Naca Report Acr l4h07

5/26/2018 Naca Report Acr l4h07

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WAIHIME lUNBOWORIGINALLY ISSUEDMgU8t 1944 asAdvanoe ConfidentialReportLkt07

CHARTsOF A

FOR ESTIMATIONOF TEE CEMWXERISTICSHELICOPTERRCILWRIN FORWARDl ZZGB lI- PROFILEURAG-LIFTRATIO

FQR UM WISi3DECTAMUTLARBLUESBy F. J. Bailey,Jr. andF. B. Gustafson

LangleyMemorialAermauticalLsngleyField,Va. Laboratory

T.NGI,EYMEMORW AFXONAUTICMw&I- l,qGTON . LABC)XUTORYLangley Fielcl, Va.

NACA WARTIME REPORTS are reprints of papers originally issued toprovide rapid distribution ofadvance 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 chsnge in order to expedite general distribution.

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NACA ACR l?O . L4H07ITATIONALADVISORY COMMITTEE FOR AERONAUTICS

ADVANCE CORFIDZNTIAL HEPORT--.CHARTS FOR ESTIMATION OF THE CHARACTERISTICS

OF A HIKLICOPTER ROT@R IN F()~flJ,RDLIGHTI- PROFILE DRAG-LIFT RATIO

FOR UNTWISTED RECTANGULAR BLADESBY 1?.J. Bailey, Jr. and F, Bc Gustafson

SUMMARYCharts showing the rotor ~i-ofil~ drag-lift ratioare presented fcr a helicopter rotor operating inforward flight and having hinged rectangular untwistedblades. Charts are given for a range of power inputcovering glides, level flight, and moderate rates ofclimb. Each chart expresses the relation between thelift and We profile-drag characteristics of.the rotor

for various combinations of pitch angle, tip-speedratio, and solidity for a particular value of a parameterrepresenting the shaft power input.A particular drag curve, represented by a powerseries, was used in preparing the charts. This curveis compared with experimental curves for typical air-foils. The method by which the charts may be used incalculating the total shaft power required for anyspecific flight condition is shown by an example.The charts indicate that, for the rotor with

rectangular untwisted blades, one effect of increasingthe shaft power input is to produce a moderate increasein the profile drag-lift ratio. They further indicate)that, regardless of the amount of power used, theoptimum profile drag-lift ratio is obtained at thehighest pitch angles permitted by the high sectionangles of attack encountered on the retreating side ofthe rotor disk.

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2 - NACA ACR ]~0 . LJ H07INTRODUCTION

Because of the pressing requirements of procurementagencies for a rational method for evaluation of heli-copter proposals and because of the requirements ofhelicopter designers for a basis for choosing theoptimum combination ofvariables, it was felt that aneed existed for design charts summarizing the effectof changes in the major variables on the characteristicsof a powered rotor in forward flight. The method ofanalysis of reference 1 accordingly was used to preparesummary charts that are generally similar to figure 3of reference 1 but cover various amounts of shaft powerinput. The present report has, for simplicity, beenrestricted to the basic case of zero blade twist.

METHOD OFANALYSIS

Parameter for shaft power input.- The primary modifi.cation made herein In the method of reference 1 is theintroduction of a new parameter P/L for rotor-shaftpower input. The symbol P represents the drag thatwould absorb the same power, at the velocity along theflight -path,as the power being supplied through therotor shaft. The parameter P/L is therefore equal tothe total drag-lift ratio, or

where

1)()i()Zp

:= ( )0+R)j(:)p(?)cprofile drag-lift ratio

induced drag-lift ratio

parasite drag-lift ratio

(1)

drag-lift ratio representing angle of climb;that is, rate of climb divided by velocltyalong flight path


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u., . , , . --by,tke method oy.tll.nedin reference 1 for any desiredvalue of P/L by inciu5ion o~-the shaft-torque coeffi-cient

whereCQ0

a

IJcryintherotor.

torque coefficient solidity; ratio oftotal blade area to swept-disk areaslope of lift coefficient against section angleof attack (radian measure)tip-speed ratiothrust coefficient

equation expressing the torque equilibrium of the(See section entitled Applic~~ion of Theory in/_,tireference 1. ) The eXpreSSiO~ for TfJ.- iS ~iverl inoaequation 14 ofreference 3..Rotor characteristics.- The sample rotorthe charts presented herein were pre~ared washave hinged rectangular ljntwisted~jlades. Athe mass factor y of 15 was usjjd. The chartsidered applicable to rotors having values offrom O to 25.

for whichassumed tovalue ofs are con-y rangingAirfoil characteristics.- The airfoil characteristics

assum~d m reference 1 were used in preparing the charts.The equation representing the section profile-drag coef-ficient iscd = 0. 0087 - 0.021&a. + 0.400a02o

where CCois the section angle of attack. The corre-sponding profile-drag curve is shown in figure 1 withexperimental curves for several typical airfoils.


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4 NACA ACR NO. 4.H07Limits of validi~ of theory .- As was explained inrefer~e 1, calcu~a~ions based on the representation ofthe airfoil-drag characteristics by a power series of-thrce terms become optimistic when high blade angles areencountered over too large a portion of the rotor disk.It should be ncted, however, that very little improvementin (D/L). is to be expected by operating beyond theconditions to which the theory is limited, as a resultof the rapidity of growth of the region of high angleof atback. This fact is readily demonstrated bygraphical treatments for both au.togiroand helicoptercases.In the example given for the autoglro in refer-ence 1, a satisfacto~y limit was found to be the con-dition in which a blade element at an azimuth angle ofZ700 and having a relative velocity u&R. equal to four-

teenthsthe rotational tip speed reached an angle ofattack oT 11.750 The use of this locus line has beenretained in the present example but, fcr convenience,the angle of attack has been increased to an even 12.Because the limtting angle of attack depends upon thesection and upon- the Reynolds number and Mach number,an additj-onal locus Iilnehas been included for an angleof attack of 16. For values of F/L greater thanabout 0.1, the highest blade angles are encountered attho blade tip instead of inboard; hence, locus linesfor angles of attack of 12 and 1-6at the blade tip, atan azimuth angle of 270S are substituted for those forT = 0.4 whenever the tip locus lines fall above thosefor - ook~T

In the charts presented heiein, the locus Ilnes forthe conditions for ~~hicha blade element at.an azimuthangle of 270* with a relative velocity uJ2? equal toJ-four-tenths the :eotatlonal tip speedreached a specifiedangle of attack are designated by the symbolSimilarlyj the locus lines for the ,7=@4)(2.7fJO)0conditions for which the blade tip at an azimuth angleof 270 reached a specified angle of attack are desig-nate~ by the symbol a 1. 0) 2700)

RESULTSThe charts of (D/L)o obtained for the samplerotor SLreshown in figure 2. The chart for p/L = 0,


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>>

NACA ACR ~ O . L4U07 ........,that is, for autorotation,, ;s the same as figure 3.Qfre. e.rence1 ex,cept for thechoice of limit lines. Avalue of P/L .tif0.2~a-ye eonstdered as typical ofpresent helicopter? at-ornb~r cruising speed. Valueslower than 0.2 correspond tocleaner craftor to apower-on glide. Higher values ,corrbspondto less stream-lined craft or to a positive ariglerof climb; the highestvalue covered by the present charts, P/L = 0.5, tiaybeviewed as representing a typical helicopter climbing atan angle of approximately 15 or 20.

DISCUSSION

Inspection of the charts reveals that the effectof increasing power on the optimum (D/L)o, as indi-cated by the lowest points on the liw.itlines, is toproduce a moderate but progressive increase in themagnitude of the value of (D/L). and.to shift theoptimum tip-speed ratio toward lower values. It maybe remarked that similar charts for twisted bladesshow a relatively insignificant increase in (D/L)o,up to values of P/L of 0.2 or higher.AS has already been noted, for both helicopter and

autogiro conditions, the optiml.nn (D/L). is indicatedas being obtained at the highest ,pitch angles permittedby the section angles of attack encountered on theretreating side of the rotor disk. The choice of pitchangles materially lower than those corresponding to thelocus lines for an angle of attack of12 results inextreme inefficiency.

SAMPLE PEIU?ORMANCECAI&~TION. . ..Power absorbed by main rotor.- In order to illustratethe manner in which he charts may be used to estimatethe power required by a helicopter under a given set ofconditions, an example has been included.Assume ahelicopter to be operating i.nlevel flightat sea level under the following conditions:

Forward speed, feet per second ,. .* .. *...,......: @%?QsTip-speed ratio, .,..0...*.,*..6*...*. . 0 . . . . 0 , . .Disk loading, poun s per square foot ............... 215 ,6s~~%p \%


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Gross weight; pounds ~t.*,...9..9 ******+**........**.* 3140Rotor radius, feet .........0 ******4 *******9.. 9*.*. 20Blade plan form ...................}....... . RectangularBlade twist .... ... .... ...........,... **.*.,.*. Nonec Solidity .......................................... 0.07

9Parasite-drag area, square feet ~ .? . . . . . . . AO. OOOO 15, . , - ,- . . , ,For these asswptions, /-CL = 0.32 and ~ = 4.70.In order to obtain a first a~p%m+lm%l%on to (s/L)8igforuse in equation (l), P/L is assumed to be 0.2. -ure 2(e) then gives a value of 0.086 for (D/L)o at theintersection o.fthe curve for v = 0.2 with the line for~ = 4.70. The value of (D/L)i, as indicated in refer-Wence 1, is simply CL~ or 0.082. The parasite drag-lift ratio iso 0. 001139 x 15 x 80)2Z*= 3140

= 0. 036Since the rate of climb is assumed zero, the valueof P/L from equation {1) is

P- = 0. 086 + 0.082 + 0. 036 + oL = 0.204As a second approximations the value of (D/L). maybe obtained by interpolation between the charts forP- = 0.20 and for P- = 0.25. The value so obtained is,L Lwithin the limits of accuracE in reading the charts, equalto the original value of 0.0 6 and no further approxima-tions are necessary.The total rotor-shaft power required for the specifiedcondition may now be calculated as

0. 204 x 3140 x 80550 = 93.2 horsepowerPower absorbed by auxiliary rotor.- The charts mayalso be used to estimate the power absorbed by the tailrotor.Assume that the torque of the-main rotor is beingcounteracted by an articulated auxiliary rotor havingthe following characteristics:

Blade plan form .. .. . * 0.. . RectangularBlade twist None.. ...0. ... ..***** *..,.... ,......Solidity .,.** . .* *. * ** ******* * ** 0.10


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NACA AC?? I?o . 4H07 f~j 7Spindle angle, a,-degrees , 00. . 0. 0. . . . . . . . . . . . . . . . . oDistance between spindle ...and.ain .._

rotor axis, feet .*....*,...................*,..* 2Radi~~s,feet .*.*....* .***.*.* . . . . . . . . . . . . . . . . 0. . , . . zTip-speed ratio ..*,..*..* ...............*.... *,... 0.2The tail-rotor thrust, based on the main-rotor poweralready calculated, is 102.7 pounds and the correspondingthrust coefficient CT iS 0.00536. The inflow-velocityfactor A may be obtained from equation (8) of refer-ence 1

a A %= -+v 2W2Substitutl;n of the values for the present case gives ava~ue of = - 0. 0134. By using a lift-curve slope aof 5.73 per radian, substitution of this value of A inequation (6) of reference 1 gives a blade pitch an@e 6of 4.470.

in order to permit the use of the charts of figure 2,it is convenient to calculate the value of CL-O from therelationCL 2C Tl=5 2GvCLwhich gives a value of ~= ,Zo6~. The value of P/L

corresponding to the specified cow.bination of values ~,e, and CL/O is found by interpolation between fig-ures 2(c) and 2(d) to be 0.138.

The auxiliary-rotor shaft power is then0. 138 x 102. 7 x 80 = 2.1 horsepower550

Since the auxiliary rotor may also be producing a drag,the total power charged to torque counteraction should.be calculated from the sum of the values of (D/L) and(D/L)i. The value of (D/L). at P/L = 0.138, bjinterpolation ~rom figure 2, is 0.120.(lI/L)i is The value of


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= 0. 067The total drag-lift ratio is then 0.187 and the corre-sponding power Is 2.8 horsepower. The difference betweenthe two values ofpower results from the drag on theauxiliary rotor and hence must be supplied through themain-rotor shaft; the revised value of main-rotor shaftpower is then 93.9 horsepower.

If a particularly rigorous treatment is desired,the difference between the auxiliary-rotor values of(D/L). + (D/L)f and P/L should be converted into adrag-lift rati; bas~d on the main-rotor lift, that is,0.049 = or3140 0.002 for the present case. Thisvalue should then be added to the original value of(D/L)m used in the nain-.rotor calculations, and theentir~ proced-me repeated. Examination of the problemhas shown, however, that the differences so obtainedare negligible for normal ranges of variables, sincethe rotor profile drag-lift ratio is not particularlysensitive to tinevalue of P/L used.

CONCLTJSIONS

1, The profile drag-lift ratio of a power-drivenrotor in forward flight can be completely specified forvarious combinations of pitch angle, tip-speed ratio,and solidity by a series of charts for different valuesof power input. On the charts, the profile drag-liftratio is plotted against the ratio oflift coefficientto solidity for specified values of pitch angle and tip-speed ratio.

2. For a rotor with rectangular untwisted blades,the theoretically derived charts indicate that oneeffect of ir.c.reasingthe shaft power input is to produce.a moderate increase in the profile drag-lift ratio.3. Regardless of tfi.eamount of power used, theoptimum profile drag-lift ratio is obtained at the


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highest pitch angles permitted.by the high section anglesof attackencountered on the retreating side of the rotordisk.

Langley Memorial Aeronautical LaboratoryNational Advisory Committee for AeronauticsLangley Field, Va.

REFERENCES~ 1. Bailey, l?.J., Jr.: A Simplified Theoretical Methodt) of Determining the Characteristics of a LiftingII Rotor in Forward Flight. NACA Rep. No. 716, 1941.I

~. Jacobs, Eastman ~., and Shep--an, Albert: AirfoilSection Characteristics as Affected by Vari-ations of the Reynolds Number. NACA Rep. NO. 586,1937.~. Jacobs, Eastman IT.,and Clay, William C.: Chara~-teristics of the N.A.C.A. 23012 Airfoil fromTests in the Full-Scale and Variable-DensityTunne1s. NACA Rep. No. 530, 1935.4. GOett, Harry J., and Bull.ivant, W. Ke~eth: Testsof N.A.C.A. 0009, 0012, and 0018 Airfoils in theFull-Scale Tunnel. NACA Rep. No. 647, 1938.5. Tetervin, Neal: Tests in the NACA Two-DimensionalLow-Turbulence Tunnel of Airfoil Sections Designedto Have Small Pitching Moments and High Lift-DragRatios. NACA CB No. 3113, 1943.


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&

NACA ACR No. L41i07 Fig. la.048

:044 ., -. ...

.0400 iVA(2A 230J2 /t .036 %/. 1

/ i; .032k

/oQ .028~bI .024q Ig NACA 00 12 ~ , / f /

zzt ~1& .020 /~NLQ .0/0 -% /

.0123, ----

.008 - Cd* = 0.0087+0216 CCo+Q400Eoe

NAl l ONALDVWRY.004 RMWEE FORAHgNAuncs

-2 o 2 4 8 8 10 /2 14 @Section angb of aTtQck, @70, dega Data from NACA variable-density tunnel; Reynolds number,

2.6 x 106; reference 2.Figure 1.- Comparison of the power-series profile-drag curveused In the analysls with experimental data on representat~vealrfo l sections.


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NACA ACR NO. L4H07 Fig. lb

I IV--r 4 ///1//& .020 /f //~ ,/\k }$ .o~6 . //9 / /

.0/2 ~ ~

IVACA23012.-~. ~-------- -------

- x NATI ONALD1 S I RY.004 - NACA 00/2 cOMM TTEEORAfRONAUTI CS

o -2 02 4 6 6 /0 4/2 /4 16SecT ion angle of at fuck, Go, deg .-(b) Data from NAGA Ihll-soale tunnel; Reynolds number, 3.4 x 106;references 3 and 4.

rl~e 1.- Continue&


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NACA ACR No. L44H07 Fig. lC.048

,044 . ... . .. .... ., .- .,..-,.+ .

.040

.036

.032 .

.0261 /

Cdo=0.0087-0.0216 GCO+Q400cC02 \.024

.020 I

J/ /.016

/1I

.012 I ~ NACA230/S

.008 I

.(W4 + A AL7A3-H-13.5m CA 2301 2 (l?=3. OxmyNATI ONALOVI SORYCOMM TTEEO AERONAUTI CS

o-2 0 2 4 6 8 /0 /2 /4 ,Sect~on ang/e of attack, (XO, ciegData from NACA two-dimensional low-turbulence tunnel andNACA two-d mens~onal low-turbulence pree8ure tunel;

Reynolds number, 2.6 x 106; referenoe 5 and unpublisheddata.Figure 1.- Continued.


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IVACA ACR No. L4H07, Fig. ld.048

curve - P++ ,Fl Fffbric-covered bl@de with solid

Ieadin edge; NACAOO12 -se@w;feyno ds numbe~ 1.72 x /0.0+0 B PI wood-co verea b/~de sNACA 00/2 section; eyno/ds Ylwnbef j .7L9 X 0

0z .036K~.Q .032~ Cd o= 0.0087-00216 Q?O+0.400CCOaalo0 .0282

/

+ .02+ /*g

//

~ .020 /

.8 RaQ .016% /

P

/ /// //.012

.008 -., A /. -MTDWLWKORY.004 COMM l Tk0RAERONAUTI CS

-2 0 2 4- 6 8 /0 /2 /+ /(

(d) Data on practical-constmction rotor-blade specimens, fromNACA two-dimensional low-turbulenceunpubl~shed data. pressure tunnel;FQzjure1.- Concluded..


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NACA ACR No. L4H07 Fig. 2a.2(

.2t

.24

.22

.2(

.18

.16

.)4

.12

./0

.OE

.Oe

.04

.02

0

0

K I LI I I I II I IY l\ln. I I I

11111111 f l ATI i 3NAdI s0Al l II I 1, 1 1 Ill I 1 1 1 .2 F-J- lb ~~ ;_~o f~o /Qo fioL i4 coefikf%- 3JA:o *A

CJJM l i E ORARONIUTNsI 1 1U_L1r 1Ill I

Illully I Ullu bL/ u, C-L9 (a)~L = Q -Figure 2. Profile drag -fift ratio for sarnp[e rotoc.


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NACA ACR No. L4H07 Fig. 2b.2t

.26

.8?4

.22

.2C

.18

./6

.14

./2

./0

.06

.06

.04

.02

0

- b \ \ \ \ \ \

\\ \\

\\ \ .

(b) P/L = .05 ~Figure 2. CocVin.iea.


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NACA ACR No. L4H07 Fig. 2C

.28

:26

.24

.22

.20

.18

./6

.14

.12

./0

,06

.06

.04

.02

0Lift coefflcien?- so~d~ ratio, ~/o--

(6) P/L= ./0.Figure 2.- Con7727uecf.


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NACA ACR No. L4H07 - Fig. 2d1.2&

.%

.24

.22

.20

./8

./6

.14

./2

./0

.08

.06

.04* .02

0 .

(d) P/L = .13Figure 2- Continued.


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I

II1 NACA ACR No,. L4H07 Fig. 2e

.2[

.2(

.2A

.22

a

./8

,16

./4

.}2

./0

.08

.06

.04

.02

() ,i. e P/L=.20. . .

Figure 2. Continued. b


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NACA ACR No. L4H07 Fig. 2f

.2&

.26,24

.22

.2C

./8

./6

.14

./2

./0

.08

.&

.04

.02

0

\ I \\ \l \ I \K I \ I I Iv I 11111=X 1

Lift coefficient soh ;fy ratio, ~/&-(f) P/L =.25

Figure 2. Conjinued.


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NA13A AcR NO. L4H07 ~ Fig. 2g

,

.21f

ix

.24

.22

,2(

.18

.16

./4

./2

./0

,08

.0(5

.04

.02

0

0

@) I L= .3L Figure Z.- ConTinu~d. ~

.


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II 1111lmlmn-m-mm 1 ,,, ,., , ,, --., . ,, . . ,---- --- .- .,-.. .,

NACA ACR No. L4H07 Fig. 2h

i28

.26

.24

.22

.20

.18

,/6

,14

./2

./0

.Ot

.Ot

.04

.02

II

1. \ l \ \l l\ I l\ IN I I I I I I I~

(h) ~L = .35 Fiqure 2- Continueci.


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NACA ACR No. L4H07 Fig. 2i

.2&

.26

.24

.22

.20

./8 1./6

.14~

./2.10

.08

.06

.04

.02

0Lift coefficient sohdi~y ratio, ~/E

(i) P/L = .40.Figure 2. Continued.

~ - - m mm-l mmmm -mmm mnm , mmmm m I .mI NB I I m III mu .8 , ,,, , , .,,, --., -..-, . ,,,,. -, ,,,. . ,, ,,,. . . . .. . . . . . . . . . .


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.. ..- ... ....-

NACA ACR No. L4H07 Fig. 2j

28

.26

.24

.22

. 20.

./8

,/6

./4

./2

I I I II 8

.06

.04

,02

0Lift coefficient - solkiity ra~io, ~/b-

(j) P/L = .45.Figure Z.- Continued. Y~IW

.


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.

NACA ACR No. L4H07

.2{

.2(

.24

.22

.2C

,18

./6

./4

./2

./0

.08

,06

,04

.02

0

Fig. 2k

i? .4 .6.8 1(9 M 40 r . . , Zo ao 100 KOLift coefficient sofidity ratio, ~/o- -(k] ~L =.5o

17qure Z- Concluded.

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Naca Report Acr l4h07