.— — .—.- ..-

~ny ‘M 1947” ..- >

NATIONAL.–-—.,

ADVISORY,.

COMMITTEE FOR AERONAUTICS

W“I’’IWW1E RIIPOR”ORIGINALLY ISSUED

October 1945 asConfidential Bulletin 5H31

COMPARISON OF THE ENERGY METHOD WITH THE ACCELEROMETER

METHOD OF COMPUTING DRAG COEFFICIENTS FROM FLIGHT DATA

By Thomas L. Keller and Robert F. Keuper

Ames Aeronautical LaboratoryMoffett Field, California

‘, ~.. ..... ..- -..:,., ,..,.,:.,,... . .;,,*,..,..,J. .

‘“’”““~NA(aKii~~’-”-..’. ,.

.,. ,’ N A C A LIBRARY.. .,’. ..,1-,. LANGLEY kfEMO~fi AERONAUT1~! .,,.,

.,.LABORATORY

WASHINGTON Langleyk’ield, V&.,’.

NACA WARTIME REPORTS are reprintsofpapersoriginallyissuedtoproviderapiddistributionofadvanceresearchresultstoan authorizedgroup requiringthem forthewar effort.They were pre-viouslyheldunder a securitystatusbutare now unclassified.Some ofthesereportswere nottech-nicallyedited.All have been reproduced withoutchangeinordertoexpeditegeneraldistribution.

A-57

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https://ntrs.nasa.gov/search.jsp?R=19930093566 2018-05-26T12:14:17+00:00Z

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ITACA CB HO. 5H31

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NATtOtiL “:hVI SORY”fiOMMITTmm.. . .. . . . .. ,, ------.I ... “.. , - .. ,

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Ft3B AERONAUTICS

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ADVAMCE COlW~IDE19TIAL REPORT “ ‘. ...”. .. . .. . J - ,.. . . ..

- COiPARISOi O? TEE. ~M@~.~.;;TH@ :WIT~”.T~” ~CCELERO~T= METHOD..

03’ COMPUTING DRAG COE3’IPICIEN!PS3’ROM FLIGHT DATA

By Thoma6JL. K6’ller aqd Robert 3’:“K$tiPer..

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...”. ““SUMKMW ‘.. 1“.

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A a“ompari$oh vasi made between the energy and the aacel-eromet6r mekhod,s of computing “drag c.oeffictient”sfrom flighttests of.the P-51B and the W39111 airplanes. The energymethod was found to be unreliable with the present types ofinstrumentation except under the praqtlaally unattainableconditions of very nteadar flight at conetnnt Indicnted air-speed within a vertically n+atlonary air mase-”

. . .

INTRODUCTION

In the pabt, many ueasureaents of the drag of airplanesIn flight have Involved the use of so~e variation of the so-aalled Henergy. methodn (deearlbed in the appendix) for thereduction of the dat.ao The results obtaine~ by this methGdare frequisntly very erratlcm odcaelonally even gi+ing.neg-tlve drag. ooefficlentso . -

Since the.res.kits from the Ilaccklekometer m6thodH(described iri’the. appendix). appear to be” consistent with -computed and wind-tunnel data~ t’he flight-test Pesulte r+ported in reference .l. offer”bn excqllent opportunity forcomparison of the two methods to determine the aause of thediscrepancies. This report presents such a a-omphrlson andInaludss supplomen~al data o%tklned from two epealal divoaperformed “at constant india~tbd tairepeed. in the k39AJ-1airplane. . . ..

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2 .“ IJACA CB ~o. ”.5H31

. . . . . .-DESCRIPTION/” 01’ EQUIP.~HT. “. . -

~iiplanee. .. ..

The airplanes u8ed for the tests were the North AmerloanP-51&L-HA and the Bell P-39%1. Complete deecriptibns e-f “these airplanes are given in references 1 and 2.

.. ....

.. .. Instru~entation

Standard NACA ph;tographlcally recording Instruments,installed in both airplanes, were used to obtain airspeed,pressure altitude, normal and longitudinal acceleration,and (for the P-39JJ airplane only) nngle of attack as func-tlcns ,of tine. Vqlues of. fre~air temperature .at differentaltlti:vdes“were .o.btzine.dduring ascent from the ptlo.t~.s indi-ctit”lll~iIls.trUiieIlt,and wore corrected for temperature rleedue to ilapqct of,the air. stream. .

.,

The air.sp6ed~moaeuGi& systems utilized., as. sourcee ofpl”th”t-dtaiic and tbtal. pr~ssur.es, free.1~ swiveling pitot-statio hOads moimted on booms located beneath the wing tips.These booms exteaded approximately 0,8 of the local wingchcrd ahead of the leading ~dge. Rach pitot-static bendconsisted of two static-pressure tubes and one total-.pree-sure tube, which per~itted tho use of indopandent sources ofstatic prossure fcr both the airspeed and the altituderocordera, ..

,.““l?hp pres~ure llnes from the. pitot-ptatic head to the “

recordlhg. ln~tduments wereafiade ns short as poesible inor”der to miuimiae lag, and the lines tp the recording air- “speed meter wero belancod to give equal flow rates in thestatic qqd total--pressure tubes during rapid changes in”pressure: (Wound t?sts of moc~ups of the airspeed andthe altitude pres~ure lines indicated that .tbe lag in the . .systame at the maximum rates of descent caused an error inthe rocordod altitude of &bout 20 feet at 15,000 feet(negligible) for.tioth airplanes .: . . , ..

.“

A co$recctiou four the pos”~tiori error of the pi.tot-statictube was determined from flights at various airspeeds pasta fixed visual reference point of known constant pressurealtltude. It was assuned that the meaeureinents of totalpressure were correct and that the variation of recordedaltitude with airspeed (obtained by a special sensitivealtimeter) at the constant pressure altitude resulted froa

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..NACA OB BO.. 5H31

the position of.,the static! tube only. Slnoe the maximumerror in alt~tllde, pe.+eternined by thta calibration, vafllone than the accuracy af 6h,+.recoT.dln~:dl%imeter used in thedive teats, no attempt wae made tb”cor”rect the altimeter recui-ings for position error-

!l!heaccuraoy of the swiveling pitot-etatlo head hae been “inveetlgated at Mach numbers up to O*8O Sn them.16-foot wind-tunn~l at the Ames AOrOn&Utldal ”LalOrhtOrY. The re-suits showthat thq effgcte of-compressibility not. tncluded In the regu-lar afrspeed callbrat~on ar# hegligl~lk over the flight 14aohnumber range investigated, .“ ..

The correat indicated alrepeed wag computed >?.uee ofthe standard formula

1%/$17031( = + 1)

o .aeevi = -1

L Po..

whore

Vz correct indicated airspeed, miles her hour,

H. free-stream total:pressure

P free-str~am static.”pressure ..

P. standard atmospheric pressure at sea level

METHOD OF ANALYSIS

If accurate drag data ara ~vailaale for nn airplane Inflight it Ie possible to mhalyse, Iridlrectly, the errorsinvolved in the use of the energy method by working bsckwct~d

from the drag data, through the energy method equations, toobtein values of airspeed or altlttide- “A comparison of thesevnluee with the actual v~luem”recordod during” the flightoffere so~e insight as to the nature of the errorta. The fol-10Willg discuaaion gives.a derivation of the neceasnry eQUatiOUSand a detailed explanation of”the proceaa. “

The equatlcna for the drag coefficient, based on theenergy and the accelerometer ffiethods (excluding pOpelleI?

thrust) have been derived In the appendix- The equation fromthe energy nethod has been shown to be

—. —

—.. .—-— --- .—. - -. —— ——

●

✌

✎ ✎

4 ....,.. . ., 19ACA-CB Ho. 5H31..3. . .:, , .. .... . .. . .u, :+...... :“

.“ il~: ‘f. r“””.:..”. :- 1...... ..-.. ... ;.;1 .

.. .1, ‘..

w ““(

.dh/Jt

)

‘TT/~t ‘. ... ~ “ “-c =— -.— {1)D q? VT

, .“%“:. .-. .:. . .. . .:..,. . .. . :m

-: .,: “ . .. . ,..whor@.’. “ ; ‘ . . . “

-- ... .. ..i

.J’”

.

w“-’”.“wei%ht of a-irplane, .pounds ... .

q free- etreem dynamic pressure, pounds per” square foot, ..... ..... . .

s. wing area, equare feet ‘ . .

h true altitude, feet,.) . ....VT t~ue airspeed, feet per ~ecend .

t tifile,seconds

g acceleration due to gravity, 32.2 feet per sectind persecond . ... .

In this discussion the slope of the altitude curvedh/dt will be assu~ed postive when h decreases, and the “slope of the airsFeed curve dVT/dt will be assumed posi-tive when VT increases; hence the Einus sign in equation(1), Equation (1) ,can he tr~nsforne~ as follows:

(2)

or .. .

.:-... . . .,... . dh

(

CDqS dV~/d~ .:,.. — = —+—

)VT. i3)

,.“1 at . w. ~’. . .,.,

“The.f.ollowing expressions, solvable by grnphlc~l in-tegratlon, .can be derivsd froti equntion$ (2) and (3):

Cnqs.—

w )g ,Llt

rlv#4t ’) VT dt “—/g’

—

!. . ... —--- —

. -,0.

I4

Thus-, If the “drag .datq obtn~ned by the accelerometer”method are apprbxinately correct and the “reaorded valuea. ofaltitude are aaeumed to be correct, the corresponding” air-speed-time curve can be computed by a Beriem of approxi-mation and integrations. In the ~ame manner, the correeponding altitude-time curve can be aomputed If the recordedvalues of alrepeed.are aaaumed. to be _correctm The dif-ferencs; l)etween.the copputed. aind recorded airepeed or altl-tufle.cuzvesi..theg;. is t@e, am”cmnt of error which-would pr-duce thb corresponding, error in.t.hs drag-coefficient curve.. .

. .

t TESTS, RESU~T%S,AED DISC.USSION-. .

Unreetrlc.ted” Ylight Conditions ..,

Yigures 1 and 2 show exnmplee uf airspeed and altitudecalculated ly the foregoing method from the data of apropeller-off dive of the P-51B airplane (diva Nom 2C ~reff3rence 1)s Ylgures 3 and 4 show drag curves for the saneflight, ccilculatod by the ener~y end the accelerometer methods,from which it Is apparent that the energy nethod yields iextremely erratic remultsm

The errors In the altltudo curve (flgo 1) or In theairspeed curve (fig. 2) necessary to produce the variationof drag coefficient shown in figures 3 and 4 are very small,and It is apnarent thbt n small error in either airspeed oraltitude could cause sufficient change in slopg to ~roducea vkr~ large error in the computed drag coefficient, Infact, even small errors in f.airing these curvee could leadto appreciable errors In drag aoefflcient. 11’urthernore, itshould be noted that the curves of figures 1 and 2 representthe outside llLlits of the error:. that 1ss the error in eachquantity was couputed on the baels of no error in the otherquantity, Actually, the error probably Is divided betweenairspeed and altitude and thus IS less than that shown foreither,

The dives r“eported in reference 2 did not follow anydefinite flight teehnique: that Ls, airspeed and altitudewere allowed to vary tinreatrained, the Sole obJective of thepilot being to attain as high Mach numbers as possible. Thequestion has been raised, however, aS to whether dives atconstant Indicated airspeed would yield data amenablo tothe energy methodO It was believed that this type of divewould yield the smoothest possible variation of true airspeed

.6 HACA CB HO. 5H31

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.. with time, w~~h the r.eeultant .increase In accuracy of the..-.me~surbdslopems dVT/dt and decrease In any unknown errors

.. $ue to rapid preesur.s changes.... .. . . ., . . .“.. . . . . Rdsitricte~ 9’1ight. Conditions .. . . .

... . . .Im. order to a“ec”er.tainthe effect of.a definite flight

ttichniqtie.on the results of the energy method, therefore,two dives at nearly constant indica~ed .airspeed”were per-formed In the P-39N-1 airplanes A sensitive longitudinalaccelerometer Was Included in the Instrumentation for theseflights, so that a dire,ct comparison cculd be made betweentho doubtful quantities involved in tho energy method andcorresponding quantities of established accuracy used in theaccelerometer method.

Time historios of variables measured during the two divesare presanted ~n figures 5 and 6, The necessFry correctionsfor free-air temperature wero applied to the ’f.ndicated values..of airspeed a.hd Pate of change of pressure dp~dt to obtfiin

. the true values of .nirspeod pnd rate of c“h”angeof altitudedhfdt used in tho computations of the longitudinal foroe.fnctorm

.. . .

Fl&ura 7 shows a .comp’arlson of the.longitudinal force.frlctors (Az sin a - AX COO. a) from the accelerometer method

.

(.iih/dt-and. — - w)

from the energy method.. . Theoretically,

‘T g. .~urlng any one dive, these quantities should be Identical.The resultant drag coofflci-ent co~puted from these data is.. .presanted in figure 80 It will bo observed that during thetime interval for each dive in which the contltions wereextremely eteady (70 to 145 seconds in dive number 1$ and55 to 150 seconds In dive number 2) the maxluum differencein drag coefficient Ac~ is approximately 0.0021 nnd theaverago ACD ifI very small. The agroeffient in results isconsiderably improved over thnt of the unrestricted fiivea(See fl~ure 3.) Jt is apparent, hnwever, that the slightest“.variation from steady. Conditions CnUSOP wilo variation b-

tween the cofiputed longltu~inal force factors and rendersthe onargy method unr~liablee

Furthermore, .sinde the derivation of tile energy ncthoddoes not allow for any. extraneous acquisition of energy,

MACACB ~00 6E3”1 ?.

suoh as that duo to vertical air ourronts or changes of-mert’icdl air cufTente,- conslderable error .-aould be intro--auced by tho alrplaneto transit through a rising or de-scending nir;icat!a..- ‘ .‘- .“. ‘

. .. .“j “

.. .

i It ia be~loved tha$; .if sztremely steady flight cond~tione (including constant indl’oated alropeed) could be main-tained by the pilott the energy”rzethod of computing drag :.coefficient would be of value.z In practioal flight-retaoarchwork, especially at high MaGh numbers, howevor; the roqulredconditions nre seldom achieved and are diffioult to recognizewhen they are anhlevado. Thus,. i-t Is believsd that theenergy method cannot be rolled upon for conclusive results,

CONCLUSIONS .

Fro~ cckparison with the accelerometer method, the .energy method of couputing drng coefficient from flight dntais believed to be unreliable with tho present instrumentationfor the following reasons: ‘

10 Tho condltione of conmtant Indicated airepeed andvery steady flight, which appear to be es8ential for accurate

application of tho energy method, aro impractical for ordi-n~.ry flight-research work (especially at high Mach numbers)

and are difficult to achieve nnd to recognize

2. The energy method is correct only for flights iE airhaving no vertical volooity.

&mae Aeronautical Laboratory,

National Advisory Commlttoe for Aeronautic;, “,. Moffett R’ield, Califo

-. —— ——------- ——-.——-———.XIt is Inbtructivo to note that, since, theoretloally,

the energy method should be exact. for flight in still air, It18 poss’lblo that tho altitude and airapeed curves of figures 1and 2 represent a type of preseuro calibration and that therecording syetems aro actually In error by varioue amountm.The differences shown In figures 1 nnd 2, however, only cangive a qumlitatlvo picture of tho errbr because the relativeamounts of the total error attributable tc altltude and to air-speed are not kncwn and tho vertionl motion of tho air massduring the dlvos could not be detorminedm Further study alongthis line might be of oonslderable lntereote

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.-:, . . !., . .-m. .. .. . .APP@DIX A : ‘ .’”. . . “ m . :

Symbols..

.1. ..-.. .: Symbols ue-ed. throughout .thls rbport. a.r”eli8ted 8s follows:

r

vi “ oorrec.t infli.c.a$edstirape~d, miles pb”r”h“cur “.... .

.fre&stz&ap total” pressure IE“..: .. .

,.

P. fre-stream statio pressure ..

PO standard atnospherlc pressure at sea level

w Weight of nirpla~e, pounds.,. . .

q’ “fre%strdah ilynafiiopressure, pounds “per squere foot

s ving data, square feat ..

h“ .,tr”uealtl.tude o; airp’la.n’d,feet ““ ““ “. . . . ....,. . .

v;.. ....~ru”e ai~sip:eai”,~eet” pm s~cqnd ‘

t time, seconds”- ‘. -. .

.. ..i “acceleration due to gravity; ,32.2 feet ,per second per..

second

E energy, foot-pounds

D.. .

drag, “pounds.“

.

Az the ratio of the” net nerodyn~mic force along the al-,..,plane. Z-axis (pos.tive.when d~~ectq~zupward),tmo the,.,. ,. :.. welg~t ‘of .the.:airplano

r.. .. . .Ax. the: ratio o; the ,n’~tqe”~od~pafi”~~fo~ce a-1.~ngth.q air– “

plane. X-axla (posi”ilv:e wheq dire.ctsd.forward) .to..”the wq.lght cf “th~ airplwie .“ .. .

,

.

,.Ii. the reau~tant ,of AZ

.’... ~nd Ax.l. . ,.

f“Light-p~th anile ~roi ““hnrizantnli “~.’.

do.grees .... . ,.

a angle of at”tack”, degrees

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lVACA CB Moo 5H31 9

APPENDIX B- . . . ......, .. ,.

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:1

DERIVATION OF THE lKUliR(3YAMD THE A“CCELEROMilTERMETHODS

03’ COMPUTI?IGDRAG COE3’FICIEMT S’ROMFLIGHT DATA

Derivation of Energy Method

Th~ total energy (excluding that due to propeller thrust)of an airplane in flight in still air with respect to a point

-on the earth mt sea level may be expressed by the eauation

W(VT)2 “

.E =Wh+—2g

(El)

The rate at which energy is axpended by nn airplane In flightis equal to the drag multiplied by the voloclty, or

(l;’} i VU

(B2)

Differentintlng equation (El) with respect to time gives

dE

(

+ ~ dvq~=W.Q-’ (B3)—dt dt g dt }

Combining equations 032) and (B3) yields

or

and thus=0

1 dh/dtD

--w (y )+ dVT/dt-- ,

~

.10

I

?JACA CB ~Oc 5H31 ~.

Derivation of Accelerometer Method

The diagram of the accelerations (excluding that due to ●

propeller thrust) acting on an airplane in flight is givenbelow:

The resultant acceleration acting on the airplane Is R,Its components along the airplane RXOS are AX and AZ*

Tho external (aerodynamic) forces which produce Axand Az are equal to WAX and VA z and act in the samedirections as Ax nnd Azs.

Positive drag is defined ne qn oxtornal force actingre.nrward along the flight path’ Therefore, since the CO*ponent of positive WAX ccts forward qlong tho flight path

and the component of positive WAZ ects rearwnrd, for p~ei-

tlve, vnlues of a, the drag equation becomes

D = WAZ sin m - VAX cos a

and

.

L

CD.& ~S /Az sin G- AX cos a)

. .

— —.- —-— ——. I

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HACA CB ~0. 5H31 11

REYEREIJCES

.- -., .7

1. Hisson, James M., Gadeberg, Burnett, L., and HamiltonWilliam 9!.; Correlation of the Drag Cheracterlatlaaof a P-61B Airplane Obtained from High-Speed Wlnd-!lhmnel and 3’light Teatsm liACA ACE MOO 4K02, 1944.

,J

2. Gaafch, Welko E., and ClouGlngO Lawrence A.$ YlightInveatigatlon of the Vnriation of Drag Coefflclentwith Mach ITumber for the Bell P-39H-1 Airplane.NACA ACE NO, 5DC4, 194G0

.

MACA OB Mo. 5231 q .g.1

— — RecordedCalculated

.. _—.,

v

/

/ \ . /

/ -

/

Q.!I ,

0

gaoo2m

@ “/ H

100

14 18 2e 26 so 34 3a 42 46 50 64The, see

rigurel.- Time history of ohan6e in altitude and rate of ohange in altitudeshowing comparisonbetween value- recorded and calculated by the energy method. North AmericanP-5M-1

airplaoewith propeller removed.

llACA .a

Time. mo

Figure 2.- Time history of alrnpeed and accelerat&on along the flightpath mhowlng CO* arimon ofvaluem recorded and calculated by the energy method. fNorth American P-51B- drp?ane

with propeller removed.

(

i

mAooeleromet er method :

---------- Emorgy method +a

5.04

$ ITT?II li\lll 1,’ 111

&1

.03

.02

.01

0

, . , , ,

II I /I 1.

II 1! , /\

II \ -/’\ J \ / /

\/ ‘

\/

10 ,20 30 40 50 60 0Time. t, 080

1 I

I

8.

NATIONALADVISORYCOM-MITTBEFOR A3RONAWTICS

,02m

2.m

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.

.07

.06

.05

It

.04‘N /

IfI ?I \ /

03 8 /\

1’ 1 /’

\- .1{\./

.02

.01

0. x.s. 4 5 6 7 .8 .9

“Mach n&ber, H 0

Figure 3.- Timehiotory of drag coefficient 86 calculated by the Figure 4.- Variation of drag coefficient with Mach number asaccelerometer and energy methods. North American P-51 B-1 calculated by the accelerometer and energy methods. ~

airplane with propeller removed. North American P-51B-1 airplane with propeller removed.&

cd

“+

I

I

I

I

24

/ ~1

22

3, / ~

~ 20 A

IiF

$ 1*

c

m wm%

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; 16 / ~d /

$

+ ~r 4

14“A

12 P

({ (>- v ‘

/( 0

560-/

\ 240

) \

m

/3 540 / 9 vi.I + — i- —+ —+

i .+ —+ —+ —+ —+—+—;—w —;— + —+.— + —+ — +—+ + +— .i—— +— +’ — +— +

300.s / 1> I.

): 520 /

/

\ \ 760

s [I

EL

2XhTIONALA nVI:ORYCOM1ITTI;E

FOR AER ONALTICS\ :VT

U 500‘S \ 220

: ( <)

480-10 20 30 40 50 60 70 80 90 100 110 120 130 140 1SO 160

Tifie 9 ec

Tigure 6.- Time hietory of dive No. 2 in which the pilot attempted to hold constant indicated airepeed !3ell P-39N-1 eirplane, eng$nethrottled, propeller in high pitch.

Aa6.

.4+

2m.m

I

o

.3

-. 1

?i.gure 7

-C4

~

0ml=0

~e

\\\

(~ \ <t,, 1- -( ~ + ~ ~ - — (- + -.-- <,,., \

,’

-,(Az sin tz - AX coo &)-”‘..

( dhfdtjVT - dVTidtl~)-””:. ,’, !, ,, ,, ,,

.,,

\ NAT:ONAL AD ‘11S0IY o2MUITTEE: \ F()FlAERONAUTI2s

\,\

\ _ — ——.-— ) 7)\ 4 - - “= - - - - - ‘~ G - 7 + - ==%m - ~ ~ — ,- 4 - +,

/ “Y - ~ \ 4

){

I

/

/

10 20 30 40 50 60 70 80 90 100 110 1?0 130 140 150 150 170Time, aeo 9

Variation of longitudinal force f actorg f’?tl!r accelerometer and energy methods for two dives at approximate ely constant lnclicat ad ~

t-

,-airapead. Bell P-39 N-1 airplane with propeller in high pitch. -a

.

I

L-Q

1 1 1 1 1

“*g

.05 *c1m

1 gli

.04 \.

\mxuw

/ \y — — —

—-—

— — “ “ — - - —- V -- -I /1

‘.02

1Aooeleromete? method

#m.—— - ___

\

Energy method1

.05 - \

\.}

I.04 \

\

1t

L< . - -. -- -— \- — — — -— r

— . — - +,

)-/

/

.02NATIONALAD VISORY COUMITTES!

EJ- Efttm$u’ff C9

.01

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

iiJn$z&~ “ ‘P.<

Time, sec :

Figure 8.- Variation of the resultantdrag coefficient calculated by the energy end accelerometer methods for t *o dives at approximate ely ?constant indicated aizspe~d. Bell P-39 N-1 airplane with propeller in high pitch. @

—. —.

: IlllllllllllI31176014392790 ,

—.,

4

. c’●

,

I..—. _ I