Effect on helicopter performance of modifications in profile-drag characteristics of rotor-blade airfoil sections

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Material Information

Title:
Effect on helicopter performance of modifications in profile-drag characteristics of rotor-blade airfoil sections
Alternate Title:
NACA wartime reports
Physical Description:
23, 14 p. : ill. ; 28 cm.
Language:
English
Creator:
Gustafson, F. B
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Laminar flow   ( lcsh )
Rotors (Helicopters)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Performance calculations are presented for a typical helicopter rotor in which three types of airfoil section were successively used. The types represented are the rough conventional, the smooth conventional, and the laminar-flow or low-drag sections as developed for helicopter use. The performance items covered are rotor thrust for fixed power in hovering, range and endurance at cruising speed, and power required at a relatively high forward speed. Contours showing the conditions of operation encountered by the blade section and weighting curves showing the relative importance of the various section angles of attack for specified flight conditions are included as an aid in the interpretation of the results. The calculations indicated that the use of a smooth conventional section will result in marked performance gains throughout the flight range. Definite, though smaller, additional gains in take-off weight and in range and endurance may be realized by the use of a low-drag section. At high forward speeds or at moderate forward speeds and high loadings, however, losses are indicated for the low-drag sections in contrast with the smooth conventional sections. It is demonstrated that, if these losses are to be avoided, the low-drag sections must be designed to avoid the extreme rise in drag coefficient at the higher angles of attack which is characteristic of the low-drag sections now available for use in helicopters.
Statement of Responsibility:
by F.B. Gustafson.
General Note:
"Report no. L-26."
General Note:
"Originally issued August 1944 as Advance Confidential Report L4H05."
General Note:
"Report date August 1944."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003617559
oclc - 71341806
sobekcm - AA00006289_00001
System ID:
AA00006289:00001

Full Text


I.~


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS






WAlR'LTI ME REPORT
ORIGINALLY ISSUED
August 1944 as
Advance Confidential report IABD5

EiECT ON HELICOPTEl PEIFOR MACE OF MODIFICATIONS
IN PROFILE-IDAG CEARACTEISTICS OF EOTOR-BLADE

AIRFOIL SECTIONS

By F. B. Gustafeon


Langley Memorial Aeronautical
Langley Field, Va.


Laboratory


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.

DOCUMENTS DEPARTMENT


T.- ?6


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Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/effectonhelicopt001ang




*- z .



.ACA ACR T'o. LIHO5 COCIIFTD ':.TAL

IATIOiAL A VISCFY COl.! ITTEE FR AE"RCiA.UT CS



;.DVA'CE CO PTDEiTTAL REPORT



EF'FE .JT CII MHELIC F P -LE FE :FI'R -.i:CE F' Hl,' DIFI:. I IC i3

TIJ F':;'FILE-DFAG CHALRATE RI.'T'iCS. CF R''TCR-3.L EE

AIRFICI SE TIC. IS

.y F'. E. Gus'i::fson





Pcrfor-a'r'n:nce c a I, tion ar': ]:rs.- s tei fo o a t ;:i '.l
helicopter r-ot.or in wl;vicih three t;,-l:e ci 9irI-oil se Lio:n
vwere success ivel, used. T ttyp' renres rted .re the
rough ccn'c e t ioncal, tlih s.ro',tl-h c:.'V rLntlcrL al, an:i the
laminar-flow or I c~w-drE secti i-ns aS dev~ lj-Ld for hell-
ccpter us The pe rf r'?rrance it-.m? oc-:ered i e i-ttr
thrust for fixed p. e'-r in !'overin,., rLan.e sad enduran.e
at cruising sp ed.J, and pc.AC : re-:iu.ir-eJ at a rielit- reiy
high forward spe.e;,. Cot.:,urs sno~ ,I g she conditions of
operation er-nc..ountcre.: b;: thie b aile sec"ti.c.n ar.d '.vwe i- tin J
ci rves sh owviing the relIat i-:e irl.r'op f-.t ,rce cf the var'Lous
section angles o7 att--ck fo spoecifie. piet :nL 'itions
are included as *n a J in:- thei i -ter:re:a ti:. of the
re sult .

The calcul nations indic :te D tha t th1e Lie f a sr .c'th
conventional sc t.on. r ill result in r3crl:ed cerfranrce
g-.ins throughout the ii- ht r nse. Definite, thnu.h
stialler-, add.ti t io al ,ai;n- in take-off ei:'ht and in
range artn: endLur-re E'i," be re .izs-ci by th ie uis of a low-
drag section. AC. hi i'c,'Ar- spe.ds or at moderate
frrwar-d speeds and hi i-g las:irigs ho.G'verr, losses are
indicated for the lovw-,lraig s-ctions in c'_-,ntr: t vilth} the
smooth conve-nt io nal se:-ctions. It is d-i.monstr.- 'ited that,
if these losses a:re t tLe avoided, the low -i:'e' ,tectiDrns
must be des.i:ned to avoid the extirene rise In dr-c cocffi-
cient at the hi, -ir angles of attack wtiich is cnar!iter-
istic of the low-dr; sections now available fcr '-ue in
helicopters.


CC, F IDENTIAL







2 COFFIDEiTTIAL NACA ACR No. L4H05


INTRODUCTION


It is generally recognized that an important part
of the power required to operate a helicopter is absorbed
by the profile drag of the blade elements; consequently,
considerable interest has been shown in the possibility
of using laminar-flow, or low-drag, airfoil sections in
helicopter rotors. A recent report (reference 1) described
the characteristics of several low-drag sections that
were developed especially for use in helicopters. Pre-
vious low-drag sections had either excessive pitching-
moment coefficients or low drag only at extremely low
lift coefficients. The sections of reference 1 were
designed to give the maximum lift-drag ratio (L/D)max
obtainable with zero pitching-moment coefficient, over
an appropriate range of Reynolds number.

In order to indicate the magnitude of the performance
gains that might result from the use of the new sections
and to provide a guide for the development of additional
sections, an analysis has been made for several condi-
tions of flight for a helicopter of assumed character-
istics. The method of analysis used for hovering flight
differs considerably from that used for forward flight.
The results for the two flight conditions accordingly
are presented separately. Material that is not essential
to the analysis but provides substantial aid in under-
standing the results has been incorporated in an appendix.


SYMBOLS


R rotor-blade radius

b number of blades

c blade chord

r radius of blade element
r
x-
R
6 pitch angle of blade element

01 difference between hub and tip pitch angles (posi-
tive when tip angle is greater)


CONFIDENTIAL








IIACA ACOR io. L[HC05 COc'lTDEIT.IAL 3


0-c. blale pitch angle at x = 0.75

Q rotor angular velocityy, radi-ans per se.-o,.nd

V forward sp.Ded

Ij tip-speed ratio aV ..

G eagle of &ttac:: cf rotor disk

C2.R speed of axIal rlow tihru-.ug rotor cdil-- positivee
upward)

ao section nc ,i le of attack.-: (absclutQ)

Cd section pr:file-drs 'i efficient

CL section lift c'effic ie.t

a slope of lift coefficient as.inst section arnile of
a ttac (r a d i n mr 3s u re

a solidity; ratio of tocal blade are to swept-disl:
area r (bC ,

T rctor thrust

Cm thrust coeff icienrt -( -
\ F'^ TTni4/
C,- torque coefficient (Rotor to-rque .
-t -
P power

Cp pover coefficient (t ft p r inut


CL lift coefficient (Rotor 1i ft


ap angle of attack of blade ele,.ient from. zero lift

aR angle of attack of blade element at tip

uTRF, velo ity component at blade clement perpendicular
to blade span and parallel to rotor disk

p.QR velocity component st blade element perpendicular
to blade span and to UTQR

CONFIDENTIAL







NACA ACR No. LHo05


p = tan-I1 -
uT
'V blade azimuth angle measured from down wind in
direction of rotation

S gross weight, pounds

/S rotor disk loadlnF, pounds per square foot

f parasite-drag area, square feet

p air density

Subscripts:

i induced

o profile


HOVERING FLIGHT


In order to indicate the effect of variation in air-
foil section drag characteristics on the useful loyd that
can be carried, the rotor thrust developed by a fixed
shaft power was calculated for an assumed helicopter
rotor in which three different types of airf:'il section
were successively used. The calculations were, in each
case, carried out for a series of blade pitch settings.


Sample Helicopter Rotor

The sample helicopter was assumed to be in hovering
flight at sea level. The rotor characteristics vwere
taken to be as follows:

Rotor radius, feet . 20
Solidity . . O.07
Blade plan form .... ...... .Rectangular
Blade twist . . cne
Power available at rotor, horsepower ... 20


COFI TDENITIAL


CONFIDENTIAL








IUACA ACR ITo. L+H05


Airfoil Sectcin Characteristics

The UACA 5--1H-.5 section was chosen as representa-
tive of the new lorv-ldra sections of reference 1. The
NI'ACA 2501 section, for which data are also given in
reference 1, was inciuded to permit comrrparison v vith a
smooth conventional section. In c;'..der to permit compari-
son with a c conventional section in a condition believed
to be typical of present-day r'oors, a "rouIogh" con'ren-
tional section was included; the dra cu :rve for, this
section is a composite of data fr.lc vrarioufs soir-'ces.

The curves cf profile-drag coefficient against angle
of attack. used for the three sections are shown in fig-
ure 1. These curv are e repres-.rtat-ive .o:f ,eynol, ds
numbers corresp.ondi.ng to the o:.t.-r psrt of th-e rotor disk,
in which most of the profile-dr-g losses occur. As is
shown in the appendix the Reynolos nntumer, IMach number,
and angles of yavw encountered b; the rotor blade vary
considerably over the rotor disi:. :.o attempt wvas made
to modify the curves o ffi.ure 1 to a lci.j for these
variations? tthe analysis is thus a coI:parison of drag
curves representative of certain types of airfoil section
rather than cf specific sections.

The profile-drag values available for high angles
of attack were incomplete, esTsciali- for the IIACA
5-H-15.5 section. The drag data of r.fer- rce 1 reach
an angle of attach,: of 15 for th-e iAC, t53'- 15 section
and of 10 for the IC A 3'-H-15.5 section. The follvwng
relation, which is based l1r-ely on a composite f all
the data for high angles of attack of reference 1, was
used to extend these data as neces.siry:

Acdo = 0.25 IcZ' cI)

where

acd increment in profile-drag coefficient atve value
at upper end of straight-line portion of lift
c r. ve

c7' lift coefficient as given by extension of straight-
line portion of lift curve

This method gives results that agree with the available
values for high angles of attack for the low-drag sections
of reference 1 within about 20 percent. It is also in


CONFIDENTIAL


COTNFIDEITT TAL







6 COTFID.ETIAL NACA ACR No. L4HO5

approximate agreement with drag data for other airfoils
at angles of attack beyond the stall.

The slope of the airfoil section lift curve was
taken as 5.85 throughout the analysis.

Method of Calculation of Thrust for Fixed Horsepower

Thrust.- The rotor thrust T is
[-2
T = CTPTrA-!

or, for the assumed rotor,

T = ll95CT2 (1)

The value of CT for a given blade pitch setting
may be obtained from equation (14) of reference 2, which
may be written
2 A5 a\2 A5 2a
CT = a2a + +- 2 25
L5222 L \ 62;i

where

A = +4 a

In order to obtain an expression for t, the power
required and the power available may be equated as

P = 260 hp = pTR52 Cqi 0 + p1T5Q2 CQo I5

hence,

S= 26o ( 2)
V3.46(cq + Co)

Induced torque coefficient.- The value of Ci
for a given pitch setting may be obtained by using the


CON FIDENT IAL








:!ACA ACR LC:iO5 CO.F':DZ:ITIAL 7


fiFur3-of-merit equati on ,o .rferncrCce 2, which ma'; te
w.ri tteni


;:= 0o707-


hence ,

./2



Val..:ue-s of 1'. f' a: i7 -,r i ".i :. .. -.' ? cf 1 itch :'a1, c
obtai d fr-..,, fi- e 17 o ._-er. The f'ct:r in
th- ab.-ve cqi .i... .7 I r- t .f 1 /2 a n re a;'-
rice'. 2 E in,:: .... '.. 3 u i: t"-,- ," e finii.t t .. ..f LT
a:-i C in rf:'er::- vh reads p is used in the
def'nij ions t l-ro -- t. :e ; .- t r:p..rt.

1 'P- .file tor .e :effi: t.- In n ,i-:rC t:, cbti: n the
*desi i '.r ,valu -es o o.. for a ra curve oi arbit rn,'," r.,ri,

it is nicezas.r-, fi-t to culccu-.te tn_ in:noux angle of
fI'lo. at a Jer, es :.f r:.--.ii fo, -=...: t.-e specified -.tch
anil-z. :-ias calc'.;. L cn w- ; :... r:7 r.-i.ns f eque-
ta-. (1 ) of ref :.- -.. ch.-. ; i .. rit -r


2 8 1 .


''iere an u-?/ard in-lnnrin.li r: of t;h; flow is associated
v..'i u: ",sitive v i;]l..V=s of C; 0h(.:


-P (0.751 o.:,-5 + 4l.Uex


'The a,- les of atrac!-: ar-e thei. o'ai.n.ed from the rletion

S= 9 +

Sinle curves of ..-e3 olf at.tck aain:lt fraction of
radl ius are shown in figure 2.


COI:FIDE::TIAL







NACA ACR No. LL-H05


The torque coefficient per foot of radius can then
be cdx2
be obtained from the expression .- The torque
2TrTR2
coefficient for the entire rotor is then readily obtained
by graphical integration.

After both CQi and Co 'are obtained, equation (2)
may be solved for Q and equation (1) may then be solved
for T.


Results of Hovering Analysis

Rotor thrust was calculated for a range of pitch
angle from 70 to 210. The results are shown in figure 5.
Curves for zero profile drag and for the still more ideal
case of zero profile drag together with uniform induced
velocity have been included for comparison. The maximum
section angle of attack, that is, at the blade tip, is
indicated in figure 3 along with the blade pitch. At the
higher pitch angles, the slope of the airfoil lift curves
falls off and the calculated thrust values are optimistic.
These portions of the curves have been drawn as dashed
lines.


Discussion of Results of Hovering Analysis

It is apparent from figure 3 that, within the range
of tip speed corresponding to present practice, the rela-
tive merit of the three sections being considered remains
virtually fixed. A change from the rough conventional
section to the smooth NACA 25015 section results in an
increase in rotor thrust of more than 300 pounds.
Changing from the smooth NACA 25015 section to the smooth
NACA 3-H-13.5 section results in a further increase of
approximately 200 pounds. It is noteworthy that only
about 500 pounds more could be gained if the profile
drag could be made zero.

The calculated values of maximum available thrust
shown in figure 5 are greater than the gross weight
assumed in the forward-flight analysis. The lower gross
weight was assumed because, in a practicable machine,
the ability to hover at altitude and the ability to
take off with an overload are considered desirable
features,
CC1I IDEIiT IAL


C Oi FTDEI'T IAL








'',A ,.C P : O. LL C,5 COITFITDETTTAL


C'R7',..D FLI .1GHT


cf the1 various e .r: .r-rmiL-n. c ace cbca ct r-ist 1ics assocI. ted
viitr forward fiijlit, .r':ge and endurance seer:i of
r-.eate:t interest at the ores :nt_ tim. C.I J il: 1A con ot f
r nF ze1; r e. uriice at pa rr-ticals s1.. e (. aprc":-
mately tt for' minimrirm po.er) cc nse :iue cntly Vere nad
for a samL, S he licopF ter in ,hich the tlire C.irfDil s.c-
tions prev ou. -- de..cr ibed w.ver use: .z.cce :.si'vel .
fuel iead :' ,1) p-ercent C:i' T. r-js v. -i:t was s su,ned
in such :cse. T e pc'.'er- a' -b by ll i es other
than the rcto.r, i ncludin. c1. in- .fa?.ns andi tor-u,-:.-
compera tirt g de'. .- :, '." s ]i .. :! for :,- isu. ing a

hor se'ower -hour, f.nic i s n. pr ma t'ly tc 20 .er nt
higher than the rior-:'-.al v' a n. f r- cru.L i; -n p-Cw.I

BecaJ.se of the irre1i.Lr s1-qe Uf the dri a curve rcr
the lc,-drag a ir cil, -n. L ,ti:?. L tre..i.tr:,rnts of the ro,trr.
prcnfil-dr:."g l ses, sucih as th ht o.f r-t er:.nce 5, were



Sa1.1plee 1lic opt c r- ani .JT,' ,, L:n it ions

The s -in.ple h: licopter v."aZ 2 su:ared to b, in l:v1-l
fligh. at sea 1:,T. 1 and t: i.e r': tiii nd. r the fol-
lowing conduit ics :

Forward spe-cd
e t -r. s.ond . . 0
'Miles : rc- h .our . . '.
Rot, or- tip p ed, feet r s c . 00
Tip-sp,, ed r-.ti . . 0.2

The geomietr ic c ciractzr-is tcs t ssmLed ca-ere eas
fcllowvs :

Rotor r- adius, feet . 20
Disk lo'-ding, pounds per s1'juer-e foot . 2.5
Gross weight, pounds . 140
Blade plan form . Rectangular
Blade twist . . one
Solidity . . 0.07
Parasite-drag ar-ea, square feet . 15


CCI FIDT'T RL







NACA ACR No. L4Hi05


Except where otherwise indicated, the foregoing
assumptions apply to all results presented for forward
flight. It will be noted that the geometric character-
istics assumed for the rotor are the same as those used
in the hovering analysis.


Method of Analysis

The power absorbed by the rotor may be considered
as the sum of the power required to overcome the parasite
drag, the induced drag, and the rotor-blade profile drag.
The power required to overcome the parasite drag is

1 V
P = 2-pVf5-
9 2P 550
= 16.6 horsepower

which is considered to be constant. The horsepower
required to overcome the induced drag is


P = a
L i 550

As explained in reference 3, the induced D/L is simply
CL/4,. Because the change in weight is small, the use of
the average weight is considered permissible, and the
average induced power is then

8o
Pi = 0.0735 x 2980 x -6
550
= 55.9 horsepower

The calculation of profile-drag losses is much more
complex and is described in some detail.

Calculation of s3ngl-.s of attack.- Any graphical
treatment of profile-drag losses recui'es knowledge of
blade section angle of attack at various points on the
rotor disk. In order to calculate the angle of attack
of a blade element at any given point, it is necessary
first to calculate the required blade pitch, the inflow
velocity, and the blade flapping coefficients. The
pitch and the inflow velocity were determined by means
of the analysis described in reference 4. This analysis


CC F IDETIAL


CONFIDENTIAL








'..CA A "1~ o. LHO.5 C OIIFDEI'TIAL 11


e::tends the an.alysi of reference 5 by the addit-o'.n of a
sparaTimeter tha t rrreen-ts tne shaft Cpv.cer su.:lied to
the- rc'tcr. The flapping coefficirents were then deter-
mrined by e.qu tions (1 ) t (o (") of ref rerce n .

in determining, the itch:! and inflo,,. v'eioc.it-, it
was necessary-tr to esti:nmte the r.otor: prc f ile-drag losses.
This est i:.-tion i. 4as a ccmrplishEd b- use of a s"e. ifi
airfcil drt-ag curve as repreentd by a po'' ser1ieLs.
The drag cur'.e u;se:. co--rresponds to that e:i loyed in tie
example of referer.ce ?, but the r~ultitr: values of
r-tor ;c filc dra N w frCe cecreased a:'LIt 10 i3 ...er.c-cnt to
provide a better appr' xi.i a ticn o th1 cI-r.?ter-i tics
of the Si::.:.oth Secti ons in- ~:' ins -,ere in trhe ore; en t
scudy. In a strict Sa-:e, a d.1iff rent c:. tir.stio'n of
pitch and Ii[low'. ve.-1 ior;, should be d ter mrin d for each
sect-,ion, p. rti _iarly for th-:- r':u71h1 ::'nvnt iOucnal section,
because of the dli _ference in rqu ired power input ; how-
ever, the effects cf such c gnnges in Lhe co m'ation 0
pitch and inflow velocity are nr.El ibe e:c--:t in cases
in which the retreatin.' tip-section nles become hig:i
enough, to produce ece:sive :.ra's. TI effect of n
extreme change in pce r inpout an.- in the r E-u ltinn co-rcbi-
nation of p. tch arni' i.iflo21 velccity m riy rr.c ted by
r-eferring to the e:.i.pl:oi- given in the e ppendix: this
example co:p-re s the roror profile -dry losses tZ.-1 hen
15 square feet of p .ra- ite-dreg aIrea ani:'. zer'o artas. ite-
drag a rea :e,- su cess- -'ely assum..d a-t : relatively hih
forward scee ..

The nor-i.mal and tan-gent i.1 conpcnents of velocity
relative to s b.ladc element uer? obtained from the fol-
lo in, expression, v.hich :a-e mo:ifications of equa-
tions ( ) and (9) of Ire-erence h:

li = + x

up = -2 + {x
-'A
whe re

K1 = 1 sin f

1 I i 1
K2 = + al + -pa~c +pa cos j+ 23 sin + t ipa cos 21

1 1 1
+ 2-kbi sin 24 +2. a2 cos 35 +7pb2 sin 5W


COIJFI P TDE TIAL







NACA ACR No. 4HJ05


K3 = bi cos al sin + 2b2 cos 24 2a2 sin 2*

and ao, al,- a2, bl, and b2 represent coefficients
in the Fourier series expressing the blade flapping
motion.

In reference 6 the angle of attack of an element ar
is shown to be equal to 0 + tan-1 U-. In the present
UT
analysis, the tangent was assumed equal to the angle in
radians; hence, the angle in degrees is


ar = 57.35( +


Values of a, were calculated at every 100 azimuth and
at intervals of 0.1R over the blade radius, so that
values were provided at a total of 360 points on the
rotor disk.

Profile-drag power loss.- The rate of profile-drag
energy dissipation for a blade element of unit length is
the product of the drag and the relative velocity, or

1 uTU R uTQR
Po pP) bccdo C-
S cos cp/ Cd cos p

For the conditions of operation covered by the present
analysis, a negligible error is introduced by the omis-
sion of cos p and the profile-drag power loss per foot
of radius becomes
o= -puTnR) be cd

By using the assumed values of solidity, blade radius,
and tip speed, there is obtained in foot-pounds per
second per foot of radius

PO = 554,000uTcdo (5)

In order to obtain the total power for a given airfoil,
the drag coefficient corresponding to the calculated
angle of attack at each point in the disk is used succes-
sively in equation (3). The details of the integration
of the 360 values are omitted.


CO FIDE iTT AL


CONFIDENTIAL









.CA 'C3 "o. 4I,.H' Co I irEiTTI T_.L 15


Tr or-der to obtain curves of pr.ofile-d-: g p1c. r- loss
aga inst wei Yt, '~.ic. ul1-'. toi s of an.!.i of att.-ck ;fni: energy
loss '.re a:re ied. oLut 'or e V-iiLes of gross weight.
Tei r it in curves are shev.wn in f iure 4.- T''he "aulues
for tae r.u.rh air ,'c ,il cot1 3 ined a,-Il':tic'-lly are included
for c.;:-'ericcr.n viLth t!he '.- lues obtained r.' i, l-.l In
order t: c c nit -uL)ch -I 'al .ul." ticn:- the drc a curve of
fiL ur 'or tr e ,: U 5ij .irfIoil 'a mai'e t. -,i -.-e, u. to
an an:rl of stt'ci: :f h('' ti!e S -,Jie I"fr; as thEst .- the
exI.,mple SYiven in .efe'rnc? 5 t-: cI .:rdi t- e re, however,
increa. s d p:.rc nt in crj.e,-' to m-:. the e.s ir 3d allov.ance
for su-fi :- ce i' ughnt ess. Val.l'- ,. D.,'L obtL -ined as
desc r ib-ed in r -frre nc, c co.ullo th.-l ": us.-j.d after' bF ing
i ncr.eas-d '; 2' e rE:ft.


C. lc'. U, ti o f ,- n K. rai -.L n- c :.

E- ; usi.g thie 3"-..:- e rd -.fil -dr. is in horsepower,
as given by % i u e L, for th..- r.:--e .f w i-i.t i ro
510 topounds c Dti- a-.r-a. total rotor di-rag
looses f',or e c;. airfoil SE', -ic .i '" [ ,-v i u. ted. as
follows:


.. Airfoil
Dr.ag.
losses 's,
(hp)

Parasi te
Induced
Pr.cfile

Total


2;ounch SIrmooth
convenrtion-.l I!ACA 2d0



.? I 53.


I ~ ~ '- '- 1,'-


.3 t h
15 i. ,.C,. 3-h-1 .5



-"'.9
c!ii.,


7C.5


By assuming. a Sp- i ifi : ful 1o.su:irtion Of. 0.5 pound
per rotor horsepY..:.'-er-ho-ur, ti'- valuis of r an'e and
endurance are c. s follows :


irTfoil
riRouh Srnuoth Smoothl
c onvent Ional :IACA .-2015 IIACA 5-H-1.5


Range, miles
Endurance
hours


U23
5.8


i7.5
?.5


S.1







NACA ACR No. 14H05


High-Speed Condition

As an indication of the effect of tip-speed ratio
on the relative merit of the airfoil sections, calcula-
tions were made for the sample helicopter at a tip-speed
ratio of 0.5. The corresponding forward speed becomes
120 feet per second, or about 80 miles per hour; all
other assumptions are as previously given. The drag
losses then are as follows:


Airfoil
Drag Rough Smooth Smooth
losses conventional NACA 25015 NACA 5-H-13.5
(hp)

Parasite 56.0 56.0 56.0
Induced 25.0 25.0 2.
Profile 67.5 35.5 54.5

Total 148.5 114-5 155.5


The high profile-drag loss for the low-drag section
results from the high drag values above the low-drag
notch; this point is demonstrated in the appendix.


Discussion of Results of Forward-Flight Analysis

It is apparent from figure 4' that the relative merit
of the airfoils depends on the loading used. Certain
aspects of the comparison are brought out more clearly
by plotting the profile drag-lift ratio (D/L)o instead
of power loss. Figure 5 shows this factor plotted
against the loading factor 2Cm/ia, which is more
general than but is proportional to weight or loading.
It is evident that the optimum (D/L)0 occurs at a
considerably lower loading for the NACA 3-H-15.5 sec-
tion than for the NACA 25015 section.

Although a relatively small portion of the rotor
disk is affected, it should be pointed out that the
assumption of constant lift-curve slope is not strictly
valid at the high loadln s and at [ = 0.5. The calcu-
lations for the NACA 5-H-13-5 section, in particular, are
increasingly optimistic as these conditions are reached.


CC:J' T TIAL


CONFIDENTIAL









I'AC\ 'AC o. LE4 -05


CO,. HIC LUSIO S [


Thel effect of modi'fications in the airfoil section
drag characteristics, as indicated b:r .he the oretical
performance enaly-sis made 2for the sample helicopter, may
be s.uimari.zed as follows:

1. Tne use of the section characters t ics taken as
representative of a smooth :;.onf veti ona section instead
of those t.i.l:en as representative of a rou;n conventional
section resulted in an increase orf .~ :.::i:nmately 9 percent
in the rotor thr;ust availa":'l with fixed shist po'er- in
hovering, -an increase ,of f per"cen..it in ruan2L. and endurance
(with equal fuel load) at cruising s:.peed, and a reaction
of 25 percent in the po.oer requi-H'e, at a relatively high
forward speed ('.O mph; tip-Ji, ied rstio, C.3j.

2. The use of the section characteristics taken as
representative of the lcA-dra- air-fooils of' IACA CS
Ho. 5115 inste-sd of t"-ose fi ti- smoozch conventional
section resulted in a furtl-.Lr increase of approximately
5 percent in the rotor thrust available witiit fixed shaft
power in hovering snd an a.lditional increase of 10 per-
cent in rEn.e anda endurance at cruising speed: however,
at the high-speed. condition, 5r in crease of. appro-xima tely
18 percent in the .po'er rs quired wJ.s indicated.

5. If the losses show-- n for the lowv-draR section at
high speeds and at moderate speeds and high loadings are
to be avoided, the low-dra2 section ;imut be designed to
prevent the extreme rise in dr;a. -oefficient at the
hifgh'er rnzles -:f attac': exhibited hb the lo '-drag sections
of I;ACA CE !!o. 5112 .


Langley Memorial Aeronautical Laboratory
National Advisory Co.nrittee for Aeronautics
Langley Field, Va.


C O FIDET:IT IAL


COPITIDEliTIAL







NACA ACR No. T1O05


APFPE DIX


CONDITIONS OF OPERATION ENCO;N;TERED BY THE BLADE

SECTION AND EFFECT OF VARIATIONS IN ASSUMPTIONS


Contours of angle of attack and power loss.- In order
to make the reason for the results obtained in the forward-
flight analysis more evident, contours of angle of attack
and power loss were prepared. The source of the values
of section angle of attack has already been sufficiently
explained. In order to show the relative importance of
a given increment in drag coefficient in the different
parts of the rotor disk, the expression previously given
for power loss per foot of radius was modified by dividing
by the area of the annulus at the appropriate radius; the
resulting expression for the power loss in foot-pounds
per second per square foot of disk area for a profile-drag
coefficient of 0.01 is

UT5
P = 26.60 -u
0 x

Contours for the set of conditions initially assumed
are shown in figure 6(a). Figure 6(b) shows the effect
on the contours of increasing the assumed value of
solidity. Changes in loading produce similar effects,
since the higher solidity is com~narable with lower
loading. Contours for the original solidity but for
p = 0.5 (V z 80 mph) instead of p = 0.2 (V = 55 mph)
are shown in figure 7.

Weig-hting curves.- The contours in figures 6 and 7
indicate that a given increment of profile coeffi-
cient is more important at low than at hic-:. section
angles of attack. It is difficult, however, to judge
the significance of certain factors for example, the
abrupt rise in drag coefficient at high sngles of attack
shown for the ITA"A 3-H-15.5 section (fig. 1). In order
to permit more rapid quantitative judgement of such
factors, the data may be combined for the two sets of
contours into a single curve showing the relative ir:por-
tance of different parts of the curve of airfoil section
profile-drag coefficient against section angle of attack.
This weighting curve is designed to show the amount by


COI'F LEPT IAL


COUFIDESTITTAL









T ACh ACR No. L4i HOS


which the power consuLned in overcoming the profile drag
of all the blade elements operating at any particular
angle of attack is increased if the airfoil section drag
coefficient corresponding to that angle of attack is
increased by some convenient increment, for example, O.C1.
Such a curve has the further merit of permitting rapid
calculation of total rower for ain airfcil section; it is
necessary; only to multiply the oridinates of the curve of
profile-drag coefficient against angle of attack charac-
teristic of the airfoil section by the ordinates of the
weighting curve and obtain the area unLder the resulting
curve.

In order to obtain such a weighting curve, the range
(or ranges) of aziir.uth angle ('in1 to 2) through which
a given range of angle cf attack (Car to ar2) was
maintained was determ-ined for a ie.en radius by using a
plot of angle of attack : against azimuth angle for that
radius. The nrocess was repeated for successive ranges
of angle of attack until the entire circumference was,
accounted for. The apDoro riare average value of UT-
for each range of azimuth angle was then read from a
plot of UT5 against azimuth angle. Ordinates for the
weighting cure for the specified radius were then obtained
by means of the expression for the energy aer second per
degree angle of attack uer foot of radius

1 '1 1
-pbc cc uTp R3
2 5 0 a 2- oar

where uT5 is the average value of UT5 for the range
from )l to '2. It was found that increments of angle
of attack of 0.20 provided amnle detail in the final
curve.

The process was repeated at intervals of 0.1R over
the blade radius. The resulting weighting curves for
representative radii and the over-all weighting curve
obtained by a summation of the curves at the various
radii are shown in figure 8 for u = 0.2. Values of
power obtained by use of the curve of figure 8 and other
values obtained from each of a number of other weighting
curves were checked against corresponding values obtained
by the more laborious point-by-point method already
described, and the answers agree within 0.5 horsepower.
C nNPTDFNT TAL


C CITrF DE T IAL








NACA ACR 1:o. 14105


In order to permit ready application of the weighting
curves to rotors differing from the sample rotor in chord,
radius, or airfoil section and likewise to rotors oper-
ating at different tip speeds and altitudes, the curves
have been plotted in nondimensional form. The use of the
curves for calculation of the profile-drag loss for a
particular rotor and a particular airfoil section involves
the following steps:

(1) Multiply the ordinates of the weighting curve
by the ordinates of the curve for airfoil section profile-
drag coefficient

(2) .-iltiply the resulting ordinates by 100 to allow
for the fa t tha the weighting-curve ordinates were
given for do = 0.01

(5) Obtain the area under the resulting curve and
thus obtain the total value of CGp/

(U) Multiply the value of Cp/o by the factor


550

Steps (2) and (4) may of course be combined; the factor
for the sample rotor is then

100 x 0.07 x 0.002378 x (20)3 x n x (20)5 6
= 2.43 x 10
550

Effect of variations in helicopter characteristics
and flight conditions.- The weighting curves provide a
convenient means for indicating the effect of changes in
assumptions on the airfoil requirements. The effects of
tip-speed ratio, loading, solidity, blade twist, and power
input are thus indicated in figure 9. Corresponding
profile-drag losses for the drag curves under considera-
tion are given in table I.

Source of losses indicated for low-drag airfoil.-
Comparison of the weighting curves of figure 9 with the
profile-drag curves of figure 1 shows that, for the
conditions in which the low-drag airfoil shows losses
instead of gains, these losses result from the extremely
high values of profile-drag coefficient at the high angles


CON FI DENT IAL


CONFIDENTIAL







I'ACA .ACR Ho. Lc-H05


of attack. The point is brought cut more clearly in fig-
ur;e 10, which shows the u'.ves th;t result from multi-
plyig c s o the drag curves of ur 1 by the corresponding
we'ihtin: urves of figure ''(a) for |i = 0.5.

Pr-e] iminary results (unpublisled.) of additional low-
drag airfoils intended to reduce these losses at hi g
angles cf actack. indicate Lh'ct zonrsiderable f.pror'&ss mray
be expected.

Conditions of cpe ration i2gnordr in an-,lys is.-
S ime lif ing a szsunlpti-i ons -ior proc- :.i' e 1hic'; have been
used in the analysis but hvE'. nut been discussed an.d 'aii&
be suspected c-f endang;r'inr the. siiJ.it of the comipari-
sons made, include:

(1; Use of sc-ticaly mel-i suedJ s action ct-ar.:acter-
istics with nc alilo':n'ce for .ff' cts dico to iotaeton

(2) Assiumptlon of uniform inflow velocity (forward-
flight analysis only)

(35 Use of section charact-ri. t.Le co-r-rsponding to
a single Reynclds numibe-r an a inerle Ta'ich n, umriber ,s
applying at all points on th rtotor dis;:

(4) liHelect cf effect of angles ofr -a. --n section
characteristics

Past experience indic at-es thu t airfcil sections used
in rotating blades exhibit clar-cteristics similar to
their statically measured section characteristics. P s-
sible effects on thl chs racteristics of the low-drag
sections are conjectural.

The effect ?f rucnunifor.-ity ofi inflc'. velocity- was
examined in reference 6, an- it w-as concluded that the
net effect on the rctor forces was secondary.

The method of analysis used '.would permit study of
items (5) and (j), or even inclusion of the effects in
the analysis if such were deemed desirable and if suffi-
cient section data were available. Although the data at
hand are insufficient to penrit complete calculations,
it is of interest to note the magnitude of the variations
of Reynolds number, Phach rumblrr, and angle of :Iaw.


COIGF IDEJiT IAL


C OI! F IDE'TT IA L







NACA ACR No. L4H05


The Reynolds number, which was taken as approxi-
mately 3 x 10 in choosing the drag curves, actually
varies from 0 to 4.5 x 10 in a typical case. The value
2.8 x 106 corresponds to the mean value at x = 0.75
when the number of blades is taken as three. Figure 11
shows the variation of Reynolds number over the rotor
disk for two tip-speed ratios. Radial components of
velocity are ignored. Comparison with figures 6 and 7
indicates the regions in which the greatest differences
might result if the drag curves were varied with Reynolds
number.

The contours of figure 11 may also be used in esti-
mating Mach numbers. For this purpose, the values shown
on the contours should be multiplied by 0.000014QR. For
the sample rotor in forward flight, OR = 400; hence,
the :':i.h number is approximately equal to the value shown
on the appropriate contour line times 0.0056. For
= 0.2, the maximum tip Mach number is thus 0.42 at
S= 900 and the minimum is 0.28 at V = 270.

The variation of angle of yaw over the rotor disk
at a tip-speed ratio of 0.2 is shown in figure 12. The
same contours can also be applied to any value of p,
above 0.2 by placing a new outer boundary at a radius
equal to 0.2/k times the original radius; the tip
circle for p = 0.4 has been drawn in as an example.
It is of interest to note that the regions which appear
in figures 6 and 7 to be the most critical that is,
the region of high power loss per unit drag coefficient
on the advancing side and the region in which tip stalling
is approached on the retreating side include relatively
low angles of yaw.


CO-iTFIDENT=W


CONFIDENTIAL








T'-.CA .-_ CR iTo. L.FIOS


REFEElEICES


1. T'eLervii, Heal: Te-ts ii- the Il:-CA Tw'o-rimenricnal
Lo r !-Turbu-le-nce Tur nneil of Air-foil Secti iorns Desicnaed
to Hav'e Sinuall Pitchin ri i'-,m rits and hji-ch Lif't-Dr.a
;. tis. Ji.LCA CS 'Io. 511,, iA 3. .

2. I:ni .ht 'int .r.er and He FRalph : Statc
thrustt An'i .'si .of t W U Lit 'tir.: Al"sa e ew U/IlCA 'THI
lio. 2' lY37.

3. Baily, F. J. Jr. A .imrplil -d T'h-c.:oretical ine thod
of D'eter.,,i.,inr t -: Chari tc .r is tics ,f -a Liftingt
Rotor in c.r.-wa d FI.i-t. i s ; .. Cer F. 71., i'7i.

4. aPIl ].., F. J., Jr. sar Gu3st s.n. F. F.: Charts for
Es tim i aL ion of the Ch-is.c ti:-ist ics of a Helicopter
Rotor inr Forviary --J F'li' l-t. I p.-ofile Dr-ag-Lift
Ratio for Untwiste.j Ri-ctDan-uler Bla.des. II.CA ACR
io. LHC7, 1?<4.

5. Wh tle; Johin E..: An A'al ytic and E:.per imetnt1
3tudry of the Eff'ect of Feriodic Blade Ti''ist --on the
Thrust, Torque3, a :, Fi ,ppin '..otion of -in utogiro
ic tor. il-. p:.. n. 591, l?17

u. Wheat iy, John E -. : nr. t .e- ody.akriilc ni- lysi. of the
Autogir ao Rotor iwiitlh a Coiimprison betn'een Calculated
and Exeriimental Fresults. Ii'.LCA Rep. F!,. 437, 1 35.


COF'?IDEI TIAL


CO'FIDET l' TtL












I.AC.A ;C Fo. Li.HO5


CCl T r 2iT IT L


C/)






E--












< -"
r'3
C-,







C'-



E
C'



I2







CI---1














C
HU

















C).
I -I
O 0




r- -
i _
c.1E-
S S^












rr


I *










rri
I- I 0





:- .-.





-, .I .





.- ; .- -










5
.--




-- -













SI 1 ,









1 r















Ci)
i.i



*l' T


S .-.I ,, u"'- ,







.-- -
)--- I11





I-.







i u



c

'I. 'I IU



C_.

*I.-
I 4 1 C J
i I












K 1----

""I I "'

_ -- '-
* -I
4 ____________


4_'1 *

***] *7 S '::

.l r,,?\ --
**-


*


i




,-t,


COI'FITDEi!T I.''L


- -'I r- J I








"' i .








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..i I

, 4





' I i




i0C I C '

















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""'
-,' r ,N ,-, ;i


r-CJ CJ C'.~


C'-.~C1 CC".

u~ C'- ~-I
r~j I


J~i CT ic


,.-I C1] N


CN


-4-i







o
CL



4,-





0





















O






II o o







;:
0
-i* 4-1









) C)
cr,
'-4 -
-i
-)I O
4-H




















o
0 '-


I ^

"C'
0






r-
c,

c


~ ~ ~ ~2__ __ ~ _


_


I r- r-i-












"-.C CR "o. LHC 5
















'. L '.

















-4
,., 1



I-0 1:., :1



D.-,
, ,J





1I.
o r -
I ,II




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E'' *
II K-
E; -- -


C T ., 'T, .I L


r,~
,- ^


I--, I


1r1







, 3
' I,,
I-4




L- 1-


-;j


CI 01P FT" lT L









NACA ACR No. L4H05


,b









.049








.07
I


CONFIDENTIAL


Fig. 1


CONFIDENTIAL Section anqle of a//acK (abs), cr deq
F/ are A-P-ofile-draq curves used in the analysis.





NACA ACR No. L4H05


20


NATIONAL AD ISORY
S_ MMITTEE FOR A RONAUTI I Pitc
angle, 8
(deg)

_/ ....~t.9.- -







c





0 .2 rQ .6 .8 /O L
Frmcf/on of vdJc/s, x


Figure Z.-- ection /7ngl/e of attecK for
three pAich hetfings. Jamp/ helicopter
rotor /n hovering f//hht


CONFIDENTIAL


Fig. 2


CONFIDENTIAL






NACA ACR No. L4H05


Of 1 I I II1 I I.I [IJIJ1I1 I I I 1 I
300 340 380 420 460 500 '40 S90 620
Tip speed, fps
Figure 3.- Rotor thrust -For 260 slwft horsepower. Sarin hel/copeer in hovering
Flght. CONFIDENTIAL


CON:IjF IDENTICAL


Fig. 3





NACA ACR No. L4H05"


2A Z40


2800 3200
Gross weight, /1


Airfoil


3600


Met


wsh conwmtalul Grqp
Rouyh conventional Arnl
nooth #/A 3-H-S.5 Grap
mooth NAt 23015 Grap

NATIONAL ADVISORY
COMMITTEE FOR AERONAUTIS


4000


Figure 4-.-Rjter ,orofile-dray Ioss for a range of gross weight.
Sample hehcopter; j,=42.


ic. 2 14 / .7
R 2 & 5 2. 8


.036


/'
I v
/I.


Pitch angle, 0

Omox at tip

W/3 (tb/af)


Airfoil
Rough conventioand
- Rough conventional
Smnooth AA CA 3-H-135
/Smodth NACA 2390/


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS



CONFIDENTIAL


.040


Figure 6.- Roatr ptof/1 drat-lft ratlo as affected by loading.
Sample hehcopter rotbr j.=O. .


460


f40


ti


0 1
/IQ


thod


ico/
ica/


/7
1.9


S.1








.ozl


Methled
Graphqcx
AnGewco/
Graphical
GrqA*cal
@rvap'UcGI/


- h ..-J-LL- & L


.0 OZ 28 .032
ZCr/-ra


S S,'
wool


90


4-5 8
/ ,/



* -- L


Figs. 4,5


CONFIDENTIAL


0







NACA ACR tlo. L4H05


Power lose
(ft-lb/sec/sq ft/O.Oicao)


(a) Original solidity; X = -0.0385;


Angle of attack
(deg)


6 = 90; 0= 0.07;


NATIONAL ADVISORY
COMMFIFEE FOR AERONAUTICS


(b) Increased solidity;


X = -0.0350;


8 = 70; c= 0.10;


Figure 6.- Contours of power loss and angle of
helicopter rotor and for an alternate rotor
solidity and lower pitch. V = 55 miles per
A = 2.5 pounds per square foot.
S


attack for sample
with higher
hour; I 0.2;
CONFIDENTIAL


S= 0.0321.
oa


2CT
oa


= 0.0225.


CONFIDENT. TIAL


Fig. Fa,b







Fig. 7 NACA ACR No. L4H05











0 0


I- s 0L



00d 0










0- I gl o

O4 o
C, ; E-4
420 1 i=)


o :


4 1, o
0 :

o ~~e




o
00 0---- V -- 4 I --lci
4-0 Os














SI i I S\
i, / / +, *
0 4








0a
+7 +~ I
$40
cuH
go I I oI 4







NACA ACR No. L4H05


/.t OrO


~~lb


Sectin atile of attack, or,,de
Figure 6.- Weghtng curves for reoresentatrve rwd, and for entire rc-r. Sampl
helicopter rotor; /--O.B; 6 =9;9A= -0.038S.
CONFIDENTIAL


COiFI DEN TI AL


Fig. 8






NACA ACR No. L4H05


I I I--- i I


p LCO. R
e9" A= -o0.0385








6
u-= 0 o K

--- ----N'-------s



PMMM I FOR O RONM cs_

S Z 4 6 10 / /4 A/
Section angle of attack w)., deg
(a) Effect of tip-speedratw. W/,S=2.5-;o'=0.07 4,=Of CCN :FIDENTIAL
Figre 9.- The effect of mnous changes in the qperni g coramfes Pd~geome~ rc
characteristics assumed For hes saprLe vrota as shown hb the
correspo mi/ weighting curves.


CCNFIDENTIAL


Fig. 9a


5x







CONF IFDNTI AL


6




= 7" A= -0.03/0



2-









W/12.
I e =19 A=-0.0385














4 -- 9 A-0.0-469


NAT AL A VSORY
S- OMMI I E FOR Ai RONA-I CS


0- -
A a M I_ IA 0


Secetir avgle of aftac, 0, dray


IH I'r IU


(b) Effect of loading. .0.2O a=-a07oj =0.


Figure 9.- Continued.


1(3


NACA ACR No.


L4HOG


f


CONFIDENTIAL






NACA-ACR No. L4H05


6



4



2.



0





O



6




24

2.


e= 9" A=-003=5'





















9= 7' A-0.036L



S- IIA1NAL A ISORY
SMM I FOR ENA ICS


0 4- 6 6 0 I
Section angle of attack, w.C, de


(c) effect of solidity. 4~=&. W/S=Z.5 -,=0.


Figure 9.- Conmnued-


CONFIDENTIAL


L( I.M t i l l f i l l l l i l i l l


:= -


Fig. 9c


CONFIDENTIAL






NACA ACR No. L4HOF.


,. 4.' 1 I


l -(s / A= -00680
4--==


O
0 4- 6 /o 72 14, 16
Section argle of oatacrts, dae
(d) Effect of blade twis*. A/ 0.3; WA,=2.5 OS0.07.
NATIONAL ADMVSORY
SCOMITUU FOR AEDOMAInIC
iramsme-draq area 5" fs
,= /ao" A '-e.0680





I lul llE


Sween angle ofttacmk deg
(e) Effect of redaucton u# rewred power mt. 2i 3; W/S I -,s .=-B6


Figure 9.- Concluded.


CONFIDENTIAL


Fig. 9d,e


CONFIDENTIAL





Fig. 10 NACA ACR No. L4H05




-_____s y-


o*\
0 -"j







.IJ -- .I "
So '



z 0

o -o









2 'I
... r- I i



I rri I


,
CV V




I ____ __, _______--_







z---LL-
^ ^ ^ ^ o S>q-





6ap/44








NACA ACF No. L4H05 Fig. 11



















0
(a




s o ..





-a a *r





Ao






r 0-* t 0







*S
4


dW

/ H
Owe

0 0










d r
rr 2w d






NACA ACR No. L4H05


Direction
of flight


Direction
of rotation


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS



Figure 12.- Contours of rotor-blade angle of yaw for A = 0.2.
Angles shown are in degrees. Contours may be used for any
tip-speed ratio p above 0.2 by placing a new rotor boundary
(x = 1.0) at a radius equal to 0.2/& times the radius of the
boundary shown for i = 0.2. As an example, the boundary for
L = 0.4 has been drawn in.
CONFIDENTIAL


Fig. 12


CONFIDENTIAL







UNIVERSITY OF FLORIDA

3 1262 08104 982 6




I ~.'Er.SiTY CF FLCFJDA
DOCUMENTS DEPART MENT
120 MARSTCON SCIENCE LIBRARY
,:0. BOX 117011
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