Naca Report 749

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REPORT No. 749

PROPELLER CHARTS FOR THE DETERM INATION OF THE

ROTA TIO NA L SPEED FOR TH E :MAX Il\1UM RAT IO

OF THE PROPULSIVE EFFICIENCY TO THE

SPECIF IC FUEL CONSUMPTION

By DA.VID BIERKANN and ROBERT N. CONWA.Y

of the ratio of the propulsive efficiency to the specific

A 8et of propeller operating e.:fficiency c harts, based on fuel consumption is also included.

a c oeff ic ie nt from which the p ro pe lu r r ota tio na l speed hall

been: eliminated, i8 presented. These c harts were pre-

pared 'W ith data ootained from tests of full-Biu m eta l p ro - P

peller8 in th e NACA p rop eller-re8earc h tun nel. W orking T.

c ha rts fo r n in e p ro pe lle r-b od y c om lrin aiic m 8 a re p rese nte d, Tin clud in g resu lts from tests of d ual-rotatin g pro peller8 . AD

These c harts are to be used in the calc ulatiffn of the W

range and the endurance of airplane8 equipped with 1 1 .

c onsta nt-speed pro pellers in w hic h, fo r given }ligh t c on di- LID

OOn8, it is d esire d to d ete rm in e th e p ropel le r r eoo lu tio n V

speed that gires the maximum ratio of the propullJive D

ejJiciency to the specific fuel cO'M'llmptio-n. The coejficient p

on whic h the charts are based may be written in th e form Po

of a thrust c oeffic ient o r a thru st-p ow er c oeffic ient. tr

A method of using the cham i8 outlined and sample q

c omputatio-ns for a ty pic al airplane are inc luded. C

SUM~URY

INTRODUCTION

Inthe calculation of the range and the endurance of

airplanes equipped with constant-speed propellers, the

thrust horsepower required for flight at a given gross

weight, airspeed, and altitude is known. It is desired

to determine, from the propeller-engine operating char-

acteristics, the propeller rotational speed that gives the

maximum ratio of the propulsive efficiency to the specificfuel consumption. The usual propeller coefficients are

insufficient for use in such calculations because knowl-

edge of both the engine power and the rotational speed

is required and these quantities are unknown.

In order to facilitate the calculations, the Bureau

of Aeronautics, Navy Department, requested the NACA

to prepare working plots of a thrust coefficient that is

independent of propeller revolution speed. The present

report contains such working charts for nine propeller-

body combinations and includes results obtained from

tests of dual-rotating propellers. .A . method that

can be used for the determination of the maximum value

SYMBOLS

power of engine, foot-pounds per second

effective thrust (T-IliJ), pounds

total propeller thrust

increased drag of body due to propeller slipstream

weight, pounds

propeller rotational speed, rps

lift-drag ratio

airspeed, feet per second

propeller diameter, feet

mass density of air, slugs per cubic foot

mass density of air at sea level (0.002378)relative density of air ( pI ~

dynamic pressure (lpVJ)

engine specific fuel consumption, pounds pel"

brake horsepower-hour

Q engine torque, foot-poundsC. speed-power coefficient ( { / ' _ p = v a ~ / P = - n - I )V/nD advance-diameter ratio

T. thrust coefficient G~~)Cp power coefficient ( p J ~ 7 3 = p . , i )

r, power disk-loading coefficient G r ~ V i ) ·

DISCUSSION

Inthe calculation of the range and the endurance of

airplanes equipped with constant-speed propellers it isdesired to determine, from the engine-propeller operat-

.ing characteristies, the propeller speed that gives the

maximum ratio of the propulsive efficiency to the

specific fuel consumption. The thrust horsepower re-

quired for a given flight at a given gross weight, air-

speed, and altitude is already known. .

The usual propeller coefficients of power, thrust, and

propulsive efficiency that are defined as

373



374 REPORT NO'-- 749-:-NATIONAL ADVISORY COMMITTEE FO~ AERONAUTICS

orOp=~- __pn _

Ol'=~·---pn-.u{ _

GT V.,,----=o.s»are insufficient for this purpose because neither theengine power nor the engine speed" is known.

In order to solve these special problems with the least.

work it is necessary to use plots of propeller coefficients

that do not involve the rotational speed. Suitable

forms of the coefficients may be obtained from the usual

thrust or power coefficients as follows:

TC7' T.

c=V / n D ) 2 p D 2 P

C' Cp pP =t t / n D ) 3 P . l F V 3

Because the brake horsepower is unknown, the equa-

tion for Op' should be multiplied by ." to obtain a thrust-power coefficient:

C, T. T

." p=~= e

The two general forms of the coefficient are ."P/plJ2V'

and TJpD 21T2 , which may be converted into engineering

units as follows:

."p 73300 thpP 1 J f V i = t 1D2(mph) 3

and

PROPELLER DATA

The propeller charts were prepared from data. ob-

tained in the NACA 20-foot propeller-research tunnel.

The tests that provided the data were made with tractor

propellers of approximately 10-foot diameter operating

in conjunction with various representative body types.A list of the charts and the basic propeller data are

given in the following table; principal model dimensions

are given directly on the propeller charts.

FigurePropeller drawing

number Rotation

Totalnumber

ofblades

Hamilton Standard:81M-6 _6193A-3_ •• ~ __31lilHL _

~---- ._-------3166-6, r,h._- _._ . ~318& -6, L h. • _8166-6, r. h. _ . __. _:&l8&-6, L h•. . _

Bnrean of Aeronautics:1 3 , 1 4 __ _ _ __ 6868-11 __ • _16,17 • ~ __. _

16 ,18_ ._____ 1i8e1H l ~

Body condition

Blade·anc Ie

r&IlItI at0.7SR(derl

Approxi-mate pro-oeller

diameter(ft)

1,2 __ . _3,4 _6, G •

7,8 __. _9,10 _

11,12 •

3 _ Streamline body, with spinner, on symmetrical wing .. ..:..._3 Streamllne body, with splnner ~--. .-- __-4 . _ Streamline body, with spinner, on symmetrical. wlnK. __._. .G do •• ~_

4 do ~

11IIII

II

2..do · ~-__..___---

3_ _ !Jqu id-ooo led engine nacel le , wi th sphlDe r_ .. •r__••__

3 Rad1aI en&Ine nacelle • ~ __ ~~-_-

4 Llquld·oooJed engine nacelle, with spinner. _._._~---------- __

10 Sln(le_. ____.. ~ t o l l S1l.lItI

. _ • • _ do________l I Q l o 5 l

10.____do ________

Z l t o l D10

_____do_______2l1o~

10 Dual. ___._•• _ ~ t o 5 l

10_____do. . . _____

2lto06

10 Slllf!le... .. . __ IUo e o10 __._do ___.__._ IIi to 4010 _____do._. . . . . . . . . 16 to 43

S4

3

PROPELLER CHARTS USE OF CHARTS

Two charts are provided for each of the propeller-body

combinations. One chart contains curves of. VjnD

plotted against Tc between 0 and 0.10 with contour

lines of constant.". The other chart contains curves of

T; between 0 and 0.40 and curves of ." plotted against

Vlnl). The same quantities may be read on either type

of plot but greater accuracy is obtained by the use of the

first type for the range of Tc values that it covers. Thesecond type of chart. is included because it offers greater

convenience in extending the range of T,values.

Itis possible that propeller charts of the typo given

in this_report may have a number of uses that- are not

anticipated at the present time. Also, it is quite

likely tha.t different methods can be devised for using

the charts in solving any specific problem. The chip!

object of these charts is, however, to furnish 8 means of

determining the optimum propeller speed for given

flight conditions to obtain the maximum ratio of the

propulsive efficiency to the engine fuel consumption.A method of obtaining the optimum propeller speed is

presented in the following outline, .



4.6

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3.6

3.4

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REPORT NO. 749--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

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1 _ I i ' \ . ~ r x k'V 7 ' .i 1 \ \ i\ / :04 '> '\1,-'"

~~~~~~~~H+~4-+H~~4-~~i~~~~i~~-H1'_~r+~'_r'~~

~o~ i f ? • ~Olo ,I .; P t a " 45° 150 1 /55· 1 /50 ' : :P-;;5S·-af() '7SR~~~~I~,Ii~/~I~II~I~/~~~I~~/~~~~-*~~~/~~-~+-~-rI'--'-a .2.llU 1.0 ie 1.4 /.6 1.8 2.0 es 2.4 es ee .!J.O se .3.4 .3.6 .J .8

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FlOUBE2.-Chart of, against VlflD for tbree-blada propeller 31M-e. streamline body, with spinner, ODIIJlIIIIletricI wing; a I n J l a rotation. rrupelltrdati. taken from rel6'enc6 1

Ie ../.. f " \ . \ ~ \ \ / V 1\ L'I\;::'3 V '\, ...OC=T}Cp-To .~_I-

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o .2 .4 .6 .8 1.0 /.2

FIQ\1U 4.-Cbsn. of If a g a t m ' t VIlllJ lo r tbIee-blade propeller 6lWA--3. Streamline body, with sPinner; I ! i n & l e rotatioD. Propel ler data \ akeI l . fromrefereDoe 1.



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REPOR'f NO. 749--NATIONAL ADVISORY COMMITTEE FOB AERONAUTICS 379

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FIo!:BI G.-Chart of, against V / f 1 . D 1 ' 0 1 ' fonr-bJade propellel' 3IH Eti:'eiImlIne body, wlU! SPU!OO!',on 9l'mmetrieal wfnz;

slng!e rotat ion. Prope llel' data taken. from reference 2.

.M~-+~4-~~~~+-~-+~I£~_~~74~~_~~9,~~-~~~~~_+-~-+~~+-~-+~4-+-~

V r-...'./ ........-. . . / , , > < . . . . . . .- . . . . _

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'h./ \/ '\If \ \ \ \.~_f<..80~~+-~~+-.t~~+I~~~~~~\~~~\~~\~I~Y~~I~A~~~~~~~~~r+~~-+4-~~

I t .-J-~'\ , 1 \ 1 \ r - . , I \ 1 \ ' \ - , ' \

~78 .29{.1 1 - 1 ' - 1 1 \ I) 1 \ Y \ !.'\ \ \ I 1 \

~ I-+-I-+-+--+-22{/fr-!-l. \ \ i/ \ 1\ .~ II \.~76 ~~V 'U 1 \ J \ W

~74 .28i~ .....1 \ 1 \ Y '. . . . . . r e u - t .1l\ \ ,/ 1 \ 1 / \ I

I

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1 \ /I-t-

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I I I / I i . I I I ..64~-+~+-~rl~~Hffi~H-~~~i~~~~~~~~~+-~-+~~~~-+~+-~-+~

~~~ar~~/~,~~/~~~~V~~h~/~~kd~~~~~~~~~+-~~.62 25" / 1.301/35" 1r40·1 4 5 ' 50· l i55" rso: ,; {Ja65"afQ75R.

I I I I I 1 / 1.5%~-.~c_L~.4~~.5~-~~~lO~~/,C~~/'~4_Ll~.6~~1.8~~c.~.O_Lc.~~~c.~A~~e~d~c.~~~3.~.O~~3.~C~3.~.

V/nDl! 'roUD: 8. --cbar t oC, apImt V/1ID for m-bJade propeller 3U6-G. StreamlIne body, with splnnet , on symmetrlcal wing; 5 I n s I e ~tIon. (The m" ell !.cfenor

carve was InterpoIated.) Propeller datil. taken. from reference 2.



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: / 1>!c"1- - t-- •N~~:: : '<~ i'-. ~£.

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_ "e;: -7;.,J'JOtJIIJl:e . -Cha r t of V/fiD apIllit !l'. ro r t w o t w o- b ll d l p r op eU e ra 8 l J5 1 i. -ta n d 8 1 11 6 -8 . S U ' eI U l I ll n e body , with ap lDMr, Oil I Y JID I lt I; rI a a Iw l Il B ; d l l~ r ol a tl o ll . P r op e ll e r data t aken troD! r e tenm.c. i,



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REPORT NO. 74g.... .., ..NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

/' r-/ ) 1 \ ~ \ \ . ' \ / \ . -7 --- f--

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. .3Z r-,"\ It-+-t-+-t-t'-+-'-:-f~\rt+-ltrrlHt-+t-tt-/:-+t+t-iH+~·O!-:;-7+t-t-+++-+-tiH-t--t-+-+-+-·t-+-I---t-·· -.-

~--+-t-+--I-tI--I+--M+\-H--t+-IIt-flI--tt--f-I--t+t-tII--H--t--fl++-I-I--!:=+--II-+-t-t-+-+.. --I-~-+--f-- 1 - -- - .I ! II

1-t-+-t--t-t-+t-t+~-h'tt-+-HHH-tt--t--++H-i-tt~-1+±:-I+t-+-7I---t-t-t-+-+--I--I-I~-"' ..-_.".I I I I: 08

.4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8VlnD

FIGURE lO.-Char t of ~qalnst V/flD fOl'two two-blade propellers 31M-(! and 3151H1. 8tresmlIne body, wl.tb spinner, on I)'mmetrlca1 wing; dual rotat loD.

PropeIler data taken !rum n!fereooe 2.

VlnlJ

FIaURE 12.-Chart 0( ~ aplost l'/IID for two three-blade prope lle rs 31~ sod 3156-6. Strelmllne body, with :<pinner, ODIymmetrlcal 'lliDg; dual rotatlou.

Propellel' det& t aken f rom reference 2.



3.8 5. •

3 . 8

S3.~j_

. . . . .

3 . 4 ~.78- . r-,

3.2 150 ·

3 . 0

4 8 . S ; _

:8 2

30 ·/.B 29.6·

= : : ~

1.4 2! 0

2

a .008 .016 .024 .032 .040 .048 .058 .064 .072 .080 .088 .096 ./04

TlC/-r .J 't ou u l l. -< lb .r t 0{ V/nDAPlDlt T. ( M WD t hr ee -b la d o I lI 'o pe ll m 3 1M - II ~ d 8 lM - i1 . S1.reImJlIIll bod)" wn h lP lm:wr , 011 1) '1 II1II11I1oa1wbIJl dua l r ol il t. lo n . P ro pe ll er a a La t II ke n tram m8l'lllDII 2.

I .

II

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MAXIMUM RATIO OF. PROPULSIVE EFFICIENCY TO SPECIFIC FUEL CONSUYPTlON 385

1-[...< I-.88~-+~+-~-+~+-~~~~~.~~~K~~v_~+-r_~-+~~+-~-+~-+-~-+~+-~~

/ f. 1 1 \ \ I\t!'-v X·~·~-+~+-~-+~~~~~~~~~\~~~-r/~~'~i~kl~~~/7-~~~~~~_+-~-+~~~~

; ' r V ' \ \/!\ v [f r x•..r

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. . . . .'II 1 / I I IES" pa " \ 5 " 1 0 ' "'I..~ I hive I / s s · 1/'Yi = 50" af Q75R

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O~AEAWaU$m~UUUS~UM~~V/nD

FrGuu l'--Charl 01. aplDsl; VIIlD ro c three-blIIde ~ o~ ~ L1qllid-eooled endne nacelle, with spinner, sIni Ie rot&tfou. Propeller data. takenf rom r ef er en c e &.



IUJ1-H--+-+-+--+-+--+-+-H"""",+-'+-+-+-+-+--+-HH-I--+++-+-~I-f--r-+

;

~----- 116" -------o!-1-f-j---J.-+-+-+--+-+--+--+--I-+-+-+-I-lH--+-+-+-+-+-+--+-+-i-

1

-+-+--i-+, PrOfH!lIer diameter, 10'

26~~~-4-+-+~~-+-+--+-~+-~~H~-+-+~~+--+-+-+-r-~~~-+I-+~~-+-+--+-+-~-~~~~-4-+~-~~-+~

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1; r

,: ,

I I.016 .024 .032 .040 .048 .056 .064 .072 .080 . 08IJ .096 .104

7 J £ ? , ' . T ,.



1. 6 J ,.'0"'1--

1 - i1:5

1.2

E . G ! . .1. '0

.6

.

~

.76

- _ - r = : : : : : ~ : 1 5 J~5'

I'--~ .-'I-:~ BO- - " " ' :

~ -_- -. r-. .,_"l-_.'8

.B5~ i . '04

-- I

- '~.-.. --e, --. fje - : : : = : : : =.~

e8~-+-q~~~.~76~+-~-+~~~+-~-+~-r~+-~-+~~~+-~-+-r-r~+-~~-+-r~+-+-~-+~~,~+-~~

• i ·:1,9e6r~~-+Hr~~80~~-+~~~+-r-~~-+-r-r~+-r-~~-+-r-r~+-r-~~~-+-r-r'_+-+-~~-+-r-r~+--r-~

r - . . . . r . , ' . r,Be

L./.86. ---:r· _._ /_

--r·_,.....-- r-- -r." '"" •

. ! " 7 . - r -= , : . :: z . " -, . .. . , .. . 7---

~ ~8 ~f ~.' - •.II

'0 . '098(){)8 ,016 .032 . '040 .048 .0567 7 f 1 . ' - r ,

, '064 .'072 . D B D .(J88

I'IQtJJt. Itl.-Ohar~ IIrVIII»apiDllt T.forrom·blad. propeJlH I 1 1 I I I & 4 , Llqllld~11!d m!la, lI.ceU~.wltII Iplnner; . J J I I I e rotaUOD, Data taken from rafIrIDoe &.

, I

.~

. .5·

p I .I)•

./04



388. REPORT NO. 749--NATIONAL ADYISORY COMlfiTTEE FOR AERONAUTICS

Given: Aerodynamic eharacteristies of airplane and

flight conditions:

(1 ) LID for speed of flight and altitude (or thrust

power for speed of flight and altitude)

(2) Weight, W

(3) Airspeed, t'(4 ) Diameter of propeller, D '

(5) Density at altitude, p

(6) Engine gear ratio

Characteristics of engine, including:

(1) Brake horsepower for altitude of flight as a

. function of engine _ speed and manifold

pressure

(2) Specific fuel consumption as a . function of

engine speed and manifold pressure or torque

.86

.8

f : : : . . kI ~ , , - ~ r - , I ? 1 " \

'"~ ~ I '\ . r \ . . r - ,'~4

.Ic.j. h < fil\f/ r\ ~05

'2 I £ - t\ "') \\1/:~,,~W ' _ ~ I V ~07

.,~ \ U '\ \ I V '.08

p n : - I . . " \~ T \ Ii'8

.c~.b-- f . . , . \ \ j

.c4. ' - 11 \ T .09"1]£;-r.0 .~ r-. \

.c 8 N \ ftjv'4

!\ 1 \ \I

'2I I

I I

o I II Ii

I ! I! /

I I ,- i I I

: ! j " I!

4I I

cO - I I

'2zs· ~ .

!'i! .p_-40·01 a75R

I

. 8 .

.80

~.7.

~g . . 7 1

& :

.68

.66

.6

.6

.800 .e .4 .8 .8 LO ie 1.4 1.6

V/nD

FIOUBJ: 17.-Chart of 'Iagainst V/nD for three·blada propeller~. Radialengine JlIICeIIc;single rotation. Propeller data taken from reference to

To obtain: Propeller speed to effect the maximum ratio

of propulsive efficiency to specific fuel consumptionSolution based on thrust coefficient, To :

(1) Determine effective thrust T. from LID and W

(2) Solve for thrust coefficient

TT, 195.4 T.

.=~= uD2(mph) 2

(3) For several values of propeller speed n, solve

for V/nD

(4) For several values of V/nD computed under

step (3), read from propeller chart values

of propulsive efficiency II

(5) For several values of n, compute propeller

QT.V

torque =2m'l

-(6) For several propeller values of n, compute

n/n'IJw and Q / Q r I J r e 4 (nrIJkd and Q " . r t l l corre-spond to rated engine speed and torque values

with gear ratio taken into account)

.88

,68

1 . . < : l< - i-

I f " " " " " r-,"r-, ~ -"

'"t t - . . . . IX K r-,.// !J. r- ~ 1\ ') < f\ _ _ I '~04

liz . II r - , r 1 \ V : ! l 5

J4· N, 1 1 \ 1 \ I V I \ \ l./~.[ 7r-, II 1 \ \ ~06

1 6 1 ' / ' rt- !\ ~.CO s . J \If V II

.ee»

"1 \ A 1:07

.~4 l' ' \ \ 1 \

.26- s : ~I\ \- ---.e r . J . · f . , . I " f . .

-1'00

30 : · 1 > " 1 \ 1 1 \ Y

~ f/. : \1 \ \ I.~ If \ . ! \ II :Q9.1JC;-r .

I ~ - ,/; JI I I I Ii

I T r r! I . ' / 1

[ T I T 1 i II

-I

I "_.f

:5 " i 1 72~ I

1 7 Z s o r x l 3 ! i ; # C f o /J-4S·ot .7SR

.86

.84

.82

.80

~.78

f,! ! .76. \ ; !

~1l1.74

~~.7Z

: : : l

8 -c l : : . 7 o

.66

.64

.6c

a .c .4 .6 .8 1. 0 I. C /.4 /.6 1. 8 eo'Y/nD

FJ:oUBJ: 18.-CIw1 01, apInst v/nD f«Iour·blade pt'OPfller~. Llquld-GXIlcd

ellifne naceIW,wIth spinner; slncIerotation. Propeller data taken r r o m refer_ 6.

(7) From fuel-consumption data, determine values

of engine specific fuel consumption C cor-

responding to engine speeds and torques

computed under step (6)

(8) For several values of n, compute and plot

values of 1 1 1 0

(9) From curve obtained in step (8), determine n

for maximum value of ' 1 1 0

Solution based on thrust coefficient, II Cp:

(1 ) Determine thrusa power liP or thrust horse-

power from curves of power against speed of

given data

,_ liP 73300 th p(2) Solve CorT jC p -pJ)2~"3--IT[)2(mph)3



!U.XIM.UY RATIO OF PBOPUI8IVE EFFICIENCY TO SPECIFIC FUEL CONBUMPrION 389

(3) The rest of the solution corresponds to steps in

the solution based on thrust coefficient,

except that Q=2f1P

r1l.f1

SAMPLE CALCULATION

A calculation for a . sample airplane-is herein performed

to demonstrate the use of the charts. Values of ' 1 1 .cor-

responding to the maximum value of 71/0 were deter-

mined for three flight speeds; the computations for only

the condition of flight at maximum LID of the airplane

are included. Range computations have also been

made for the three :Bight speeds based on a specific fuel.

load.

In addition, range computations were made for the

same flight speeds but with the engine torque and speed

I

I

S

'/ r-,V <,

'2_j r - ,

r - ,

0r-,r-,

<,

~80 100 120 140 160 180 200 eeo

Air ~d at 10,000ft.mphFIOOD I9.-Varlation r1 LI D with airspeed f«IIIIll1pJeairplane.

adjust-ed according to the relation Q c x : n ! to demonstrate

the value of adjusting the engine speed to obtain the

maximum engine-propeller operating efficiency. (The

relation Qcx:nt corresponds to the operation with a

fixed-pitch propeller.)The two charts necessary for the calculations are in-

cluded: One chart is a plot of LID against airspeed for

the sample airplane (fig. 19); the other chart is a fuel-

consumption chart (fig. 20). The fuel-consumption

chart was prepared from data taken during NAC. ! . testsof a 1340-H cylinder from a Pratt & - Whitney 1340-

S1H1-G engine.

Calculations were made for three conditions of flight,

namely; maximum LID, 50-percent power, and 75-

percent power. "Given: Weight: gross=17,500 pounds; gas load" 5930

pounds "

Power plant: two 700-horsepower engines; en-gine speed=2380 rpm, geared 16:9

Propellers: two three-blade Hamilton Standard

3155-6 propellers; diameter=l1 feet; pro-

peller speed=1340 rpm

Maximum velocity: 210 miles per hour at 8100

feet

Flight altitude: 10,000 feet

Solution for flight at" maximum LID based on thrust

coefficient Tc (calculations are shown for one point on

fig. 21; other values are given in table I):

(1) Maximum LID=15.1 (from fig. 19)

V for ma.-mnumLID=116 miles per hour=170

feet per second

W 17500 -T.=t/,tJ 15.1 =1160 pounds or 580 pounds

per engine_

195.4X580(2) T,. 0.738X121X(1.346X10.) 0.0945,

(3) If it is assumed thatn=20 rps,

V/nD 201~01l.....0.773 '

(4) For V/nD" 0.773 and 2\=0.0945,f1=0.823 (fig. 1)

" 580X170

(5) Q=2rX20XO.823 953 foot-pounds

(6) ' 1 1 . , & , , 4 = 2 2 . 3 3 rps,

Q5 5 0 b h p ' & l e d 550X700 r

~u& 2 r n , . & l u I 2rX22.33 2750 foot-

pounds

At '11.=20rps,

20n / n ' & l u I = 2 2 , 3 3 =0.897

and Q/Qnll4=O.34fY

~.80

I

t 7 0:Q

.

Percentage of

rated torque40

I--. -~53

B6

-~ 80b-

tl

f~. . .s o

!1 " 4 0~~ o 60 70 80 90 {(X) 110 le o

Percentage of rated .'!Ip6ecf

FIGlTU 2O.-EIfect of e n c I n e speed on mfnImum fue l consumption 01 several

t«qUP vaIllM. The I34O-H cYlInder.

(7) From figure 20, by extrapolation,

at ' 1 1 . / ' 1 1 . 1 & 1 1 4 = 0 . 8 9 7and Q / Q , & 1 . 4 "0.346,

• 0=0.600 pound per brake horsepower per

hour

(8) 7I/O=~:~~=1.37



390 REPORT NO. 749-NATIONAL ADVISORY COMMtTTEE FOR AERONAUTICS

(9 ) 'f}IO is plotted against n in figure 21, together

with the corresponding values of Q , 0, and

~, which have been added as a matter of

interest. From this figure it is seen that the

maximum value of 'f}/O occurs at n=13.7

The results of similar computations for flight at. 50-.

percent and 75-percent power are given in table 1.

The range for the three flight speeds was calculatedfrom the Breguet range formula:

L fI WoRange, miles=863 1 5 ( ) log 10n',

where H'o is the gross weight and We is the gross weight

less the gas load. .

In the Breguet formula, LID is assumed constant

and the values of 'f}/C are average during flight i whereas,

the values of file as used in the problem are for the

start of flight.

For maximum 'fI/Oat maximum LID,

Range, miles=863 X 15.1X 1.62XO.181=3820

With the data from table. I, the range at 50-percentpower was computed as 3680 miles and at 75-percent

power the range was 2940 miles. The variation of the

1.3

,. ,/56

/'/

C'\v '/'r 54

_ ,0 ../ . -- -

~\. ~ - r! l- 62-, ff' l-i--> S . . ~'IC

- -

/ V<, . . . . . .'- -

60r-,

V / r-.< <,~. ,/

. . . . . . . . < 48

r - . : . . <

t--f--

/46

j

IClO(r

1.9.88 2000

1.8 .86 IBOO

1.7.84

i '7

1.6 ;8Z

1.5.80 teoo

1 .4 .78

162 /4 15

n.rps

FIGL'KE 21.-Varlatlon of eIll1ne-propenor operating characterilltlOll for 1lIJht

at maximum L{D of 5 8 D 1 p J e airplane.

13 17 /8

I I I .'

.Cantrollable-P/!-ch p r c ; -t- 7S-percent- r pef/eii# 8ef for- cOnclitionfXJ .WEr r-:: : : : : : : :~ -:«maximuin'r,!C'

-

<~ <,

<,r-,50-percen~ower ...-

'\.

"-"I.

Fixe)pi,!", . l - o p 9 / ~ set'" 1 \ - \ t--to absorb rated power at \Qted engine Speed for high-3peed-fllght condilion I

JI Moximiln L/~

I

180

120

100NOO Z6IXJ ZBOO 3000 3ZOU 3400 36IJO 38G IJ

Range. miles

FIOVBIi:22.-ComlJ8l'lson of flight rang!'S for fixed· and controllable-pitch prolX'lJers

on sample airplane at 10.000teet. The foregoing comparisons were based on

\'a lu es o f "IC fo r the start of tI lif ht. I ns te lld o f on a v er & gC v a lu e s Il!I stipulated In

the Bregoet formula .

range with the airspeed is given in figure 22. For

comparison, figure 22 contains 8 plot of the range for the

same airplane equipped with both controllable and

fixed-pitch propellers, the fixed-pitch propeller being

set for the condition of high-speed flight. Because the

gain in range by the use of controllable-pitch propellers

Bet for maximum engine-propeller efficiency was rela-

tively small for the conditions assumed in the samplecomputations, it would appear that the optimum blade-

angle setting is fairly close to the high-speed setting.

The stating of such a generality is hazardous, however,

chiefly because the fuel-consumption data herein pre-

sented may not apply to engines in general.

TABLE I

CALCULATION OF . " / e

Flight constants , . 11 Q() C

at start of Jllght (rpI!) l'/nD

" Kr.t.' (rt-Ib) Q;. . . . (l~rl~e

--

r0.77 ( ) _ 8 2 3 (I.m e~ 0.345 ( ) _ 1 i O O Lr;

LlD-lli.l : 1 1 1 . 1 1 2 • ! 1 28 .&2 D I M ! .3Il2 . lI86 LU18 .!II .831 • ! 10 7 10.50 .382 . 8 7 1 1 1.45

t' -116 mph ! 17 .;1 .8311 . 7 63 1100 .400 . s e a 1 . 1 1 116 . g n .MIl .718 1110 . 4 2 1 1 . 5 4 & I.M

T -1l601b I l~ I .DI •MIl .1Ii2 12 30 .U8 • S I l l 1 .871.10 .84% , 1 ! 28 1330 .~ . 5 2 1 1 I.I i : !

: : = - i II r.is .RI0 . 1 1 8 3 1(90 .M2 . 505 1.811.211 .760 .&38 17 :10 .8211 • o I8 D I.m

~--L/ !

.90 ( ) _ 1 1 4 7 1.03 1 2 1 1 0 ()_~ o .m 1.40

.; 4 .8IiO .1lI7 1300 .471 • & 1 1 0 LS2

.fill .8M .~ 1360 .4!15 .646 1.57I 20 1.03 .880 .!f11 142 0 .515 . 530 1.82

V -llllimph 18 l . 0 I I .8&7 .852 14110 .638 .617 1.ilII18 l . 1 6 . I 1 1 I I I .IBT 1M O .M7 • S O li 1.72

T -l3IiO Ib; 17 1.21 .8G6 .iU 11150 .Il0:l .~~ 1.7&16 1. 5 .887 .718 liS) . 1 1 - 1 8 . 4 1 1 0 1. iR

T, ~0.OOI6 16 1.38 .84% .872 IG3Q . '1l!2 .W 1.81It 1.48 .1124 .Im 2110 .7t1 .480 1. 'Ii13 l . 6 f I •is) .1i83 ftOO .m .m 1.71

-----_.----f------2lI 1.10 0._ 1.03 11UO 0.705 n . 1 I I I l ' 1.71

LlD-W.O 22 1.111 .871 .® 2020 .73a .497 1.7521 1.20 .1172 .!K2 2 12 0 .770 • - 1 85 I.S!

t· ~ll1Omph 20 US .871 .So 2:llO .1110 .470 1.&Ig 1.33 .865 .852 l I850 ,W .4!!2 1.87

T - l7I!O Ib 18 1.40 .M1 .807 3610 . 1 1 1 3 .4~ 1.8817 L,", :844 .763 2700 .Q82

:::~~:I. ~()_0530 18 Lilli .830 .71816 L8!I . 800 .1!72

LANdLEY :MEMORIAL AERONAUTIC.'.L LABORATORY,

NATIONAL ADVISORY CO:r.UUTTEE FOR AERONAUTICS,

LANGLEY FIELD, VA., December 11, 1940.

REFERENCES

1. Biermann, David, Hartman, Edwin P., and Pepper, Edward:Wind-Twmel T~t-8 of Propellers Equipped with Spinners,Cuffs~ Airfoil and Round Shanks, and NACA IS-Series

Sections. N ACA Rep: to 00 published.·2. Biermann, David, and Hartman, Edwin P.: Wind~Tunm'lTests of Four- and Six-Blade Single- and' Dual-RotatingTractor Propellers, Rep. N o . 747, NACAr 1042.

3. Biermann, David, and Hartman, Edwin P.: Tests of TwoFull-Scale Propellers with Different Pitch Distrlbutlons, atBlade,Angles up to 60°. Rep. No. 658, NACA, 1939.

4 . Biermann, David, and Hartman, Edwin P .• Tests of FiveFull-Scale Propellers in the Presence of a Hadial and aLiquid-Cooled Engine Nacelle, Including Tests of TwoSpinners. Rep. No. 642, NACA, 1938.

5. Hartman, Edwin P., and Biermann. David: The AerodynamicOharaeterlstica of Full-Scale Propellcrs Having 2, 3, and

4 Blades of Clark Y and R. A. F. 6 Airfoil Sectlons, Rl 'p.

No. 640. NACA. 1938..

Documents

Naca Report 749