C
F
cF(e, r6,
H2 FBA
2SA' SA
(2-5)
The three-dimensional moments may also be written in
coefficient form similar to equation 2-la or

16
= C (¡3, Re,
^PUA SA CpF
H2 FBA
2SA ' SA
(2-6)
where Cpp is the planforra 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, 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
mutually perpendicular to and C^.
The corresponding moments C , C and C represent moments
c 3 mx my mz r
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 A=0) as
FWD
= C sin
y
(6)
- C cos
X
(6)
(2
-7a)
HL
- C cos
y
(6)
= C sin
X
(6)
(2
-7b)
Equations 2-7 will be used in later discussions regarding
potential yacht performance.

17
Finally, only one size yacht model is correct rela¬
tive to the fixed onset velocity distribution [UM0D^Z^
used here. However, slight extensions of the scale
factor (1 ) 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, 1 becomes approximately 11.
n
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
18

19
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

20
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.

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.

22
TABLE 3-1
Experimental Force and
Moment Coefficient
Maximum Uncertainties
Coefficient
Cx
Range
Uncertainty
0.0 to 0.2
+ 4.3%
0.2 to 0.4
±3.9%
0.4 to 1.0
±3.1%
Coefficient
Cy
Range
Uncertainty
0.0 to 0.5
+ 6.0%
0.5 to 1.0
±4.9%
1.0 to 1.-5
±3.8%
Coefficient
Cz
Range
Uncertainty
-0.4 to -0.2
±2.0%
-0.2 to -0.1
±2.1%
-0.1 to 0.0
±2.2%
Coefficient
Cmx
Range
Uncertainty
-3.0 to -2.0
+ 4.8%
-2.0 to -1.0
±5.8%
-1.0 to 0.0
±5.9%
Coefficient
Cmy
Range
Uncertainty
0.0 'to 0.2
+ 6.1%
0.2 to 0.5
±5.8%
0.5 to 1.5
±4.6%
Coefficient
Cmz
Range
Uncertainty
-0.2 to 0.2
+ 3.1%
0.2 to 0.4
±2.6%
0.4 to 0.6
±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
23

FIGURE 4-1 ERAU Subsonic Wind Tunnel General Arrangement.
ro

25
interior. The rectangular high-speed test section is 24 in.
2
wide by 36 in. high with an area of 5.96 ft . 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 120ft gauges which were
wired as two arms of a four-arm Wheatstone bridge circuit on

26
the Model 225 Switching and Balancing Unit for each of the
six channels monitored. The remaining bridge circuit was com¬
pleted using two precision 120P "dummy" resistors. Strains
were read directly from the Model 120C Strain Indicator in
microinches per inch, yin./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 ±1°F 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.

28
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
HIND TUNNEL DATA REDUCTION PROGRAM
SAIL BOAT DATA INPUT
INPUT SAIL DIMENSIONS (for model) I J P E (Inches)
25 8 22.5 9
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 J - 8.00 P v 22.50
E - 9.00
SAIL AREA (ACTUAL) = 1.82ft**2
SAIL AREA (100 '/. F.T. ) = 1 .40
PERCENT OVERLAP = 1 .50
FRACTIONAL RIG FACTOR = 1.00

29
TABLE 4-1 -continued
SAIL AHGLES(DEG),VELOCITY(FPS) .REYNOLDS HUMBER, DYNAMIC FORCE
COURSE
ANGLE
Delta
jib
Delta
main
VELOCITY
REYNOLDS
NUMBER
DYNAMIC
FORCE
8.0
12.0
0.0
'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
12.0
0,0
81.35
417675.
13.44
30.0
12.0
0.0
81 .50
418426.
13.46
35.0
12.0
0.0
82.01
421015.
13.58
40.0
12.0
0.0
82.34
422739.
13.69
46.0
12.0
0.0
82.71
424646.
13.81
FORCE AND
MOMENT
COEFFICIENTS RELATIVE TO
THE WIND
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
j 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
1.4891
-.2095
-1.0961
.2723
-.0408
46.0
.9575
1 .4652
-.2202
-1.1495
.4645
-.0164
FORCE AND
MOMENT
COEFFICIENTS RELATIVE TO
HEEL
THE BOAT
PITCH
YAW
COURSE
DRIVE
HEEL
VERT.
MOMENT
MOMENT
MOMENT
ANGLE
COEF.
COEF.
COEF.
COEF.
COEF.
COEF.
8.0
.2056
.4104
-.0427
.0871
.0675
.0769
15.0
.0943
.7016
-.0773
.3711
.1620
.0538
20.0
.0070
.9185
-.1086
.5994
.2774
.0206
25.0
.1649
1 .1918
-.1402
.7668
.4373
-.0032
30.0
.2626
1 .3733
-.1672
.8932
.5873
-.0430
35.0
.3503
1.4840
-.1878
1.0313
.7953
-.0571
40.0
.4130
1 .5973
-.2095
1.0148
.9132
-.0408
46.0
.3887
1 .7066
-.2202
1.1327
1.1495
-.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
30

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¬
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

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 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
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 * 7
u o
(5-3)
where z
U(z)
K
z
o
vertical distance above the water plane
velocity at height z
von Harman Constant taken to equal 0.42
roughness length

33
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 [U^p] and the vertical position (z) for any
profile velocity as
U (z) = 0.1086 U1Q In[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 (1^ = 12)
yields
= 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 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=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
Similarly, sloop rigs which have fore-triangles that do
not extend to the vessel masthead are termed "fractional
35

Head
Luff
Clew
Foot
FIGURE 6-1 Sail Geometry Nomenclature

rigs". To classify these geometries, one can define a
fractional rig factor (FRF)
37
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.
The foresail triangular area (SA ) can then be written
r
as
SAp = -y(I2+J2)*(OR) (J)
The mainsail dimensions are designated P and E. Its triangu¬
lar area (SA^) is
sam =iPE-
The rig planform area used for all of the force and moment
coefficients is the sum of the foresail and mainsail area
SA = SA + SA
F M
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

38
defined by the particular sail being referenced. The main¬
sail aspect ratio is taken as
arm = I
while the fore-triangle aspect ratio is
AR
J
I
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
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
'PF
1 saf
= it-/ +
’V
Jib
SAm
c = L—1 .
PF P ‘Main
Test Reynolds numbers for each wind tunnel test run are cal¬
culated using this chord length. It is reasoned that Cpp
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

39
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 (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
g
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

TABLE 6-1
Planform Geometries
Configuration
Reference
Code*
Planform Nomenclature
Rig Description
FRF
I
J
P
E
PO
T00CB1
Finn-Type Sail
0.0
0.0
0.0
24.80
15.30
0.0
T15MH1
Sloop - Masthead
1.00
25.00
8.00
22.50
9.00
1.52
T15781
Sloop - 7/8
0.875
21.88
7.00
22.50
9.00
1.52
T15341
Sloop - 3/4
0.750
18.75
6.00
22.50
9.00
1.52
T15121
Sloop - 1/2
0.500
12.50
4.00
22.50
9.00
1.52
TOSCBl
Catboat
0.0
0.0
0.0
22.50
9.00
0.0
T15MJ2
Sloop - High AR
Jib and Main
1.00
25.00
6.00
22.50
6.43
1.52
T15MJ3
Sloop - High AR
Jib Alone
1.00
25.00
6.00
22.50
9.00
1.52
NOTE: Dimensions shown are in inches ± 0.016 in.
*Configuration Reference Codes are used throughout this work to cross reference
test information.

SECTION LIFT COEFFICIENT
41
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.

42
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 (!„) is taken as 12 to per-
n
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

FIGURE 6-3 Wind Tunnel Yacht Model Configurations.
(All dimensions given are in inches)
CO

44
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

45
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
r = ^ [ARCCOS —--7) ] (6-1)
£ 1+4(d)
2 2 h
For the headsail, (I +J ) 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 1 A 1 2 ARCCOS t1"4(d)?]
1+4(d)
'F LP* -
o
2 2 h
(I +J )
- z
1-—
F ' LP'
o
and
(6-2)

46
where
1 *
ZF = ~J [ 2 ]
o (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. zl and z' are foot and leech bounds respec-
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.

47
FIGURE 6-4 Sail Surface Description.

48
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 (ó,„) 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.

49
Headsail
Twist
4» = 24°
J3
4> = 22.
J2
4> = 21°
J1
V 12
Mainsail
Chords
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.
50

51
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 10° to
45°. 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 (3=10°. The model was ro¬
tated through 45° 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 5yin.
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 5° increments from
10° to 45°.

TABLE 7-1
Mean Sail Shape and Trim
Parameters
Configuration
Reference
Code
6 J
(Per Span)
dJ
ÓM
(J) w
(Per Span)
dM
T00CB1
N/A
N/A
N/A
0°
32°
11%
T15MH1
12°
16°
12%
0°
30°
12%
T15781
12°
18°
10%
0°
31°
12%
T15341
12°
20°
11%
0°
33°
11%
T15121
12°
H1
00
0
11%
0°
35°
12%
T0SCB1
N/A
N/A
N/A
0°
36°
13%
T15MJ2
12°
14°
10%
0°
O
CN
CM
7%
T15MJ3
12°
14°
10%
0°
24°
11%
Ul
tv)

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 5yin., 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 =7) fabric scale model of the Finn sail to experi-
mentally investigate the effects of boom vang tension and
resulting sail shai 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.
54

55
The sail planform is given in Table 6-1, Configuration
Code T00CB1. 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.

56
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 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.

57
z(in.)
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.
FIGURE 8-2 Finn Sail Upwash Observation.
Position assummed by a long yarn on the
leeward side of the sail as viewed from above.

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 (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

COEFFICIENTS
59
FIGURE 8-3 Effect of the Planetary Boundary Layer on
Gail Toot Data. Finn cail for Re= 1.8 x 105
vs. Marchaj'c data for Re= 2.? x 105.

60
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
(Cz) can be thought of as the net reaction of the span-
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 C , C , and C are concentrated at dif-
x y z
ferent x, y, z locations or
F
x
F
x
)
F
y
Fy(x2, y2,
)
and
F
z
Fz(X3
y3'
)

COEFFICIENTS
61
10 20 30 40 50
HEADING ANGLE(Degrees)
FIGURE 8-4 Finn Moment Coefficients With and Without
the Planetary Boundary Layer.

62
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
mz
ICyx2
+
W /CPF
mx
(cyz2
+
Czy3*/CPF
my
(Cxzl
+
CZX3I/CPF
Applying the conditions of equation 8-1 to equation 8-2 gives
z
2
(8-3)
From the plots in Figure 8-3 it is noted that
C > C
y x
It is logical to assume y^ <_ x^, therefore, the z-moment
coefficient can be approximated as
: = C x / C
mz y 2 PF

63
Solving for x2 yields
x
2
(8-4)
Using equations 8-1, 8-2 and 8-4 the vertical height to the
x-force location can be approximated as
It is clear that the uncertainty of z2 is less than that of
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 z-^ is estimated at ±11.09%.
Using these uncertainties to generate weighting factors
and W2, a sensible vertical distance to the force center
is defined as
z(nominal)
*W1Z1*2 +
(W2Z2)
+
W„
(8-6)
Where W-^ = 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.

Ratio of Height to Luff Length (z/P)
64
FIGURE 8-5 Finn Sail Center of Effort Location.
Center of effort locations at various attack
angles with and without the simulated PBL.
flote: 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.

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
65
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 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 be 0.48 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 values at or near stall.
At an angle of attack of 30°, three tests were conducted cor-
5 5
responding to Reynolds numbers of 2.3 x 10 , 2.9 x 10 and
3.3 x 10^. The Cy 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.

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
T15MH1 -- Full hoist masthead sloop
T15781 -- 7/8 hoist headsail sloop
T15341 -- 3/4 hoist headsail sloop
T15121 — 1/2 hoist headsail sloop
T0SCB1 -- 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

67
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.

COEFFICIENTS
68
FIGURE 8-6 Masthead Sloop Test Results. R = 280,000.,
FBA/SA =0.23 (T15MH1) e

69

COEFFICIENTS
70
FIGURE 8-8 7/8 Sloop Test Results. Re= 240,000.,
FBA/SA = 0.27 (T15781)

or
71
FIGURE 8-9 7/8 Sloop Polars. Re= 240,000. ,
FBA/SA = 0.27 (T15781)

COEFFICIENTS
72
FIGURE 8-10 3/4 Sloop Test Results. Re= 210,000. ,
FBA/SA = 0.32 (T15341)

or
73

COEFFICIENTS
74
FIGURE 8-12 1/2 Sloop Test Results. Re= 90,000. ,
FBA/SA = 0.43 (T15121)

or
75
FIGURE 8-13 1/2 Sloop Polars. Re= 90,000. ,
FBA/SA = 0.43 (T15121)

COEFFICIENTS
76
FIGURE 8-14 Catboat (with hull) Test Results. Rg= 90,000.
FBA/SA = 0.60 (T0SCB1)

or
77
Re= 90,000. , FBA/SA = 0.60 (T0SCB1)

COEFFICIENTS
78
FIGURE 8-16 Masthead Sloop, High Aspect Ratio Main and
Jib. Re= 260,000. , FBA/SA = 0.32 (T15MJ2)

or
79
FIGURE 8-17 Masthead Sloop, High Aspect Ratio
Main and Jib, Polars. Re= 260,000.
FBA/SA = 0.32 (T15MJ2)

COEFFICIENTS
80
HEADING ANGLE(Degrees)
FIGURE 8-18 Masthead Sloop, High Aspect Ratio Jib and
Standard Main. Re= 270,000. FBA/SA = 0.28
(T15MJ3)

or
81
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
82

83
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

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 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=35°). In this same region, the
drag coefficient values are seen to be under predicted. This
is to be expected with an inviscid solution.

COEFFICIENTS
85
FIGURE 9-1 Masthead Sloop Theoretical C , C , Câ„¢,.-,, and
Cy/Cx vs. Test Results. ' ^
(ref. T15MII1)

or
86
2.0 -
u
u
M. 5
1.0
0.5
LEGEND
Theory,Sails Alone —
Test,Complete Rig
â–¡ C vs.C
3 -*•
0.5
KIH
IT
vs.C
HL
J—rV
77V
C or C„T
x HL
FIGURE 9-2 Masthead Sloop Theoretical Polars vs.
Test Polars. (ref. T15MH1)

87
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
a heading angle of 21°, 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

TABLE 9-1
Rig Configuration Test and Theoretical Results
Description
Aspect Ratio
Rig Ratios
Sails Alone
Complete Rig
Rig
H2/2SA
Main
P/E
Jib
I/J
l/P J/E
' cy
C
X
CFWD
CHL
c /c
y x
C
y
C
X
L/D
Masthead
Sloop
T1SMH1
0)
(2)
(3)
(4)
1. 14
1.S0
1 .SO
1.14
2.50
2.50
2.50
2.50
3.13
3.00
3.00
3.13
1.11
1.10
1.10
1.11
0.89
0.89
0,89
0.89
1.04
1.25
1.25
1.15
0.18
0.26
0.22
0.32
0.46
0.45
0.51
0.20
1.01
1.24
1.21
1.33
5.62
4.73
5.83
3.56
1.24
0.40
3.10
7/8
Sloop
T1S781
(1)
(2)
(3)
(4)
1.40
1.82
1.82
1.40
2.50
3.00
3.00
2.50
3.13
2.78
2.87
3.13
0.97
1.02
1.02
0.97
0.78
1.10
1.10
0.78
0.9S
1.24
1.24
1.16
0.15
0.26
0.21
0.35
0.24
0.32
0.36
0.12
0.91
1.22
1.20
1.18
6.40
4.80
5.96
3.31
1.30
0.41
3.17
3/4
Sloop
T1S341
(1)
(2)
(3)
(4)
1.63
2.04
2.04
1.63
2.50
3.00
3.00
2.50
3.13
2.63
2.63
3.13
0.83
0.96
0.96
0.83
0.67
1.10
1.10
0.67
0.91
1.24
1.24
1.02
0.13
0.26
0.02
0.41
0.29
0.33
0.37
0.10
0.87
1.22
1.20
1.10
6.85
4.68
5.77
2.49
1.15
0.50
2.30
1/2
Sloop
T1S121
(1)
(2)
(3)
(4)
2.21
2.58
2.58
2.21
2.50
3.00
3.00
2.50
3.13
2.25
2.25
3.13
0.56
0.82
0.82
0.56
0.44
1.10
1.10
0.44
0.91
1.24
1.24
1.18
0.14
0.28
0.22
0.46
0.24
0.32
0.36
0.12
0.78
1.23
1.20
1.35
5.86
4.49
5.54
2.57
1.34
0.57
2.35
Catboat
TOSCBl"
(1)
(2)
(3)
(4)
2.50
2.50
2.50
2.50
2. SO
2.SO
2.SO
2.SO
N/A
N/A
N/A
1.44
1.42
1.42
1.48
0.21
0.22
0.21
0.53
0.46
0.45
0.51
0.20
1.37
1.35
1.33
2.00
6.77
6.56
9.57
2.97
1.72
0.70
2.46
High AR
JSH
Masthead
Sloop
T1SMJ2
Cl)
(2)
(3)
(4)
1.65
1.67
1.67
1.65
3.50
3.50
3.50
3.50
2.78
2.75
2.75
2.78
1.11
1.10
1.10
1.11
0.95
1.41
1.41
2.95
1.03
1.23
1.03
1.15
0.13
0.2S
0.20
0.37
0.35
0.34
0.38
0.20
0.97
1.21
1.19
1.25
8.14
4.92
6.13
3.11
1.28
0.47
2.72
High AR
Jib
Masthead
Sloop
T15MJ3
CD
(2)
(3)
(4)
1.44
1.44
1.44
1.44
2. SO
2. SO
2.50
2.50
2.78
2.75
2.75
2.78
1.11
1.10
1.10
1.11
0.67
1.01
1.01
0.67
1.09
1.24
1.24
1.25
0.18
0.28
0.23
0.45
0.34
0.32
0.36
0.20
1.0S
1.23
1.21
1.38
6.19
4.50
5.47
2.78
1.38
0.50
2.76
Legend;
(1) Sail-3 results.
(2) Milgram's results with a pressure and viscous drag estimate.
(3) Milgram's results without the pressure and viscous drag estimate.
(4) Wind tunnel test results.

89
the apparent wind speed. There are also minor differences
in rig dimensions, as noted. Nevertheless, comparison re¬
mains of interest. To facilitate this comparison, 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.

TABLE 9-2
Finn-Type Sail Results From
Experiment and Theory*
Coefficients
L&ft
^x
Drag
CFWD
Forward
CHL
Heel
z/p
Side
Force
TEST
(T00CB5)
1.050
0.280
0.230
1.130
0.52
SAIL-3
(After Register)
1.258
0.232
0.424
1.196
0.518
MILGRAM
(With Viscous and
Pressure Drag
Extrapolated)
1.405
0.271
0.410
1.372
0.522
MILGRAM
(No Viscous and
Pressure Drag
Extrapolated)
1.405
0.208
0.450
1.350
0.529
*B-X = 27°
o

TABLE 9-3
Masthead Sloop (T15MH1) For Various 6
Experiment vs. Theory
6
Source of Data
Coefficient
C
y
C
X
(1)
SAIL-3
0.96
0.14
o
in
CM
(2)
MILGRAM
1.20
0.25
(3)
TEST
1.05
0.30
(1)
SAIL-3
1.05
0.18
27°
(2)
MILGRAM
1.25
0.26
(3)
TEST
1.14
0.32
(1)
SAIL-3
1.16
0.23
30°
(2)
MILGRAM
1.27
0.26
(3)
TEST
1.22
0.38
ASPECT
RATIOS
MAIN
JIB
(1)
2.50
3.13
(2)
3.00
3.00
(3)
2.50
3.13
NOTE:
VO

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

L/D
FIGURE 9-1? L/D Ratios From Theory and Test. Comparison of wind tunnel test
data with potential flow theoretical predictions.
VD
U>

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.

CHAPTER TEN
CONCLUSION AND RECOMMENDATIONS
Wind Tunnel Test Conclusions
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 perfor¬
mance 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 and, apparently, of the correct magnitude
95

96
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.
In two-dimensional water tunnel tests, Milgram (11)
found that the 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 will be greater for single sail catboats than for
sloops.
Recommendations
Having summarized what has been investigated, the
following parameters have not yet been adequately defined.
"''Sloops 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 the
headsail is nearly that predicted by a no mast 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 layer interference.

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.

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 Um(z), boat speed Uc, and the
true wind angle, y, to determine the apparent windspeed U .
UA = [uj(z) + Ug - UT(z) UB cos(180-y)]h (A-l)
Similarly the apparent wind angle, f3 , may be defined
using the law of sines as
6 = arcsin
UT(z)
”UT
sin(180-y)
(A-2)
These relationships describe the wind triangle for the sail
ing yacht (see Figure A-l). 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
UB = Ko VH) (A"3)
98

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

100
where Kq is the constant of proportionality. From Chapter
Five the true wind speed at any height, z, may also be
characterized in terms of the masthead wind speed as
UT(z) = Ut(H)(A In z + B)
(A-4)
where A and B are constants (see Appendix D).
Substituting equations A-3 and A-4 into equations A-l
and A-2 and combining gives the apparent wind angle as a
function of z alone for any selected Kq and y as
B = arcsin
K
siny
K
[ (1 +
A In (z) + B
+ 2
A In (z) + B
cosy)]
(A-5)
For the present analysis consider UT(H) to be (the wind
speed at 30 ft), A = 0.1086, B = 0.4918 and Kq = 0.6 (after
Milgram). As a specific example let y = 45° and then B can
be calculated for the heights z^ = 3 ft and z^ = 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
AB = B(z2) - B(zx) (A-6)
From equation A-6 for z2/z.^ = 10, AB 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

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
(cu ) can be approximate in terms of the local induced down-
wash velocity w(z) and the freestream velocity UT(z) as
w(z)
UT(z)
a.
i
(A-5)

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
k
w(z) = -U E, nA (AA - BB )
o m=l n n n
where
Uq = wind velocity at the sail mid span
A = Fourier coefficients
n
AA and BB = numerical solution points of the Glauert
n n integral and the image sail integral
respectively.
From Milgram's solution the values of AAn and BB^ for k = 3
gives a representative downwash velocity at the boom and at
the masthead, respectively, of
w(z,) = -0.189 U
1 ° (A-6)
w(z2> = -1.096 Uq
The freestream velocity at these same locations may be ap¬
proximated using Milgram's linear model
U (z ) = U - 0.115(z„ - z ) (A-7)
T 1 o 2 1
and
Ut(z2) = Uq + 0.115(z2 - zx)
Selecting Uq = 6 ft/s as representative of the test condi¬
tions of interest, equations A-6 and A-7 can be evaluated

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% reduc¬
tion 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.

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^) and the unit tangent vectors e^)
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
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
j 1 1 2 2 3 3
The corresponding elemental differential surface area vec¬
tor (dSj) at this location has a magnitude (ds) defined as
ds = e.ds.
3 3
such that the differential force applied to this elemental
surface can be written
dfj = Tjds; j = 1, 2, 3 (B-l)
104

105
Equation B-l represents a vector described in local
coordinates. Let be the direction cosines between the
local e-coordinates and a global coordinate system. Then
is a function of the surface parameters and the differen¬
tial force in the global coordinates becomes
df.
i
A..T.ds; i = 1, 2, 3
i] 3
(B-2)
and the total force applied over all of the free surfaces
is given in global form as
i = 1, 2, 3
f. = IS A. .T .ds; j =1, 2, 3
i s 13 j
(B— 3)
The moment about the global origin resulting from the
applied local surface traction at is defined as the
vector product of the position vector and the element force
df
It is convenient to introduce the permutation symbol
e . .. such that:
13k
s. ..
13k
e. ..
13k
e. ..
13k
0 if i, j, k do not form a permutation of 1,2,3.
+1 if i, j, k form an even permutation.
-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.
1

106
From equation B-2
dM.
i
e . c • A. .T.ds
ljk^i kl 1
(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
Mi = "s Eij^i\lTlds ,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 pres¬
sure 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

107
similar aerodynamic center or "center of effort" cannot
be obtained, in general, by measurement of orthogonal force
and moment triples alone. As proof, let be a force vector
applied at a location in space denoted by the position vector
such that:
i
M. = E . .. c*F.
i k
From equation B-5 then
(B-6)
eijk5jFk "s
e . .. z, . A. ,T.ds
íjk^i kl 1
For static equilibrium
Equation B-6 may be expanded to yield a set of simultaneous
scalar equations in M, c;, and F of the form
M, =
F r * - F r *
3^2 2^3
M„ =
-F r * + F r
3Q1 1^3
M_ =
F r * - F C *
^ 2^1 1^2
(B-7)
Now, consider the vector equation
M.
l
B. .
i] ]
(B-8 )
where the coefficient matrix B^^ is singular skew-symmetric
which, by definition, has no inverse and is subject to the
following conditions:

108
B. . =
13
= “Bj ¿i i#j
and
B. . =
13
= 0; i=j
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
Mi =
B12C2 B31C3
II
CM
IS
-Bl2q + B23í* (B-9)
m3 =
B31^1 " B23^2
By comparison, equation B-9 is seen to be identical to
equation B-7 for
F1 =
B23
F2 =
B31 (B-10)
F3 =
B12
Therefore, equations B-7 may be thought of as a vector
equation of the form
M. = F..£* (B-ll)
1 13 3
where the numerical subscripts on the matrix F.. are related
13
to the F^ as indicated by equation B-10. The desired solutions
are the components values of or

109
í* = [F. .] 1M.
i i] D
(B-12)
The solution indicated in equation B-12 exists if and
only if the inverse of exists. But, for equation B-ll
to represent the moment components of equation B-7, F^^ must
be singular skew-symmetric. As such, equation B-ll 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 com¬
ponents is known from symmetry or can be estimated from
some physical constraint of the experiment, a unique solution
of equation B-ll 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 (C*=0), in
equation B-7 allowing position vector components and
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.

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
6
6
(C-l)
110

Ill
where is the net reading (load cell output, electrical
resistance, force, etc.) for any one channel in terms of the
actual applied calibration load or moment on any one
channel and the cross coupling influence coefficients 9R^/
9e^ of all six channels. The calibration equations for any
net, single-channel, reaction is then obtained by inverting
equation C-l or
T
eD
(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,
yCj e 3
dependent on all six R^ channel readings and each of their
respective individual uncertainties. Employing the methods
discussed by Holman (22) and assuming a uniform odds distri¬
bution, the single channel uncertainty, w^e^, is then given
in terms of the individual reading uncertainties, wR^ as
6 9y
„ , ei
(C-3)
w
9ei
If the coupling effects are strong and the uncertainty of
all the readings are approximately the same, the final net

112
reaction uncertainty is then determined by any one typical
channel uncertainty as
W3ei WR
6 9Yei 2
K.
(C-4 )
3y
01
For the worst case, all the -rrr— are considered of equal
9Rk
magnitude and equation C-4 reduces to
w
ye
Ir)
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
by decreasing (elimination is the optimum) the cross coupling
terms of equation C-3 and/or by reducing the reading un¬
certainty, w .
R
The pyramidal balance is classically offered as a means
3y .
0 i
whereby all of the -r-r— coupling terms of equation C-4 approach
9Rk
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

113
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
least a portion 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
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-l.
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, six-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

114
floating beam balance has been designed, constructed, and
is employed as the data acquisition tool.
Six-component Floating Beam Balance
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 tech¬
niques. 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
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-l 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)

115
FIGURE C-1 Six Component Floating Beam Force
Balance In Schematic.

116
which measures Fdirectly. The moment about "z" is reacted
at F by a sixth beam.
The subsequent force calibration equation takes the
form
F
y
= cari
+ CBR3
+ CAFR6
+ CBFR6
F
X
= CBR2
+ CER4
+ CCFR6
+ CEFR6
(C-5)
F
z
= CHR5
where C,, , etc. are calibration coefficients determined
A B
by application of known loads to each of the independent
channels. Rearranging equation C-5 for the individual
flexural element contributions gives
F = Fa + Fd
y A B
Fx = FC + FB
F = CuRc;
z H 5
The principle moments are then functions of the known dis¬
tances (h and n) and the measured forces or
M
II
&
1
+
(n
+ h) F
X
A
M
y
= hFc +
(n
+ h) F
M
= C„R,
z
F 6
(C-6)

117
Problems one would normally encounter with change in the
model angle of attack or heading angle are avoided because
the z-axis 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 displacements 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 over ball bearing pulleys. The pulley hysteresis
and "stiction" were measured at ±0.2% of the applied load.
Any single strain gauge channel could be statically read
to an accuracy of ±0.2% of the scale of interest. The net
accuracy of a calibration coefficient over a range of chan¬
nel readings for all six channels used is adequately repre¬
sented by an uncertainty of ±1.1%. The useful output un¬
certainty of the balance for any one force or force

118
coefficient is seen, from equation C-5, to be dependent on
as many as four such calibration coefficients. In addition,
the output load (F^, Ffi, F , 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 C„ defined as
r
The uncertainty of q, the dynamic pressure, is dependent
upon a water manometer reading, ±0.010 in. of *^0, and
a temperature reading, ±1°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 ±1.15%.
Each channel resistance, R. through R,, 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

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.

APPENDIX D
WIND TUNNEL DATA REDUCTION
COMPUTER PROGRAM
"BOAT"

F IMX ,L
AFILES (0,1)
PROGRAM BOAT 121
C
C WIND TUNNEL TEST DATA REDUCTION PHASE
C
C ( •note*
C The main program is written to be general
C with the only arrays and/or
C variables being stored in COMMON that are
C applicable to any type of model that can
C be tested in the wind tunnel.
C
C The subroutines are geared
C towards sailboat analysis. )
C
C PART GF
C WIND TUNNEL / DATA ACUISITIGN UNIT / HP1000L PROJECT
C
C J. LADESIC
C
C CRIGINIALLY WRITTEN
C 26 MARCH 1882
C
C MODIFIED
C 8 APRIL 1982
C 12 APRIL 1982
C 15 APRIL 1982
C 21 MAY 1982
C 9 MAY 1982
C 15 JUN 1982
C
C
COMMON NR,ANGLE(30),V(30>,RE(30),CX(30),CY(30),CZ(30),
/ CMX(30) ,CMY(30) ,CMZ(30) ,QA(30)
REAL MZ,JS,IS,EPSLN,AM,B2M ,CM,EM,R6F
INTEGER FNAME(3) ,DESC(30)
. DIMENSION CDR(30),CHL(30),CVT(30),CMHL(30),CMPT(30),CMYW(30)
/ B J(3 0),BM(30)
DATA VK/.000157/
C
C COMMON data table
C NR : Number of wind tun' '1 runs for
C model being tested
C ANGLEj: Angle model is moynted relative to wind,
C can be X - Y plane or X - Z plane
C Vj : Airspeed
C CXj ,CY j,
C CZj : Force coefficient's X Y Z
C coordinate system
C CMXj,CMY j,
C CMZj : Moment coefficients X Y Z
C coordinate system
C REj : Reynolds number
C QAj : Dynamic force
C
WRITE (1,5)

non
5 FDRMP.T (" INPUT NAME OF FILE RUN DATA IS STORED IN" / 122
/ "(UP TO SIX CHARACTERS,FIRST CHARACTER START IN COLUMN 1,"
/ / " JUSTIFIED LEFT, INCLUDE TRAILING BLANKS, IF ANY)")
READ (1 ,6) (FNAME(I),1 = 1,3)
6 FORMAT (3A2)
OPEN (UNIT=6,I0STAT = IERR,EPR=S98 ,F ILE=FNAME ,STA.TUS='OLD' )
’GOTO 50
S98 WRITE (1,55) (FNAME(I),1=1,3) , IERR
55 FORMAT (" ERROR ON OPENING DATA FILE ",3A2
/ / " ERROR * ", H)
GOTO 999
50 WRITE (1,7)
7 FORMAT (/// 5X, "WIND TUNNEL DATA REDUCTION PROGRAM")
READ (8,10) NR,(DESC(I),1 = 1 ,30)
10 FORMAT (14,30A2)
WRITE (1,15)
15 FORMAT (////)
ICNTRL=2
CALL SINPT (IS,JS,P,ES,PC,FRF,AR , CHORD,SA,ARTD)
••••KINEMATIC VISCOSITY CORRECTED FOR TEMP AS 1 .083VK(STD)=VK
CONST=CHORD/(1.083*VK*12.)
C
DO 1 J=1 ,NR
EPSLN = 0.0
READ (8,20) ANGLE (J) ,T,PS,PT,R1,R2,R3,R41RS,R6,BJ(J),EIM(J)
20 FORMAT (F5.1,FS.0,2F7.2,GF7.0,2F5.1>
fi-((R1-4000)/(12.1 1 )) + ((4000-R6)/307.656)
B=((4000-R3)/(8.11))+((4000-R6)/1589.35)
C=((R2-4000)/(83.3333))+((4000-R6)/300.0)
E=(MOOO-R4)/(87.500))+((4000-R6)/4050.0)
MZ=M000-R6)/56.8627
H=((RS+(.276*R1)-S104)/161.8) ,
QA(J)=(ABS(PT-PS)/12.)«62.4*SA
EPSLN = 1 +.027»(SA+.45)*SIN (ANGLE (J) / 57.3)
QA(J)=(EPSLN**2)»QA(J)
IF (QA(J)) 100,200,100
100 CX(J)=-(C+E)/QA(J)
CY(J)=-(A+B)/QA(J)
CZ(J)=H/QA(J)
CMX(J)=((-4.625«A)-(16.063*B))/(QA(J)•CHORD)
CMY (J) = - ((- 4.825*0 - (18.063*E)) /(QA(J)«CHORD)
CMZ(J)=MZ/(OA(J)«CHORD)
GOTO 300
200 CX(J)=0.
C Y (J) = 0 .
CZ(J)=0.
CMX(J) = 0 .
CMY(J)=0 .
CMZ(J) = 0 .
300 V(J)=2.905*SORT(ABS(PS-PT)*T)
V(J)=EPSLN»V(J)
RE(J)=V(J)«CONST
1 CONTINUE
C
CALL SCOEF (CDR,CHL,CVT,CMHL ,CMPT,CMYW)
CALL SBOUT (IS,JS,P,ES,PQ,FRF,AR,CHORD,SA,ARTD,CDR,CHL ,CVT ,

nonnnnnnnnn onooooooooooooooooo noooo
C
/ CMHL,CMPT,CMYW,BJ,EM,DESC)
CLOSE (UNIT-6)
999 STOP
END
123
SUBROUTINE SINPT (I,J,P,E,PO,FRF,AR, CHORD,SA ,ARTD)
SUBROUTINE Sailboat INPuT
Accept sail dimensions data from CRT,
compute sail area (actual), sail area (100 V. F.T.),
mean aerodynamic chord, aspect ratio
( * note ♦
subroutine is designed for sailboat app1ications ,
however subroutine can serve as a model for
aircraft / missle / rocket type
applications )
SUBROUTINE WRITTEN
12 APRIL 1982
MODIFIED
9 MAY 1982 TO INCLUDE THE CATBOAT
COMMON NR,ANGLE(30),V(30),RE(30),CX(30),CY(30),CZ(30),
/ CMX(30),CMY(30),CMZ(30),QA(30)
REAL I, J,JSTAR
data table
I.J.P.E :
CHORD :
SA :
ARTD :
AR :
P0 :
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
WRITE (1,5)
S FORMAT (/ SX,"SAIL BOAT DATA INPUT" //
/ " INPUT SAIL DIMENSIONS (for model) I J P E (inches)
READ (1,0 I, J , P , E -
WRITE (1,10)
10 FORMAT (/ " INPUT PERCENT OVERLAP, FRACTIONAL RIG FACTOR")
READ (1,0 P0 ,FRF
IF (FRF) 30,50,30
30 JSTAR - SORT((P0**2)/((1./(J**2))-((P0**2)-1.)/(I* *2)))
H = I/FRF
SA - (.5» JSTAR*I+ ,5*E*P)/144.
ARTD - (.5*J*I + .5*E*P)/144.
GOTO GO
50 ARTD = .5»E*P/144.
H = P
SA=ARTD

oooonoooo r~> n o o o r~i o o nnnnnnnnnnnnnnnn nnnnnn
60 AR = H**2/(SA«H4.)
CHGRD = SA*144./H 124
RETURN
END
SUBROUTINE SCOEF (CDR,CHL,CVT,CMHL,CMPT,CMYW)
SUBROUTINE Sailboat COÉFficients
Computes coefficients when rotating wind tunnel X - Y axis
to DRIVE - ATHWARTSHIP axis
SUBROUTINE WRITTEN
12 APRIL 1982
MODIFIED
(none)
data table
CDR, CHL, CVT : force coefficients
CMHL, CMPT,
CMYW : moment coefficients
COMMON NR.ANGLE (30),V(30),RE(30),CX(30),CY(30),CZ(30),
/ CMX(30),CM Y(3 0),CMZ(30),QA(30)
DIMENSION CDR ( 30) ,CHL ( 30) ,CVT (30) ,CMHL (30) ,CMPT ( 30) ,CMYW (30)
DO 1 J - 1,NR
CDR(J) - CY(J)*SIN(ANGLE(J)/57.3)-CX(J)«COS(ANGLE(J)/57.3)
CHL(J) - CY(J)*C0S(ANGLE(J)/57.3)+CX(J)*SIN(ANGLE(J)/B7.3)
CVT(J) - C2CJ)
CMHL(J) - CMY(J)«SIN(ANGLE(J)/57.3)-CMX(J)*COS(ANGLE(J)/57.3
CMPT(J) - CMY(J)*C0S(ANGLE(J)/57.3)-CMX(J)*SIN(ANGLE(J)/57.3
CMYW(J) - CM2(J)
1 CONTINUE
RETURN
END
SUBROUTINE SBOUT (I,J,P,E,PO,FRF,AR.CHORD,SA,ARTD,CDR,CHL,CV
/ CMHL,CMPT,CMYW,BJ.BM,IDES,FNAME)
SUBROUTINE SailBoat OUTput
SUBROUTINE WRITTEN
14 APRIL 1982
MODIFIED
(none)
COMMON NR.ANGLE(30),V(30),RE(30),CX(30),CY(30),C2(30),

125
/ CNX(30), CMY(30),CMZ(30),QA(30)
REAL I,J
DIMENSION CDR(30),CHL(30),CVT(30),CMHL(30),CMPT(30) ,CMYW(30)
/ B J(3 0),BM(30),IDES(30)
C
WRITE (1,5) (IDES(K),K = 1,30) ,I,J,P,E
5 FORMAT (///// 5X, "WIND TUNNEL EXPERIMENT, DP.TA REDUCTION ",
/"OUTPUT" // " TEST MODEL : SAIL BOAT" // 1X,30A2 III
/ " SAIL DIMENSIONS :" / " I = ",F7.2,7X,"J = ",F7.2,7X,
/"? = ",F7.2,7X,"E = ",F7.2 )
WRITE (1.10) AR,CHORD,SA,ARTD,PO,FRF
10 FORMAT (5X," ASPECT RATIO = ",F7.2 / " MEAN AERODYNAMIC ",
/"CHORD = " ,F7.2," in." / 5X," SAIL AREA (ACTUAL) = ",F7.2,"f
/ / 6X, "SAIL AREA ( 100 7. F.T.) = \F7.2 / SX,"PERCENT OVERLA
/ ,F7.2 / SX,"FRACTIONAL RIG FACTOR = \F7.2)
C
WRITE (1,15)
15 FORMAT (/// " SAIL ANGLES(DEG).VELOCITY(FPS).REYNOLDS NUMBER
/"DYNAMIC FORCE(a*SA)LE)" //
/ " COURSE",1X,2(3X,"Delta") ,18X, "REYNOLDS" ,
/ GX,"DYNAMIC" / " ANGLE",6X
/" j ib" ,5X, "main" ,4X , "VELOCITY" ,6X, "NUMBER" ,8X, "FORCE" / )
DO 1 K - 1,NR
WRITE (1,20) ANGLE(K),BJ(K) ,BM(K),V(K),RE(K) ,QA(K)
20 FORMAT (1X,F5.1,5X,F5.1,3X,F5.1t4X,F7.2,7X,F8.0 ,5X ,F7.2)
1 CONTINUE
C
WRITE (1,25)
25 FORMAT (/// " FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE
/"WIND" // " COURSE" / " ANGLE",6X,"Cx",7X,"Cy",7X,"Cz",7X,
/"Cmx",GX,"Cmy",6X,"Cmz" / )
DO 2 K - 1,NR
WRITE (1,30) ANGLE(K),CX(K),CY(K),CZ(K),CMX(K),CMY(K),CM2(K)
30 FORMAT (1X.F5.1,G(2X,F7.4))
2 CONTINUE
C
WRITE (1 ,35)
35 FORMAT (/// " FORCE AND MOMENT COEFFICIENTS RELATIVE TO THE
/"BOAT" // 37X,"HEEL",SX,"PITCH", SX , "YAW" )
WRITE (1,40)
40 FORMAT (" COURSE",4X,"DRIVE",4X,"HEEL ",SX,"VERT." ,
/ 3(3X,“MOMENT") / " ANGLE", 1 >(,G MX , "COEF . " ) / )
DO 3 K = 1,NR
WRITE (1,30) ANGLE (K) ,CDR (K) ,CHL (K) ,CVT (K) ,CMHL (K) ,CMPT (K) ,
/ CMYW(K)
3 CONTINUE
C
c
RETURN
END

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 U(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 Az yarn spacing and the
resultant change in velocity
U(z) ]
U30 J .
screen/yarn
measured in the test section (TS-0) for the same relative
height (Figure E-l). From the initial arbitrary yarn place¬
ment and experiments mentioned above, a discrete empirical
predictor was developed by least square curve fit to the
formula.
126

TS-C-52)
126
127
52
TS-0
r
¿¿¿¿iiimmuiLiLL
Fairing
Impedance Screen
Position Where
A(U(z)/U3Q) is
Measured
FIGURE E-1 Correlation of Screen Impedance With The
Resultant Downstream Velocity Distribution.
FIGURE E-2 Yarn Spacing And The Resultant Flow
Impedance Distribution.

128
b A,
Ak(z) = ae
U (z)
U
30
(E-l)
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.

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
g-L (z)
g-L (z) /
Vz)'
o < z < a^
•
i
i
a -1 < z < a
n — — n
where i = 1, 2, 3, . . . ,n
and g (z) is an admissible function meeting the correlation
requirement over (a^ - 1) < z < a . The required profile is
known from equation 5-5 and may be written as
f (z) = = A ln + B
30
where A = 0.1086, B = 0.4918, z(in.) is the vertical height
above the tunnel floor, U^q is the velocity at z = 30 in.,
and U(z) is the velocity at any z. The required local kth
impedance is then a function of the velocity difference at
U(z)
U
30 J
= g . (z, ) - f (z, )

130
in which form equation E-l becomes
Vz)
eb(®ilzk>
£(zkn
Taking A^(z) = a, initiates the marching scheme. Successive
values of the independent variable were determined by the
regression from
z
k+1
zk + Ak(z)
In an efrort to ensure smoothness of profile in the
vicinity of the piece-wise continuity points (g^'s) the
marching was slightly over extended. Any significant dif¬
ferences 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

131
FIGURE E-3 Dimensionless Velocity Ratios (Measured
and Desired) and Turbulence Intensity
Distribution (TOT).

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
AP = 1.22q
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.

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
f z dL
— o
2 = H
/ dL
o
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
dL = q (z) CL(z)C(z)dz
where
q(z) equals the local dynamic pressure,
C (z) is the local section lift coefficient, and
Li
C(z) is the chord length at z
133

134
Then
z Q(z) C (z) C(z) dz
z = -g (F-l)
j Q(z) CL(z) C(z) dz
The local length of chord is adequately represented by the
linear model of the form
C(z) = Kxz + K2
where and K2 are constants determined from the sail
planform. For the uniform velocity, dynamic pressure is
independent of z. Therefore,
H
/ z C (z) (K z + L) dz
z = -g ±^ — (F—2)
f CL(z) (Kxz + K2) dz
J o
It is now a matter of selecting a sensible relation¬
ship for lift coefficient. As a first approximation C 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

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-l with
uniform flow density reduces to
S z (A In z + B)2 (K..Z + K») C (z) dz
O -L z Lj
j.H (A In z + B) 2 (K^z + CL(Z) dz
(F-3)
where A and B are constants of the onset velocity distribu¬
tion. 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:

136
Approximating Polynomial
Degree
Height to Force
Center, z (in)
z/H
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.
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
stanchion in place of the sail model, dead loads of the
same magnitude (±1.0%) 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 ±8%. 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.

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 Symposium, 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 Desigr. of Yacht Sails,"
Proceedings of the SNAME Annual Meeting, 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,
1981.
(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, Highly Cambered
Airfoils in Incompressible 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

138
(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 New 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, Cambridge, 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.
(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. 185-
190, 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 Rural
Atmospheric Boundary Layer in a Wind Tunnel,"
Fifth Australasian Conference on Hydraulics and
Fluid Mechanics, Christchurch, New Zealand,
December, 1974.

139
(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. 389-
395, June, 1979.
(27) Wippermann, F., The Planetary Boundary-Layer of the
Atmosphere, Deutscher Wetterdienst, Offenbach,
a.M., 1973.
(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 Engineering, 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.

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
aerospace industry in mechanical design and research/develop¬
ment activities, Jim entered graduate school at the Florida
Technological University in Orlando (now the University of
Central Florida). A Master of Engineering degree was con-
fered August 1973 in engineering mechanics. During graduate
studies Jim began teaching 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

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

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.
- . «a-i
Ricnard K. Irey, Chairrmaiy
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 Doctor of Philosophy.
- 7^
Richard L„ Fearn
Professor of Engineering Sciences
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.
Q/hvt d C-.
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 Doctor of Philosophy.
Calvin C. Oliver
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 Doctor of Philosophy.
Research Professor of Mechanical
Engineering
This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council, and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
January, 1983
Dean, College of Engineering
Dean for Graduate Studies
and Research

UNIVERSITY OF FLORIDA
3 1262 08554 0903




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