Charts for determining propeller efficiency

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Title:
Charts for determining propeller efficiency
Alternate Title:
NACA wartime reports
Physical Description:
19, 26 p. : ill. ; 28 cm.
Language:
English
Creator:
Crigler, John L
Talkin, Herbert W
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:
Propellers, Aerial   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: A short method of estimating propeller efficiency for a given operating condition is described. The efficiency is determined for any design condition by evaluating separately from charts the induced losses and the profile-drag losses. The estimated efficiency is compared with experimental results for a wide range of operating conditions and found to be in agreement near peak efficiency. The present analysis covers single-rotating propellers of two, three, four, six, and eight blades and includes charts showing the rotational-energy loss for the given operating condition in order to assist in estimating the gain in efficiency for dual-rotating propellers. The change in efficiency to be expected from body interference is discussed. Two examples illustrating the use of the method are given in an appendix.
Bibliography:
Includes bibliographic references (p. 19).
Statement of Responsibility:
by John L. Crigler and Herbert W. Talkin.
General Note:
"Report no. L-144."
General Note:
"Originally issued September 1944 as Advance Confidential Report L4I29."
General Note:
"Report date September 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 - 003614447
oclc - 71258783
System ID:
AA00009506:00001


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Full Text


ACE No. L429


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS






WARTIME REPORT
ORIGINALLY ISSUED
September 1944 as
Advance ConfidentialdReport L4129

CHARTS FOER DEiRMIIN PROPELLER EFFICIENC
By John L. Crigler and Herbert W. Talking

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


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.


SL 14
.


DOCUMENTS DEPARTMENT


L:::vi;;;i::.~ j : .;:;.i i:





































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http://www.archive.org/details/chartsfordetermi001ang






3 GA IqeT7:

[ACA ACR I~o. L4I29
IIATIOIIAL ADVISORY COMf ITTE- FOR AERCIJUTICS


ADVAIICE C',:IIFIDEI:TIAL REPORT


CI:ARTS FOR DETRFLTIIIIillG PROPELLER EFFICIE'CY

E-' John L. Crigc'lr andi Herbert V. Talking


SUMiRY


A short meth.ti:.' of esti:nating propeller efficiency
for a given operating condition is described. The
efficiency Is deterit.ined" fjr any Cesign cniditio-i, by
evaluating separately froi': charges the ind'.uced losses
and the proflle-dra, losses. The estimated efficiency
is compared with excerimental results for a wide ranje
of operating conditionsa.nd found to ,be in agreement
near neak efficiency.

The present aniialyzi covers sinr-lt-r:.tatin- pro-
pellers of two, three four, six, and eight blade. and
includes charts showing the rot.aziccnal-enerWy' loss for
the given operating cronditiorn in order to assist in esti-
mating the gain in efficiency for cli..ai-rotating propel-
lers. The change in efficiency to be expected fro'.i] body
interference is discussed. T'.vo ex2nmplee illustratln.o
the use of the method are fiven in an appendix.


I'T PRODUCT IC:


In reference 1, ai-alytically determined propeller
performance is compared with experimental results for
propellers having four, sFx, and ei'ht blades of con-
ventional design. The calculated results .s-e in
agreement with the experimental results over the com-
plete range of blade angle investigated (5h to 65' at
0.75 radius). The calculations were made by a strip-
theory analysis by which the thrust and torque contri-
butions for several elements alon.. the radius are
graphically integrated for each operating condition.
The time required to analyze a single operating condi-
tion by the strip-theory method is negligible compared
with the time required to obtain experimental data for
the same condition. The time required to analyze the









NACA ACR No. L4I29


complete range of operation is considerable, however,
and a shorter method is desirable.

A method of estimating. the propeller performance
supported by the results of reference 1 is presented
herein. By this method, a large reduction in the time
and effort required for propeller analysis is effected
as compared with the strip-theory method. The results
obtained are in agreement with those from experiment.
The basic propeller parameters are interrelated in
charts that aid in the selection of a propeller for a
given design condition. The charts are useful in
analyzing data for any propeller and aid in the deter-
mination of excessive losses.

The induced power losses for a conventional round-
shank propeller are compared with the losses for the
optimum load distribution. The induced losses are
divided into axial- and rotational-energy losses so
that the maximum gains possible by the use of dual-
rotating propellers instead of optiinum single-rotating
propellers can be estimated. The effect of profile
drag is treated separately. Because drag losses are
evaluated secirately, increased losses due to compres-
sibility can be estimated directly when airfoil data
at high Lir-h numbers become available.

Detailed applications of the method are illustrated
by examples in the appendix.





a axial-velocity interference factor

a' rotational-velocity interference factor

B number of propeller blades

b chord of propeller blade element

CD section drag coefficient (Do/qS)

CL section lift coefficient (L/qS)

Cp power coefficient (p/pn3D5)


C CI7T ID T:T'PIAL


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HACA ACE Io. L4I29


CQ torque coefficient (Q/pn2D5)

CT thrust coefficient (T/pn2,:4)

D propeller dia;-meter

Do drag of propeller blade element for infinite
aspect ratio

Ea axial energy per unit time in rli trearn

Ep rotational energy per uni.t time in slipstream
F Coldstein corrections factor for finite number
of blades

J advance-dia'meter ratio (V/nD)

L lift of blade section

n propeller rotational speed, revolutions per
second

P input power to propeller

Pc power disk-loading coefficient (P/qSV)

q torque of propeller

q dynarric pressure of air scream.

R tip radius

r radius to any blade element

S disk area of propeller

T thrust of propeller

uo axial velocity in plane of propeller (propeller
removed)

V axial velocity of propeller

x radial location of blade element (r/R)

dCQ/dJ element torque coefficient dQndx
Cpn'D
COIFIDEUTTIAL


C 01 IF IDEI T IAL









4 CONFIDENTIAL EACA ACR No. L4I29


dCT/-x element thrust coefficient ( nD4

a0 angle of attack of blade element for infinite
aspect ratio

Q propeller blade angle at 0.75 radius

7 propeller or element efficiency

p mass density of air
a propeller element solidity (3b/2ir)

aCL propeller elencnt load coefficient

an-le of resultant- velocity to plane of
rotation ( a t

Subscripts:

0.7R at 0.7 radius

D due to drag

i for zero drag


FORMULAS

The derivation of the formulas for element thrust
and torque calculations is even in reference 2, from
which the element thrust coefficient is


S_ B2 b ( + 2 ( C cos CD sin (1)
dx R sin2


and the element torque coefficient is



S )2 + C( cos (2)
_B J-, b( (I1+a-' (I + snacos (2)
dx 16- R s i112 L


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YACA ACR No. L4I29 COI FIDENTIAL 5


The expression for the axial-velocity interference
factor a is


a OCL cot
1 + a 4F sin


The values .of the correction factor F as used
in the present report are given in figure 1. The values
of F for two-, three-, and four-blade propeller. are
taken from reference 3. Tihe val-3-.es of F for Six- and
eight-blade propeller- v.ere extrapolated from these data
by the method developed in reference 3.

For calcu lations sho.winng, the effect of drap on
propeller performance, the follor'.ig formulas wJere
obtained from equations (1) to (3) for CL = 0:




dx -CD 0 J Jv + (Cx)



S D TT- T (4)
4 sin ()




dCQ 2x3 1
= ---'J + (x)


O TZXO J
= CD in (5)



Equations (4) and (5) are derived for zero loading
without inflow and consequently are not exact for a
finite loading. The formulas show, however, that the
error in estimating the loss due to drag is negligible
for light loadings which occur near peak propeller
efficiency.
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NACA ACR No. L4T29


i"e formulas for the rotational-energy and axial-
energy losses from reference 4 are


.0
E5 a-_ T dx
P CQ F_ dx
C)


Ea J
P Cp


1a0 dCTr
f a-- djx
O dx
JO


(6)




(7)


dCQ 2
a =-
dx 2Jx3(1 + a)F



dCmr/dx
-1 + 1 + 4 -
\l TT7XJ2F


These formulas fr::m reference 4 have been modified herein
by inclusion of the correction factor F.




Charts for Induced Losses


The basic propeller performance charts are presented
in fi..:re 2 for two-, tbree-, four-, six-, and eight-
blade propellers. T'..: cr.inates represent values of the
efficiency for propellers operating without drag and the

abscissas represent values of D--. Against
V ci
these scales, curves of constant element load coefficient


CC1-WIDE;.TIAL


where


and


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NACA ACR iro. L4I29


("jOC R are crossed ty long-dash lines of cons-tant
V/nD and short-dash lines of constant power coeffi-
cient CpI. The O.p,-curves shlow the variation or
(oCL).* with V/nD for constant Cpi and are included
for convenience of computation for constant-speed pro-
pellers. The curves were attained from calculated *:,ptLilum
torque and thrust distributions rrraEphically integrated
from the tip of the blade to x = 0.2. Thee performance
charts are the same as thpep-ropeller selection charts in
reference 5 E.cert that the dra. losses are not included.

In the present report, the value of the solidity at
0.7R, G0. R, is taken as a conv-nient r,measure of the
propeller solidity. The value of (O' T is corre-
spondingly taken as a measure of the overvr absorbed.
The activity factor has freqr. ntntl7: been taken a. an
index of the power-absorbing qualities of a propeller.
For the Hamilton Standard 3155-6 propeller reported in
reference 6 (for which comparisons are made in the present
paper), the activity factor is 9'.' (per blade) and o .R
is C.034EB; that is, for propeller-s of this design, the

activity factor is 2GnO--- This number is approxi-
mately the same for all conventional propellers. If the
exact relationship is desired, however, the activity
factor A.F. may be obtained from


A" x= 1.0
1000,C0 0r0 I b -z
A.F. = 16 -/ DX ,x
yO .2


Breakdown of Propeller Power Losses

In the calculation of propeller efficiency, it has
been customary to compute the thrust and torque at a
given value of V/nD for a fixed blade-angle setting.
The analytical determination of proreller performance
may be considerably simplified in many cases, however,
by evaluating the several sources of power loss rather
than by attempting the direct computation of thrust and
torque. In the present paper, the efficiency is


COrF IDE7:TIAL


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NACA ACR No. L4I29


determined by deducting the sum of the power losses from
unity. The total power losses are divided into induced
losses and profile-drag losses; the induced losses are
subdivided into axial- and rotational-ener;,- losses for
use in evaluating the efficiency of dual-rotating pro-
pellers. The blade drag has no appreciable effect on
the induced losses for normal propellers but must be
considered in obtaining the total power losses. This
method of analysis has the advantage that compressibility
corrections can be included when the airfoil section
characteristics at the operating I7ach number become known.

ERctal-'n Il- .rn I1 -Ir .- The losses of efficiency
due to rtI 't.i -ial v 'L.,ci:- are shcwn in figure 3 for
three-, four-, six-, and eight-blade propellers. The
rotational-energy loss for a given operating condition
(constant Pc and V/nD) is seen to increase as the
number of blades decreases. This increase in power
loss arises from the increase in the tip loss as the
number of blades decreases.

Calculations for a 1irc number of load distributions
show that overloadi:6. the inner radii is of secondary
significance at values of operatinrg V/nD < 2.5. As an
illustrative case, the calculated rotational energy for
the four-blade Hamilton Standard 3155-6 propeller of
reference 6, which has round blade she'nk, is compared in
figure 4 with that for a four-blade propeller computed
from the charts of figure 3. The rotational energy
for the Hamilton Standard 3155-6 propeller was com-
puted for several blade anr-es up to 655 at 0.75R and
the value of V/nD for peak pro. eller efficiency. The
values of Er/P for the optimum propeller were taken
from figure 3(b) at the same values of V/nD and Pc
as for the Hamilton Standard 3155-6 propeller. Figure 4
shows that no appreciable difference in rotational energy
exists between the two load distributions at V/nD < 2.5
and that the losses differ by only 1.5 percent of the
total power at V/nD = 4.5, which corresponds to a
blade-angle setting of 650 at 0.75R. 'The rotational-
energy losses given in fli'u;-e 3 are therefore close
approximations to the expected losses for conventional
round-shank propellers over the usual present-da-!
operating'ran-e. Similar results are found even when
airfoil sections are used over the inner radio v':hern
V/nD < 2.5. It cannot be e-.phasi.ed too strongly,
however, that if cuffs are used to cover the round


C 3G TIDSETIAL


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EACA ACR i!o. L4129


shanks, the loss may become serious at high values of
V/nD unless. the cuffs are set at an angle .f attack
between 0 and the opcirr.u:n to si''e low loading over
these sections. This dependence of the rotational
energy in the slipstream on the l ading c-:ver the inner
radii is apparent from equation (.6), which shows how
the effect of overloadir. the inner radii increases in
importance as the operating V/nD increases.

Axial-energv los-es.- The axial-energy los. for
any operating condition may be obtained from the rela-
tionship


-=1 -7,-----
p "~ p
P P


where the induced efficiency ri is obtained from
figure 2 and Erp/F is obtained from figure 3. The
axial-energy loss shows but little variation among
propellers in present-day usage operating near peak
efficiency. As an illustration, the axial-energy
losses for a four-blade propeller obtained from the
charts of figures Z and 3 are compare-i in figure 5
with the calculated values for the four-blade Hamilton
Standard 5155-6 propeller operating at peak propeller
efficiency and for the ideal propeller (actuator disk).
The values of Pc at V/nD for peak efficiency for
the Hamilton Standard 3155-6 propeller were taken fror.
reference 6. The axial-energy losses for the optimum
propeller load distribution and for the ideal propeller
were determined at the sare values .f V/nD and Pc as
for the Hamilton Standard 3155-6 propeller. The axial-
energy losses for the optirmumn distribution of loading
(figs. 2 and 3) and for the loading obtained with the
Hamilton Standard 3155-6 propeller are nearly equal and
are about 1 percent higher than for the ideal propeller
over the range investigated. A part of this increase
in axial-energy loss is due to the finite number of
blades and therefore bec.-mes less as the number of
blades increases. A small part of the difference occurs
because the load distribution differs from that of an
actuator disk. The axial-energy loss for optimum distri-
bution, obtained with the aid of figures 2 and 3, is
therefore sufficiently accurate for application to
conventional propellers.
CONFIDENTIAL


COITFIDE ITIAL









NACA ACR -o. L4I29


Blade-drag losses.- The effect of blade drag on the
characteristic .f li htly loaded propellers (near p-a!-:
efficiency) can be estimated from equations (4) and (5).
These equations were obtained by eliminating the axial
inflow and putting CL = 0 in equations (1) and (2).
The equations are not exact but, near peak efficiency
for modern high-speed propellers, the omission of the
inflow factor a causes a negligible change in the
calculated propeller efficiency. Equations (4) and (5)
show that, for a given radius and value of V/nD, the
element thrust and tor'.ie coefficients dL- to crag are
directly proportional to the drag coefficient.

The profile-drag coefficients for -infinite aspect
ratio for several sections along the Hamilton Standard
3155-6 blade are shown a-int lift coefficient in
figure 6. These data were taken frcm reference 7. The
profile-drag coefficients cb1-. with lift coefficient
but, since the change is very small for a wide ranre of
lift coefficient, average values were used in the calcu-
lations for operation near peak efficiency. The profile-
drag coefficient increases rapidl:- near the stalling
angle of the section and the average values are accord-
ingly not representative for such conditions.

Figures 7 and 8 show the effect of drac on the
thrust and torque coefficients, re-:ectively, for
several values of V/nD. The values of the section
profile-drag coefficient shov-n in figures 7 and 8 were
used in the calculations for the Hamilton Standard 3155-6
propeller. Curves of the differential-thrust and
differential-torque corrections due to drag, for the
drag coefficients shown, are plotted acir.st the racial
location x,and the inte-rated corrections are also
included in figures 7 and S. "Thse integrated values
apply for one blade and the correction is directly pro-
portional to the number of blades and to the blade chord.
The element thrust coefficient and the element torque
coefficient due to drag at a :iven value of V/nD are
directly proportional to CD, and a change in CD at
any radius is represented by a propo-rtional change in
the ordinate of the differential-thrust and different-Ial-
torque curves. For this reason, the method of analysis
is adaptable to any blade section for which the airfoil
characteristics are available. The s-''r:stion is also
made that the loss in efficiency due to ir&- at high
speeds at which the blade section drag becomes large


C Ci DD-T :A'T


CO! FIDEI-TIAL










HACA ACR No. L4129


can -h. predicted when the drag coefficient- at hi.ph
!'ach ni.u-.:bers become available TL.e calcZ ilat ion-- -:.-w
that the drag correction to the thrust is chiefly due
to the high draz of the inner -secti.,not (sef fiU. 7)
and that a change in the dria com efficient of th.-
principal workinF part of the blade du.e to I. change
in the lift coefficient near peak efficiency (see
fig. 6) results in a negligible clhan.e in the correc-
tion to the thrust coefficient.

The effect of dra, on the- eff cicncr envelope and
on the integrated power-c coefficielrt for o:oerration at
peak efficiency, in LunIobstr'._.cted air- flowv, i' hl'wr-I in
figure 9. The values of' rl an'.L the c rr-s.p:-ndlr o,.
without dra vere ta.:en frJ' fi'ure C2 or f.'oir-olad
propellers at oCL). = 07.0'" Fr p t i d
bution of loadinT alon- the radius for tn' e --;ol of
the fourl-blaLe 1Hmilton S3tan ar. J.1.,5-C r r_-. l: i -, tnis
value of (C'-).,, corresponds to C: ,- .1.
The solid lines ir. figure 9 ive tie '- :. .: e''iency
and the correspondir. power coef icier--': -_ .in-t V/-.D
for ortimrTum Clistributicrn for a four-bisafe friction:less
propeller at (o L) .- = 0.07. The sh.rt-'tash line
show T] and Cp as modified by blade C.ra7 integrated
from O.2CR to the tip. The curve for rj for blade
drag integrated f rom 0.45R to the rip is .bh.:'n by the
long-dash line. The Cp-curve is inot shown for the
latter case but falls between the other- Cp-curves.
The introdu.?ri on of tlade drag of :he magnitude s~-own
in figures 7 and 8 has little effect on the total p.:'r
absorbed during .-peration near pea; efficiency, regard-
less of V/nD; the effect of the drag. on the integrated
thrust and hence on the efficiency, however, is i.r.:'rt-ant
and increases rapidly with V/nD. For e:xa.ple, the loss
in efficien-cy for the entire blade varies from 5.5 rer-
V V
lent at -- 1.0 to 2,.C percent at = C.O. n the
nD r-"
other hand, the loss in efficiency due to the drag of
the principal v'orking s-ections that is, from 0.45R co
the tip Is relatively unim:portant. The loss in effi-
ciency for this portion of the blade (see long-dash
line,, fig. 9) is thus seen to vary from 2.5 percent at
V 't
1.0 to 4.0 Percent at 6.0 these losses
nD "nD


CO:NFIDEUTIAL


CO F IDEIITIAL









NACA ACR No. L4I29


represent the upper limits for increases in efficiency
that may be achieved by reducing the profile drag for
the working sections of the blade operating at
CL = 0.51 with optimum load distribution. The thick
inner sections of conventional round-shank propellers,
which are used for structural reasons, are therefore
the chief source of blade-drag loss, especially at
high values of V/nD. This.loss in efficiency due to
drag may be greatly reduced by covering the inner
portion of the shank with a spinner and the outer
portion with cuffs, if the cuff angle is properly set.
It is emphasized that cuffs may result in a loss in
efficiency instead of a gain unless set at the proper
angle of attack. Overloading of the inner radii results
in a large increase in the power in rotational energy
for single-rotating propellers, and the blade-drag loss
also becomes large for blade sections operating near
the stall.

The losses due to the thick irner sections are also
reduced when the propeller is operating in front of a
blunt body, such as an NACA cowling, because.of the low
velocity over these sections. Calculations of thrust
and torque coefficients have therefore been made at the
same values of V/nD and for the same distribution of
the element drag coefficients as in figures 7 and 8 but
with the inner portion of the blade assumed to be
operating in a region of low-velocity air as in front
of a conventional air-cooled installation. Ths velocity
distribution in the plane of the propeller, as used in
these calculations, is given in figure 10, for which the
data are taken from reference 4. The region of low-
velocity air depends on the ratio of the nacelle diameter
to the propeller diameter, the conductance of the engine,
and the distance of the propeller in front of the cowlirg.
The ratio of the nacelle diameter to the propeller dia!.eter
in the setup in reference 4 was 0.417. The effect of
operation in front of an open-nose cowling (velocity dis-
tribution of fig. 10) is shown in figures 11 and 12 for
a four-blade propeller. Thrust and power coefficiernt
due to the distribution of drag in figures 7 and 8 are
shown for free-stream operation by short-dash lines in
figure 11; the long-dash lines represent operation in
front of the 1TACA cowling. The value of the power
coefficient due to drag (ACp)D is seen to vary but
little with V/nD whereas (ACT)D rises rapidly.


COCF IDE TTIAL


CONFIDENTIAL










NACA ACR No. L4I29


Equations ( ) and (5) also show this effect. The effect
on the efficiency of operating a propeller in the velocity
distribution of figQure 10 is shown in figure 12 and com-
pared with the efficiency computed for operation in free
stream. The increase in propeller efficiency' resiulting
from the presence of the cowling varies from 1.0 percent
V V
at -= 1.0 to 9.0 percent at = .0. In the calcu-
nD nD
lations for the curves shown in figure 12, the only
variation considered is the draq of the blade shanks.
The low-velocity jjr causes an increase in lift over the
outer sections of the shankl and, accordingly, an increase
in the rotational-energy loss, which may result in a
somewhat smaller gain in propeller efficiency than indi-
cated by figure 12. Tn order to determine exactly the
magnitude of the charge in propeller efficiency, element
calculations for each velocity distribution are neces-
sary inasmuch as a change in velocity distribution pro-
duces an effective change in pitch distribution.


CO1MPARISCOU WI-T. EXP2:.Ii.TIEiT


The experimental efficiency envelopes for four-,
six-, and eight-blade Hamilton Standard 3155-6 propellers
are compared with the calculated results integrated to
0.20R in figure 13. The experimental result for the
four- and six-blade propellers were taken from refer-
ence 6 and the results for the eight-blade propeller
were taken from reference 8. The single-rotating
propellers were made up of two hubs mounted in tandem.
The spinner in the setup for all the ex 'erimrental data
covered the inner 0.1E9R of the front unit of one-half
the blades and the inner 0.232R of the rear blades.
The results are in agreement over the entire ranre
investigated for each set of blades. The calculated
efficiency is about 1 percent lower than the experi-
mental efficiency at low values of V/nD and is higher
than the experimental efficiency at very high values of
V/nD; the calculated curve crosses the experimental
curve at V/nD r 3.5. Part of the discrepancy is due
to the use of the short method.


CONFIDENTIAL


COLFIDDEITI .L









NACA ACR No. L4I29


CONCLUS IO S


A short method of estimating propeller efficiency
for a given operating condition has been developed by
a theoretical analysis. The efficiency is determined
by evaluating separately the induced losses and the
profile-drag losses. A comparison of the estimated
efficiencies with experimental results indicated the
following conclusions:

1. The performance for operation at values of the
advance-diameter ratio equal to or less than 2.5 may be
accurately predicted.

2. The approximate performance of conventional
round-shank propellers may be predicted to values of
the advance-diameter ratio much higher than 2.5.

3. The upper limit of possible performance for
other types of propeller (airfoil sections over the
inner radii or the use of cuffs over the round shanks)
is shown for values of the advance-diameter ratio up
to 6.0.

4. The cause -of excessive losses may be determined
for any propeller design.

5. The maximum .;';in in efficiency to be realized
with dual-rotating propellers over optimum single-
rotating propellers is evaluated for a wide range of
operating condition.



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


C;r'FTIDEI;TT.AL


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HACA ACE Ho. L4I29 C CIFIDEFITIAL '-

APPEUDIX
A P F IT E I(

APFLICATIOH OF T.-E !'EiTHCL

The problem of determining the prop-ell-cr efficiency
for a given design condition by the methods of the present
report iay be resolved into two parts: (1) determLinai.Tion
of the induced pouer losses and (2) determination of the
profile-dragi loscFs. The induced power losses for a given
design condition are available from figure 2 as 1 r,.
The induced losses obtained from ft.zurn e 2 at V/rnD < 2.
are very close aprroxi nations to rt.-he obtained with
conventional proc,: ie rs. This ranc-- of V/nD cover most
current hi-L-g-speed designs. The bl1ade drag is hai-?dled
separately and can therefore be u-ed fr hiph I'..ach numbers
and high drags if the correct airfoil section character-
istics are used for the corresponding 1.ich n.umbers. The
profile-draq losses are obtained from figure 11, which
shows the variation of the thrust and rower coefficients
due to dra_ for the values of the element drag coefficients
shown in figures 7 and S. These drag values are repre-
sentative for the Hamiltcn Stsndard 3155-6 propeller
operating near peak efficiency. The ordinates of the
curves in figures 7 and 5 are directly proportional to
the drag coefficients at each radius so that, if other
drag values are used, new curves .:ivinr the thrust and
power coefficients due to drag may be easily plotted.
Since the total power losses are divided into induced
power losses and profile-drag losses, the method aids
in determining excessive losses for any design condition.
Excessive losses may be due to the fact that the propeller
is either too heavily loaded or too lightly loaded, to a
poor load distribution along the blade, or to high blade
drag due to compressibility. The use of the perfor-mance
charts determines the lift coefficient at a representative
station and thus the loading.

Two examples are given to illustrate the use of the
charts in the determination of the propeller efficiency
for a given design condition.


Exam-le 1

In example 1, the propeller selected operates on a
liquid-cooled installation in the tractor position and
all the sections are assumed to operate at free-stream
velocity. Ho compressibility corrections are applied.
CCITFIDEIiTIAL









NACA ACR No. L4129


The following design conditions are assumed:


Power, hp .. .. .
Altitude, ft .
Velocity, miph .
Rotational speed, rps .
Propeller diameter, ft
Number of blades .
S- Bb
0.7R 21r .
Activity factor .. ..
V/nD . .
SP
pn3D5


are


. . 2000
S. . 25,000
S . 425
S . 23
. .. . 12
. Four
. .. .. 0.1380
. . 90
. . 2.26
S. . ... 0.342


The calculated values for operation in free air


(ACp)D (fig. 11) .
Cpi = p (ACp)D .



C iO.7R (flg. 2(c))
CLO.7R .
Tli (fig. 2(c)) .
Er/P (fig. 3(b)) ,

S= iCpi
CT = ......nD

(ACT)D (fig. 11) .
CT = CTi + (CT)D

CT V
1' p= T D .


. .. 0.006
. . 0.336

..... .. ... .. 3. 7
* .. . 0.07
. . 0.51
. . 0.931
. . 0.039

S. .. 0.1385

. . -'..01 3
. 0.1.232


0. 843


In order to determine whether the propeller selected
is loaded properly, the value of CLO.7R is first deter-
mined in the selection chart in figure 2. Since the
design conditions are given and l/Tci and V/nD have
been predetermined, the value of (CL)O.7R is read
directly from the chart. The value of CLO.7R required


COMF' I DE7 TIAL


CC IFIDE TRIAL


. 4









NACA ACR No. L4!29


is found to be 0.51 and indicates a satisfactory design
condition. This lift coefficient has been found to be
that absorbed near peal: propeller efficiency for the
Hamilton Standard 3155-6 propeller for operation at the
given V/nD. The power loss due to rotational velocity
Er/P, which is equal to 0.079, is the maximum increase
in efficiency to be expected from the use of dual-
rotating propellers of the sar..e cdia-reter and solidity.
The induced efficiency is 0.C3 but the introduction of
drag of the rragnitude of tIh-.t sho.-'n in figures 7 and S
reduces the over-all propeller efficiency to 0.848. The
use of 1/\/F with drag included, instead of 1//Pc,
results in negligible chsnces in r.i and (CL)TC .


Example 2

The only difference between example 2 and example 1
is that the propeller in example 2 is mounted in front
of an open-nose co-wling (air-cooled installation) with
the inner sections of the propeller in retarded air flow.


The design conditions,
example 1, are


which are


the same as in


Power, hp . .... .. 2000
Altitude, ft . . 25,000
Velocity, mph . . 425
Rotational speed, rps . 25
Propeller diameter, ft . 12
Number of blades . .. Pour

ctvity factor. ................. 1390
Activity factor . . 90
V/nD . . 2.26
P
Cp = --- .. . 0.342
nI- D"


The calculated values for operate
NACA cowling are


(ACp)D (fig. 11) . .
Cp = Cp (AC )D . .
1/ P4 T . ..... .


ion in front of


. 0.006
S. .336

3.67


CO 0NFIDENTIAL


CO1FIDEITTIAL









CCIFIDLEITIAL


CLO. R ....
OT) (fig. 2(c)) ...
C3 O/ . .

Er/P (fig. 3(b)) . .
'iiCpi
CTi V/nD . .
(ACT)- (fig. 11) . .

CT = CT (ACT)D ......


NACA ACR No. L4!29


S 0.07
S. 0.51
. 0.931
. 0.039

S. 0.1385
S. -0.0065


CT V
p D .
Cp nD


. 0.872


CO :IDET TRIAL










IIACk ACR INo. L4I'12


_FEFEfEI'ZC E-3


1. Cr'i eler, J:hn L.: T Ccmpari Os.-i o- f Calculated a-nd
:per-imental Propeller1 Characte ri t ic f:,r Four-,
Six-. End Z1ght-B3.lade Sinr:le-Rotat ing, Pro eller..
li-:.CA .A.CR lio. 4304, 1 -' 4.

2. Gla".rt, H.: Airplane P opeleers. V1o. IV of Aero-
d;.rnarrlc T!ihe-r; ,iiv. L., '. F'. Durand, ed.,
JulFius -prinrer ( erlic) I0?, pp. 189-.3.0.

3. Loc:, C. I:. H., a&.i Yefat.a r,, D.: Tatle- f- .r Usl in
-n Im proved .'et.hd o Airs .rew Str'ip Theor-y
Calculation. 3. t- .' c. 17'74, r .iti-h A.:?.C.,


4. Stic:le, e r-1e V.., and Cri-lt-r, JotLn L.: Pr:.pller
Anialy "l from L.:xperiertaenl Dta. .AC. ep.


,IT-. r, :
!r. 1l2, 1941.

e. Cril-r.. T J:hn L., ard TallJ:in, l r-- .* .: Frrecll r
l.: i :- tior f r..rr: Aer od;rnr: ic Con -ratio c.n C
[kR, Julr: 10iE.

6. Bier.iiRann, D .avi", c .-i H.-rtmf.n, EL .i,' P. YI:.: -.':J- -nrnel
Te t ?, F ';. I- !, l-T- :"do E in ,a-e- and C u l-
tetin;. Tractrc r Pro.peL- rT' .. ac.T Fc 2I' -,
i9 2.

7. Pincer-ton, F,.o h rt :., and 0 r :- t'b r I-i. r- : .-ai 'i'y-
n -.'C:1 Ch- acn -: i oi: f a T".r i. .. o : rf ?iio
Tc-t--l in t 'X.*:.*i..le-L. n.. i c-. ind ui.inn- I. ..ACA
f. I G6 ,

8. Biier.ar-n.n D-"'ii, d Grey, i. : ; 'in-i-T'.unr- : Tests
oaf ''.. t- it. .in ,-c rn.. D-..a.1 -R: t -' rPrje liD ers
in t.- e Tr-act.: r -Z.osit ron I aCt. AR-, -,i0 1941.


r"017!IDETIAL


COI)n rFTLETTI AL









NACA ACR No. L4I29


CONFIDENTIAL


(a) For rwo-b/ade prope//ers. (Dt~a Orom reference J.)
Fiyure 1.- Curves od Fayama/nt .


Fig. la



i. 4





NACA ACR rio. L412'J


CO I TEE IR A uTO
------------ ---I




















I V7wsre / -am----
\ \ _\ __ _,_ -
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\ \ \ __ ^__ ___ ^a __ -
\ -s^_"'-; z rz=


CONFIDENTIAL


Fig. Ib







NACA ACR No. L4I29


1 3

.S/ I
---------f













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\1 J-9 70 90

Fly&n[re roo nn jKaunc
i''',' ~~ ~ Fo or--ie prp /er:,. rv fo rfeeni. -
\iur -..oniuid


Fig. lc


CONFIDENTIAL







NACA ACR No. L4I29


/0 w j0 o4 4,,a'eqg S 60
1d) r r-' 61g' /;rirpe'/erJ. (rbtraoc. biea froTr reference 3.)
'-Ure /.- C':t.,nued.


CONFIDENTIAL


Fig, Id







NACA ACR No. L4I29


III
COM ITIEE

CONFIDENTIAL
o I_ I I I I __
0 /0 w 30 40 0,deg 0 60
(e) For eyhl-blode propelelrs. (EXT/rpolt/ed from reference J.)
-,gure / Coaluded.


CONFIDENTIAL


Fig. le





NACA ACR No. L4129


Ch

8
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34
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Fig. 2a






NACA ACR No. L4I29


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Fig. 3d








NACA ACR No. L4I29


F/G6nE 4. 0fokim'/o/-ernery s or P correspoax/ 0o pe*o ed/f/vey a;
/ur-tede Ham/itoan S5rendard 3J/5-6 prope//er
1,6


- -


-- -- OPtium "/stribi /on, = 4
----- Prope//er 3/55-6, 8=4
Idea / prope//er I


/6 ~e Axio/- energy /oss at R corresponding to peao
efficiency of our-blade Hami/ton 5t-anda ~ r-
3/55-6 prope//er

CONFIDENTIAL


z
z
I
z


CONFIDENTIAL


Figs. 4,5.








NACA ACR No. L4129


as

'no


SLJ
-io
g
OL.J

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NACA ACR No. L4I29


Zl II I-II
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Fig. 7a


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NACA ACR No. L4129 Fig. 7b






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i



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Fig. 8a











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NACA ACR No. L4I29 Fig. 8b








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S5 O











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I--I














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NACA ACR No. L4129














Cp

/2 --


CONFIDENT AL


/c/6U/UE 9.- EFFECT OF Dx46 ON EFF/C/ENCy RA/O oOW-E COEFFfC/EN'T
R"F PEAK EFFICIENCy FOR rOU/R-BLADE I MILToN S STANDARD
3/1.5-6 PeOPEL ee.


Fig. 9








NACA ACR No. L4I29


d/-L a'773 dOfc!d








0
-,.
u,
uj










.r.'
"Oo
-t "
___ __ __ __ __ __ ___ __ __ __ o j __ __
5 1
rd---^-

r ^ "r"--- -----
---------- ------- ---------- --------- ---------- --------- ---------------------------------------------------------
^ \
g -- -- -


_ A__ ___
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^-- \-----


Fig. 10


4'




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-i
ft 8





































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G`


^.







NACA ACR No. L4I29


707




-.6OS


:O


V/no


'S6au /A VyA/ar/W o T10eWsT dAoPowvE co -F C/Ars oW 7
DWnS w/r# Y1W 9oeR CNwsrW9N7 r -V Ysr*/PJr4O. 0=


CONFIDENTIAL


CONFIDENTIAL


Fig. 11





NIACA ACP No. L4129


K;
I




I
r



- N


-o I


Fig. 12







NACA ACR Ho. L4I29C


- -- Ca/calated
- -- xperimenta l(erferences 6andi


CONFIDENTIAL


0 / Z 4 S 6
V/770

F/-iure /3- CnomparisoV of ca/culated acnd ejperiment-a/
prope//er efficiency enve/opes.


CONFIDENTIAL


Fig. 13














































































































































































r









UNIVERSITY OF FLORIDA

3 1262 08104 984 2




UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE UBRARY
P.O. BOX 117011
_'"AJNESVILLE, FL 32611-7011 USA




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