REPORT No. 421

MEASUREMENT OF THE DIFFERENTIAL AND TOTAL THRUST AND TORQUE OFSIX FULL-SCALE ADJUSTABLE-PITCH PROPELLERS

By GEORGEW. STICKLE

SUMMARY

I’oree mea8urement8 giving total ihrwd and toriyw,ad F0p8h% 81ip 8t%5(Z7n8wmey8 gbkg difertmiiulthrwt and torqw were tindaneoualy mude on euch ofsix fidL8caLe propelLw8 in #ha30-foot propeli&-e8earchtunnel of tb National Advi.eory Cbmmdteefor Aero-nudix. They were adjwtable-pdch &al pmpeL?4789,6 fed in diamder; three had n.todijied Clark Y Ma&8ecti0n.8and three hud modijied R. A. I’. 6 blade 8e&nw.Thti report givw tlw di$erential thrwt and torque andth8 variuiion cauwd by chmqing the propeUertip qpeed,

~, and th8 pi$ch 8dtin9. The total thrust and torgw

obtained from integration of ths thrwt and torque die-tri.lmiion CUrveeare compared with thoee obtained bydirectforce meusuremen18.

In tb above c-ompari.eonthe tor@?8 m+?a$uredby thetwo meihode were diredly c-ornpaxabfebut tlw thrwat8derived from tb 81ip&ream w.nwy di$ered from tho8eobtuined from tb force 7.%%WlW6?WTl#8~ tWOf(lCtOT8,

the drag of the hub and the imrwe of body drag due tot?w 81ip8tream. MU% 8in@?8VaJUe8of two eoqfkiemhwed to obtuin the factors browgld al-l the thrust curwmaasured by the two methods into very good agreemeni,it is believedihut thefactor8 reprtxtmt accurateI?ythe dragof ths hub and the irwream of body drag due to the 81ip8tream.

INTRODUCTION

An invedigation of propeller oharaoteristics, con-ducted in the 20-foot propelkwre.search tunnel ofthe National Advisory Committee for Aeronautics,included teats on six full-scale propellem, three havingmodiiied Clark Y blade sections and three modifiedR.A.E’. 6 blade sections. Simultaneous readings weretaken of the total thrust and torque and of the differ-ential thrust and torque at six stations along the blade.The results of the total force measurements are given’in references 1 and 2. The prwent report gives theremdts of measuring the diilerential thrust and torqueat six stations along the blade and derives factors forhub drag and increase of body drag due to the pro-peller slip stream. A later report will give the airfoil

characteristics of the propeller sections deduoed fromthe measurements given in this report.

The differential thrust and torque for each stationalong the blade was determined by measurements ofthe total head and the tit of the propelkr slipstream. The tit and torque distribution alongthe blade for any operating condition was obtainedby plotting the elementary thrust and torque for eachsection agsinst the radius of the propeller. Since itwas impossible to survey the air stieam behind the hubportion of the propeller, that part of the distributioncurves was undetermined. This made it necessary -to iind a hub-drag coefficient that could be used taaocount for the negative thrust of the hub.

The total thrust (bMgrated thrust corrected forhub. drag) obtained in the above manner differs hornthat obtained in the force tasts of references 1 and 2by an amount equal to the effeot of the propellerslip stream on the drag of the body, since only the netforce was measured on the tit balance in the forceteds. From a comparison of the thrust curve9obtained by the two methods the value of the increaseof body drag due to the slipstream was obtained.

APPARATUS AND METHODS

The measurement of total head and angular twistat a series of points in the slip stream, which are thewenti quantities required m computing the propellertit sad torque, was accomplished by the use ofyawmet.em of the ,type used by G. P. Douglas, of theBritish Aeronautical Research Committee. (Refer-ences 3 and 4.) The term “yaw-meter” is used tadesignate the combination of a yaw head and a record-ing manometar. A suitable yawmeter for the purposeis one that gives a diibrential prwmre, proportiomilto the resultant dynamic pressure multiplied by thesine of twice the sngle of twist of the slip stream, orH&=PW2 sin 2*. (See listof symbols.) A yawhead constructed of three small tubes (fig. 1) with theforward ends of the two out&de tubes turned 45° bthe central tube, was found to have a calibration thatconformed to the above standard up b approximately40° of yaw. This angle is much greater than the angle,

437

RDPORT NATIONAL ADVISORY

m——— —.-—-——. .———---——-—.

COMMCITEE

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FOR AIi130NAVITCS

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zTofalheedfGbe

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T(Aessolderedtogetherftmu#louf ---fcmgfh

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3132;0;.1; 3 64” f.D.fG4(-g

FIGUREI.—Yaw-hindbankaswmbly and detail

DIFFDREN!I!L4L ~lJREl@JNT, TOTAL TRRUST, ANTI TORQUE OF SIX FULL-SCALE PROPELLERS 439

of yam (twist) encountered in the slip stream of ordi-nary propellers. The center tube was used to measurethe total head.

Sii of these yaw heads were clamped at intervals of6 inches on a tube (fig. 1) which was mounted verticallybelow the crankshaft center in the rear of the propelleras shown in Figure 2. The vertical position of thetube was such that the yaw heads were 24, 30, 36,42,48, and 64 inchca from the center of the crankshaft.

This distance was chosen to allow a sticient clear-ance (0.3 inch) for the 24-inch station yaw head withthe propeller set 27° at the 42-inch radius. Theyaw heads were connected by small copper tubw toa photographically-recording multiple-tube manom-eter, located in a dark room under the entrancecone of the tunnel. Prcgsures were recorded simul-taneously with the readings for the force tests reportedin references 1 and 2. The yawmetefs were calibrated

FIOUEE 2-%&TuIh plO@W—M&ud

The yaw head at.the 54-inch station was thus 3 inchesubove the propeller tip.

The tube supports were arranged to allow a fore-and-aft adjustment of the tube position. The modelexperiments bf reference 3 indicated that the readingsmight be seriously aflected by the distance betweenthe tip of the yaw head and the trailing edge of thepropeller. A few position trials showed no appreciableeffect up to 3 inches between the trailing edge and theyaw heads. Therefore the tube was fixed with amaximum distance from the trailing edge of the pro-peller to the tip of the yaw heads equal to 2.5 inches.

149900-3%29

tonnelwithyaw-headbankinplm

with the yaw heads in front of the body for angles ofyaw from 5° to the left to 15° to the right for use withright-hand prcpellera.

The propeller-research tunnel and its equipment aredescribed in refermce 5. A Curtiss D–12 enginerated at 435 hp. at 2,300 r.-p. m. was mounted in atractor fuselage (fig. 2) to drive the propellem.

Results from tests on six 9.5-foot adjustable-pitchmetal propellers, three having moWed Clark Y bladesections, and three having modified R. A.I’. 6 blade sec-tions, are presented in this report. The outer thirdof all six propeller blades have sections of constant

.

, ——

AERONAUTICS440 REPORT NATIONAL ADVISORY COMMITTEE FOR

thickness/chord ratio. This ratio is used to designatethe propellers, as shown in the following table:

PROPELLER DESIGNATION1 I 1 1

LEEThe blade-form curves for these propellers are given inFigure 3. Section characteristics may be obtainedfrom reference 1. Each propeller w-as tested at fivepitch settings (11°, 15°, 19°, 23°, and 27° at 42-inchradius) to cover the range ordinarily used. The pro-peller tip speed for these tests was kept below 900 feetper second in order to minimize the compr~sibilityeffects of high tip speeds. In addition, an investiga-

1.4

/.2

1.0

.8

.6

.4

2

0

Now

Therefore

dT= dC,/m21Y

‘CT for each propeller section behindThe values of z

which Qyaw head is located are plotted against~-$ and

faired curves are draw-n through the points An ex-ample of these curve9 is given for the C-10 propeller atz= 0.526 (30-inch radius) in Figure 4. Valuea ofdCrz at even values of ~D are given in Tablw I to

to XIV. The thrust-gradient curves for even vrdueav

‘f z are plotte’d from these tables, as in Figures 6

to 7. The curves are drawn through O at 0.2 of theradius because that is approximately where the pro-

.07\

I 1 I .30SW 27” 0( 4<r

tt v I 1- 1 I 1 Y

‘i LLErEn..as

.0s 22

-mb h

D

.03 14

I=R-I-HJ8

I

@RR- 8.—Pitidishfbutionandbladeformcm-ves

tion of the effect of high tip speed was made in whichthe pitch was set to 9.8° at 42-inch radius on all pro-pellers and also to 7° at 42-inch radius on C-6 andR-6.

RESULTS

Thrust distribution.-The thrust of a differentialelement of a propelhx is equal to the increase in totalhead due to the thrust, multiplied by the differentialannular area described by the element.

dT=HdA

Substituting, dT=H(2dr)

ThereforedT~ =27mH

Letr 2r

‘-Z-D

Then !&_;~Hz

peller changes to a circular section. It is impossibleto determine exactly where this point of zero thrustaJong the blade occurs, but for convenience 0.2 of theradius was adopted as a standard. The total thrustis not very sensitive to a small shift of this point oneway or the other, but wh~tever change does occur istaken care of in the correction for the incrnased drag ofthe body due to the slip stream. &aphical integra-tion of these curves gives the total thrust coefficient~ uncorrected for hub drag, aa show-nin Figure 8.

Inasmuch as the same hub waa used for all the pro-pellem, it seems reasonable to suppose that a constanthub-drag coefficient could be applied to all propellersand all pitch settings. At zero thrust the (YTcurvcafrom force measurements and total-head measure-ments should coincide since at this point the increaseof body drag due to the slip stream should be zero.Therefore it is permissible to aasume that the sepma-

,

DIFFERENTIAL MEAf3~ NT, TOTAL THRUST, AND TORQUE OF SIX FULL-SCALE PROPFJXERS 441

tion of the curves for force messuremente and tctal-

head measurements as shown in Figure 8 at the ~~for

zero measured thrust is due to the negative area that

spending to zero thrust from the force measurements,were converted into this form they were found to benearly constant; therefore an arithmetical mean wastaken of them which gave:

d~dx

:.

V/nDFIGURE4.-Dlfferentiol-thmstcmfiident.Propdk C-KI. s=OJi20

,06

.04

.02

0 ,1 .2 .3 .4 .5 .6 .7 .8 .9 10= .=/R

FIGU’FtE5.—Thmst%mlkntCIUVW.Fro@hz C-1o. set11°atCMIIChEMU

should be added to the distribution curves between

z=O and z= O.2. If the thrust coefllcient, CT= A’Va

()is divided by ~~ it becomes &P which is in the

form of a drag coefficient. When the values of CTfrom

the total-head measurements, at values of ~~ corre-

.22

.20

.18

.16

.14

.12@dx

.10

,08

.08

.04

.02

0 .1 .2 .3 .4 .5 .6 .7 ..8 .9 [0x =rfi

FICOJBEO.-Thmst-fradlontmrvm FropmerC!-10.at W at42-hohl-adh

Drag cod3icimt =0.005== ~

v%

()C. correction= 0.005 ~

This hub-drag coefficient is approximately equal to 25per cent of that of a circular flat plate of a diameterequal to that of the hub.

—. —... _ _——> .. .. ..#Ax....#Ax. .. ...+. -- .- . -

442 RJ3PORT NATIONAL ADTISORY

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FIGURE7.—Thmt%mdknt cams. RO@ler C-10. M mat 42-fnchradfas

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orce meoswemenfs~—1- T@likqd yyysn~ I

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0 2 .4 .6 .8 1.0 12 /.4V/&

~~ 9.-Cam*n of effeotlvetlwmtwwlkdentfromfermmeosmomenteandtotafthmstccdkdent(fnt.wmtedthnwtcoeffkientcorrwtdforhubdw)fmmtotihmd mEMmwmnt&Propk o-o

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Fmuim11.-Cem*n of effectivetit oMhkmt fromforcemewmments~d comeotdtotalheed-mmsnwnenk Pm@er C-O

,

DIFFERENTIAL h9DASUWiW3NT, TOTAL THRUST, AND TORQUE OF S= FuLLA3w PROP13UJIRS 43

Figure 9 gives a comparison of the total thrustcomputid from total-head measuwaments and themeasured effective thrust from the force measurements.

The diiTerencein the two values (A(?T)at any ~ may

be accounted for by the increase in body drag due tothe slip stream. In Figure 10, AC. is plotted againstthe total CTand a straight line determined by the theoryof least squares is drawn through thesepoints. Figures11 to 16 give a comparison of effective thrust coe5-cients obtained by the two methods.

Torque distribution.-l?rom a consideration of theangular momentum in the wake of a propeller, thedifferential torque of a propeller element can be ex-pressed as:

dQ=rVldMsubstituting dM=pUdA.=pU2imdr

‘~= dv,updr2

o .2 4 .6 .8 1.0 12 . /.4V/d

FIOUEE 12—Camparfmn of el?mtfvethrustcmMdentfremferwmeammmenfsandmrreckiitotal-headmmsmwnent% Pr0p3aer c-a

But V,=wsin$u-wcos$

ThereforedQ~=2 ~pPWrnn + cos +

or =7rPPwsin2#From the calibration of the yawmeter,

pw sin 2#=KHN

Therefoie $= n-?mv

dQ n-xWKHVSubstituting ~= ~

Now dQ = dC~’P

Eence

Owing to the type of mounting and the sensitivityof the yavnneters, it was impossible to get them allto record zero diilerentird pressure in the undisturbedair stream. This initkd deflection for zero twist mustbe subtracted before the H, can be used in the above

formula. The amount to be subtracted is determinedby plotting tie yawmeter reading for each radiusagainst totil head from the 0° calibration run. Thisplot gives the yawmeter correction as a straight-line .function of the total head. With the propeller run-ning, this function is theoretically in error by the

.12

./0

.08

G

.06

.04

.02

0 2 .4 .6 .8 1.0 12 /.4v/nD

IfIGUEE18.-Compmiwnof effectivethmstcwlTfdentfromforcamwummentsendmmwtedtotal-headmewmmnen!aPmpdferc-lo

change in stdic pressure, but this error is much smallerthan the experimental error, and consequently themethod may be used with cotidence. The only placethe error could become appreciable is at low values

of ~~ J and in this range the yawmeter method of

measuring torque is admittedly not very accurate./2, I , , , , f

.10

.Ci9

G

06

.04

,.02

0 .2 .4 .6 .8 1.0 12 1.4V/d

Fmmm14.-Oom@sen of effeelivethmstomdidentfromfmmmeasmmnmfdand ‘comeakdtotal-headmawmement%PropmmR-o

The values of ~ are plotted against~D and faired

curv~ drawn through them, as in Figure 17. Values

are read from these curves at even values of ~ andnD

are given in Tables I to XIV.

,..1 ,., ..- --------

R13PO13TNATIONAT ADVISORY COMMJTIIW

!2

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YXawEEIs.-

FOR AERONAUTICS

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0 .2 .4 .6 .8 /.0 1.2 f.4V/d

-Corn- ef efktlw thmst ed3cientfi-emfermnmam.mment9and~ total-hindm I

FIQUEE10.-Cemperfs0nof effedvo thmstwafflolantfromfamemwuementiessmementsPrapelfmR-S endcematedtatel-hwdmwmwnent% PramllerR-10

.016

.014

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.008

.LW6

.004

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o

-.0020 ., .2 -3 .4 .5 .6 -7 .8 .9 1.0 1.1 1.2 /.3 1.4V/nD

FIGUBE17.—DIffmntfal torqne mfffakk Pra@ler C-IO. z =CL6M

.012

.010

.008d~

.008

.004

.002

0 J .2 3 4 .5 .6 .7 .8 .9 [.0x=r/R

FmuRE W-Tmqaqgadfmt C3Jrva. Prap3ueTc-lo. at 11”at 4z-fnehJedfm

.Cm

,018

.016

.014

.0/2d C.~o,o

.008

.006

.004

.LW2

O J .2 .3 ..4 .5 .6 .7 .8 .9 1.0x =r/R

FIGuRE 19.—Torqnwmdlont oarvm. ROPOM C-10. Sot lW at 4ZtIIOhmdiue

.

DIFFI!IMINTTAL MILkSUIUIMEJNT, TOTAL TH13UST, AND TORQUE OF SIX FULL-SCALE PItOPElLIiE13S 445

The torque-gradient curves are obtained by plottingthe tabular values against percentage radius, as inFigures 18 to 20. The integration of the torque-gradient curvca gives the torque coefficient U~which ifmultiplied by 2r, gives the power coefficient CP. TheOp obtained in this manner is compared with themeasured CPin Figures 21 to 26.

DISCUSSION

DMerential thrust and torque,—A brief study ofthe thrust and torque gradient curves for Mkrentblade settings, Figures 5 to 7, and 18 to 20, shows thefollowing :

(1) As the blade setting is increased, the thrust ofthe outer sections increases more rapidly than thethrust of the inner sections, which causes the point ofmaainmm unit thrust to shift toward the tip. Thisshift results from the fact that the pitch increases more

I I

KE~,–’

. =;

,028 ? =/.8, =1.

..024 ,2 ,

=1.

d“ 51.if

1co I I I 1 I I 1 1 !

‘.020 I I I I I I I I I I I 1/1/1 J I 1 himt I 1 1 I I I 1 I 1 , , ,, “ r ,,

/tmJ\I I.016

,012

,008

.LW4

O .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

1 F 1 , t , \ Uu-1

x =r/RFmuaE W-’l%rqnegndlent cmrms. Pm@lOr C-10. E& W at 4Mmh mdim

rapidly toward the tip of the blade than near the hub.-t-T

(2) h the ~~ is lowered from the point of zero

thrust, the increments of thrust are large “and nearlyuniform, because the propeller sections are working onthe straight-line portion of their lift curves.

(3) As the propeller approaches maximum thrust forthe high pitch settings, the tip sections begin to falloff in thrust, owing to the blade sections operatingnear their stalling angles.

(4) At the lowest ~ given for the 27° pikh setting

(figs. 7 and 20), the blade is stalled from the 75 per centradius to the tip, showing a pronounced decrease ofthrust and an increase of torque.

Effect of propeller speed on differential thrust andtorque,—The change in the thrust and torque dis-tribution resulting horn the variation of the rotational

velocity of the propeller is given in Figures 27 to 30.TT

These curves are taken for the v of maximum efH-n~ciency in order to show the results of most int+mesttothe designer. For tip speeds up to 1,050 feetpersecond(2,1oo r. p. m.), the ordinate-sof the thrust and torque

.12

.10

.08

c>

.06

.04

.02

0 2 .4 .6 .8 1.0 12 1.4V/d\

FTGTJEE21.-Oompariwn of power c=mftldantfrom force maasrem ents and yawrmtar meammmena Pm@@r c-o

gradient curves are continually increasing. Abovethis speed, the outer sections begin to fall off in thrustand increm in torque, whereas the inner sections in-crease in thrust aa before. At 1,250 feet per second(2,500 r. p. m.) and above, the outer 10 per cent of theblade for propeller C-6 is producing negative thrust

. [2

.10

.08

Cp

.06

.04

.02

0 2 .4 .6 .8 1.0 12 1.4v/nD

FmuEE=+%mpmisan of PJWWomS3dantfmmfmmmmsummentsandymY-meia mwmaman~ Pmpdk C-S

and porntive torque. At 1,350 feet per second (2,700r. p. m.), the whole outer 25 per cent of the blade istraveling above 1,o5o feet per second, and showing acorresponding decrease in thrust along the blade. TheR.A.F. 6 propeller does not drop off as much in thrusttoward the tip above 2,500 r. p. m. as the Clark Y

---- — . . ..–.. .—. -A. ..-----s . + .-.— --==-! ------- .-=

4+46 REPORT NATIONAJ ADVISORY COMMPPPDE FOR AERONAUTICS

propeller but otherwise shows very nearly the samecharacteristics.

Total thrust and torque.—l?rom a comparison ofthe total propeller thrust and torque from the force

.12

.10

.08

‘G

.061 I I I I I I > I I5-1 I W

V/d

FIGURE23-Comprfmn of mm amfOdant from form mea!mementd and yar-meti m&wremeJIts. PrqAfer G1O

teats and yawme@r tests, Figures 11 to 16, and 21to 26, respectively, the following may be noted:

(1) The constant hub-drag coefficient brings all ofthe thrust curves like those shown in Figure 9 intovery good agreement at the point of zero thrust. It

.12

.10

.08

Cp

.06

.04

.02

0 2 -4 .6 .8 1.0 [2 1.4v/nD

~auEE2L-Compatimnof WWEXmalkientfromforcnmeamranontsondyaw-metmmeammmmk PropouorR-o

should do this for ordinary prcpellera that have awashout of pitch tmvard the hub, since where there iszero thrust the slip stream should be negligible andconsequently the drag due to the slip stream shouldbe zero.

(2) The thrust curves of Figure 9 have a veryuniform separation which is due to the increase in

body drag caused by the slip stream. This difference

in the ordinates of the two thrust curves at any ~

iS called ACT ~d k plotted ~~t the total CT h

.12

.10

.m

G

.06

.04

.02

0 2 .4 .6 .8 /.0 1.2 1.4V/nD

FIGURE2S.-CamfwhonofIMrermeffidentfromforcemwstuementsondynw.metermemm—emelk% PrOpllkR-8

Figure 10. The increase in body drag due to theslip stream is approximately equal to 8 per cent of thetotal- thrust of the propeller for this particular typeof body. This relationship is independent of pitchsetting, provided that the propeller is set to have a

.12

.10

.08

Cp

.06

.04

.02

0 2 .4 .6 .8 1.0 1.2 1.4V/nD

FIOIJELE!M.-Comrmrfwnof wwer cwfffdent from f&ca mownrements and yaw-meter memumments Propafk R-10

washout of pitch toward the hub. If, as with the 9.8°and 7° settings (fig. 3), the geometric pitch is constantalong the blade, or increases toward the hub, thecurves of integrated and measured thrust do not go

through zero at the same ~ ~ consequently this

relationship does not hold. In such propellers, when

.

DIFFER13N’lZAL ~URll&U3 NT, TOTAL !TMHJST, AND TORQUE OF SIX FULL-SCALE PROPELLERS 447

the total thrust is zero, the velocity of the slip streamover the body is greater than the ffee-air velocity,because of the positive thrust on the inner sectionsand negative thrust on the outer sections of theblades. These low pitch settings are rarely used in

.004

,003

fY@2I I I I I I I L

,001 I I I 1X1 I I I

o !!! I I I I I I I I I I I I I

.05D=Z%3T\

.04

.mCILJdx -w

.01

0 1 .2 .3 .4 .5 .6 .7 .8 .9 1.0x =Iyn

FIGUREZ’.-VmfatIon of thrust and torqm dkhibntion due ta change fn r. P. m.PrOpelferC-@. Set ~ at 4Z-fnohradfox Mr. p.m.

d.!jCix

d~dx

x =rflFmuaE 2%,-Vorfatfon of thrnst and torqne dfstrfbntian due to changefn r. p. m.

Propeller C-& Sat ~ at 4$inti radfrm. Hfgh r. p.m.

practice, consequently the above relationship issticiently accurate for practical purposes.

(3) The agreement of the effective thrust coefficientsobtained by the two methods indica~ that the

above factors are very satisfactory in predicting totalthrust from total head measurements.

.ax

.005

.004dr:

.003

.m2

.001

0

.05

.04d~

.m

.02

.01

0 J .2 .3 .4 .5 .6 .7 .8 .9 1.0

.-001

x =rfiFIGURE ZiI.-Variation of thrust and turqm dkbibntfon due to chancein r. p. m,

PropellerR-6. S&P at-fnch radfns-hw r.p. m.

.006

.005

.a94dcJ

‘X.003

.002

0_iI I I I I I I I 1

“2700~.~.rnI

-–-–-2600+=1ti/nl)+ 0.251

F—-—2500 =

.05 —._2400- , I I I .

——-2300’ ‘w.04 ,–y–fq-r .&% I

>“us!

‘z .03

.02

.01

0x =r.

FmuEE W.—Variation ofthroet and torqno Wkfbntfon due to cimngEfn r. p. m.Pi-OpaIlerB-9 %t~at~fnehradias- H&hr.p.ro.

(4) The power curves are in good agreement.

LAiTGLRY MBaIORLAL AERONAUnCAL LADOMTORY,NATIONAL ADVISORY COW~EE FOR AERONAU~CS,

WGLEY l?~LD, VA., Apti ib, 1$%%?.

.

. .. . . . . . . . ....—

IUIPORT NATIONAL ADVISORY

LIST OF SYMBOLS

Hp—reoorded differential pressure in yaw headtubes due to the twist of the slip stream

H~reoorded total head behind the propeller withpropeller rum@g

H.O—reoorded total head at the same point with the

COMW’ITMI FOR A13RONAUTICS

Q-torque of the propellerPower

cp”—pn3PT—thrust

C.=&

AC~=Prepeller thrmt-eflective thrust

pn21Ypropeller off‘ H—total head added by the propeller =HT –H=.

Z&axial velocity through the propeller planeV~tangential velocity though the propeller planeTP-resukmt velocity through the propeller plane

REFERENCES

Wood, DonaldH.: Fu.U-ScaleTestsof MetalPropeller atHigh ~p 8yeda. T. R. No. 376, N. A. C. A., 1931.

Freeman, Hugh B.: Comparison of FulMoale Propellershaving R. A. F. 6 and Clark Y Airfoil Seotions. T, R.No. 878, N. A. C. A., 1931.

Doughw, G. P.: 13xperhenta on Model Airsorews at HighTip Speeds. R. A. S. Jour., June, 192S.

Douglw, G. P., and Ceombee, L. P.: The Measurement ofTorque Grading along an Airsorew Blade, IL & M. No.992, Britiih A. IL C., 1925.

TVeiok, Fred E., and Wood, Donald H.: The Twenty-Foot

f-angle of twist of the slip strea& - -K+onstant for each yawmeterp-mass density of the air~radius of any blade element

D-total diameter of the propellerR—tip radius of the propellern—revolutions of the propeller per unit timeP—propeller pitohh—blade thiclmessb-blade width

V+iwe-air velocityL&mass of air passing through the propeller

1.

2.

3.

4.

5.Propeller Res-earohTunnel of the National Adviso~ Com-mittee for Aeronautic. T. R. No. 300, N. A. C, A., 1926.

perunittime

Values of’~ and’~ for pm@kr C-& (From faked cnrvm)

2+X31 %-0.7-27 Z.o.w r=o.C47

Settlnr3v

~D

Z-o.m2=0.421

dCrz

W&

am.awls.m’&s.C9Wll.Wo73.W7re.OxEa.ml.W&no.W55.QIlm.WW3.mW7:%%.Coml.W.W.Wlm.Otm.Ollu.OU45.Olw.Oloza.Wlm.Cn)7bo.W.550.m.CQlw.0104s.015s.01497.014M.01314.Oulo.01076.W3&3.WtJo.cul?s

dCbx

dCr-—&

O.msxl.W66.m.W301. CW31O

0.1030.U370.U&06. a315. CO1O

CLW7W. W570.Co4m.01240.Omdli

ll” --------11”_______11”----------ll”---------11”----------

0.20.30.40.K1.ea

:%’.40.m.00.70

.al

..M

.40

::.m.&l.W

.m

.30

.40

.50

.eo

.70

.al

i%L 10

%.5).eo.70.f?l

i%L 10L%

a 0S09.0491.m:%%:=.0s4s.W.ozm.0M3.O?W.075s.mm.=.Oua.0343.0213.W75

:%%.OW.0765. m70.0533.W.02E3.Olm.W3s

. 1M9

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.OW

.0314

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:%.02eo.0140

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:%%

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a axd.0777.&u.m.Wo

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-: %!

.. . . . . . . .. ll?a. 1a57.0311.0663.OzeJ

.. . . . . . . ..1240.1206.llzo.1016.0723.O.MLl.0316

.. . . . . . . .

.. . . . . . . .. 10EO.IMO. la46. llQ6. lm.0310.mu.0416

.. . . . . . . .. Km.1186. U76.1316.IzM. E41O.1076. cwo.0720

o.m6cm.m.Cm80. WU1O.m

16”-_____-—w-----------Iv--. -—–.-.l&-----------lcP---------lr_________

lw_________lT-_.__—__lw---------lw--..-—––.-w __________1’3+----------m-. —-----W-----------

23”----------33”---------23”-- .---—..23”_________z3”----------w--------23”_________23”----------‘zw.-. --—---Zw----—–.-.

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; ;42&

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.......... 14m. 14W. L&50. lWI. lfxa. lW.13&9.1025.0770

...........O%wl.03140.02s10.Q7&K1.OzW.021ea.Ols.m.Olw.01070

D-RENTL4L MEASUREMENT, TOTAL THRUST, AND TORQUE OF SIX FULL-SCALE PROPELLERS 449

TABLE II

VfdnwI of ~ and’~ for propeIler C-S. (From fahwl curves)

-1Setthg vn—D

Z=o.al z.om r-o.ml zmO.7S7 Z-O.842 S-O.047

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.03970

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o.as15.W$3.0610. a317.0102

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. 0L55

. 1s3$

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. 16s9

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.. . . . . . . ..mlo.amm.Omw.02sm.027Zo.crwm.022@3. 01’W. Olmb

dcrx

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0.1146.CK@o.0760

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TABLE III

Vdnesof’+ md ~ barpropaller C-10. mm faked curved)

.Z-O.631t-o .421 Z.0J20 2=0.737 Z-O.842 S=O.W7

Settingv

n—D d_&&

0.B’55

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ADWSORY450 Cohmrrrlm FOR AERONAUTICSRDPORT NATIONAL

TABLE IVVzhms Of %G and %Q fca pqdler C-O. Set 9.W at 4Mnch radk. (From Wed cnrvea)

Z= O.737 I z.oa42 S- O.’J47s-o.4nI

z- 0.626 z- 0.631

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-: %%. . . . . . . . .

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R. p. m.dCgx

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-: %%.. . . . . . . . .

. mfbs7,0Q410.mmo.m.ml16.m.00497

:E.W373. W312. W@.al?m,QWm.W076.m6fr2.Ww6. W416.MG20. mo

l,’m --------Ill. -.. —-----lm. -.._ —..-l#xL -----l,m. ——---l,mJ--_-—-l,4f0--.—----l,4m--_-—-1,400-------l,4m——-----l,4m--—---1,403 —-----l,6w -------I,W--------l,em ----------l,Eu9---------l#mI--------l,6w --------I,sw--------l,8w -------l$crl_–.–___-l,&m---–__–l@L-.–.-__L8a3-–..-.__

a 10-.m

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am.0640.0493.CR?3.0178. clu7

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-. m.W4so.W434.m.01%3.mlaz

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:%%

:=.OcQM1.00260

am.om7.G?31.0410.Om

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–. m20

:%%?

:%’%.00127.c05m.m.Wfo7’.IB316.W2m.0M22.00404.K@a.K@15. m16

:=.m

:=.mm6

aaw:%%.0410.0104

–. w.m.a’M6.Wm.Oim.014s

–. 0140. lm. W’s.0$.$4.Mm.0162

–. o122.1003.QJ17.0$37.04m.0162

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DIFFEREN!ITAL MEASUREME NT, TOTAIJ THRUBT, AND TORQUE OF SIX FULL-SCALE PROPELLERS 451

TABLE VI

Values of ~ and’~ forpropllerC-10. Sat9S at K/&h radhm (l?rom W mrWO

R. p. m.

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dCo

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. . . . . . . . . . . ..-14m._-..._ ---

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452 REPORT NATIONAL ADVISORY COMMFITDD FOR AERONAUTICS

TABLE VII

Vd~ of’~ and ‘~ for IXWAIer C-6. Set Tat 42-fnchradk (From faked cnrws)

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. @1243

.m

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DmRENTIAL MOASuR EMIINT, TOTAL TFIRUST, AND TORQUII OF SIX FUL&SCALO PROPELLERS 453

TABLE VIII

Vd.esof ‘~~ and ~q for propeller R-O. (From W IXXIVW)

r=o.’347

JSetting vn

——

r-o.431 2-0.626 r-o.lm Z- O.787 r=oM!2

dCr=

‘CrT

a a313.W.59.0476.0273.m

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. Ill%

. mm

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.W226

.W

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.1470

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. C816

. W24

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dCr72-

dCox

clcQ7&

. mm

.m

. mm

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.mm

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. mo

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. 0m40

.01720

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a Oiisl.0496.am.0231.C4m

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‘m----------- .w . .. . . . . . . . . . . . .27 . . . . . . . . . . . . . .!27— -. -. . . . . . .v. ——------zr’_ .. . . . . .._- -w — - . . .. -. -.. . .P — . . . . . . . . . . .w . . . . . . . . . . . . .w — -. -. . . . . . -w. —---------- .

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coMraTPEENATIONAL ADVISORY454 RDPORT FOR ADRONAU!ITCS

TABLE X

Z= O.737 r=o..w r-o.647

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TABLE ~

Valnm of ~ and’+ for propelk R-O. Set 9.8°at 42-innhradiua. (From fdred curve$

.

2=0.842 I r=o.947I

Z-O.421

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=

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:%%

2=0.526 Z- O.631 Z= O.737

R. p. m. vm S!.g ,g

I % I!2.g

: ~4g

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.O?a

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.m

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:=.m343. ml. WISU.f0w3.aucm.aW8.MrZG.mm9Al&

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:U3&l

. Om

–: E.Wi8.0710.6i85.0241

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a wm.fmn.m24.0315).axm

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DD?I?I!IRWWT.AL M33ASUREL5NT, TOTAL TEWJST, AND TORQUZl OF SIX FULL-SCALE PROPELLEES 455

TABLE XII

Volnmof ~& and~ forpropdferR-8 W 9S at 4&lnohrodfns. (FromW cnrvw)

-1R, p. m. vG

Z= O.421 r-o.620 z-oml Z= O.727 Z-6442

-dfl%‘iiF

am-m7.m4Eo:W!.mzm

.Ca5m:%.maa.mzm.W.@Wm.m4m.m.za.m

.W40

.Wm

.m4z

.m

.m!i35

.msm

.OE.m

.W

.amz

.W

.m522

.mlm

.m

.Wm

.m12

.W

.mW1

.mmo

. WI

.al.xa

d% d~7iF x

— -—.. ——-——- —.- .

0.0S70 O.oomo.olm.mm :%%awl .mm

.—. — -. --—.mm .mfm.W .mms.0262 so!&.m4s

——— ——..W .W

.W:= .m.mm .mz88

—.-—— —.-..mll .W45.04m.0270 :%%.Wa5 .mma

—.—_— ..— —..mm.Wa :%%.mos .m=

—-.----— —. —--.mm .MW76.W2 .mm.0K&5 .W

——— —-. —--.mm . 0M14

:%% :%

.mm .0Q5&5

.mm .CWt5

.mm .03296

dCrx

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.W95

.0497

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. Wlm

.amm

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. m242

.m140

.mm

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----------lam--_.–-.-–.

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. m74

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lm)-.___.._’_lCJ%._._.__-lmo_________

--. -.-.-—16m_-.—___

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m..-. -—-....--- —. —..

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!!!!!+_TABLE XIII

ValUesof ‘~~ ond’~ for propeller R-1o mt 9.F at 4Xnoh mdIu% (From fefred cnrves)

I I r-o.~1 “Z= O.Z37I

Z.0M2I

zmO.947S-o.m r-oml

dax

aw.rx&l.m+75.M.mmo

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:=

. mm

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.W

.03s28

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dCrZF

df%z

dCa7F

—.—.Clan&.CmfJ.Oma.mm

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—----.mm.W.wml.mS&J.Omlo.mlo.007J5

——.—-.mma.msm.M.m

———..m.mm

.- ——...m.m576.0m12.mw.mm.mzo

Km_. _.__-—lm_.__–...-KKo_...__..._lm_.._-.-..mm--------

......... ..m--.---—-–

-.-. —-.—-.l!4m--— -----

.— -------

14m...___-...lam_. _-... -..lam-_ . . . . . . . . . .14m_. . .. —_-.–1401---------

Iom----------.-. .—. -.—.

.— .- .. -----.—---------. —.. .-. —..

.— . --------Iwo- . . .. —.-...law-----------

-.. -.-. —..IBM-.. .._..._

2m_________—. —.. -.. —.-. .— .- .-. .

am2_._-—.-..

:;4.--.__ . . . .-- —--------

2100_ .--._.21m--------

22m—._______. ..-- —.—...— —.--...

o.16 am%.25 .0405.35 .CG62.46 .02m.6.5 .maa

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149900-3%30

456 REPORT NATIONAL ADVTSORY COMW’ITE E FOR AERONAUTICS

. TABLE XIV

Valnw of ~ and’+ fca propeller R-6 W P at 42-indI radlw. (1’rom fahwl mrws)

R. p. m.

Ire________lm--------lm_______mo__-.—--

ImL-------~---–—~-_-—-12w-.--.–––

14m_..__.__,:~:__:::

14m_:L___

lw&-------lm--------lImI_________16m-------

———.—DEW_–.-.--..

--------~--–—-..

~-------——.——

am3_--.-.——2m&-------

2103 ----------2100________21@L______21@l--------

2m--------2m-------~--.-–-2m--------

-.-----Zm–.__.–._-.2.m--------

.--. —. .

Z4m-----------.--—.

24@L– ______.—-. .-—

--- —-..2KL_______

——.-.—.

m3L_______.—-— ——

Km---------

2m––--–.––..-. --. —.

2mL_______

va

0.15

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