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RESEARCH MEMORANDUM

EFFECT OF ~OWJWASH ON THE ESTIMATED ELEVATOR DEFLECTION,., ,. ,,

.’

jj&ijtiRED FOR T13M OF THE Xs -1 AIRPLANE,.,,,,’,,,,;,.,, ,:’ ,,$-.

,;/;,.‘ AT SUPERSONIC SPEEDS;:{ ‘<;, i,b:!. ,

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James T. Matthews, Jr.5..’~

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NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

~WASHINGTONNovember 1, 1948 [ *Qq;;’i;’; (

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NACA RM No. Mi06a

NATIONAL ADVTSORY COMMITTEE FOR AERONAUTICS

REW3ARCH MFMORA.NDUM

EFFECT OF DOWNWASH ON THE ESTIMATED ELEVATOR DEFLECTION

REQUIRED FOR TRIM OF THE X&l AJRPLANE

AT SUPERSONIC “SPEEDS

By JameE T. Matthews, Jr.

smMARY

This report contains the results of an investigation to cktermlnefrom linearized theory, which has recently become available, the do~–wash at supersonic speeds at the tail of the XS-1 airplane ar.dtheeffect of the downwash on the elevator def’lectlon required for trim.The results are”presented in the fozm of c~es sho~ng the variation

of downwaah angle with angle of attack & and eleva~or def’1’.(ti~rl

required for trim plotted against Mach number.

The average value across the sp.n of the horizontal tail (negkctlng

the fuselage) of ~ is about O.~ at a Mach number of 1.1 and ciccrt:aw:’

rapidly to a value of about 0.08 at a Mach number of 1.4. The valw; ofdc~ then gradually decreases to O at a Mach number of about 1.9 wlLh

the possibility of a very slight amount of upwash in the Ma.k ~/Wb’21”range from 1.9 to 2.2. Above a Mach number of 2.2 ths Mach cor,l)>!from

‘e IS thr;[jwll.<~tht]wing tips are outboard of tht-~tail surfaceo and ~

(if the tail were in two-dimensional flow that is, * = 0’,.

The calcu.latlona Indlcat.othat i.ncxwasing up-elevator deflection i:+requirud with increasing Mach number (unstable variation) in 1,.:velflightbetween Mach numbers of 1.1 and 1.6. A slight reduction in up-;lt:vatord(>flection occurs between Mach numbers of 1.6 and 2.0. [Ii..;1:!~iliz~,r:w@thas a similar variation, that 18, umtable up to a Mach numbc:r of about1.6 and then becoming slightly stable up to a Mach numb:+rof’2.0. Thereduction of don-oh with increasing Mach number is not the main cauwof thu increaso in up-elevator deflection. The main rea~ons for thintrend are that the ~itching+noment coefficients due to the WiIW carnbor,the wing lifi, and the lift of tho stabilizer are all in a no:w-dowldirvctlon, and aB tho Mach number increaees, these pitching+omunt ~o@f-fi,:iont,oapparently decrease less rapidly t~ the elevator effcctivene33.

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Any Information that can be used to predict the stabillty andcontrol dM@3S of an airIil~O at Supersonic epeeds is urgently heededat the present time. This wwr presents the varlatfon of downwaeh

with angle of attack at suprsonic speeds for the X%1 airplane. ‘l’hisvariation was obtained by applying several.simplifying assumptions toLagertiromte linearized-theory celculatione for the downwaeh of three-dimensional lifting wfngs at supersonic speds. Several curves showingthe estimated V=fatlon of elevator deflection required for trim w-lthand without the effect of downwash are presented to give an indicationof the effect of dowwash on the longitudinal stability and control ofthe atrplene.

SYMBOLS

angle of attack

aspeot ratio

mean aerodynamic chord

lift coefficient (L/qS)

pitchfn&noment coefficient of the’wl.ng-fuselage combination

about its aero-c center

()

%

E

variation of downwash with engle of attack

stabilizer incidence, degrees

elevator deflection, degrees (measured relative to stabilizer)

tail length (measured from e.g. of airplane to hl~ line ofelevator)

Mach number

. .. . . . . . . ,,. , . .. ,’.. > -,’,.:-.. ~,.

Q dynamic pressure()

L&’2

s surface area, equare feet

x distance from center of gravity to aerodynamic center ofwing-fuselage combination (positive for aerodynamiccenter ahead of e.g.)

Suh:~cripte:

t

w

e

tail

wing

elevator

●

ANALYSIS

Calculations of the variation of dovnwash at the tail with angle ofattack ~re made using reference 1. Theoretical calculations based onthe linearized theory of su~rsonic flow EUW3presented in reference 1fO1’ the do~wash at ~upreonic speeds of trapzol~ wings and rectan@tU

wings. Since no calculations were presented for a ta~red wing eimilarto the wing of the X3-l airplane, a rectangular wing of the same areaand spn WM assumed h this investigation.

The data of reference 1 for the trapezoidal wings with ti.pecut offali~!~ the inboard edge of the Mach cones from the tig tip are morecomplete th~ those for the rectangular as. It was found by comparingtht~ curves of reference I for the case in which the tail was in the phles.Il(\Infinitely f’ar behind the wing that the domwash was almost identicalfo~-both t~s of ~gEI provided the ep~ of the trapezoidal Wing waf3taken slightly luger than the span of the rectangular wing. For this

re:lson the ~re complete &ta for the trapezoidal wing were used as 8nai(i in fairing the curves ueed to eetimate the downwa8h at the tail orth(lXS-I.airpl~.

A three-view drawing ie presented in figure 1 Bhowing the Wrtinentdimcmsions and ch~acteristics of the X&l airplene. Figure 2 presents

th[!theoretical variation of ~ with Mach number. The valuee of &da

p]’{lsentedare average values over the SeIILi3pSnor the horizontal t:~il.It is expected that the actual downvash at supersonic speeds will be lessth,jnthe thooretlcal value below a Mach number of about 1.1 and will fairint,othe subsonic velue~. Above a Mach number of 2.2 the Mach cones from

th~> WiIIg tips are outboard of the tail surfacee and ~ is the same asda

)if the tall were in tvo-d hatis, &=O.

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The elevator deflections required for trim wers computed by equatingthe pitching moments Of the airplane to zero about :1s center ofgrnvlty (0.257) using the following relation:

Figure 3 presents the assumed variation with I&h number of thepitching-+uoment coefficient C

%’the lift-curve slopes for the wing

and tY.11 C%

and C

%

, and the elevator effectiveness CL The8e “

f~xperjment~~lcurves at subsonic s~eds were arbitrmily faired into theLhooretl(:alcurves at supersonic s~eds as shown by the dashed lines.The experimental subsonic values wem used as an aid in fairing thevfd.IJcq near a Mach number of unity, as ~t is generally accepted that the.linonrizeci-ouporsonic-flowtheory 13 not applicable in the low su~rsonicrange of kkich numbers. The experimental vtiLue3 of C

%and CL were

%obtained from reference 2. The experimental values of

cLbwere obtained

from reference 3. The pltching+oment coefficient at zero ~ift about theticrodynsmic center C

%-s c~culated f’romthe form~a ~iven In reference 4

which i~ baaed on the line~ized theory f’ortwti~ngional flow. The3uper90nic values of CT were calculated from the following relation:

%.

CL== &(1 -W&=;)The values of

however, thesetal tiatato beoi’ CL6 used

e

cLbeat t3upersonic speeds were calculated from reference 5;

values wera found by comparison with unpublished experimen-about 50 percent too high”at all Mach numbers. The values

herein were reduced accordingly.

An average subsonic value for the aerod-c center of the vlng-f’u:;nlugecombination of 5 percent Of the man aerodmc chord obtainedfrom wind–tunnel tests was shifted rea~ard to 30 percent of the mean;J!:rodwywun.l.c[:hOrdfOr Supersonic speeds. The rearward shift of the aero-llynal?lil;center of the wing alone iE gho~ by theory to be somewhat lesst}l;ln25 percent of the moan aerod-c chord. The relative destabilizingcI’fecL of the .fu~elagcdecreaoes at su~rsonic speeds, however, becauseof’the disappearance of upwash ahead of the wing. The value aseumei forthe aerodynamic-center location was intended to account for this effect.

CONFTDENTti

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NACA RM No. L8H06a

tiTrGsJ&::

5

More detailed estmtion of this q~tity WaS not ‘tho@t to be ~ustlfledbecause accurate theoretical treatment of a ~g-f~elage combination insupersonic flow iB not available. The angle of attack of the wing forzero lift was assumed to be zero. The wing incidence was taken as 2.5°.The effect of the 1.OO twist of the &l wing and the Interference ofthe wing body were n~glected. The angle of attack of the tail used inthe pitching+normmt equation includes a constant 2° downflow. It isbelieved that this downflow exists becauge of the flow around the fuselage.The 2° dovnflow was found from wind-twel &ta to occur at subsonicspeeds. The mum value hassince theory Indicates thatIs very sitilar at subeonlc

been assumed to exist at supersonic speedsthe angle of flow in the region of the tailand supersonic speeds.

DISCUSSION

Figure 4 presents tvo palre of computed curves of the elevator-deflection variation vlth Mach number. One pair of curves is for level–flight lift coefficients with and vjthout the effect of downvash and theother pair of curves is for a COIMtant lift coefficient of 0.27 with andwithout the effect of dovnwash. All the computed curves of elevatordeflection are for a stabilizer incidence of 2.2° leading edge up, awing loading of 80 pounds per square foot, and a pressure &ltitudeof 49,000 feet.

The calculations indicate en unstable variation of elevator deflec-tion with l&ch number (Increasing u~levator deflection is requiredvith increasing &ch n@er) in level flfght between hch nubers of 1.1and 1.6. After a Mach number of about 1.6, there is a slight reductionin the amount of up elevator required up to a Mach number of 2.0, whichis the extent of this Investi@tion. The vulation of stabilizerincidence for trim (tie= O.OO) with Mach number iS presented in figure 5and indicates that the variation is unstable in the Mach number rangefrom about 1.1 to 1,5 and then becomes slightly ,gtablein the &ch numberrange from about 1.5 to 2.0. The calculations also shov that the reductionIn dovnwash with Increasing Mach number lEJnot the main cause of theIncreaee in up+levator deflection. The main reasons for this trend arethat the pitching-moment coefficient due to the wing cambe?, the wing lift,and the lift of the stabilizer are all in a noatiovn direction. As theMach number increases these pitching-moment coefficients apparentlydecrease leae rapidly than the elevator effectiveness.

It appears that in level flight at a pressure ~tltude of 49,000 f’cetwith a wtn?, loadir)gof 80 pound~ per Oquzlre foot wld ~ ~~~bilizer

incidence of 2.’2’0 (leadtig edge up) the UMXILU~ up elevator of 11.OO

will be reached at a Mach number of about 1.6. Ample stabilizertravel is available, hovever, to change the trim so that the elevatordeflection may be reduced to ~qqo,

,L)o,~~FL~$~[d~~hn~ber. Under the-..

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6

conditions etated previously, but by use of ~ tier

It appears that level flight could be maintained withavailable from a Mach number of 1.3 to 2.0.

NACA RM No. L8H06a

stabilizer incidence,the elevator travel

Langley Aeronautical LaboratoryNational Advisory Committee for Aeronautics

Langley Field, Va.

1. Lagcrstrom, P. A., and Graham, Martha E.: Downwash and SideWash Induced

by Three–Dimensional Lifting Wings in Supersonic Flow. Rep. No. SM-1300Douglas Aircraft Co., Inc., April 14, 1947.

2. hkittoon,Axel T., and Loving, Domld L.: Force, Static Longitudi~

Stability, and Control Characteristics of a ~-Scde Model of the16

Bell XS-1 Transonic Research Airplane at Hi&Mach Numbers.NACA RM No. L&12, 1948.

3. Adams, Richard E., and Silaby, NOmELII S.:

Model through the Tm.nsonic Speed RangeNACA RM No. L~25a, 1947.

4. Smeltj R.: Note on Longitudinal Stability

Teste of a Horizontal-Tailby the NACA Wing–Flow Method.

and Trim Changes at Speedsnear the Speed of Sound. Rep. No. Aero 1911, British-R.A.E., 1944.

5. Tucker, Warren A., and Nelson, Robert L.: Theoretical. Characteristicsin Supersonic Flow of Conetant<hord Patii~+p~ Control Surfaceson Rectangular Wings Having Finite Thickness. N.ACATN No. 1.708, 1948.

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L8H06a

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NACA RM No. L8H06a

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Figure 2.- Theoreticalvariationof the downwash parameter ~with Mach

number for the XS-1 airplane.

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~06a NACA RM No. L8H06a 9

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