.. -.. C O P Y

7 RhI B57EOl Q /

"

RESEARCH .MEMORANDUM

FLIGHT MEASUREMENTS AND CALCULATIONS OF WING LOADS AESD

ILIAD DBTRJBUTIONS -AT SUBSONIC, TRANSONIC, AND

SUPERSONIC SPEEDS

"

By Frank S. Mahesixto Thomas V. COOmyJ and Earl R. Keener

JUL l U 1957

By Fk.ank S. Malvestuto, lkomas V. Cooney, and E a r l R. Keener

SUMMARY

Presented i n this report i s a summary of loca l and net angle-of- attack wing-panel loads measured i n f l i gh t on six airplanes. In addition, a compezison of these loads measured in f l igh t with calculations based on Simple theory is presented.

INTRODUCTION

A t the High-speed Flight Station of the N a t i o n a l Advisory C o d t t e e for Aeronautics, fuU"scale reseazch in the f ie lds of s tab i l i ty , perform- ance, and loads is conducted with a w i e t y of completely f n s t m e n t e d research and military-type airplanes.

In the present paper, the aerodynamic Loads aspect of this fllght research is considered. The presentation w i X L involve a summary of local and net. angle-of-attack wing-panel Loads measured in f l fght on a variety of airplanes flown during the past 5 or 6 years. In addition, a prelim- inary comparison of these lo& measured in f l i gh t and the correspondbg loads calculated by simple theory is presented. The object of this can- ,, parison is-t-o-.assess-.&&--biUty of s-le theoretical techniques t o pre- I[ dict the flight-measured la- l o r a ox cmrm at lolls. O n l c x r y comparison of the f l ight m e a s x s with c z a b l e win&tunnel resul ts has been made. In a general sense, the f l ight results verify the tunnel f indLngs . Fo~Lhe. convenience of- . t h e . r,eader, a bibliography has been added.

- Y a .I!

. t

, . .. . .. .

Figure 1 depicts d t h plan-dew outlines the airplanes to be dis- cussed in this report. The. w i n g panels are darkened t o emphasize the fact that only the wing loads w i l l be considered. An inspection of the Fndividual sketches and geometric data shows that there is a good coverage of wing sweep, plan form, aspect ratio, and thickness. In addition, the X - l E w i n g has 2' positive incidence and the D - 5 5 8 - I I w i n g haa 3' of positive incidence. The free-stream Reynom number for the f l igh ts of these airplanes varied from 1 x 106 t o 6 x 106 per foot. The al t i tude wied from 25,000 f ee t t o 65,000 feet .

c

, . e -

2

A

b'

bf

C

Cav

Cf

Cn

CP

H

iw

M

t

X

Y

a

6e

aspect ratio

wing-panel span

flap span

chord

average chord

flap chord

c .. I . . NACA RM ~ 5 7 ~ 0 1

SYMBOLS

section normal-force coefficient

net normal-force coefficient

variation of wing-panel normal-force coefficient with angle of attack

pressure coefficient

pressure coefficient differential between upper and lower surfaces . altitude

wing incidence

free-stream Efach number

free-stream Reynolds number

thickness

distance along x-axis

distance along y-axis

angle of attack

elevon deflection

leading-edge sweep -

NACA RM ~ 5 7 ~ 0 1 3

A few preliminmy remaxks regarding the theories used for the wing- panel load calculations will be made. The w i n g s are assumed t o be rigid flat plates and of negligible thickness. In addition, the effect of the fuselage hterference on the w i n g loads was approximated by assuming the fuselage t o act as a perfect reflection plane located at the wing- fue l age juncture. On this bas is , the wing load is predicted 88 the load on one panel of a symmetrical wing with i ts root chord coincident with the wing-fuselage juncture. It i s realized that this approximation t o the fuselege Interference is subject t o hrprovement; however, it is f e l t t o be sufficient fo r the present study. With these asslrmptions Fn mind, the wing theories used for load predictions are given in the fol- lowing table :

Theories used f o r calculation of wing loads - 1 subsonic

(0.5 < M C 0.85) Transonic (M = 1.0)

lifting surface lifting surface (refs . 1 t o 4) (refs. 5 and 6)

mswept WLng: two- dimensional flat plate; two- dimensional double *dge (refs. 7 and 8)

0 1 Supersonic

In the subsonic range, for all wings, lineax theory was applied. (See refs . 1 t o 4.) These subsonic calculations were made up t o a Mach number of 0.85, although in the neighborhood of t h i s Mach number, tran- sonic mixed-flow conditions no doubt exist. In the transonic range, cal- culations were made only f o r a free-stream Mach number of 1.0. In thb range, for the swept wings, the linear theory presented by Mangler ( ref . 5 ) which is in essence Jones* slender“ theory (ref. 17) m o d i f i e d for linearized sonic-flow conditions was applied. For the unswept wing, a t a Mach number of 1.0, use was made of the results of Guderley and Yoshihara (ref. 8) f o r a double-wedge section and the results of Guderley (ref. 7) for a f la t plate of negligible thickness. For the supersonic Mach number range, the well-known lifting-surface theories were applied.

4

LOADING DISTRIBmION

NACA RM H5V01

In the discussion of flight results, the chordwise and spanwise loadings for the unswept-wing X- lE airplane, the swept-- D-558-11 air- plane, and the delta- JT-102A airplane are considered and then a

Some idea of the f l tght Reynolds number, altitude, and angle-of- attack excursions f o r these airplanes can be determined from figure 2. The Reynolds number is given on a per-foot basis and for free-stream con- ditions. The open circulert. symbol represents the maximum Reynolds num- ber obtained. It is noted tha t th i s f l igh t Reynolds number varies from approximately 1 x lo6 t o 4 x lo6. The alt i tude covers a range from approximately 25,000 t o 65,000 feet . On the right-hand side of figure 2 the hatched boundary is U c a t i v e of the rnaxFmum angle-of-attack excur- sions obtained in f l ight . The discussion of the angle-of-attack wing loads w i l l be within the region shown by the dashed boundary.

In figures 3 t o 6 m e presented the chord loadings and span loadings for the X-1E wing panel. The solid line represents the theory; the open symbolfi the flight data. The dashed l ine through the open circles repre- sents faired" flight data. The sketches on the left-hand side of fig- ure 4 indicate the panel normal-force coefficient CN for the angles of attack at which the chord and span loadings are shown. Consider f i r s t the chord loadings of figure 3, that is, the variation of 4 , the l i f t i n g pressure, with x/c, the normalized distance from the leading edge. These results are for a span station = 0.46. The symbol b'

denotes the external panel span. The chord loadings are sham for Mach numbers of 0.8, 1.0, and 1.9. For each Mach number the chord loadings are shown for two angles of attack, a low angle and a high angle. The magnitude of the high angle of attack is limited by the availabil i ty of the data. The angle of a t tack is a l w a y s the angle of attack of the wing panel. A t M = 0.8, the calculated level and vaziation of the chord loading compares favorably with the flight data. For a Mach number of 1.0, there is no available finite-span unswept-wing theory. The theoretical variation shown here is t h e f l a t - p h t e two-dimensional theory of Guderley. Although the level of the lifting pressure is not predicted herein, the variation is similar t o the flight-measured variation fo r both angles of attack.

*

A t supersonic speed &ud l o w angle of attack, the comparison of f l igh t and theory i s acceptable. A t the higher angle of attack, the l o d i n g d i s - tr ibution is not predicted by theory although the level of the local load 'can be calculated. The midspan chord loadings and the chord loadings a t two additional spanwise stations, one near the root and one near the t ip, m e shown in figures 5 and 6.

NACA RM ~ 5 7 ~ 0 1 - 5

J

If the span-load distributions (fig. 4) aze Considered, it is noted that, at M = 0.8 and M = 1.9, the calculated span loading compares favorably wLth the flight-measured loading. For M = 1.0, the span loading was not calculated, since, as mentioned previously, the two-dimensional resul ts of Guderley were used; however, the f l ight data have been faired. The shapes of the span-loading curves strongly resemble each other for the three Mach numbers shown.

For the swept-wing D-558.11 airplane the chordwise asd span-load distributions f o r the wing panel are shown i n figures 7 t o 10. The solid line represents the calculations and the open cfrcular symbol, the flight measurements. The panel normal-force coefficients corresponding t o the angles of attack considered are indicated in the sketches on the left-hand side of figure 8. The chord loadings presented Fn figure 7 are for a spanwise station close to the mid~emispan location. For the subsonic and sugersonic speeds, the theory allows the calculation of the level and vmiation of the chord 10- except at the high angle of attack fo r the sugersonic Mach number. A t M = 1.0, the measured distri- bution of the l if t ing pressure SP is not calculated by the l inear

theory. Theory gives a zero loading behind the lFneerized sonic shock that starts f r o m the leading edge of the streamwise t i g of the wing panel. It is possible t o obtain a nonzero loading by minor alterations of the wing-tip geometry so that, for the portion of the WFng behInd the l ine- axized shock, the local span Increases with increasing l o n g i t u d h a l posi- tion; and hence lift is produced. (See ref . 1.7.) A discussion of t h i s a r t i f i ce is given in the report by Mangler (ref. 5 ) mentioned ear l ier . The midspan chord loadings and the chord loadings near the root aud t i p are shown in figures 9 and 10.

The span loading fo r the swept-wing D-558-11 is presented Fn fig- ure 8. A t subsonic and supersonic speeds the calculated distribution comgares favorably wFth the f l igh t measurements. For M = 1.0, the cal- culated loading, especially at the high angle of attack (1l0), does not represent the emeriment because of the inability of the theory t o pre- dict the level of the load~ In the vicinity of the root and t i p regions. A t an angle of attack of no, the % of the panel is approximately 0.8. It is possible that separation effects at the root and t i p a r e important for this configuration. In addition, the simple end-plate correction used herein f o r fuselage interferences may be approximate. In this regard the application of an a n d y s i e such as that reported by Crigler (ref. 6 ) for wing-body interference at sonic speeds would -rove the prediction of the loading in the vfcinity of the root.

The flight-meas&ed loads f o r the w i n g panel of the 60° delta-wing JF-102A airplane axe considered next. In figure ll i s shown an exploded view of the wlng. Note the t w o fences located in the forward portion of

6 NACA RM ~ 5 7 ~ 0 1 I

the wing and the elevon surface which is operative during flight. This w i n g has conical camber and a reflexed tip. For the calculation of the wing-panel loads, the effect of the fences and the effects of the conical camber and the reflexed t i p a r e neglected; however, the effect of the elevon has been considered.

I ,

In figures 12 and 13 are shown the chord loading and the span 10- for this airplane. For the lower angle-of-attack range (angles of attack from 3 O t o 5O) the calculations of the chord loadings compare favorably with the measurements. Up-elevon deflection is negative. The fac t that the loading at the leading edge is not predicted is partly due to t he omission of camber effect in the calculations. Although the effect of elevon at M = 1.0 w a s not calculated, an inspection of the low-angle-of- attack results indicates that the elevon load calculations at low super- sonic speeds such as those obtained at M = 1.2 are reasonable approxi- mations to t he elevon load. at M = 1.0. A t the high angles of attack the remarks made for the low angles of attack for the sonic and supersonic Mach numbers are still reasonably valid. For the subsonic Mach number, the angle of attack is 20° and the calculations do not predict the f l i gh t measurement p r i m r i l y because of leading-edge separation. For the case of leading-edge separation, calculations of the loading should be made within the framework of the approximate separation flow theories such as reported by Brown and Michael ( ref . 18) . The panel span loadings f o r the JF-102A are shown in figure 13. The inabi l i ty of the calculations t o produce.the flight trends at M = 0.8 and a, = 20° is clear from the remarks relat ing to the chord loading at this Mach number and angle of attack. A t M = 1.0, since the elevon load was neglected, the calcuLations overestimate s l ight ly the level of the distribution. The effect of the fences on the span loading distri- bution can clearly be seen at M = 1.0 and ct = loo.

I n general, the overall impression from this preliminmy comparison i e what would be expected from similar compzisons with wind-tunnel results. Briefly, a reasonable approximation of the span loadings can be determined for the low and moderate angle-of-attack range. The estimation of the chord loadings is less satisfactory, particularly in the neighborhood of a Mach number of 1.0.

NORMAL FORCES

In figure 14 i s shown the variation of the panel normal-force coef- f ic ient with panel angle of attack. Note , i n th i s i l lus t ra t ion tha t the open circular symbol represents the flight measurements for Mach numbers of 0.8 and 1.0. The solid symbol represents the f l igh t measurements for supersonic Mach numbers. The calculations are again represented by the

NACA RM H 5 W 1 7

solid l ines. For the unswept w i n g a t a Mach number of 1, the calculated m i a t i o n is s h p l y the result of Guderley and Yoshihara (ref. 8) f o r a two-dimensional WLng w i t h a 4-percent-thick double-wedge section. The theory here does not predict the magnitudes o r the variation for the range of angle of attack where f l i gh t measurements are available. Tunnel results, however, for a similar wing indicate that the CN variation with a is not linear and Fn the lower angle-of-attack range (below bo angle of attack), theory more nearly agrees with the experimental variation.

In figure 15 an attempt has been m a d e t o show the effect of Mach number on the normal-force derivative C N ~ f o r all six airplanes that were sketched in figure 1. The theory is again represented by the solid l ine and, i n addition, the inverted "V" symbol has been used t o indicate the magnitude of % at M = 1.0. The flight data me represented by a square symbol. The solid symbol represents a low CN range; the ogen symbol, a moderate CN range; and the half-solid, a high C& range. In most cases, f l i gh t data were available f o r only one of these ranges. For the X-1E at sonic speed, the difference in the calculated and f l i gh t values resul ts from lack of f l i gh t data in the low CH range as pointed out in the discussion of figure 14.

In general, the calculated normal-force-curve slopes compare favor- ably with those obtained frm the flight data.

In general, the o=ll impression from this preliminary comparison i s w h a t would be expected from similaF'compmisons with wind-tunnel results. Briefly, a reasonable approximation of the span loadings can be determined fo r the low and moderate angle-of-attack range. The estimation of the chord loadings is less satisfactory, particularly in the neighborhood of a Mach number of 1.0. In general, the calculated normal-force curve slopes compare favorably with those obtained from the flight data.

""c""~ ,.

ET@-Speed Fl ight Station, National Advisory Committee for Aeronautics,

Edwards, Calif., W c h 5, 1937.

8 NACA RM H5p01

1- D e Y O W , John, and Harper, Charles W.: Theoretical Symmetric span Loading at Subsonic Speeds for Wings Having Arbitrary Plan Form. NACA Rep. 921, 1948.

2. DeYoung, John: Theoretical Symmetric Span Loading Due t o Flap Deflec- t ion for Wings of Arbitrary Plan Form at Subsonic Speeds. NACA Rep. 1071, 1952. (Supersedes NACA TN 2278. )

3. Glsuert, H.: The Elements of Aerofoil and A i r s c r e w Theory. Second ed., Cambridge ZMv. Press, 1947. (Reprinted 1948.)

4. Allen, H. Julian: Calculation of the Chordwise Load Distribution O v e r Airfoil Sections With Plain, Split, o r Serially H i n g e d Trailing- Edge Flaps. NACA Rep. 634, 1938.

7. Guderley, Gottfried: The Flow Over a Flat Plate With a Small Angle of' Attack at Mach Number 1. Jour. Aero. Sci., vol. 21, no. 4, Apr . 1954, pp. 261-274.

8. Guderley, Gottfried, and Yoshiharra, Hideo: Two-Dimensional Unsymmetric Flow Patterns at Mach Number 1. Jour. Aero. Sci., vol. 20, no. 11, Novo 1953, PP* 757-768*

9. Piland, Robert 0. : Summazy of the Theoretical L i f t , Damping-in-Roll, and Center-of-Pressure Characteristics of Va;rious Wing Plan Forms at Supersonic Speeds. NACA TN 1977, 1949.

10. H8smon, Sidney M., and Jeffreys, Isabella: Theoretical Lift and Demping in R o l l of T h i n Wings With Arbitrarry Sweep and Taper at Supersonic Speeds - Supersonic Leading and Trailing Edges. NACA TN 2ll4, 1950-

11. Malvestuto, Frank S., Jr., Mmgolis, Kenneth, Etnd Ribner, Herbert S.: Theoretical L i f t and Damping in Roll at Supersonic Speeds of Thin Sweptback Tapered Wings With Streamwise Tips, Subsonic Leadin@; Edges, and Supersonic Trailing Edges. NACA Rep. 970, 1950. (Supersedes NACA TN 1860. }

12. Tucker, Wmren A., and Nelson, Robert L.: Theoretical Characteristics - in Supersonic Flow of Two m e s of Control Surfaces on Trimgulm Wings. NACA Rep. 939, 1949. (Supersedes W A Tli's 1600 and 1601 by Tucker and TN 1660 by Tucker and Nelson. )

13. Malvestuto, IRmnk S., Jr., and H m v e r , Dorothy M. : L i f t and Pitching Derivatives of ThFn Sweptback Tapered W b g s With Streamwise Tips and Subsonic Leading Edges at Supersonic Speeds. NACA TM 2294, 1951..

14. Hannah, Esarg.ery E., and Margolis, Kenneth: Span Load Distributions Resulting F'rom Constant Angle of Attack, Steady Rolling Velocity, Steady Pitching Velocity, and Constant Vertical Acceleration f o r Tapered Sweptback Wings With Streamwise Tips - Subsonic Le- Edges and Supersonic Trail- Edges. NACA TN 2831, 1952.

15. M a r t i n , John C., and Jeffreys, Isabella: Spas Load Distributions Resulting From Angle of Attack, Rolling, and Pitching for Tapered Sweptback Wings With Streamwise Tips - Supersonic Leading and Trailing Edges. NACA TN 2643, 1952.

16. M a r t i n , John C., Margolis, Kenneth, and Jeffreys, Isabella: C a l c u l a - - t ion of L i f t and Pitching Moments Due t o Angle of Attack and Steady Pitching Velocity at Supersonic Speeds. for Thin Sweptback Tapered Wings With Streamwise Tips and Supersonic Leading and T r a i l - Edges. NACA TM 2699, 1952.

17. Jones, Robert T. : Properties of Low-Aspect-Ratio PoFnted Wings a t Speeds B e l o w and Above the Speed. of Sound. NACA Rep. 835, 1946. (Supersedes NACA TN 1032. )

18. Ewown, Clinton E., and Michael, William H., Jr. : O n Slender Delta Wings With Leading-Edge Separation. NACA TN 3430, 1955.

10

BIBLIOGRAPHY

NACA RM H5m1 .

m e r , Richazd D., Reed, Robert D., and W c y , W i l l i a m L.: W i n g - L o a d Measurements of the B e l l X-? Research Airplane at a Sweep Angle of 58. To. NACA EM H55All, 1955.

Cole, J. D., Solomon, G. E., and Willmarth, W. W.: Transonic Flow'Past Simple BcxkLes. (Contract fiF 1% 600) 383; NAw-61%) , GALCIT, 1953.

Few, Albert G., Jr., and Fournier, Paul G. : Wind-Tunnel Investigation of the Aerodynamic Characteristics of a Series of Swept, - H i g h l y Tapered, Thin Wings at Transonic Speeds - Transonic-Bumg Method. NACA RM ~56124, 1956

Heaslet, M a x . A. , and Spreiter, John R.: Three-Dimensional. Transonic Flow Theory Applied t o Slender Wings and Bodies. EACA TN 3717, 19%.

Henderson, Arthur, Jr.: Wind-Tunnel Investigation of the Stat ic Longi- tudinal and Lateral Stabi l i ty of a 1 / 6 2 - ~ c a e Model of the X-= at Supersonic Speeds. NACA RM L56C23by 19%.

Henderson, Arthur, Jr.: Wind-Tunnel Investigation of the Stat ic Longi- tudinal and Lateral Stabil i ty of the B e l l X- lA a t Supersonic Speeds. NACA RM L55123, 1955.

Holder, D. W.: Note on the Flow N e a r the Tail of a 'Two-Dimensional Aerofoil Moving at a Free-Stream Mach Number Close to l h i ty . C.P. No. 188, British A.R.C., June 39, 1954.

Keener, Earl R. , and Jordan, Gaxeth H. : Wing Loads and Load Distribu- t ions Throughout the Lif t Range of the Douglas X-3 Research Airphne at Transonic Speeds. NACA RM ~ 5 6 ~ 1 3 , 1956.

Keener, E a r l R., and Jordan, Gareth H.: W i n g Pressure Distributions O v e r the L i f t Range of the Convair XF-92A Delta-Wing Airplane at Sub- sonic and Transonic Speeds. NACA RM H55G07, 1955.

K u h l , Albert E., and Johnson, Clinton T.: Flight Measurements of Wing Loads on the Convair XF-92A Delta-Wing Airplane. NACA RM H55D12, 1955.

Kuhn, Richard E., Hallissy, Joseph M., Jr., and Stone, Ralph W., Jr.: A Discussion of Recent WM-Tunnel Studies Relating t o t h e Problem of Estimating Vertical- and Eorizontal-Tail Loads. NACA RM L55E16ay 3-955

NACA RM ~ 5 7 ~ 0 1 - ll

.I Lindsey, Walter F., and Johnston, Patrick J.: Some Observations on M a x i m u m Pressure Rise Across Shocks Without Boundary-Layer Separation on Airfoils at Transonic Speeds. W A TN 3820, 1956.

Mayer, John P., and Hamer, Harold A.: A Study of Means f o r Rationalizing Airplane Design Loads. NACA EM L55El3aY 1955.

Moseley, William C., Jr.: Investigation a t Transonic Speeds of the Hinge- Moment Characteristics of a 1/8-Scale Model of the X-lE Aileron. NACA RM L55F06a, 1955.

Neuma,rk, S. : Cri t ica l Mach Wumbers f o r Thin Lhtapered Swept Wings at Zero Incidence. R. & M. No. 2821, Bri t ish A.R.C., Nov. 1949.

Neumazk, S., and Collingbourne, J.: Velocity Distribution on Thin Tapered Wings With Fore-and-Aft Symmetry and Spawise Constant Thickness Ratio a t Zero Incidence. R. & M. No. 268, Bri t ish A.R.C., June 1951.

Nielsen, Jack N., Kaattari, George E. , and Anastasio, Robert F. : A Method for Calculating the Lift and Center of Pressure of Wing-Body-Tail Combinations a t Subsonic, Transonic, and Supersonic Speehs. NACA RM A53GO8y 1953-

Nielsen, Jack N., Spahr, J. Richard, and Centolanzi, €?rank: Aerodynamics of Bodies, Wings, and Wing-Body Combinations at High Angles of Attack &nd Supersonic Speeds. NACA RM A55Ll3cY 1956.

-- Polhamus, Edward C.: A Simgle Method of Estimating the Subsonic L i f t and D a m p i n g in Roll of Sweptback Wings. NACA TN 1862, 1949.

Polhamus, E d m d C.: S u n m a y of Results Obtained by Transonic-Bump Methcd on Effects of Plan Form and Thickness on L i f t and D r a g Character- i s t i c s of Wings a t Transonic Speeds. NACA TIT 3469, 1955. (Supersedes NACA FU4 L5IE30. )

Robinson, Glenn H., Cothren, George E., Jr-, md Pembo, Load Measurements at Supersonic Speeds of the D o u g l a s Airplane. NACA RM mL27, 1955.

Runckel, Jack F., and Gray, W. E. : An Investigation of at Transonic Speeds. NACA RM L5P13, 1955.

' Shapiro, Ascher H.: The Dynamics and Thermodynamics of Fluid Flow. Vol. II. The R o n a l d Press Co., 1954.

C h r i s : W" D-558-n: Resemch

Loads on Ailerons

Colnpressible

.: Spreiter, John R.: On the Application of Transonic Similaxity Ru&es t o . Wings of Finite Span. NACA Rep. 1153, 1953. (Supersedes NACA TN 2726. ) -

Spreiter, John R., and -ne, Alberta: Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils a t High Subsonic Speeds. NACA Rep. 1217, 1955. (Supersedes NACA TN 3096.)

Vincenti, Walter G.: Measurements of the Effects of Finite Span on the Pressure Distribution Over Double-Wedge Wings a t Mach Numbers Near Shock Attachment. NACA TN 3522, 1955.

Vincenti, Walter G., Dugan, Duane W., and Phelps, E. Ray: An Experimental Study of the L i f t and Pressure Distribution on a Double-Wedge Profile a t Mach Numbers Near Shock Attachment. ‘NACA TN 3225, 1954.

Vincenti, Walter G., Wagoner, Cleo B., and Fisher, Newman H., Jr.: Cal- culations of the Flow Over an Inclined Flat Plate at Wee-Stream Mach Number 1. NACA “N 3723, 19%.

Vincenti, Walter G., and Fisher, Newmas E., Jr.: Calculation of the Supersonic Pressure Distribution on a Single-Curved Tapered Wing in Regions Not Influenced by the Root or Tip. NACA TN 3499, 1955.

Vincenti, Walter G., and Wagoner, Cleo B.: Theoretical Study of the Transonic Li f t of a Double-Wedge ProfFle With Detached Bow Wave. NACA Rep. 1180, 1954. (Supersedes NACA TN 2832. )

Vincenti, Walter G., and Wagoner, Cleo B.: Transonic Flow Past a Wedse Profile With Detached Bow Wave. NACA Rep. 1095, 1952. (Supersedes NACA TN’ s 2339 and 2588. )

WiUmarth, William W. : The Lif t of Thin Airfoils at High Subsonic Speeds. OSR TEiT s4-168 (Contract m-18(600) -383) GALCIT, June 1954.

IJACA RM ~ 5 7 ~ 0 1 -

L

A = 8.1

NAGA W A O O ~ m m m A,. 23'

MOOVIED "tit =Ox145

TIP "NACA =-Ole'

Figure 1

FLIGHT REYNOLDS NUMBER AND ANGLE OF ATTACK

0 .4 .8 1.2 1.6 2.0 0 + .4

IPREsENT STUDY 1 I . l I

I I

I I

.8 1.2 1.6 2.0 Mach number, M Mach number, M

Figure 2

14 NACA RM H 5 W 1

X-IE UNSWEPT W I N G . ( tk=O.O4)-GHORD LOADING AT y/b1/2 = 0.46

THEORY -; FLIGHT 0

M= 1.0 M= 1.9

a4t t O Q l t - -1 " 1 .2 .4 .6 .8 1.0 0 .2 .4 .6 S 1.0

b YC

X-IE UNSWEPT WING (Vc=O.O4) SPAN LOADINGS THEORY-; FLIGHT 0 , -- 0 --

, , , I M=!c/ca"l;b-

'N .S p'Lf- 0

0

Figure 4

NACA RM ~ 5 7 ~ 0 1

X- IE UNSWEPT WING-CHORD LOAD DISTRIBUTIONS THEORY-, FLIGHT 0

M = 0 8 MW.0 a =4* a=4O

M= 1.9 a = 4 O

X-IE UNSWEPT WING-CHORD LOAD DlSTRfBUTlONS THEORY - , FLIGHT 0

M = 0.8 NI 51.0 M = 1.9 a= 80 a-7- a = 140

3.0

Figure 6

16 NACA RM ~ 5 7 ~ 0 1

D558-1- SWEPT WING (f/c~O.O9)-CHORD LOADING AT Y/b&=O?ll THEORY - ,FLIGHT 0

M=Q8 M=ID M=1.8

O O

. . .

a =So

b

D-558-II. SWEPT WlNG(t/cflO.Og) SPAN LOADINGS THEORY - FLIGHT 0 , " 0 "

Figure 8

3Y t

D-558-I-SWEPT WING-CHORD LOAD DISTRIBUTIONS THEORY-, FLIGHT o

M= 0.8 M = 1.0 a= 4 O a=3O

,2.0 72.0

M = 1.8 a = 5-

,2.0

,2.0 72.0

D-558-IC SWEPT- WING CHORD LOAD DISTRlBUTION THEORY - , FLIGHT 0

M-OB M= 1.0 M = 1.8 a = 7°+1) U = I [ O as go

h2.0 f 2.0

\”

Figure 10

18 0

JF-102A AIRPLANE-SCHEMATIC OF WING

NACA RM ~ 5 7 ~ 0 1

.

A

Figure l l

JF-IOLA DELTA WING (?k&.04)-GHOAD LOADING AT %4=0.34 THEORi"(N0 CAMBER), FLlGM o

M. .a w1.o M=1.2

Figure 12

NACA RM ~ 5 7 ~ 0 1

JF-[02A DELTA WING (t/c=O.04) SPAN LOADINGS THEORY-; NGKT 0 , --"o --

.2 0

"1.2 .6r a

VARlATtON OF NORMAL-FORCE

THEORY - ; UNSWEPT WING

X-IE

COEFFICIENT WITH ANGLE OF ATTA(;K

FW3-m 0 M, 1.0 0 M = 0.8.1.0

SWEPT WING DELTA WING -8-ll JF102A

1 . 2 ,

0 4 8 1 2 0 4 8 I 2 0 4 8 12

WING ANGLE OF ATTACK, a, DEG

Figure 14

20 NACA RM H57EO1

VPIRldWN OF FORCE COEFFtClENT DERlVATlVE WITH MACH NUMBER MEORY--.A; FLIGHT CN = MOO LOW

UNSWEPT WINGS

gn- X-IE

cNamY= .04

HIGH SWEPT WINGS DELTA WINGS

r 0-558-11 [- JF-IOEA

I F-'mA I XF-92A

L .. ". 5 1.0 1.5 2.0 .5 ID 1.5

MACH NUMBER

Figure 15

HACA - Lmtgley Field, Va.