NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

REPORT No. 712

PROPELLER ANALYSIS FROM EXPERIMENTAL DATA

By GEORGE W. STICKLE and J OHN L. CRIGLER

1941

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 AERONAUTIC SYMBOLS
1. FUNDAMENTAL AND DERIVED UNITS

Metric English

Symbol
Unit Abbrevia- Unit Abbrevia-
tion tion

Length ___ I meter __________________ m foot (or mile) __________ ft (or mil
Time ________ t second ___ ______ ________ s second (or hour) _______ sec (or hr)
Force ________ F weight of 1 kilogram ____ __ kg weight of 1 pound ______ Ib

Power _______ P horsepower (metric) ____ __ ---------- horsepower ___________ hp

Speed _______ {kilometers per hour ______ kph miles per hour _________ mph
V meter persecond ____ ____ mps feet per second _____ ___ fps

2. GENERAL SYMBOLS
w Weight=mg JI Kinematic viscosity
g Standard acceleration of gravity=9.80665 m/s2 p Density (mass per unit volume)
or 32.1740 ft/sec 2 Standard density of dry air, 0.12497 kg-m- 4_s2 at 15° C
m Mass=-
TV and 760 mm; or 0.002378lb-ft-4sec 2
,q Specific weight of "standard" air , 1.2255 kg/m3 or
I Moment of inertia=mk 2 • (Indicate axis of 0.07651Ib/cu ft
radius of gyration k by proper subscript.)
C,oefficient of viscosity
3. AERODYNAMIC SYMB OLS
S Area Angle of setting of wings (relative to tbrust line)
Sw Area of wing Angle of stabilizer setting (relative to thrust
G Gap line)
b pan Q Resultant moment
c Chord n Resultant angular velocity
b2
A
V
.
Aspect ratio, S
True air speed
R Reynolds number, p Vl where l i a linear dimeo-
J.L
sion (e.g., for an airfoil of 1.0 ft chord, 100 mph,
standard pressure at 15° C, the corresponding
q Dynamic pressure, ~p V2 Reynolds number is 935,400; or for an airfoil
L Lift, absolute coefficient OL= :s of 1.0 m chord, 100 mps, t,he corresponding
Reynolds number is 6,865,000)
D Drag, absolu te coefficient OD= q~ 0. Angle of attack
E Angle of down wash
Profile drag, absolute coefficient ODO= ~S
Angle of attack, infinite aspect ratio
Angle of attack, induced
Induced drag, absolute coefficient ODj= ~ Angle of attack, absolute (measured from zero-
lift position)
Parasite drag, absolute coefficient ODP=~S 'Y Flight-path angle

o Cross-wind force, absolute coefficien t 00 = q~

2626°
 l

REPORT No. 712

PROPELLER ANALYSIS FROM EXPERIMENTAL DATA

.~. I

By GEORGE W. STICKLE and JOH N L. CRI GLER

Langley M emorial Aeronautical Laboratory
 NATIONAL ADVI ORY COMMITT EE F OR AERONAUTICS
HEADQUARTERS, NAVY BUILDING, WASRI NGTO ,D. C.

Created by act of Congre approved March 3, l015, f or the upervi ion and direction of the scien tific tudy of the problem
of fligh t (U. S. Code, Title 50, Sec. 151). Its membership was increased to 15 by act approved Ma rch 2, 1929. '.rhe members lire
appoin ted by the President, and serve as such without compen ation.

V ANNEVA R BUSH, Sc. D., Chairman, RORERT E. DOHERTY, M. S.,

Washington, D. C. Pittsburgh, P a,
GEORGE J . MEAD, Sc. D. , Vice f'JlOinnan, ROllERT H . HINCKLEY, A, B.,
Wa, bington, D. C. As istant SecI' tary of ommer ce.
HARLES G. AnBOT, Sc. D., J l!.'R OUE C. H UNSAKER, Sc. D. ,
Secretary, Smithsonian Institution, Cambridge, Mas. .
HENRY H. All ' OLD, Ma jor General, United States Army, SYDNEY M. lUlAUS, Captain, United State Navy,
Deputy Chief of Staff, Chief of the Air Corps, War Bureau of Aeronautics, Javy Department.
Department. F RANCIS W, R EICHELDERFER, Sc. D.,
GEORGE H. BRETT, Major General, United State Army, Chief, nited tates Weather Bureau.
Acting Chief of the Air Corp, War Department. J OHN H . TOWERS, R ear Admiral, United States Navy,
LYMAN J . BRIOGS, Ph. D., Chief , Bureau of Aer onautic, avy Department.
D irector, rational Burea u of , tanda l·ds. RJ)WARD W AllliER, Sc. D.,
DON ALD H. CONNOLLY, B . Wa hington, D.
Admini !'; ( rator of ivil Aeronfl1ltic . ORVTILE WRIGHT, c. D"
Dayton, Ohio.

GEORGE W. LEWTS, Direct01' of A eronautical R esearch S. P AUL JOHNSTON, Coorclinato7' of Research

JOHN F. VICTORY, Secretary

HENRY J. E. REID, En,Qi!l1. eer-i1t-Charg e, Langley M emoda.l Am'onautical L ab01'atory, Langley F ield, Va.

S:IIflTH J. DEFRANCE, Engineer-'in-CJw1'g e, Ames A erono,lItica.l L a borato)'Y, M.offett Field, Calif.

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II
 REPORT No. 712

PROPELLER ANALYSIS FROM EXPERIMENTAL DATA

By CEOHOE W. 'l'TC){LE and JOH N L C lnQ[.l~ R

SU MMA RY prow·lI er bu (, al 0 Lhe disLribuLion oC Lhese forces a.1 ono '

the radius. A method of ob taining Llw d istr ibuLion ~1
T he opeTation oj the propeller i analyzed by the use
tho 0 forces from measurements in the wake of the
oj the distri bution oj j01'ces along the radius combined
propeller is given in r eference 2.
with theoretical equations. The data were dbtained in
I n th c pre ent papcr the eli tribu tion of thru t and
the NACA 20-joot wind tunnel on a 4-joot-diameter,
torque along the radi u i used to compare the act ual
two-blade propelia, opeTating injTont oj jour body haJJes,
pcrfo rmance of a p ropcllcr with thc calculated perform-
ranging jrom a sm(~ll shaft to uPJJort the propeller to a
ance . The energy losses in thc wake oC tile p ropdJer
c()rlIJerl.tionaZ NAOA cowling. A method oj estimating
as ob ta inecL from experi men tal measurements a rt' d is-
1~I.e a.rwl and the rotational energy in the wake as a /1'ac-
ells eel. A m thod of determining he. e los os from
t~?nal part oj the prop ller power is given. A knowledge
~he . total thrust and torque of the completc propcJ] el'
oj the total th1'ust and torque is nece sa1'y jor the estimation.
I S gIven; the m ethod permits an analysi of the d recls
TAe loss oj efficiency due to the rotational velocity is
of propelle)' olidity on th e axial and t.he rot'a/ ional
always small jor a propelle1' oj optimum design, being
108 c of the propc11('1' to be mad e from the toLal thru Et
only oj the order oj 1 percent jor a low-solidity propeller.
and torque. Th e repor t. pr esent rlata that show how
The loss of fficiency from this source may become qui te
and wby the prol Uer effi r. iency is affect d by tbe bod y
la:ge, .however, at hi gh blade-an gle ettings jor a propeller
shape. Thc data u ed in the analysis were obta.ine~1
W'l.th ~mproper load distribution. Counterrotatin g pro-
in tbe N ACA 20-foot tunn el on a 4-foot-diametcl', two-
pelleTS are shown to be attractive jTom con ideTations oj
hl ad~ propell er opel'nting in front of fom body hapes,
aer?~ynamic efficiency only when propellers of high
rangmg from a small shaft to sn ppor t Lhe proprll cr to
soluhty aTe used. Ij high- olidity propelle1's are selected
a conven tional NACA cowling-.
becau e of limitations on prO]JelleT diameteT, it may be
useful to TesoTt to counterrotating ]J1'opelle1' to eliminate S YMBOLS
the flect oj the ngine t01'C[Ue on the flying cha1'acte1'ist?'cs
V veloci ty of air stream
of the ai1'plane, but only a small gain in p1'0pelier effi-
Uo velocity in plane of propeller (propeller
ciency is n01'maUy to be expected.
removed )
. The average angle oj twist in the pTopeller slipst1'eam
t::,. V velocity increa e clue to propeller
w shown to be a function oj the tOTque coefficient Qc and
p mass densi ty of ail'
chaTts aTe given to help estimate the angle. The increase
q dynamic p ressure of ail' s t.r ea.m (J /2p V 2)
in total preSSUTe along the Tadi?lS behind the propelle1' i
n revolu tions per second
/!J
given as a function of the power coefficient 1 P c j 01' us
D diameter of propeller
in esti mating the avai lable pressure that may be obtained J advance-diameter ratio (V/nD )
f01' ai1' intakes behind the propeller. The effect oj the P input power to propeller
propelleT-body hape upon the th1'ust and the t01'que clis- Q input torque to propeller
t1'i bution oj the propella is hown. T thru t of propeller ( ranksh aft tension)
INTROD UCTION uoT useful work pel' unit time
Op power coefficient (P /pn3D 5)
Th e th eor eti al analysis of pr opeller operation h a CQ torque coefficient (Q/pn 2D 5)
been invcstigated anel th c r csul t of the inve tigation 0 7, thrust coefficient (T/pn 2D 4)
ar c summarized in r efcrence 1. Many exp erimenta.l 1/ true propellcr efficiency
studies of th e operation of the cntir e propeller have also
been made. In an attempt to combine the r esults of 1/a apparent propeller efficiency (TJ = g:Xn~)
~h~ inve tigations with thosc from theol'etica.! ana.ly e , S disk ar ea. of propeller
It IS nece sary to know not only th e total force on th e T c th rust eli k-loltding coeiflcien t (T /qS)
1
2 REPORT NO. 712- A'fIONAL ADVISORY COMMI'l'TEE FOR AERO A TICS

Pc power disk-loading coefficient (PjqSF) From the value of dOQ/dx and of a, the value o r the
Qc torque coefficient (Q/p V 2D 3) rotational interference factor a' may be compu Led:
-1- -V~- P
3..jpc - 2P
lIy differential pres ure in yaw-head tubes due to
twist of propeller slipstream (4.)
lIT total pre sure behind propeller plane with
propeller operating The values of the axial and the ro La Lion al interference
II 7,o total pressure behind propeller plane with factors obtained from these formula are the average
propeller removed value. The flow at the propellel' being continuou 0,
II mcren.se in total pres ure due to propeller this average value clo ely approximaLes lhe Lruc valut'.
(IIT-II To ) The amounL of LoLal pre sure added by Lhe propeller
r radius to <tny blade element to the slipstream in terms of the dynamic pre lU" o[
R radius to tip of propeller Lhe air stream may be obtained directly from eq uation
x =rjR (1)
p geometric pitch JI= 2pn2D 2 dCT
(3 propeller blade-angle setting at 0.75 R 7rX d.r
K calibration con tant for each yawmeter dCT
dT difl'erential thrust coefficient (7rHx/2pn 2D2)
dC [] 4 dx (5)
x q= 7rJ2x
dZ Q
diITerential torque coefficient (7rKIIvx2 / p1l
2
D2) From the force measurellwllls, th' value of Lbe
u,pparent propeller efficiency is
- 1+ 11 +4 dCTj~X
. l'III tel' f erence f ac tor
a aXla -V ~ 7r.cJ 'IT
(6)
TJ{I= P
a' rotational in terIerence factor[ dgo 7r2J r ~l + a)]
If the velocity in the propeller plane w j tu Lhe pro-
Ea axial energy per unit time in slipstream peller removed Uo j equal to V at all radii, then the
Er rotational energy per unit time ill slip tream value of TJa obtained by mean of equation (6) i the
1f angle of twi t in the propeller lip tream twe propeller efficiency, If Uo i differen L from V, Lhe

[ 1 4* ]
tan - 7r(1 +CL)2X2
twe propeller efficiency may be computed from TJu by
the use of the elU"ves of the thrust eli tribution tWcl Lbe
velocity distribuLion with the pl'opeller removed,
according to the following relation:
n angular velocity of propeller (27r1l)
(IUD dOT d£
DERIVATION OF FORMULAS _ ) 0 V dx
TJ - 7j a IdC7 , (7)
The di.lIerenLial Lhru 1, and torque coefficients mny -- dJ'
o dx
be computed as follows ( ee reference 2):
dCT 7rlh The energy imparLed to Lhe propelle l' lipsll'eam per
dx =2pn 2D2 (1) unit time may be computed from tbc curve of Lhrust
and torque distribu tion and the in terferenee vcloei tics.
dCQ _7rIUI/x
Tx- pn 2D2 (2) The energy 10 t per unit time in axial velocity may be
written
From the values of dOT/dx , Lhe axial inLe) ferenc ( )
factor a may be compu led:
CT If Ea is divided by the power inpu t to lhe propeller,
dd =7rxJ2(l + a)a
l' the fractional part of power lost in axiH l energy is
obtained:

(3) (9)

_J
 PROPELLER ANALYSIS FROM EXPERIMENTAL DATA 3
The en erg lost per unit time in rotational velocity But
may be Wl'i tien

f la ,dOQd
/~',= J CL"''''dQ = ')~7rpn3D sJo dx x (10) Therefore
4dQc
The fl'acLional pa.rL of the power lost in rotational d:r (15)
C'11C' I'O-Y may (.hen be "TitLcn

J<;, 27rpn3JYll, d Qdx Equation (15) oxpre ses the relationship between the
-=--- (L -
P p 0 dx
torque coefficient Qc and the ano-le of twi t in the pro-
= .) J'1a, d/'f
_7r - L.-- Q
. d:r (11)
peller slipstream, which will be used later.
('p 0 dj

= ~ r 'a,dQcdx ( 1111 )
Qr.J O dx

The fracLional parL of the power unaccounted for

from Lhe fOl'C'going analy i may be computed as follow :

){emaitlcler ;F=1- (E
11+ p a+ E)
pT

Thi l' mainder of the power consi ts of the error

in calculation of energy in axial and roLational velocities
cau ed by the nonuniform charactcr of tbe wako and of
Lh o energy rcpl'esen Led in the profile drag of the blade ,
,,-hi chiin the form of random velocities and of heat.
FIGUR E 2.-Free-a ir body.

APPARATUS A D TESTS
Mounted on flo a llng frome
The tests were conducted in the JACA 20-foot
Lunnel described in reference 3. FoUT body shape
13.5"
wore te ted: a free-air body, a propeller-hub body, a
body of revolution, and a body of revolution with an
Mounted on fixed frome A A cowli.ng_
Figure 1 is a lin e drawing of the fre -air body; a
photograph of it is shown in figure 2. The propeller-
hub body (fig. 3) consi ts of the propeller-shaft housing.
FIGURE 1.-'rest arrangement of free-air body. which is 9.6 inches in diameter; a spinner band wbicb
Lums with the propeller and ,,,,hich is mounted on a
The angle of twist in the propeller slip tream im- f10aLing frame; and a spinn r mounted on the fixed
mediately behind the propeller may be computed from [ram. FigUTe 4 show the body of revolution that
Lh e axial and the angular velocities: hou e the motor and the propeller shaft. Figure 5
27rxa' hows the body of revolution with an. .NACA cowling,
(13) Lhe maximum diameter of which is 20 inches. A model
J ( l +a)
of a J-5 engine, composed of dummy wooden cylinders,
, - 1 27r:ra' (14) was mounted inside Lhe cowling. Th e body of l'evo-
if/ = tGt.l1 J (l +a )
lulion ,vith the cowling will hereinafter be referred to
l~'l'om quation (4) and (13) a the" ACA cowling." The propeller, which had
dOQ two blade , was a 4-foot model of BUTeau of Aeronautic
4 drawing ~ o. 4412_ The blade-form CUTves of th pro-
dx
Lan if/ = JrJ2 x 2(1+a) 2 p Hcr are given iu figure 6.
 4 REPORT NO . 7 12- NA'l'IONAL ADVISORY COMMI'I'TEE FOR AERONA TICS

' imulLaneou m a lll'rm en Ls w r1'e mad of Lhe t otal diameter a th e pinner bu t " as mounted on Lh e fixed
Lbru t and torqu c and of th e diffcrential tbl'u t and frame. In the ca e of a pl'opellel' moun Led on a lon g
lorque along th e radiu. Th e m rLhod of mrasUl'ing th e sh aft ah ead of a body , th e difference b etween th o drag
di fl'cr ential th l'u t and tor q ue from m ea UJ 'em ent in
t he pl'opelirl' wakc wa the arne as u rd i n refer n e 2.

F W1J Il.E 5.- ll od y ofrovoluLion; N A C A cow li ng.

Itl(;t' I<I!; 'j, Propollcr -hll h bod y. of t he pro peller ll ub and tb e s pinn er 1I'0u id h e r eH l j~(>d
ill Lh (' propell er l:ffi cicllcy.
T h(, posi LiOIl or L1w tll b(" \\ us s uch thaL yaw-h ead a uLi The efficiency obtain ed with l'i Lh er Lbe body of revo-
total-b ead read il1D' wrre observed at 22 .2, 33 .3, 44.4, lu tion 01' th e NACA cowling i no t t h tl'U, but t he
55 .6, 66. 7, 77 . ,[mel .9 p erc nt of tb e prop eller radius
f rom tbe center of th e crank h af t. b h r--y /'" I p
75 Ii H-jl\-
h t~~1~t~~jZ
fJ~-~3;7;;-:'yo~:-t"-_'+-_Tt--,f-I.:"/"'i..-f-/::...-t:+/~"In~
.08 .3Z f-H 7i /' 3Z ...---r 0 .
RESULT
~ v.A--1--t---I-v-=-i 1
.07 .281-1f-\1-+-t-+-+-l/++-l-1rl-+-+-+-- t-1-
f,-----
-j/.4
Tll() ba ic 1'(' uHs of th e for ce te t <He O'iven in
-- , ~~V~~~V~~~~~+/~~~~~
V Z7 0

§
figul'r s 7 L ]0, Tlw efficirll y em -elopes Ior th e foul'
.06.24:-;; -r-: A--I-
1/-,-i--7.o(-j-+--+--1j>"<ri:v-::?i""'T-r-i-r--J/.2
I
.05.20
j 4V.J X.,__ ~. I 2"'f"2':=+~~1.0
I ' I '-41----=-
1

.04 .16 }y+ ~1 1== ~ i ~-f

I ""l+~--Ir--.+1 7--J<- .8

.03./2 EVh . 1i:~·6 I

f? .~
-1 : ,
~~
.OZ08 - / ---- . I ~ ~:=L--1.4
I I I ~ 2
.01 .04 \ I I, I -4.

7 .8 .3 1.0
o
3 .4 .5 .6
TI R
FWURE 6. - Propc\l er blade-form cur ves. D , diameter; R , radius to t he tip ; r, sta-
F WU lt E 4.- J3ody of rovoluLion .
tion radius; b, section chord; n, section th ick ne ; p , geometric pitch; (3, blade
a ngle of O.75R .
b ely b apes ar c compared in figUl'r 11. The efficiency
ob tained \I-ith the propeller-hub body i abou t 6 p er- apparent , propeneI' efficiency. Th e propell er ouLpuL
cen gr ater th an th at with th e free-ail' body and this u ed to compu t lhe apparent efficie ncy wa TV;
increase i. due to th e elimination of the drag of the wher eas, th tbJ'ust wa obtained in a region of veloci ty
prop lior hub and the :inner por tion of tb e bl ade h anks Uo and tb e useful work p r emit tim e wa uoT. The
by covering th em. Th e spi nn er coycr ed two-tenth of change from a pp a.rent efficiency to true effi iency will be
the prop lIer blade; th e h aI housing had th e ame discu sed later.

L~
 PROPEL.LER A A LYS1S FROM EXPERIME ''1' L D ATA 5
Fig ure 12 to 15 give Lh e Lhru t-gr aclien t and Lbo /B T 1 :r
I~_~UT
I
t 1
LOl'q ue-gr adient curves for the prop ell r-hub body. The
/6
I I
1
urv ar e given only to O.2R because the ilmer t V,lQ- /3 17' 22' 27' 1
ten th of th e propeller blades was over ed by th e pro - Cp-o--x
.14 Cr- + - O- O !
peller-hub body . The thru t-gradient cm-ve for Lh e · 17 ---6 - -- -<]- -- <J
other body shap es in th e ubsequent figures ilr e also
1-
.12
Lerm inated at O.2R becaus no p res LIre reading wer c ----c. -c--l--- - - f - - -
--0- _____
Laken in ide tha t radiu . . /0 ~~t~ 10

n .
I

_~~~J~ ~: ~~'~~~ ~t&

Cr
.OB B
cp ~~.I/ \(~~ • <5.

./8 l I ' _ ~,t*.f!l~ ~ ~ '( ''II

I
.6
12' 17' 22' 27' 32' 37' -j--t---t--H
.06 .~
. f'
~
.r),,, ir. ....
_Ji_c -<l L ~
J'\'f'_ ~ -'-:'-,1 ...-L.-, ' 7
C
c
p ~ !---!---!---I--1H .: ••..),0' .1, I '''-~ I I, 4
.04
~."l- : ~ :~ \:iT I
16 - ' <J-+-O-O-(7-D
- - I '7r O---·6----\7----<)----Q- -- -{> I--t -t - t - H f----;-::.;·/I
. I 4~=t~~~_+_t__+_..,--Crl-__+++_+___t---l-__h ,,'.' I 'Th~' \;
.02 ~-~,f~-I- I ~ --1 _ : '~~
I
"\\~ I 2
\~ tr\ r\i It
o
-.020
§ I

.2-
I f1i. ~~\
'---'-
.4
I
~
o
.6
I
B
1\ ~L ~~-.L'
1.0 /,2 14 /.6
Vl nD
---t--t--t--!8
FIGUIIE g.- Curves of CT', CPo aod q agaiJlst V I"J) for body of revolu tioll.

"8,>--t--+-I .6 . 18.--- r- -I I-I I I I I 1 I-I I I

T] I- fJ 12' 17" cc· 27" ,]2' .]7" 1---
~
+---1---1- Cp
.4 . 16 Cr <J- -+- -,--0- -<>-- -(7---{)
1--1--11--1- T/ o----t:.- --9---(J- ---<;>- - -() -t--t--t--H

.2

-.o2ot=±:;:===~,
2 .4 .6
±P:=:;~;::=~=;J;tt:;J;;ij
1.2 1. 4 /.6 1.8

F rGURE 7.- Cur ves of Cr, Cp, and q against Vl n D for free-ai r body.

18

16 I-- I-
·1- ~I- t--

r-- l--- -

14 (.3 17" 22'

Cp o - - -x
Cr + - - 0
.12 T] LI----- - - -\7

FrG URE IO.- Cun-es of CT, Cp, and ~ against V llI D for NACA cowl ing.
.10 /0
1---:' I~ 1.0
Cr
~~ ~
~~.
". IS-, --= r-i= --- -
.8
.08 'K I,\\<. \
.--- --- - -. --- -- -- -
G, A
+>.!
#f.
>1
1'\. .
~
,
.,
- f - -I - --
6
.8 -
.06 -M·e--- 11~ -----rt"
,--" '1<-
h.\ h r 17
Ii '\ i'x: ' \> 6
- -- - -- Free- o ir bo~
·04
- 4' -o- tn... \ r:, ,
I
,
.4
7] - - -Propeller-hu b ody
- -' - Bo~ of revolution
.02
, ,
,~
~
, :. I

\~
~'(
I~I
.~
I
.2
.4 - - -NA A c owling
o NA CA co wling. veloc lfy
correc t ion applied
.

o"
" 0 .2
\
\ );
- 02
o .2 .4 .6 .8 /.0 1.2 1.4 /.6
o .f? 1.0
.4
Vj nn
1.2 .6
1.4 1.6 1.8
V/ nD FIG URE lI.-Comparison of apparent propeller efficiency envelopes for four body
FiG Vil E .-Cur ves of Cr. Cp, and ~ agai.nst Vl lID for pr opeller -buD body. sbapes.
6 REPORT NO . 712- ATIONAL ADVISORY COMMITTEE FOR AEHO AUTI S

./8
1

! I
I I 1\
.16 1
, I
I

I Jr J..-- t----
f-..-
I Vj nD .I V-

.14
1 V/ nD J./~I /' VI t----.. \
1 /6 1 ~ '\
1 ///.3 V 1\ l\
. 12
I 1/ /1 /.4 1
.10
I
I //~ Y Y I 1\
11;11 Y /5
~
V/ / A
.08
d Cr V/i /6 \ \\ '"
dx ~ j / / ~ .~
.06
//// '/17 / -. 7 Im-
"
I 1 \ ,,\\1\\
04
W/(/ / /~
~~V/f V /--L...J ~ ~ \\
. 02
~ )"'.
/i / ~~
./f,V V /'
L~
I, ~
V V J---!--. l'\
oV V I

/>/ l / ( 1 ....-
VV.9 !--- I---'

-.02 /'"
V
IL-V ""--,
l--n 1
.2 .3 .4 .5 .6 .7 .8 .9 1.0
x x:
F IGURE l2.- C ur ves for dCrldJ: agai nst z for propeller-bu b body. {J,17°. F JOUIt E l3.-Cur ves for dC" ldx against z for propeller-hub body. n. 17°.

----r T- r - .-- , - r-r- -,-

.036 r---t -

.1
.032

V/ n D .I- ' y ~
.028
\

.024 I ~ 1\
il '~ !Z f7 ~\~
I ! .3 "-
.020 I ~
I :;;;r- t---- N ,.'.4
.016
i ~~ I-- b ~
~V/I/ J..-- t--- 1
I \ &
1\ "~\~,t-
t-

~ !/.7VII/
J
.5'
.0/2
deo ~V vs lljl.o J..-- t--- \ 1\\;\ ~
r 17
dx
.008
l#V I/. I I/- '/.1 1\\\\\
I ~ V/ /'
V .~ / I.'; \ \
.001 LU ~vV .../
V II VI I"'" 1\\
~V'
V V 11/ 1.3 "\ l"" \1\
:::=PI V--
~

~ V) ~ ~~
o
~7 .....- V ~
-.004
\'\J 1/ / V
./
V

, ~
/v
-.008 l\'F=VY
I
"lY I
I 1 1 I
-.0/2
! ! i ii
- .0/62 .3 .4 .5 .6 .78 .9 1.0
x
FIGURE 14,-Cur ves for dCrldz agaiDstz for propeller-hub bod y. (J,22°. FIGURE 15.-C ur ves for dCQld.x against x for propeller-hu b body . {J,22°.
 PH.OPELLER ANA LYSIS FHOM EXPEHIMEN'l'AL DATA 7

Fig ul'C 16 gives a comparison of th e thru st cocfficien ts A comparison of th e valu t's of power coeffieil')1 L 00-
fo /' the propeller-hub body obtained from the force tained from th e fmee and th e yawm etel' Dlea Ul'eD1CJl Ls
meas nremen ts and the total-pres nre meaSlU'ements. is givpn in figur c 17. Since the yawmetcl' meas ure-
T he val ue for tbe total-pre sure m easurements are a ment indicatc yaw in th e slip tream at zero input
d ir ect integration of the thru t-di tribution curvcs ill power to the propeller , DS shown by tl1l' discI' pa.n y
a t zero mcasured pow er , it i concluded Lhat thc direc-
. /2 -
-=-ITlrJmJasJem~[I,
~
tion of th e main air str eam w a ch anged owing to Lbe
-
presen ce of th e propeller. This amc efl'ect was noted
- - - - - - - - Totol-pres:sure measuremen ts in a serie of test on a differen t test set-up usin g full-
. 10 r ~
calc propellor s. Figmc 17 shows th e effect on tbe
t--- - - integrated power coefficient of applying a con tan L
.08 - ~~ --- ~ -
cOlTection OlTe poneling to 0.5 0 anO'le of yaw. TIl is
sm all ch ange in th e direction of the tmmcl air str eam
~
~f:J' ~- .....

.06 ~~
'""'\ brings th e in tegrated r esul ts in to substantial agr c-
m ent; th ese con ccted values arc u sed in th e further

~
/J~ /r·-· 2c~ .0.'3
Cr -
i\ - - I I I I
/ r" ' '\
~
.04 -- ~ '8 - !3 Vj nD

\
~
/co----- - 0.515 ,r-
, - 17"- - - - - .728 / '\\
- ' Ij
" \\\'
~
2c·---------- .946 ,..- -
.0 7 -
\ ''\ 27"- - - I. 198
j Ii
.02
\~ I-

~. - . 06
32° 1.448
I - 37"------ 1.753
17/
~ t: --
" .. ...
-- -,
_\ \\
:'-. \ \ \;
o , -' ?t 1\
\ .05
V / :-; " \ '1\
- -- f--- -
1\ \ .04
l/ / //t! \" :
-.02
0 .4 .6 .8 !.O 1.2 / /' /; l/,' \ "

V(nD
.03
,/ '/1/ \,
FO URE 16.- ComparisoJ1 of thrust coeffici ents from force measurements and total-
pressu re measurements . Propeller-h ub body.
dCr /; / / ~;/ \ \\
d.x
.02 r// I i' \\
, 10

rI-1 FoCLs~J I - -i . 01
~
/; :1;1// I
,
\ 1\
\1:
~
II:' / ,
_08 f-- - - - - - - Yawmeter measuremen ts ':'1
( " " corr ec ted o
- - - for as· chonqe m r -s,":':~ d,~cf'=_
.,f/I 1
.06 ", -- ~
-.?~f-- ---
__- ::.:: - _ _ _ f--- f-- -0 1 l: '/ :
fI II /
- -:'::~I- -- /
~ - , - 02
-- --- - / II
.04 -
~
-_
~ -- -
r-~ ~ -
" ;'
~ - ----K- - - .03
.B$ 170 _ ~ -' , c2· ,,-- ' \ .3 5 .6 7 3 10
2 .4 8
.02 f-- 1\ \,
,,--
_L. , " X

- " '\' \,
"
~' lG HE l~.- \ ·a .. iaLion ill Ihru~L di~L .. iiJL1tioll wiLIl I>ropelier blade-augle ~et tillg a t a
constant \,A lu e of C ,. of \).0320. N A" A COWling.
, ' \'
o .c .4 .6 .8 1.0 1.2 analysis of the propellcr ch aracLe J'istics. Th e uir-sLruull
Vj nD c01'l'ection appa,]'ently varies \vith th e propeller 0PC1'-
FIUUltE 1~.- Con l\)a r isoJ1 of power coeflicienls from force measurements and ating condition b ecause tb e constan t 'olTec~i on of 0. 5 0
yaw meier measurements . Propeller-hub body .
ov l' OlTeets th e values for high valu es of V /nD and
fig lU'l's 12 and 14. No corrections were nect' 'aiT to lIndCreolTccts th e value for low val ul's of Vir/ D. Th e
Lbeso i ll LegraLecl valu os b ecause Lhe propellel'-llLtb a ngle of Lhe ail' sti'eam ahcad 01' llJ(' propeller is prob-
body hicldecl Lh o innc1' p~\J.'L of th e propellel'. Tb e ablyal 0 changed by th c body ize HIle! ShtlpC.
large difi'cl'eHc(' eLL low values of VlnD eLl'e caused by Th e comparison of force and in Lcgratccl nwa UJ'l'-
an error in Lb G rrH'aSUl'C'm('n t of toLal prps ure behind llWlltS a J'c' valu able as all ind icatioll of Lhc Hc('uraC'y
I,hc' pJ'o pell('l' due Lo large u,ll gk of sl ips rt' lUll yaw. of ~IJe di sLribu Li oll ('lll'VCS. TIl(' proppil r /'-hub bod y
3J774-4 1- 2
 ------------- --------- ----- ----I
I

REPORT ro . 712- NATIONAL ADVISORY COMMI'I"l'EE 1<'On AERONA TICS

because of the hub drag. The fact that Lbo integra Led
~~--I-
1.00
[ -- - - -- -- - - -- power coefficients need a correction to bring them inLo

:'-1 it~~!
~ - agreement with thC\ mea ured power co fficients indi-
.90 f-- t--- cate that the intrO'rated power measm'ement are
1-- 1 q nantitativcly inaccurate. Ina much a a constan L

~2 ~+ -t_____
correction to the angle of yaw of th e tunnel airstream
.80
u.
/
7 -I
Fm-oir body bring the 1'C ult; inLo substantial agreemenL, Lbe eli -
v. 70 -NACA cowltnq / tl'ibution of the torque along th e blade is believed Lo be'
/
-S!
---QJ ,-
-~
-
l' I I ~
llfficiently accurate for u e in further analy is .
Figme 1 hovv the variations in thl'u t eli Lribu tion
I 1 g
c: c-_ IT
J- .~ with propeller blade-angle setting for the A A cowl-
.60
§ I--
T ~
QJ
§-
ing at a con tant value of CT of 0.0320, which i approx-
.§ imately at peak efficiency for the blad e-angle setting
.50 : ~ 1--1-
ct of 12°. The eHeeL on the thrust di tribution caused
~
.3 .4 .5 .6 .7 .8 .9 1.0 by the chan ge in the pitch distribution (fig. 6) is shown .
x
A the blade-angle ettmg is inerea ed, the lope of
FIGURE 19.-Velocity distribution in plsne of propeller (propeller remo'-ed). 1 ',93
m ilas per hour . the pitch-eli tl'ibution curve is increased, wbich cau es
the thrust to move toward the tip of the propeller.
fUl'lli he the best opportunity to determine thi accu- The velocity li tribution in the plane of tbe pro-
racy, no COlT chon being nece saTY to put th inte- peller with th propeller removed i bown in :figure H)
grated and tb e measured result on an equal basi [or two hody h ap£.' .
.--.--
I- I--

1- -
-
-
II/
--0.6
V/nO 1141':
1.16£: - l-
V/nO liPS; - - - - - .7 1.391
O.C 0380 - - - - - - .8 1.654 - I-- 1 -
----- - .3 .571 fI - - - - - - .9 1.983
---------- .4 .766 q -----/.0
-------1./
2.495
------ .5 .961 .7 3.375
-
If --- .6 1.16c 1--/ I-- r- '--...
q
9.0 .6
,/ !'--.
lL/ [\
j--
V ~ l' \
8.0 .5
1\ /1
/
\-
7.0
/
\ .4
/
I
v/ - '- - - "-
\
I--

6.0 / 1\ .3
I ,/
" ,
1\

1
/ \ .I
, ,- -- '=-- -- - I-- -- -
,
\ \
5.0 \ .2
11/ / ',,- \
/ ,
-- -- r--,
, 1\\
40 I 1\ .I II
1/ // l]
- ti, ~-// ,.- , - '--- --r-- -- ~
r- --
--- ~~,
f--
I- i-- \ /"
---.........

3.0 I 1 >/ '''['..\ 0

'--
(
'--
I-
'- ;---- -- I-- - 1--
-:~\
I yl '~ :-. -
-I--
~ 'I'
I V
. -- - -- - -
1\
2.0
II / ,-
-- -- -- ,
-- -- - \
,
-. I
7ff
,- .:1
I. 0 - .- -I - I- -- 1- - .2
1/ , - -
-
.- r-- I - --~
I

,I /
/'
- .-1--l - II

0
I , ,Y ---- K: -.3
II
?'
I
-/.
[;1' /
01/ All
.3 A .5 .7 .8 .9 1.0.2 .J .4 .5 .6 .7 .8 .9 1.0
x
FIGURE 20.-Curves of IlIa against x for NACA co,vling. P,22°.

i
_______________________ .-1
 PROPELLER ANALYSIS FROM EXPERIMEN'l'AL DA'l'A 9
DISCUSSION VELOCITY INCREASE DUE TO THE PROPELLER

TOTAL PRESSURE DUE TO THE PROPELLER In order to st udy the inflow velocity ahead of thc
propeller, sUl'vey m ea mements wer e mado with and
Thc eff ect of the propeller slipstr eam on th e body
without the propeller operating. Figme 22 shows the
bchind thc propeller may b e studi ed by determining the
r esults of these m easmem ents for two body h apcs
increase .in total pre m e du e to the propeller. This
with the propeller operating n ear p eak efficiency at a
iDCl'eaSe in pres m e divided by the dYDamic preSSUTe
blade-angle setting of 22° at O.75R. For the ACA
of the undisturb ed air stream mn.y be computed
cowling, th e ma;...rimum inflow velo city at the centor
directly £l'om the thru st-distribution curves and equa-
l.ine of th e propeller is 7 percent of the free-stream
Lion (5). Figme 20 shows the distribution of H/q along
velocity and is only 2 percent at a di tance one-third
th e radius for the 22 ° blade-angle setting with the NACA
of th e propeller diameter ahead of t h e propeller. The e
cowling. The magnitude of H/q will r emain essentially
curve al 0 show bow the NACA cowling increases the
th e same for equal value of 1 /~'J.5: r egardless of blade-
angle settiDg; the ma:\'1mum value, however , will shift ./8
toward the tip a the blade-angle se tting i increased.
For optimum design th e shift will bo smaller than is d e"
./6 dx
shown for this test propeller. The valu es of V /nD are r- ---------- VU , dd Cx T --- -,
hown on the curves for compar ative pUl'pO es, but it ./4 V
must b e k ept in mind that the CUTves of H/q again st L \
V /nD can be 11 ed for only the blade-angle setting given. ./2 1/ \
The magnitude of the increase .in total preSSUTe .in the / \
r egion in front of the body p ermit a rough approxi-
mation of th e in c1'ea e in body dJ'ag due to the propeller
./0
/ -·to
. -/7"
Vi n E
1.40
.65
\
slipstr eam, provided th at th e type of flow over the /
.08
body i not critically a ffec ted by the slipstream. If th e / V V
~
d C"
slipstr eam changes t be flow ovel' the body, the change dx V
/'
1\
.06 £.
in drag cannot be predicted. Il' ~/
The CUTves of H /q are useful in .indicating th e .increase ) ~-
in total pres m e that can be obtained .in a scoop or .04
other ail' intake located b ehind the propeller. / if
Because of th e increase .in total preSSUTe that can b e .02
/j-
obtained behind good propeller blade sections, the coo]- l' !l
ing of engin es should be taken into acount in the de ign o
of tbe inner sections, e p ecially when the enginc ar c l ,/
JllO lin Led in open-no e cowlings. -.02
,I:
,/
P RUPE LLER E~'.F1CIE ' CY I THE HEGION O~' ItEVU CIW VELO(JJTY
- .04
:;
.2 .3 .4 .5 .6 .7 .8 .9 1.0
Computation of the t rue propeller efficiency from x
h e apparent propeller effici en cy for the NACA cowl- FIGUR E 21.- Ex8mple iIltis tra tin ~ the metbod of determin ink true propeller eflicioncy
ing can bc made by the usc of thrust-eli tribution in presence of body. NA C A cowling.

CU1'ves (fig. 19), equation (7), and 1.to/ T! data. Figure

angle of attack of the pl'opeller sections by decr ca il1 g
21 illu tratos tho results of oalculation for blade-angle
the axial veloci ty over these innor sections.
se tting of 17° anel 37° at 0.75R for th e p eak-efficien cy
poinLs. The ratio of the areas l.mder the CUl've gives A GLE OF T WIST I TH E SLIPSTU EAM
the factor by which tho apparent propeller efficiency
mu st be multiplied to give the true propeller efficiency. A knowledge of th e magnitude of the angle of Lwist
The correction amounts to approximately 2 percent if; in t h e propeller slipstream is h elpful in the intcr-
foJ' tbe 17° blade-angle setting but disappears for the pretation of the action of airplane parts, such as in take
37° blade-angle sotting b ocau e of the shift of the scoops and wing fillets. The angle of twi t immediately
thrust distribution from the low-v elocity region to the b ehind the propeller plane may be calculated from equa-
high-velo city r egion n ear th e tip. The r esults of this tion (14). This angle of L-wist will vary with Lhe di s-
correction to the p eak efficiencies of the two blade- tance from th e propeller plane. Two separate effects
angle settings are shown a points in figUl'c 11. that change th e angle of twi t are: The conver ion of
The disappearance of this correction i particuJarly static pressure into dynamic pressure increases th e
applicable to the test conditions and should not be axial component of th e v elocity, whicD r educes th e angle
applied as a funct.ion of blade-angle setting for other of twist,; and th e contraction of the slipstream combined
conditions. with th e change of the cross section of the afterbody in
10 H,EPOIt'!' NO. 71 2- ATIO r A L ADVl S0HY OMMl'rTEE FOIt AEHO AU' l'l CS

l.il c lip trCll.m. changes the radiu of the streamlin es l /-JQc of 10. It may be see n from fig ure 2:3 (b) lh a t
a nd 'on equen lly , ch anges the a lw ul ul' velocity of th e th e ano-Ie of t\\"i t for th i operaLin g condition is Ie s
lip LJ'cam, Th cfreeL of p eecling up Lhe axial vdocity th an 3°. Thi . angle of wi t is repre entaLive of th e
amoun ts to only a m all chan ge iJl h e angle of tw i t. valu e obtained wiLh a propeller operating in lilt'
If Lite propeller i operaLing in J1'on t of a blun t boel y like cruisin g or Lhe high- peed co ncl i Lion of [Ji o·h L
aD A A cowling, Lhe angl e of twi t in Lh e lip ream
D ISPOSITION OF PROPELLER POWER
clo e to th e udace i lc s than Lh at ealculated immedi-
ately b ehind the propeller. Tbi lifTcrence in th e angle The eli po iLio n of Lhe power inpu t Lo tbe Pl'o peller
of twi t j clu e to th e acceleration of the ail' goin g over wi th the propeller-hub bo Iy i given 1'01' th e ]7 0 bl aclc-
the co wling alld to th e in cr ease in the radiu s of the an gl e setting in fi o'ure 24 (a) and foJ' th e 22 ° blade-angll'
s tl'l'amlin s, which decr ea e h e ano' ular vcloci y of t he tting in flg ure 24 (b) . The p erce nlage of power bt'-
all'. twee n tb e propeller-eff-i eiency 'urve and uni ty r epre en L
Fi o- ut' 23 hows th change, at val'iou op erating th e 10 e of th e propellel'. The thru L-l istribu tion a ncl
conditions, of the angle of twi t wi th x in th e propeller the torque-distribu tio n curv es in onj un ction wi til
lip Team immediately b ehind th propeller comp uted equation (9) and (11 ) p ermi t t he calculation of the
for t wo blad e-angle settin gs. Equation (15) give til e encrgy go in g in to the propellcr lipstr eam in the form
a ngle of twi Ii in th e propeller slipstr eam as a fun ct ion of axial an cll'o tation al v C'lo ity, Equation (9) m ay be
of Lhe torqu · coeffici ent Qc. An estima e of the an o-le r ewritten a
of twi t in th e lip tream for any propeller-body om-
bi naLion may b e obtain ed by computing Qc for the
propeller op eratin g condition de ired and by usin g fig ure
I'd
1'-'".= 11 a - 'I 'dJ'
P OT, o dJ.'
2:3 Lo e timaLe th e an gl , l ' mu t b e k ep t in mind,
however, th at th distribution of twi t alon o- tl1<' rael i u IL may be seen th a.t EeL/P, Lo th e fir L ortler, is pro-
varie wi tb pitch distribution , bod y h ape, aJlCI operat- por tional to th e procl uct of 'f] and a.
in g conw tion ; consequently, an exact value of th e angle Equation (3) m ay b e rewri tlen in tIl(' form
of t wi t for oth er propeller-body combination can not
be obtained from :fio-ure 23,
- 1+ 1 1 +~ dT,
For th e 22° bia Ie-angle ettin g, th e m aximum propel-
CL = -
-V 2x elx
ler effici ncy occW' at V /nD = O. 03 or a valu e of 2
~

1~
l
32 I- I- - I - ..... ,
Q

-l- I - "tl~ - I -
0:::::
~~ - I -
28 ~
:::::
a l. l- I-
~g.
.~ o-9!
~
g. ~~ ~ ~ - f---
~g.
QJ'
I
\) 24
b ~ ,
<')0..
l. I
I
"'"' I

~
~i
i:;l I
I

"t/?O l - I--
i) I -

~ I

j
16 I-- I
- I-

-! i- l -I - - l-
41 I
I

~ +I I;
12 l - .-l - I - - 1- - - -
.~.
I I I
I

~
I
I I
l - I-- - t - -

- A
,[
I I

'-§. I-i- - ~
I

- : - ,
I

I : ,
I

I-- - ,, I I

~ III
4
-- - - --- .-
_ _ _ 0- f--j---,
_ _ _ _ _<1..
- i-=---' -./ 0 -.2 -.1 0 -.2 -./ 0 ,I
- - - -- -- - .1i 'l V

x- - - - - - Free-air body
O---NACA cowlmq

-
I
 ~-~- --~- -- --- ---

PRO PE LLE R ANA LY SI ' FROM EXPERIME TAL DA'r A It

•~
1.0
VJJL VI//, VI//I '1//1 1111, rill! vlJ~ '(/111 '1111 IIII

lml ~~ \\lli ~ ~ ~ ~ ~ ~
~ ~
1111/ 1111/ rili/ 'ill/
V 1111. 11/// V/IJJ
Wi 1$
/~ ~ ~ ~
WI.fll//
~ ~I ~~ ~\\ ~\m ~ WI, Ijl~ 'I \\\\\ \\W \\\\\ \\W ~\\\\ ~\\\\ ~\\\.\ 71(j,

If; ~ I/III~
.9 f---
.,...... \\\\ ~ ~
\~
~~ (Uj, fl//;
-.......;.:
~ WJ.V1!J
.Y
~W
fY' "-l.I..I;
.8 - l- i -
~~ IJ/; fiJ/ ~~
£Ii
~~ ~
'--- 1- - ~ I--
~ ~I "
.7 - f---
I-- l- e- ~ 1-

.6
- -
r; .5
i -I- -
.4
=
== Thrus f power
.3 =
==
Axial momentum loss (E./P)
Rolationol momentum loss(Er/P)
Other losses

.I

(a) (b)
o 1.2 1.4 1.6 1.8 e.0 e.2 2.4 2.6 I.e I. 4 1.6 I.B 2.0 2.2 2.4 2.6 2.8
11$5;
OO ~~ OO ~ W.
F IGU 't E 24.-Dis posiLioll of p ro peller input powe r. Propeller-hub body .

. 024
cO ----- 1 - --- - - /
1
'---
.020 /
16 I'l 1/..;0: J
--~ !!! VlnD /V
r---- I-- .016
12
---- - -
.233
r- t- -
s....O/2
~< )"
/
IV

fJ. deg
8 - 6 .0 o 17
.452
V
--
x 22

4
- It- .008
/
100 .650
i'----
17.0 1-"""" .004
V 1
~ .800
--- (a)

V
/
o .004 .008 .012 .0/6 . OeD .024 .028
Cq LJ
V 1'\ 3. (,
"-... .288
16 ------ '\
~ V - ,--
I..---' F IGU RE 25.-Experimcntal cur ve showing relationship of E./I ' LO CQIJ .

12 I-
wbich bow Lh~~L (L i a dir cL flllction of clT c or that
EalP i a funcLi.on of T o and 'I) , if change in the dis-
8
60 .552 tri.buLion of thrust are n eglected ,
From equa tion (110,) i t i seen hat Lbe fractional
/" I-----
4-
--..
f--- - - 19. 0 .8b3
"" par t of the power going inLo rotational velocity in th e
wake is pl'oportlonal to a'_
o "-
'--, l...:--'"
V
.3 .4
--
17.0

.5 .6 .7
.!J80

.8
- I-----
.9
(b) Equation (4) may be written in the form

(a) (1, 17·,

( b) (1,22°.
, d Q 2
j.' IGUltg 2.1.-C ur v of a ngle of twist iu the slipst ream, Propoller-bub bod y, a = -d-x 7r zJ"-:t Cl---'+'--a---)
"""'-;

- ___ .-J
12 ItEPOIt'l' NO . 7I2- N A'J'IONAL ADVl ORY COMMI TTEE FOR AERONA TWS

.09
/"
V

.08
V
,1/
,/ V
.07
,V '-Theoretical curve
,'~ 12 I I· 1
--Points from expen -
1 I . 1
.06 mental curve, .B ~22·
" I/' I....--
, / - c--
, 5 1/ V
;?; ,'/

p/
V
0' V
.03
//
"1/ "
.02 , '/
~-; "'Str aight -line approx imation
1)1'
.0 I
1/
o
V .04 .08 ./2 ./6 .20 .24 .28 .32 .36 .40 .44 .48 .52 .56
Pc
l"GUlt" 26.- I{elaLiolls hip hetween P c a nd ax ial eue rgy ill the I))'opcllcr wa ke.

H the small effect of the facLor (1 + a) i n eglected , te t propellol', ha al 0 been plotted in figw'c 26 . It
a' i proportional to ~a J or Er/P i proportional
may b e noted that tb e agreemen t i very good ; the
differ ence in -no ea e excoeds one-half of 1 percent of
to GaiJ, if the effect of torque eli tribution i n eglected. th e total power lost.
Figure 25 is a plot of Er/P as a fllnction of GaiJ for the The difference b etween theory and experiment shown
17 ° and tbe 22 ° blade-anale ettings of the propeller-hub by figme 26 may be due to one of two effects. Fi)'st,
body, any change in the thru st dis tribution from the optimum
From figure 25 for ideal efficioncywill 1'e ult in a mall change in
axial energy in th e wak, For example, if thru t is
Er/P= G~a added whero the axial interfernce factor a is larger
than the av erage a for the entire propeller, th e frac-
\ h er e G= l.06 lor the test propeller at the bJ9 de an gles t ional power los t in th e axial vcIo city " rill be in creased ;
j('sLed. whcl'ea , if thrust j added where a i malleI' th an Llw
The va.lue of in LIte fo regoing equaLion primarily aVel'!1ge a for the entirC' propeller, Lite 10 s will /)!' de-
d epends on the torque dis tribution and wi ll rapidly creased. econcl , a dcC' rease in propeller em cien cy aL
in crease for a poor torque distribution, a given Pc will decrease h e proportion of power in
axial velocity in the propeller wake, and an incr ease in
A ALYSIS OF PROPELLER POWER LOSSE propeller effici ency will have the oppo ite effect, It i
FRACTIO NAL PART OF POWER LOST J ' AXIAL VELOCITY thus seen that the two effects tend to counteract each
other and that tb e theoretical curve gi ves il, fail' approx-
Figm'e 26 gives th e th eoretical relation bip bet,ween imation of the value of Ea/P in the wake of a normal
the coefficient P c and tb e power lost in axial velorityin pJ'op('ller. If a morc ('xaet r esult is r equired, the lmown
thc wake of tb e propeller for ideal propeller efficiency. thru st di tl'ibu tion und th e kno\\ffi propeller operating
( ee r ef rence 1, p. 1 9.) The high-speed rang of pro- conditions mu t b e ubstitu ted in equa tion (9) .
. 3 -
pell r operatIou (P c= O t o P c= O.16 or 1/ P c=o:> to
1/ 3 Pc= 1. 5) may be approximated by a s traight lin e FRACTIONAL PART OF POWER LOS T J ROTATIO NA L VELOCITY

tbrough th e origin, This r esul t shows that for thi It has been hO\\ffi that a good approximation of the
range Ea/P i.s proportional to the power di k loading, u}"rial-energy los encotmtered in high- peed propeller
that is, if th e power i doubled, tb e 10 s is doubled. operation may b e obtained from th e theoretical curve.
The exp erimental curve for (3 = 22 °, obtained with the The 1'0 'ational-enel'gy los is very greatly affected by
 --=-- -~- - - - - - - - -- ------

l'HOIJELLE l1 ANALYSI S }i'R OM EXPERIME 'TA L DATA 13

change in Lhe eli tl'ibu Lion of p ropeller lo ading h ow- long cyl indrical body wi th a tl'eam line no e an d Lail
evcr, and DO th eoretical estimate can b e ma,de of Lbj th a t \ITa uppor ted free of th c propeller . The pro-
ell ergy 10 from th e to tal power f the propeller \\rith- p Uel' effi ien y \Va m ea ured. The 1'0 ul t for pro-
out a kn owledge of th e torq uc el i trib ution. p eller C on no e 4 ,\Ter c tak en from r efer en ce 5.
The Lotal 'orqu at p eak offici on y fo r thr ee type of ose 4 ex tended tnrough th prop eller el i k in the form
propeller i given in fig ure 27 , v{hi ch is a ploL of Cp a t of a la rge sp inn er a nd covered th e J'adi u to approx i-
F/nD fo r p eak effieiency and the p eak-efficien cy en- m a Ldy 0. 25R. Propell er i Bu!"C'au of AeronauLic
velop e ao-ain t l1/nD. 0 11e of th e e, th e two-blade clrawin,; TO. 5 6 - 9, is [ 0 fee L in d iameLer , an d h a
GoldsL in p1'opell l' (r eferen ee 4) \Va specially de ign eel three blades. The pl'Oput ive efficien y was ob tai ned
Lo corre pond Lo th e " minim um energy 10 "condi Lion from LesL in r efer ence 5 and i plot ted in figure 27.
of B etz, for a cer tain relaLion b etwe n blade an gle and Propeller E (refer ence 6) wa a 3-fo ot-cl iam eL r model
working con di Lion. The hu b and th e inner po rtion of tandal'd a\' y plan fOl'm, No spinn er \Va u ed,
of th e propeller wer e covC' rcd Lo a r adiu of 0 .27 R by a Lhe propeller b ein o- entirely exposed on a long h aft.

.-/
1. 6
11. :65~';'
,

1,5
I fY:
7:
,,
1.4
{propeller E:, two .J-blade counferrofa!ing
---------- tandem propellers. (Reference 6) I
/
,
- - - Pr opeller c. 6 blades (reference 6) / '
I.J I-
- - - - "
n " • .J"
C, .J •
(
(.
• ~
) ,I :
1.2
- - - - - Goldstein propeller. 2 blades (reference 4) /:
1
AI,
1./
r 1; ,'
,
f-- - I /,'
1.0 - J-~ i-- i -I -
i--f..-
/,
,,

.-r-~ -=-=f=.!.- -- -=.LI - l-t 17 ,

/-
.9
I r-,-- f..-
.. l--
-- :J ~ ----
- ~- L___ ~~f:-_ -- -:} - J -7 ::::(_ - - - - -
- i-- I -~
T/
,8
f--
ir- I ~----....,- - -- __ • • u , _ -

-
65° I -
i I
~~=r+=r
! C-.-
:T~~-- ffi-,--
55° " '- -]7-- --

V
, ~~ -
I I =1 +-'- -+-_
,,' 1 - :-r--~
___
/
,7
---
I
I
I I I
''-/
:~< ,' T 1
'- ~ k- I-

.6 - i '-7 / i - f--
I 1/ / ,/
V

45'V{1'~
,

.5 -I -
/" I
V
I I --- V
C-, ,), /+'1 -
~/
.4 [/:4 - I- 4-
,r ./
V :p 55°
[0.7 ../'"
P ....- v' I
..J
.J5· / ~• I 45°1./""
V t- ~
(/ I
,'"
.2
v,"/
?
V ,
45°
.....
I ~
1---- I

e5'v~ .J5J V .V
~

",,' - ........-t
~

.J?~----
.1 15° ~ l..--- .JO'
- - ~'I
~. ~

~-- 12 ~-.r 1- 41.r

-5+
/5'1 ":4
20', 25 ' 27.40-
3/ 0
,

I
,6 .8 !.O /.e 1.4 1.6 /.8 20 22 24 26 28 30 3e 36 38
V/ nD
FIGURE 27.-Efficiency·curvll envelopes and values of Cp at V/71D for peak efficiency.
 - - - -- - - - - - - - - - - - ------- ----------- ------'--'--~~- . --"----- --~ -~ -~-'--- ----~

J4 ftEPOR'l' O . 7 12- ATIO TAL ADVI ORY OMMITTE E F OR AERO A TI CS

.08

/3, 6S ~
.07
1/
.06 I
[I - - Propeller E.6 blades

h so - - --
"
"
" ,3
C, • .·
.05 i- - - - - - - G08 .e ;0 p~pef/e r, 2 blodes
I

/
19' !;<'6So
45° I-
)" 7'
.03
./ 35° _)'''-5S Q

? 2S Q
14-{V P 5S Q

. 02 ---
'150 25° L.-- ~~ 45· , ,V
l---- ~
p
k-- 025° 3D· _ I ~o " l----
,0 I
15' %.-' - I~?f~ ~I -- 1- - C;6"1-- f- - -i4t8°
o
1.0 1.2 1.4 1.6 1.8 20 22 24 26 2. 8 3.0 3.2 3.4 3.6 3.8
11m
FIGURE 2 .- Relationship between 1/ ' P . and CpI27<J at V/ nD lor peak efficiency

The p1'Opelle1' effici n cy \Va mea ured in the tanford du ced wiLh a spiml cr. ccond, Lh e load di stributi on
l.e t reported in ref renee 6. Propeller E was t e t d for Lh e high bJade angle wa very poor for propellc'l"
a a Lhree-blade, a ix-blade, and two three-blad e E , whi ch gave a large in cl'ea e in lhe roLa Lion ul I.'ll(' rgy
C'ou ntet'l'o ta ting tandem propelier . of Lhe lip Leeum. The 'OW) Lerro La Ling Lan dem p ro-
The T7/nD for p eak efficiency Cor a given blad -angle peller con id e1'ably r edu ce Lhe ro taLion al-energy 10 os,
t Ling is the lowes t for propelicr E and the highe t for and it is een thaL l /nD is lightly highcr for peak
effi. iency at low blade-an gle eLLings and lhaL lh e
.28
,-
r-~ -~

t-
difl.'erenc increa e with blade angl . The H' ulL of
I-
- F-
~1
.24 -- I -i - figure 27 have b een r eplo tted in a differ en t form in
G, figm c, 2 . ote that Op/2-rrJ remain approximately
v con t~nt wi th power loading foJ' the Gold tein propeller
.20
~V
Propeller £ (calculated)
V l - I-
I-
i- D1\
I-
bu t rapidly increa c for p ropellcr E.

'~
"'I
<..i Ii. 16 ZI--i- - 1-
In the Iormlila
"t!~/2 17 V /' - I-
. - ---- - l-
.08 ,.,. L 1./ . Assumed
l- I--
1/ if 0 rcmained constan for all blade angle of a giy n
V
-- I- I- -'--
propelier, the valu e of p/2-rrJ from figHI" 2 co uld be
.04
--
V directly u ed in obtaining ET/P for th propellcr under
-
o .I .2 .3 .4 .5 .6 7 .8 .3 !.O
on ideration. Bu t, ince the distribu Lion of torqu e
J along the blade did no t remain op -imum for eiLh er pro-
peller or E , it wa n ce ary Lo e\' alualie 0 for the
Lc L eonditions.
the Gold Lein pr pelier. The order i th e ame for the A calcula tion of Lhe till'll Ii and Lh e Lorqu e disLribu-
efficiency-envelop e curve, which demon trate th e fact tion for th e te t ondi tion of prol eller E wa com-
Lhat any increa in propeller 10 e (decl'ea e in effi- pu tecl from the airfoil characteri tic. The Goldstein
cien y) in creases th e value of th power 10adinO' at correction were applied to th e 1'e ult and th e valu e
which peak efficiency fot' a given blade angle will oc Ul' weI' adju sted to give th e eorrect value of Op for peak
for a given propeller . Th ere are liwo obvious rca on effi cien cy. From th di tributions ETIP and 0 have
why the 10 ses of propeller E 'were th e greatest. First, be n valu ated. It mu t b e r ealized that thi meLh od
the propeller hub aJld Lhe bla Ie hank , which weI" only an approximation of th e till·u t and th e t orque
expo eel Lo the ail' tream on propeller E , gave exee ive di iribu tion and th at th e cxact distribu tions mu t be
to se in drag thali could h ave been con idcrably 1'e- lrnOvvn to ob tain Lhe exact r Lation al-energy los .

I
I
 -~--.--- --~

PROPELLER A ALY I FROM EXPERlME 1'AL DATA 15

A ample cW've of the torque dis tribution at peak FigUTe 32 gives th e theoreti cal curve of Ea/P and
propell er efficicncy from such calculaLion is given for the curve of Er/P for the three typ es of propeller
(3 = 65° for propeller E in figm e 29. A r evi ed torqu plotted against 1/ 3 Pc. The data for the curves for the
ell LribuLion Lhat giv s th e ame tota.! Lorque i included thr r('-hlacl c, tb e four-blad e, and the six-blad e Gold-
in Lhe sam e figure. In the r vi ed di tribuLion it i
as umed that Lhe propeller hub and Lhe inner Lwo- J 0 .--r
Lenths of Lbe blade are covered with a pinner. Th e : ~
Lmque cw·v would Lhus b e cut off at the 0.2R station. .5 l!
Th e compuLcd values of a' dflxQ for the two torque
I.
/
2 .0
dis Lribution of figure 29 are hown in figme 30. For ./
C
Lbe till' e-blade prop ell Cl' E at peak efficien cy for Y
{3 = 65°, OQ = 0.1305 and, for this condition, 11 p ercent
of t he total power was lost in rotational en ergy in the
.5
l.---' y- -- L

Revised distribution .... ·~

wake. Only 4.3 p ercent of Lb e power would be lost .0
in rotational en ergy for the a sumed di tribution th at
lI a equal toLal pow 1". Th e cW've shows the great .5
importance of unloading t h e llIDel" sections of the pro-
p eller at high blade angle . It al 0 hows that a 0
25 30 35 40 45 50 55 60 65
spinner will eliminate a larg p er cenLage of th e rota- /1 ,deg
tional- n ergy los cau cd by improper load di Ll'ibution. FIGURE 3J.- Vnrintion of C with blade augle for propeller K
!i'igur 31 g ive Lh e variaLiOl1 of 1,11 term wiLh
blad e-angle eLtin g comput d for pr pell er E. Th stein propellers wer e computed on Lh e a s umption thaL
rapid rise in C at hio-h blade angles i du e 1,0 Lhe pOOl' aL the ame V /nD th e power, and therefore th e p er-
Lorque distribution . Th e a1u e of aL (3 = 65° for entage of power, going into rotational en ergy is pro-
Lbi distribuLion is 2.94 but i only 1.15 for the as um ed portional to the munber of blade. At low valu es of
eli tribution, which i approximately tbe arne valu e as 3
1/ Pc the chief loss of efficiency is due to the axial
was obtained at Lh e 25° blade-angle setting. The velocity in the propeller wake, but this loss rapidly
torque di stribution, as computed for only three blade
decreases with an in crease in 1 ;'~Pc, becoming of th e
imgles, 25 °, 45°, an I 65°, buL Lhe 'urve a shown if) 3
order of 1 percent at values 1/ Pc corre ponding to
figure 31 was used jll obtaining 1,0 compute tbe
]'otaLional-en el'g 10 se for other bl ade angle from Lh e very high sp eed. On the other hand , Lhe loss in
effi ·ien y du e 1,0 the roLaLiona'! velociLy i alway mall
relation E,/P = 2;j· Th llJue of E r/P for propell er for il. propell er of opLimum de ign , 1 eing of the order
C " as obtained from thl'll t and L rqu e eli L,.ibuLioll o f 1 p er cent fol' th e 10\ solidity two-blade propell er .
curves of unpublish ed data. Th e till·u 1, and th torque Th e rapid ri se in rotaLionnl-cn ergy loss for propeller
distr ihu tion C1l1"ves 1'0], 1,hr Jol(l st('in pl'oprller wer r and E is due to Lbe poor load lis tribution on Lh
inner radii of t.hese propell ers wh en set at higb blil.de
.056 angles, the distribution bing m11 ch worse for prop eller
I-I_f--f-I· -I-f-l-I--+-I-·- I - I -
.048 I· f--I- - I - I - E than for propell er O.
-1-1-

.040 -1- - -- - - 1- A'I'PT.l CAT10 OF A ALYSI '1'0 co NTERROTATI G f>noP~~ LLERS

- - . - - f - - I - -- _ 1 _ - - 1-
,, -~~ - .~ I-
The fil.ct Lhl1L Lhe 1'oLil.tional-energy 10 s is gr ea Lly
.,,~032 ~. I \ !:!"ope!/~ £ to/cuk(~d)'--t-+--j -.. 1_ d ep endent on the torqu distribution of a propeller
,
\:1. \:1
024 f+- t- '\,
l-t·--j--j -1-1- and that the rotil.l:.ional-energy loss may be increased
tj '
~- - many Lim e by the use of a propeller with poor torque
.0 16 ',- -
"-
.

"'- di tribution make it pos ibl e to how a large increa c

,:.- -
in effi ciency by the use of counterrotating propell ers
.0 08 1:- -
I
I- . p-
wi th propell ers Lhat hav e pOOl' torqLle distribution .
--::::
For any given propeller it i e,ident that there hould
0'---:/ .c 3 .4 .5 .6 .7 .8 ..9 /0
be a balance between the axial-energ and th e
J.' lo ung 30.- Curvcs of a' dZ Q
against ",. CQ, 0.1305; fl. {lb0 .
l'otational- n ergy 10 e, wbich babnce is represented
by the point where tbe cUJ'ves of axial-en ergy and
computed fo], a blad -angle setting of 41. 0; C a com- rotational-en ergy 10 e ero in figuJ'e 32. At this point,
puted was 0.9. It i b elieved , therefore, that Op/27rJ tben, there can be no gain in propeller efficiency by
give a close approximation of Er/P for the Goldstein uing counterrotating propellers of double solidity be-
propell er 0 e1' the entire range, and thi valu e i used Cil.use, even if il:. j a sumed that all the 1'otational-
in th e compari ons of the following sections. nergy los may be recover ed, the axial- nergy loss
 -----~ ~ - - -~---- --~ --- - - -------,

16 REPORT O . 712-NATIONAL ADVISORY COMMITTEE FOR AERO A T I C

will be doubled. At any blade-angle etting below a the propeller olidity is increased. An e timn,te of
this point, the eili ciency of counterrotating propeller the gain, in propeller efficiency that can be realized by
j les than the efficiency of a single propeller; above the use of counterrotaliing propellers may be obtained
t his point ome gain m ay be expected. For example, from. figure 32.
uppose that two propellers, geometri cally similar to everal examples arc gi ven in table I to ill u trate
propeller C, are operating independently of each other the application of the resul ts. For the fir t example,
3-
at a valu e of 1/ Pc of 2.51 and uppo e that the axial- it is a umed that a 14-foot-diameter, three-blade pro-
energy los coincide with the theoretical CLU've of peller ab orbs 1500 horsepower fl.t a peed of 310 mile
Ea/P (fig. 32) . Then, l.5 percent of the PO\ er of each per hour. In the econd example, it is a umed th at
propcUcr goes into axial-energy 10 and l.5 percent an ll-foo t-diametel', three-blade propeller ab orbs J 500
goe in to rotational,energy 10 . In oth r words, 3 horsepower at a peed of 450 mile p el' houl'. In ea('h
percell t of the total power of both propeUel's is lost in example, the power 10 e of two propeller moullte(l
Hxial-energy androtational-enel'gy los e. N ow, if the in lepClldently of each other ar e compared with the
total power i put into cO Llntenotating propeller of los es of two propellel's, one rigb t-hand an d onc left-
th e ame diameter, Pc and therefore Ea/P will be hand m ounted in tandem, that absorb the arne total
doubled 0 that there will be no gain in efficiency even power. It i a um ed for the ca e of the prop ller
though all the 1'0 ational-energy 10 s i recovered. mounted inuependently of each other th at none of the
Above an op ratinO' condition corresponding to a value rotation is taken out of the slip tream by the wing 01'
of 1/ffc = 2.51, some O'rl in might be expected by u ing other airpla ne part, tha t i , all th rotational energy
('OUll tel'rotating propeller im iiar to propellc1' C; belo\\- i 10 t, :1nd it is furth er ass umed tllat the ('ou nterro-
3
Lhi value of 1/ P c, from co n iclel'atioJ1 s of propeller tating tandem propcllers recover n,ll t he l'otn,tionnl-
erftciency, it i more advantageolls to mou ll t the pro- energy 10 . Ea h eXlll11pJe include t he conlpari on
peller independ ntly of each other. of the power 10 se for eac h of the tl1Tee type of pro-
The curves for the thl'ee-blade, t he four-blade, and peller in fi gure 32. The losses are al 0 given lor oll e
the ix-blade Gold tein propelle)' how that cOllnter- ix -blade Gold tein propeller thn,t absorbs t he same
total power .
rotn ing propeller become more and more attractive

I ~
.11
\ ~
..Theoretical curve, £alP \?3:
.10 ~
-
-
\ I ~ I
\ / " I
.09
I
~
";:S
....0 IL
_08 1\ ~
\ ~
t '-Propeller t:. J blades

i "
~ L
.07
\\ 1/ ~ I
E,,/P ~
.DB
ErlP \\ / Propeller £,6 blades!
,
If I ,,
,05
'y / x
,,
, Propeller C ,J blades
(Dotted portion
.04
V l! ,
extrapolated)

.03 /
rI
"" "-
0.. /
j
,,
,
6 blodes '
,
,

J/ rx .- x/
,
,,
,
)/
f.C -
"
~
.02
,,/ -' '-,? I'-- /"

.01
he- - x_~

0
---
0 ,- -0- --
.............

~
+ - r-
'-
"-
-.......
r-
~ 4 blades'"
":::: ;-...; -- f--
-~ r-
-,-
i'-- L:-=-: ~
,,'
"

- , c--<>-
.] blades*

ztlates~
o!.O 1.2 1.4 1.6 1.8 2.0 2.2 2.4 . 2.6 2.8 3.0 3.2 3.4 36 3.8 4.0
!Ins;
FIGURE 32.-RelaLionship between l/":/V, and axial and rotational energy losses. ~Qq.1dstejo propellers.

;'
 PROPELLER ANALYSIS FROM EXPERIMENTAL DATA 17
TABLE I.- APPLICATION OF RE LT

Gain in efficiency with

Pow C'r inpu t co uIl tcrro ta ting pro-
pcliers
N umiJcr Dia ml' ler Velocity 1 Eu h',. E.+ R,
Propeller
or iJla des (rt) ( mph )
Of l'neh
propeller
(h p)
I ' r o ts l
(hp)
p,
VI', P l' - p-

Over 2
t hree- blade
I Over I
s ix-blade

E xa mple I
--
G o lds le in 3 1<1 310 1500 3000 0.0482 2.75 0. 0117 O. Oil S 0. 02;15 -- --
O o lcls tpin G 14 ~ IO 3000 3000 . 09G-l 2. 18 .0225 . 0235 . O,j(i(j
O oldsl r in a G 14 310 3000 . 096·\ 2. \8 . 0225 0 . 0225 o.oiJio O. () 235
(' 3 14 :l10 1:500 3000 . 0482 2. 75 .0117 . 0215 .Oa32 --- ----- -
( ' II
G 14 3 10 ...
-- 1500 3000 .0964 2.1 8 .0225 0 . 0225 . 0107 ---
I,: ;j 1'1 ;HO 3000 .0482 2. 75 . O1l7 . 114(1 . 1257 -- -
1':11 () 1'1 ;11(1 ;1000 . 09(j~ 2. 18 .0225 0 ..0225 . 1032 ---- -
-- -
E xa mple 2 I
Go lds tein .. _____________ _ 3 II 3000 0. 0255 3. 40 0. 006'l 0. 01 70 O. 023 ~ ___________ _________ __
Goldstein _______________ __ 2. 70
: ~~ ~ ----o:olli-- ----0:0340-
6 II 3000 . 0510 . Ol23 . 0340
Golds tein "oo_ __ __ ____ __
C ___________ __ __________ _ 6 11 3000 . 0510 2. 70 . 01 23 o
3 . 0255
: ~~~~ - ---:0493-- ::::::::::: -
C " ______________________ __ 11 3000 3.40 . 0064 . 0552
6 11 3000 .0510 2.70 .0] 23 o
" Hight-h nnd a nd left t hr c- ha nd blade ta nclem prope llers.

Th (' tahle how t h at, fol' the flight roudition of [n lh(, prac-Licil l 11ppli eH Lion of l!Je p rob lem , l b e ('01'('-
ex I.l, 11 I pJ e 1, ClIO power losse of two tlu'ee-b la,de propellers go ing di sel! ' ion stri ctly a pp1i(" onl y Lo (J1I hel' (1 1'0-
h avi rlO' ideal load eli tl'ib utio l1 s and operating ide by pl'ller . III the eas ' of tractor propellers, Lh e win g
ide ar e approximately eq Llal to the power 10 se of and t it Lail s urIa e' tene! La take Lh e roLation o ut. or
two tlu-ee-blac1e counterrotatin g tandem propellers the lip ' LI' am a nd t hu s Lo recov l'l' a con-id er able por-
whieh ab orb th e ame total power and r ecover all the Lion of Lhe rotational energy Lh at j onsiclered 11 1'C as
rotational-energy 10 se ; whereas, the power 10 es for 10 t. 'fhi re Lil t m eaw that counterrotaLing 1'1'0-
one six-blade similar propeller are 2 .35 percent O'r eater pellen; ill tractor po ition will not b ecom e attractivc
tha.n for the couutenotating propellers. The example from n . lJol'ation of ae rodynarni effi ciency exce pL
further shows that a gain of 1.07 percent can be reali:t;ed at E\ven higher speeds than the 'urves of figure 32
by u ing the cOLiuterrotating propell rs instead of two indicate. The fOl'eO'oing analysis how tlHtt, [01' a
propellers with the sam e load di tribution as propeller propeller of low solidity \ ith optimum di tributioD of
o and that, by th e use of the co unterrota,tlng propellers thl'Ll t and torqu , l ittle i. to be gflj ))ccl by the use of
instead of two prop ellers h aving the same 10 e a, couutel'l'ot at.ing propeller eycn at high peecl . .Fo)'
pl'opellel' E , a gain of ] 0. 32 percent efficiency can be propellers of poor di tl'ibuLion, e p citl lly propell er
experimentally sho\ n . Altbough thi large gain in having a hi gh loading ov.:/· Liw .ulncr sec tion s uch as
efficiency is real, it re ults from the initially poor torque propeller E, Lhe 1'0 taLion al-cne!'O'y losses mcl' a C 0
di tribution of propeller E when et at high blade rapidly at very 11iO'h s peeds th at a la)'o'o increase in
angle. Data for the ix-blade propeller E are not cfliciency may be shown by u ing cOlintclTo tating P1'O-
included in the table, but fig ure 32 how that the peller .
rotational-enel'gy 10 es for this condition of flight CO CL DI TG REMARK
amount to 20.5 percent.
For t h e high er p eed range cover ed in the flight co n- l. A knowledge of th e d istribu t ion of Llll'Ll t and
ditions of example 2, th e gain in efficiency by using torque alonO' th e prop 11el' blade p ermit the analysis of
co unterrotating tandem propeller in tead of two pro- propeller p erformance. The performance of th e Le t
peller havi.ng iclealloael eli tl' ibution is of the order of propeller h as been analyzed , and a m eth od of applying
1 percent, but the gain i 3.4.0 percent for one six- the analysis to other data for high C'l' blade-angle ettin gs
blade propeller. A gain in em iency of 4.93 percent is h as b een pre en L d.
r ealized by u ing co unterrotatinO' propeller in tead of 2. The 10 s in fficion y due to th e ro tational velo ity
11 ing two propeller simila.l' to propell er O. B ecan e is alway mall for a propeller of optimum d sign, b eing
of th e poor load eli tribution of propeller E, no estimate on ly of th e ordor of 1 p ercent for a low-solidi Ly propelle]'.
cn.n b m ade of t be: rotation al-e1l orgy 10 'se for Lbe The los of efficien y from thi oure may b ecome quite
fli g ht condition of exc\,mpl c 2. But t.h e t rend in the large, however , at high blade-angle Ltings for a propel-
curvo how that the los cs are Lremendou and th ere- ler with improper load eli tlibution.
fore, if .b s lmilur propeller weI' Lo be II eel und er Lh es , 3. Oounterrotating propeller ar c attracLive :from
fli ght condi Lion , , it wou ld he ne essa I'y Lo li se o un te['- consiclel'aLi n8 of aerodyn amic effi ciency only when
l'o tatlng propellers. prop 11 ers of high solidity ar e u ed . L f\,)'O'e gain s in

_____ J
18 REPORT O . 712- ATIONAL ADVISORY COMMITTEE FOR AERO AU']' I CS

propeller efficiency with counterrotating propellers may L A TGLEY M EM ORIAL A ER ONAUTI CA L L ABOHAT OHY,
be expected only if propeller of poor torque di tribution .r ATIO AL ADVISORY COMMI'l'TEE F OR A ERONA TI CS,
are used. L ANGLEY FIELD, V A., J uly 19, 1940.
4. If rugh- olidity propeller are selected becau e of
R E FE RE CES
limitation on propeller diameter, it may b e u dill to
r esort to counterrotating prop ellers to eliminate the I. Claucrt, H .: Airplane Propellc rs. Vol. IV, div. I, of Acro-
effect of the engine torque on the flying characteristics dynamic Theory, W. }I'. Durand, cd., Julius Springer (Ber-
lin), 1935, pp. 169-360.
of the airplane. Only a mall direct gain in propeller 2. tickle, George W.: Mea urement of the Differential and
efficiency i normally to be expected. T otal T hr ust and T or que of Six FuU- cale Adju table-
5. The effects of body shape on the thrust and thc Pitch Propellers. R p . No. 421, ACA, 1932.
Lorque distributions of th e propeller are shown. 3. Weick, Fred E., and W ood, D onald H .: The Twenty-Foot
6. Th e average angle of twist in the prop ller slip- Propeller R esearch Tunnel of the I ational Advi ory Com-
mittee for Aeronautics. R ep. J o. 300, N ACA, 1928.
stream is shown to be a unique function of th e torque 4. Lock, C. r . H., and Bateman, H .: Wind Tu nnel T ests of
coefficient Qc and chart are given to help e timate th e High Pitch Airscrew. Part II. Variation of Blade Width
angle. and Blade ection. R. & M. o. 1729, British A. R. C.,
7. The increa e in total prcs ure along the radius 1936.
behind the propeller i given as a function of the power 5 .• tickle, George W ., C ri gler, J ohn L ., and a iman, Irven:
E ffect of Body ose Shape on the Propulsive Efficiency
coefficient I /;;Pc' It is of u e in e timating th available of a Propeller. R ep. J o. 725, NACA, 1941.
pressure that can b e obtained for air intake behind the 6. Lesley, E. P.: Tandem Air Propellers-II. T . . (to be pub-
propeller. lished) , ACA , 1941.

U s. GOVERNM£.tlT PRINTlUG OFFI CE : 1941

 '\..
"- ....

z
Positive directions of axes and angles (forces and moments) are shown by arrows

Axis
Force
Moment about axis
I
. Angle Velocities

(parallel Linear
Sym- to axis) Positive Designa- Sym- (compo- Angu lar
Designation symbol Designation Sym-
bol bol direction tion bol nent along
9.xis)

LougitudiuaI-- _ --I
LateraL ___ ______
X
y
X
y
Rolling _____
Pitching ____
L
M
y - .....Z
Z- -->X
RolL ____
Pitch ____
cp
0
u p
q
NormaL ___ ______ Z Z yawing ____ N X----.Y yaw _____ tit "
w r

Absolute coefficients of moment Angle of set of control surface (relative to neutral

L M N position), o. (Indicate surface by proper subscript.)
Gz= qbS Gm = qcS G" = qbS
(rolling) (pitching) (yawing)
4. PROPELLER SYMBOLS

D Diameter
Geometric pitch
p Power, absolute coefficient Cp =
pn
~nr.
IF
P
p/D Pitch ratio SfV'>
Speed-power coefficient= -y ~n2
V' Inflow velocity
V. Slipstream velocity 7) Efficiency
T Thrust, absolute coefficient Gr =
pn
:D4 n Revolutions per second, rps
Effective helix an gle=ta n- {2!n )
Q Torque, absolute coefficient Ga=
pn
~D5
5. NUMERICAL RELATIONS
1 hp=76.04 kg-m/s=550 ft-lb/~c 1 Ib=0.4536 kg
1 metric llOrsepower=O.9863 hp 1 kg=2.2046 lb
1 mph=0.4470 mps 1 mi=1,609 .35 m=5,280 ft
1 mps=2.23G9 mph 1 m=3.2808 ft