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Validation of a Flexible Aircraft I

Take-Off and Landing Analysis (FAT01

Huey D. Carden and John R. McGehee

NASA

https://ntrs.nasa.gov/search.jsp?R=19780002106 2020-02-08T21:54:04+00:00Z

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NASA Technical Paper 1025

Validation of a Flexible Aircraft Take-Off and Landing Analysis (FATOLA)

Huey D. Carden and John R. McGehee

Langley Research Center Hampton, Virginia

National Aeronautics and Space Administration

Scientific and Technical Information Office

1977

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SUMMARY

Modif ica t ions t o improve t h e a n a l y t i c a l s imula t ion c a p a b i l i t i e s o f a mul t i - degree-of-freedom _Flexible Aircraft Take-off and Landing Analys is (FATOLA) computer program are d i scussed . l and ing behavior o f a s t i f f -body X-24B r e e n t r y r e s e a r c h v e h i c l e and of a f l e x i b l e - body supersonic c r u i s e YF-12A resea rch a i r p l a n e .

The FATOLA program was a l s o used t o s i m u l a t e t h e

The a n a l y t i c a l r e s u l t s were compared wi th f l i g h t t e s t d a t a , and t h e c o r r e l a - t i o n s o f v e h i c l e motions, a t t i t u d e s , a x i a l s t r u t f o r c e s , and a c c e l e r a t i o n s d u r i n g t h e landing impact and r o l l o u t were good. For t h e YF-12A a i r p l a n e , airframe flex- i b i l i t y was found t o be impor tan t f o r nose gear loading . Based upon t h e c o r r e l a - t i o n s tudy presented h e r e i n , t h e v e r s a t i l i t y and v a l i d i t y o f t h e FATOLA program f o r t h e s tudy of l and ing dynamics o f a i rcraf t are confirmed.

I N T R O D U C T I O N

Current convent iona l t r a n s p o r t a i r p l a n e s are s u b j e c t t o ground hand l ing , s t r u c t u r a l , and c o n t r o l problems caused p r imar i ly by landing-gear f o r c e s and a i r - frame i n t e r a c t i o n s du r ing t a x i , t ake -o f f , and l and ing o p e r a t i o n s ( re fs . 1 and 2 ) . These ground-induced v i b r a t i o n problems may b e magnif ied f o r supe r son ic t r a n s - p o r t s because of t h e inc reased s t r u c t u r a l f l e x i b i l i t y and t h e h ighe r take-off and landing speeds o f t h e s e a i rcraf t . S ince l and ing impact and ground o p e r a t i o n s p lay a major r o l e i n load ing t h e airframe, v a l i d a t e d methods o f p r e d i c t i n g i n t e r - a c t i v e c h a r a c t e r i s t i c s o f l and ing gear and airframe are needed t o update c u r r e n t landing-gear des ign methodology and t o suppor t advanced supe r son ic a i rc raf t technology.

Experimental and a n a l y t i c a l r e sea rch i s be ing conducted by t h e Langley Research Center t o o b t a i n a c c u r a t e p r e d i c t i o n s o f ground-induced loads and v ib ra - t i o n s and t o develop a c t i v e c o n t r o l landing-gear systems ( r e f . 3 ) which l i m i t t h e l o a d s t r ansmi t t ed through t h e gear t o t h e airframe. To o b t a i n improved a n a l y t i - cal p r e d i c t i o n of t h e airframe s t r u c t u r a l response , a multi-degree-of-freedom take-off and landing a n a l y s i s ( T O L A ) computer program ( r e f s . 4 t o 7 ) was ob ta ined and subsequent ly modif ied ( r e f s . 8 and 9 ) t o i n c l u d e e f fec ts o f airframe f l e x i - b i l i t y on t h e l o a d s and motions. The modif ied program c a l l e d FATOLA ( F l e x i b l e Aircraft - Take-off and Landing Analys is ) p rovides a comprehensive s imula t ion o f t h e a i r p l a n e take-off and l and ing problem.

The purpose o f t h i s paper is t o d e s c r i b e t h e mod i f i ca t ions made t o t h e FATOLA program t o improve its s imula t ion c a p a b i l i t i e s and t o p r e s e n t exper imenta l and a n a l y t i c a l c o r r e l a t i o n s o f v e h i c l e l and ing behavior which i l l u s t r a t e t h e cap- a b i l i t i e s of t h e r i g i d body and f l e x i b l e body o p t i o n s and v e r i f y t h e a n a l y s i s . Ana ly t i ca l s i m u l a t i o n s u s i n g FATOLA are presented for l and ings of two s p e c i f i c v e h i c l e s wi th pas s ive l and ing gears: a s t i f f -body X-24B r e e n t r y v e h i c l e and a f lexible-body supersonic YF-12A r e s e a r c h a i r p l a n e . C o r r e l a t i o n s between a n a l y t i -

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cal results and flight test data are made and conclusions are drawn on the valid- ity and versatility of FATOLA.

FATOLA COMPUTER PROGRAM

Capabilities

The general capabilities of the FATOLA computer program are illustrated in figure 1. FATOLA is a modified version of the original rigid-body program (Take- o_ff and Landing Analysis) TOLA (refs. 4 to 7). obtained the original program and added a flexible-body option (refs. 8 and 9) to generate the FATOLA program which has a core requirement of approximately 1 1 5 K octal words on a Control Data 6600 digital computer. As indicated in figure 1, FATOLA provides a comprehensive simulation of the airplane take-off and landing dynamics. The program can represent an airplane either as a rigid body with six degrees of freedom o r as a flexible body with multiple degrees of freedom. The airframe flexibility is represented by the superposition of from 1 to 20 free-free vibration modes on the rigid-body motions. The analysis has maneuver logic and five autopilots programmed to control the airplane during glide slope, flare, landing, and take-off. The program is modular so that performance of the airplane in the flight and landing phases can be studied separately or in combination.

NASA Langley Research Center-

Data which describe the vehicle geometry, flexibility characteristics, landing gear, propulsion, aerodynamic characteristics, runway roughness, and initial conditions such as attitude, attitude rates, and velocities are input to the program. comprehensive information on the airframe, state of maneuver logic, autopilots, control response, and airplane loads from impact, runway rollout, and ground operations for both the rigid-body and flexible-body options. Flexible-body and total (elastic plus rigid body) displacements, velocities, and accelerations are also obtained in the flexible body option for up to 20 points on the airplane. Complete details of the program formulation and capabilities are given in references 4 to 9.

A time integration of the equations of motion is performed to output

Modifications

Subsequent to the publication of references 8 and 9, additional modifications were made at Langley Research Center to improve the analytical simulation capabilities of the FATOLA program. The modifications are discussed briefly in the following sections and details of the required program changes are presented in the appendix.

Strut axial friction.- In the original program the force in the struts attributed to axial friction was included as the component of the resultant ground force normal to the strut multiplied by a coefficient of friction applied to oppose strut motion. This formulation is incomplete (ref. IO) because the normal bearing forces depend on the moments applied to the struts. To improve the axial friction formulation, a new friction force equation was introduced to include the moment effects. In addition, a smoothing technique (ref. 11) was included to

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preven t a sudden swi t ch i n magnitude and d i r e c t i o n o f t h e f r i c t i o n f o r c e a t t h e time t h e s t r u t v e l o c i t y changes s i g n , and a change was made t o a l low t h e f r i c t i o n f o r c e t o act be fo re s t r u t motion occur s as would be t h e case i n t h e a c t u a l s t r u t .

S t r u t a i r p r e s s u r e equat ions . - A modi f ica t ion w a s made t o t h e FATOLA program i n t h e equa t ions f o r t h e a i r p r e s s u r e s i n t h e upper and lower a i r chambers o f t h e s t r u t . I n t h e p r e s s u r e e q u a t i o n s t h e r e l a t i o n s h i p

pVy = Constan t

was o r i g i n a l l y programmed w i t h t h e r a t i o of s p e c i f i c h e a t s y equal t o 1.0 and where V is s t r u t a i r volume and t h e p r e s s u r e p is gage p r e s s u r e . Changes were made t o use a b s o l u t e p r e s s u r e i n t h e pV r e l a t i o n s h i p and t o a l low y t o t a k e on v a l u e s o t h e r than 1.0.

S t r u c t u r a l damping.- I n r e f e r e n c e s 8 and 9 t h e dynamic motion of t h e air- --- p lane body is described by t h e normal mode method. I n t h i s method t h e body f l e x - i b i l i t y is rep resen ted by free-free v i b r a t i o n modes w i t h no s t r u c t u r a l damping. I n t h e f lex ib le -body o p t i o n , an e q u i v a l e n t v i s c o u s damping formula t ion (ref. 12) o f s t r u c t u r a l damping was added t o p reven t p o s s i b l e a n a l y t i c a l d ivergence i n t h e f lex ib le -body responses .

R o l l a u t o p i l o t and c o n t r o l response.- O r i g i n a l l y , t h e FATOLA program l o g i c i n t h e r o l l a u t o p i l o t p laced the a i l e r o n d e f l e c t i o n t o a n e u t r a l s e t t i n g a t t h e t i m e o f landing impact. For a n asymmetric l and ing o f a n a i r p l a n e , t h e p i l o t would l i k e l y in t roduce a i l e r o n d e f l e c t i o n s a long wi th p i t c h c o n t r o l i n t h e impact and r o l l o u t phases of t he landing . Changes i n t h e r o l l a u t o p i l o t and c o n t r o l response l o g i c were t h e r e f o r e made t o permit t h e s i m u l a t i o n of v a r i a t i o n s i n roll c o n t r o l d e f l e c t i o n s and r o l l i n g moments throughout t h e l and ing .

New i n p u t data.- These m o d i f i c a t i o n s t o t h e FATOLA program r e q u i r e t h a t such new i n p u t v a r i a b l e s as s t r u t bea r ing spac ing , hub t o lower bea r ing d i s t a n c e , atmo- s p h e r i c p r e s s u r e , r a t i o o f s p e c i f i c heats, and modal damping v a l u e s be i n p u t on s i x data cards placed i n f r o n t o f t h e first data card of t h e FATOLA deck. The l as t t h r e e cards provide modal damping data f o r t h e f lex ib le -body op t ion and are always read by t h e program. Consequently, when t h e rigid-body op t ion i s be ing execu ted , t h e s e cards must a l s o be p r e s e n t bu t may be b lank .

AIRCRAFT LANDING SIMULATIONS USING FATOLA

A n a l y t i c a l s i m u l a t i o n s u s i n g FATOLA were conducted f o r t h e l and ings of two s p e c i f i c v e h i c l e s , a s t i f f - b o d y X-24B r e e n t r y v e h i c l e and a f lex ib le -body super- s o n i c c r u i s e YF-12A research a i r p l a n e .

Stiff-Body X-24B Vehic le

To v e r i f y t h e s i m u l a t i o n c a p a b i l i t i e s o f t h e rigid-body o p t i o n of FATOLA, t h e X-24B manned l i f t i n g body r e s e a r c h v e h i c l e , shown i n f i g u r e 2 , was used. The compact delta-shaped v e h i c l e w i t h blended wings and f l a t bottom was cons idered t o be i d e a l t o v e r i f y t h e rigid-body o p t i o n o f FATOLA. The v e h i c l e h a s been used i n

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a joint National Aeronautics and Space Administration and United States Air Force flight research program to explore subsonic and low supersonic flight characteristics of a manned lifting body with emphasis on the landing maneuver. Dur- ing landing, the X-24B vehicle is unpowered; consequently, no thrust simulation was required.

Flight test data from an asymmetric landing of the X-24B were selected for the simulation study with FATOLA. Pertinent touchdown parameters for the unpowered landing were; sink rate, 0.49 m/s (1.6 ft/sec); ground speed, 87.1 m/s (286 ft/sec); pitch angle, 13.4O; initial pitch rate, -0.8O/s (nose over); angle of attack, 13.7O; roll angle, 2O right; and initial r o l l rate, 4.4O/s right r o l l . The X-24B had an unusual offset of 0.15 m (0.5 ft) of the center of gravity toward the right landing gear. smooth since the actual dry lakebed landing surface inclination and roughness were not measured. Also included in the analytical simulation were elevator (elevon) control variations to account for pilot inputs during the landing.

The landing surface was assumed to be flat and

Flexible-Body YF-12 Airplane

The vehicle used to illustrate the capabilities of the FATOLA flexible-body option and to verify the program was the YF-12A airplane shown in figure 3. This airplane has a modified delta-wing planform and is powered by two jet engines. The fully instrumented, flexible-body supersonic research airplane was used in a NASA test program to obtain landing loads and response data (unpublished) for a flexible-body airplane.

Aircraft flexibility.- To represent the flexibility of the airplane, available modal data for an airplane in the YF-12 series were used (ref. 12). These data consist of the first 10 modal frequencies, generalized masses, deflections, and damping obtained from a two-dimensional finite-element representation of half the airplane with symmetrical boundary conditions. Consequently, the modal data are generic to the W-12 class of airplanes only and include vertical modal deflections only. The data are limited in the spanwise direction to symmetric modes. To account for the effect of aerodynamic loading on the flexible body responses, aerodynamic weighting values were calculated, as outlined in reference 8, for the 10 flexible modes using an elliptical spanwise lift distribution over the airplane wings.

Specific flight test data for two landings, a symmetric and an asymmetric touchdown, of the YF-12A airplane were selected for simulation with FATOLA.

Symmetric touchdown.- Input touchdown parameters for the symmetric touchdown of the YF-12A airplane were: sink rate, 0.67 m/s.(2.2 ft/sec); ground speed, 97.9 m/s (321 ft/sec); pitch angle, 7.2O; initial pitch rate, -0.4O/s (nose over); angle of attack, 7.65O; r o l l rate, O.OO/s. Thrust data were included in the analysis to simulate the idle power of the jet engines in the landing. Pro- grammed elevator (but no aileron) deflections were included to simulate the pilot inputs. The drag parachute deployment was also simulated. The landing surface was runway 22 at Edwards Air Force Base, California. the general runway inclination and surface roughness for approximately 1220 m (4000 ft) of the runway derived by fairing the data from a survey in which

Figure 4 presents

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measurements were made every 0.61-m (2 ft). surface elevations about the general slope are for a track 1.9 m (6.25 ft) (one semispan of main gear) to the right of the runway 22 center line and were input in tabular form as a function of runway distance to describe the landing surface in the analysis.

The general slope and incremental

Asymmetric touchdown.- Although the available modal data for representing the airplane flexibility were limited to symmetric modes in the spanwise direction, an asymmetric touchdown was also selected for evaluation of the FATOLA program. Input touchdown parameters from the asymmetric landing were: sink rate, 0.305 m/s (1.0 ft/sec); ground speed, 84.4 m/s (277 ft/sec); pitch angle, 8.3O; initial pitch rate, -0.2O/s (nose over); angle of attack, 8.5O; roll angle, 1.2O right r o l l ; and roll rate, O.OO/s. As in the symmetric landing, thrust data to simulate the idle power of the jet engines were also included. Both programmed elevator and aileron control deflections were included to simulate the pilot inputs. The landing surface for this test was runway 22 at the Edwards Air Force Base, California.

RESULTS AND DISCUSSION

To demonstrate the capabilities of the rigid-body option and to verify the FATOLA analysis, results were obtained for a landing impact and rollout simulation of the stiff-body X-24B vehicle and were compared with flight test data. Verification of the flexible-body option of the program was accomplished by com- paring results from two landing simulations of a flexible-body YF-12A research airplane with flight data.

Results are presented for the landing impact and rollout of the X-24B vehicle on a flat runway (actual surface undefined) and the YF-12A airplane on an inclined runway.with known surface roughness as a function of runway distance. Experimental data were recorded at 200 samples/sec for both vehicles. The analytical data were generated on a Control Data 6600 series digital computer and plotted at a maximum rate of 1000 samples/sec. Data are presented from initial touchdown through nose gear contact.

Stiff-Body X-24B Vehicle

Figure 5 presents comparisons of computed and flight test time histories of elevator (upper and lower elevons) control deflections, pitch attitude, pitch rate, angle of attack; ground speed, strut strokes, and axial strut forces for the asymmetric landing impact and rollout of the X-24B vehicle. Typical compu- tation time (using the rigid-body option of FATOLA) to generate all output data including the data in the figures was approximately 200 decimal seconds of central processing unit time with 115K octal words of storage on a Control Data 6600 series digital computer.

Elevator deflections.- Included in the FATOLA simulation were elevator (elevons on the X-24B) control variations to account for pilot inputs for pitch control during the landing. lated and flight test variations in the elevator deflections indicate the analy-

As shown in figure 5(a), the comparison of the simu-

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t i ca l d e f l e c t i o n rate was d i f f e r e n t from t h a t o f t h e f l i g h t test da t a ; however, because o f the o v e r a l l good agreement o f the d a t a p re sen ted i n f i g u r e s 5 ( b ) t o 5 ( d ) , no a t t e m p t was made t o match the c o n t r o l rate more c l o s e l y . As noted i n f i g u r e 5 (a ) , a t a t i m e o f 2.2 sec t h e l i f t c o e f f i c i e n t f o r the X-24B w a s a n a l y t i - c a l l y s t aged t o a v a l u e which r e f l e c t e d the effect o f t h e lower e l evons be ing expe r imen ta l ly d e f l e c t e d down t o approximate ly 160. effect aerodynamics on the v e h i c l e d i d n o t i n c l u d e a i l e r o n e f f e c t i v e n e s s ; t h e r e - f o r e , a i l e r o n v a r i a t i o n s were n o t s imula ted .

The b e s t a v a i l a b l e ground

P i t c h a t t i t u d e . - I n f i g u r e 5 (b ) t h e p r e d i c t e d p i t c h a t t i t u d e is i n e x c e l l e n t agreement w i t h the f l i g h t test data t o approximate ly 1.7 sec and agrees w e l l f o r t h e remainder o f the time h i s t o r y . s t r u t s t r o k e s and v e h i c l e geometry r e s u l t i n an i n d i c a t e d n e g a t i v e p i t c h a n g l e o f approximate ly 20.

For t he X-24B on a l e v e l runway, t h e s ta t ic

P i t c h rate.- F igu re 5 (c ) p r e s e n t s a comparison o f t he a n a l y t i c a l and expe r i - mental time h i s t o r i e s o f p i t c h ra tes f o r t h e X-24B. nega t ive and z e r o time cor responds t o touchdown. beyond nose gear impact which occurred a t approximate ly 1 .7 sec.

Nose-over p i t c h rates are The d a t a are p l o t t e d t o a time

The f i g u r e i n d i c a t e s a s l i g h t time s h i f t o f abou t 0.2 sec between t h e computed and a c t u a l t i m e h i s t o r i e s t h a t may be a t t r i b u t e d t o t h e i n f l u e n c e o f t h e a c t u a l l and ing s u r f a c e which was no t a v a i l a b l e f o r i n p u t . Magnitudes and t r e n d s of the computed and exper imenta l p i t c h rates, however, are i n good agreement throughout the t i m e h i s t o r y .

Angle of attack.- A comparison of the computed and exper imenta l a n g l e o f attack i n f i g u r e 5 ( d ) i n d i c a t e s good agreement a l though t h e a n a l y t i c a l v a l u e s are s l i g h t l y h igher than f l i g h t t e s t data throughout t h e time h i s t o r y . The maximum d e v i a t i o n between the computed and exper imenta l a n g l e s is approximately 2O b u t g e n e r a l l y t h e d e v i a t i o n is less than l o .

Ground speed.- A comparison of t h e exper imenta l and computed ground speed is presented i n f i g u r e 5 ( e ) . t o r y a l though t h e a n a l y t i c a l ground speed is s l i g h t l y h i g h e r beyond approximately 1 .5 s e c . The h igher speed is c o n s i s t e n t w i t h t h e assumed f l a t and smooth l and ing s u r f a c e as opposed t o t h e a c t u a l s u r f a c e which l i k e l y had both i n c l i n a t i o n and s u r f a c e roughness which could affect ground speed.

Good c o r r e l a t i o n is shown throughout t h e time h i s -

S t r u t s t r o k e s . - I n f i g u r e s 5 ( f ) , 5 ( g ) , and 5 ( h ) , a n a l y t i c a l and exper imenta l time h i s t o r i e s o f s t r u t s t r o k e f o r t h e r i g h t main, l e f t main, and nose gear, r e s p e c t i v e l y , are compared f o r t h e X-24B v e h i c l e l and ing . The o v e r a l l agreement between t h e magnitude and t r e n d s o f t h e computed s t r u t s t r o k e s and t h e f l i g h t test data are e x c e l l e n t f o r t h e r i g h t main ( f i g . 5 ( f ) ) and nose gear ( f i g . 5 ( h ) ) a l though t h e computed nose gear s t r o k e is s l i g h t l y h igher on t h e second peak around 3.0 sec. I n f i g u r e 5 ( g ) , however, t h e r e s u l t s f o r the l e f t gear show d i f f e r e n c e s i n t h e i n i t i a l s t r o k e bu t o v e r a l l behavior and maximum s t r o k e s are i n good agreement. A s was t h e case w i t h t h e f l i g h t data, t he computed l e f t s t r u t s t r o k e is less than t h a t o f t h e r i g h t main gear because o f t h e o f f s e t o f the ten- ter o f g r a v i t y toward t h e r i g h t gear.

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Axial strut forces.- Flight test axial strut forces and computed results for the X-24B are compared in figures 5(i) to 5(k). In figure 5(i), the comparison of axial strut force indicates that the overall shape of the time history, the time of occurrence of the peak forces, and, in general, the magnitudes of the experimental and analytical results are in good agreement for the right main gear. An overprediction of the force at 1.1 sec can be attributed to an additional analytical stroke (in excess of the experimental) of 0.014 m (0.045 ft) of the strut at 1.1 sec. (See fig. 5(f).) Such results indicate the sensitiv- ity of forces to the pneumatic component of the axial strut force during low or essentially zero strut compressive velocities. Beyond approximately 2.4 sec, the analytical main gear forces have leveled off whereas the flight data for both the right and left gears are oscillatory probably from the dry lakebed roughness which was not modeled in the analysis.

As indicated in figure 5(j), the agreement between the computed left gear force and flight data are not as good as the right gear comparison. cal forces are lower at initial contact and beyond 1.5 sec in the time history. However, the analytical results do appear to be more rational than the experimental data. For example, the left gear stroke, both experimentally and analy- tically, was less than the right gear stroke during the rollout phase. figs. 5(g) and 5(h).) At a constant stroke the vehicle is supported primarily by the force of the compressed air volume in the struts. It is expected that experimental forces in the gear with the smaller stroke would be less than those in the gear with the larger stroke. A comparison of the gear forces in figures 5(i) and 5(j), however, indicates that the experimental left gear forces are the same level or slightly higher than those of the right gear which is stroked more. This apparent discrepancy is not understood.

The analyti-

(See

In figure 5(k), the computed nose gear force shows a more rapid onset in loading but the peak force is in excellent agreement with flight data and the strut forces are only slightly higher throughout the remainder of the time history which is consistent with the strut stroke data (fig. 5(h)). The overall good agreement of the comparisons between the experimental and computed results for the X-24B vehicle indicate that the rigid-body option of FATOLA is a valid tool for the study of landing dynamics of stiff-body vehicles.

Flexible-Body YF-12A Airplane - Symmetric Touchdown Figure 6 presents a comparison of flight test and analytical time histories

of elevator deflections, pitch attitude, pitch rate, angle of attack, ground speed, strut strokes, axial strut forces, drag parachute force, longitudinal acceleration, and normal body accelerations, for a symmetric touchdown of the YF-12A research airplane. With the flexible-body option of FATOLA, typical com- putation time for generating all output data including the data of figure 6 was approximately 2400 decimal seconds of central processing unit time with 115K octal words of storage on a Control Data 6600 series digital computer.

Elevator deflections.- The elevator variations executed by the pilot to control the nose gear impact and the analytical simulation are shown in figure 6(a). The analytical variations of elevator deflections were programmed as shown to

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follow the actual flight test variations (computed from the two inboard and two outboard elevons on the airplane) throughout the time history.

During the analytical study, pitch rate was found to be extremely sensitive to the aerodynamic derivative hS which expresses the rate of change of the

q pitching-moment coefficient with elevator deflections; hence, slight reduction in the aerodynamic derivative. was made ( = l o percent) to obtain the correlation with flight data. tests on a 1/12-scale rigid model, the reduced aerodynamic coefficient is consistent with references 13 and 14 which indicate that airframe flexibility reduces the elevator effectiveness of a real airplane below that of a rigid airplane.

Since the aerodynamic data used were derived from wind-tunnel

Pitch attitude.- A comparison of the experimental and analytical pitch attitude is presented in figure 6(b) for the symmetric landing impact and rollout of the YF-12A airplane. Although the analytical results are slightly higher beyond 3 sec, they are within l o or less of the flight data throughout the time history.

Pitch rate.- Presented in figure 6(c) is a comparison of the analytical and actual time histories of the YF-12A airplane pitch rate response. The general variations in the magnitude of the pitch rate reflect the influence of approximately 22 changes in the aerodynamic control inputs (fig. 6(a)) executed by the pilot to reduce the nose gear impact at approximately 12.0 sec. The higher frequency oscillations in the flight data are responses of the pitch rate sensor to structural inputs.

As indicated in the figure, the magnitude and trends of the analytical and flight test time histories are in good agreement throughout the 15 sec of the landing impact and rollout. However, between approximately 13 and 13.5 sec, the flight data indicate a reduction in nose-over pitch rate that is not evident in the analytical results. A drift of the airplane approximately 4.6 m (15 ft) to the right of the runway center line placed the airplane on a track which may have had different surface roughness from that simulated (fig. 4) in the analysis and may have been responsible for this variation.

Angle of attack.- The comparison, in figure 6(d), between the flight test and analytical angles of attack are similar in behavior to the pitch attitude (fig. 6(d)) as would be expected. The magnitude of the analytical data is within l o or less of the flight data throughout the time history. At nose gear impact, the flight data become erratic and are not plotted beyond that time.

Ground speed.- In figure 6(e) the comparison between the computed and experimental ground speed of the YF-12A for the symmetric touchdown and rollout indicates excellent agreement throughout the 15.0-sec time history presented. During this time the airplane traversed approximately 1189 m (3900 ft) of runway 22 at the Edwards Air Force Base. (See fig. 4.) The effect of drag parachute deployment is evident in the sharp decrease in ground speed beyond 6.0 sec. At the end of 15 sec the computed speed is only approximately 2 percent lower than the experimental speed.

Strut strokes.- Shown in figures 6(f), 6(g), and 6(h) are the experimental and analytical strut strokes of the right and left main gears, and nose gear,

8

r e s p e c t i v e l y , f o r the symmetric l and ing o f the YF-12A. A s i n d i c a t e d i n f ig- u r e s 6 ( f ) and 6 ( g ) , there is g e n e r a l l y good agreement between the f l i g h t data and a n a l y t i c a l r e s u l t s . dur ing approximately the first 8.0 sec of touchdown and r o l l o u t . ences between t h e exper imenta l and a n a l y t i c a l s t r o k e s were e v i d e n t . For example, between approximately 1.5 and 3.0 sec, one s t r o k e p u l s e was i n d i c a t e d i n t h e a n a l y t i c a l r e s u l t s and a series o f f o u r small s t r o k e p u l s e s w a s i n d i c a t e d i n the f l i g h t data. d e v i a t i o n s i n the runway roughness or s l i g h t v a r i a t i o n s i n p i t c h rate ( f i g . 6 ( c ) ) could produce s i g n i f i c a n t changes i n s t r o k e behavior .

I n both cases there was minimum s t r o k i n g o f the gears Some d i f fe r -

Although the exac t cause of such d i f f e r e n c e s was n o t e s t ab l i shed ,

Major s t r o k i n g o f the main gears, both expe r imen ta l ly and a n a l y t i c a l l y , occurred beyond 8.0 sec i n the r o l l o u t . The t r e n d s compared w e l l and t h e maximum a n a l y t i c a l s t r o k e s were only approximately 10 t o 12 percen t higher beyond 12.0 sec.

I n f i g u r e 6 ( h ) t h e comparison of exper imenta l and a n a l y t i c a l nose gear s t r o k e s is n o t as good as t h e comparisons f o r the main gears. Although t h e times o f nose gear c o n t a c t are t h e same, the i n i t i a l peak a n a l y t i c a l s t r o k e was less than the exper imenta l s t r o k e . For subsequent s t r o k i n g , t h e f l i g h t data had three small s t r o k e p u l s e s between 12.5 and 15 sec whereas t h e a n a l y t i c a l had a subs tan- t i a l second peak i n s t r o k e w i t h a smaller t h i r d pu l se . T h i s d i f f e r e n c e i n nose gear s t r o k e s could have r e s u l t e d from t h e nose gear encounter ing a d i f f e r e n t runway roughness than was i n p u t because of t he d r i f t o f t h e a i r p l a n e a c r o s s t h e runway.

Axial s t r u t f o r c e s . - Comparisons of t h e exper imenta l and a n a l y t i c a l r i g h t and l e f t main gear and nose gear a x i a l s t r u t f o r c e s are p resen ted i n f i g u r e s 6 ( i ) , 6 ( j ) , and 6 ( k ) , r e s p e c t i v e l y . I n f i g u r e s 6 ( i ) and 6 ( j ) t h e main gear a x i a l s t r u t f o r c e s show e x c e l l e n t c o r r e l a t i o n i n magnitude and p a t t e r n throughout t h e t i m e h i s t o r y . Between 5.5 and 6.5 sec both t h e exper imenta l and a n a l y t i c a l f o r c e l e v e l s decreased; however, t h e a n a l y t i c a l r e s u l t s i n d i c a t e d t h e t i r e s b r i e f l y l o s t c o n t a c t w i t h t h e runway.

I n f i g u r e 6 ( k ) t he c o r r e l a t i o n of t h e exper imenta l and a n a l y t i c a l nose gear a x i a l s t r u t f o r c e s was no t a s good as the main gear f o r c e comparisons. The t r e n d s o f the nose gear a x i a l s t r u t f o r c e s are, however, c o n s i s t e n t w i t h t h e nose gear s t r o k e s and p i t c h rate behavior because of t h e i r i n t e r r e l a t i o n s h i p . Conse- q u e n t l y , t h e d i f f e r e n c e s noted i n f i g u r e 6 ( k ) are a l s o a t t r i b u t e d t o p o s s i b l e d i f - f e r e n c e s i n runway roughness d i scussed p rev ious ly .

Drag parachute force . - During the symmetric touchdown of the YF-12A air- p l ane , the p i l o t deployed t h e drag parachute of t h e a i r p l a n e approximate ly 6 sec after i n i t i a l main gear c o n t a c t . F igu re 6 ( 1 ) p r e s e n t s a comparison of the expe r i - menta l and a n a l y t i c a l drag parachute f o r c e t i m e h i s t o r i e s . The comparison i n d i - cates e x c e l l e n t c o r r e l a t i o n i n magnitude and decay of t he parachute f o r c e s from i n i t i a l deployment. The agreement shown i n t h e f i g u r e is a l s o c o n s i s t e n t w i t h t h e

the i t y

e x c e l l e n t c o r r e l a t i o n o f ground speed o f t he a i r p l a n e ( f i g . 4 ( e ) ) .

Long i tud ina l body a c c e l e r a t i o n s . - F i g u r e 6(m) shows t h e comparison between exper imenta l and a n a l y t i c a l l o n g i t u d i n a l a c c e l e r a t i o n o f the c e n t e r of grav- of the YF-12A a i r p l a n e . E x c e l l e n t c o r r e l a t i o n is shown between the magni-

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t u d e s and v a r i a t i o n s of the computed and f l i g h t data a c c e l e r a t i o n s . Although some h igh f requency response is p r e s e n t on t h e f l i g h t d a t a , t h e primary response of t h e l o n g i t u d i n a l a c c e l e r a t i o n is a rigid-body r e sponse and reflects t h e effects of v a r i o u s d rag f o r c e s a c t i n g on t h e a i r p l a n e i n t h e l o n g i t u d i n a l d i r e c - t i o n . s h o r t l y af ter 6 sec is t h e effect of t h e d rag pa rachu te deployed a t t h a t t ine . ( l g = 9.8 m/sec2 or 32 ft/sec2. ) A s t h e speed o f the a i r p l a n e decreases (a long wi th t h e drag pa rachu te f o r c e , f ig . 6 ( e ) ) , t h e a c c e l e r a t i o n s lowly i n c r e a s e s t o less nega t ive v a l u e s throughout t h e remainder of t h e time h i s t o r y .

For example, the sudden change i n a c c e l e r a t i o n t o approximate ly -0.55g

Normal body a c c e l e r a t i o n s . - Comparisons of f l i g h t test and a n a l y t i c a l normal a c c e l e r a t i o n s a t t h e c e n t e r o f g r a v i t y , t h e c o c k p i t , and l e f t main gear-body i n t e r f a c e on the YF-12A a i r p l a n e are shown i n f i g u r e s 6 ( n ) , 6 ( 0 ) , and 6 ( p > , r e s p e c t i v e l y . Although d i f f e r e n c e s are e v i d e n t i n t h e f i g u r e s , there are impor- t a n t p o i n t s of s i m i l a r i t y t o be noted . For i n s t a n c e , i n f i g u r e 6 ( n ) t h e f l i g h t data a c c e l e r a t i o n s , shown on an expanded time scale i n t h e i n s e r t s k e t c h , i n d i - cate t h a t t h e first and n i n t h exper imenta l modes a t 3.4 Hz and 23 Hz, respec- t i v e l y (refs. 15 and 161, were t h e predominant modes c o n t r i b u t i n g t o t h e acceler- a t i o n r e sponses of t h e a i r p l a n e . S i m i l a r l y , t h e a n a l y t i c a l r e sponses a t 2.5 Hz and 18 Hz were t h e first and n i n t h a n a l y t i c a l symmetric modes of the 10 two- dimensional modes used t o r e p r e s e n t t h e f l e x i b i l i t y of t h e a i r p l a n e .

F igu re 6(0) p r e s e n t s a comparison of exper imenta l and a n a l y t i c a l accelera- t i o n s a t t he c o c k p i t . Acce le ra t ions exper ienced by t h e p i l o t can affect h i s c a p a b i l i t y t o c o n t r o l the a i r p l a n e and monitor t he c o c k p i t i n s t rumen t s du r ing take-of f and l and ing . A s i n d i c a t e d i n t h e f i g u r e , t h e predominant modes c o n t r i - b u t i n g t o t h e exper imenta l a c c e l e r a t i o n response were the first and seven th symmetric modes a t 3.4 Hz and 12 Hz, r e s p e c t i v e l y . L ikewise , t h e a n a l y t i c a l r e sponses were t h e first and seven th a n a l y t i c a l modes a t 2.5 Hz and 14.5 Hz, r e s p e c t i v e l y . t i ca l and f l i g h t data is good. The d i f f e r e n c e s between t h e a n a l y t i c a l and f l i g h t t e s t ampl i tudes could be a t t r i b u t e d , i n p a r t , t o a p p a r e n t l y higher a n a l y t i c a l modal damping than t h a t e x h i b i t e d on t h e a i rcraf t (compare t he decay of o s c i l l a - t i o n s ) and t o d i f f e r e n c e s between t h e a n a l y t i c a l and exper imenta l modes ( t h a t is , d i s s i m i l a r nodal l o c a t i o n s , modal ampl i tudes , and f r e q u e n c i e s ) . S ince similar modes are being e x c i t e d i n both t he a n a l y s i s and t h e f l i g h t t e s t of t h e YF-12A a i r p l a n e , t h e use of more a c c u r a t e modes and f r e q u e n c i e s would l i k e l y improve t h e a c c e l e r a t i o n c o r r e l a t i o n s .

A t t h e time of nose gear impact , t h e agreement between t h e ana ly-

I n f i g u r e 6 ( p ) on ly a segment of t h e f l i g h t t e s t a c c e l e r a t i o n a t the l e f t main gear-body i n t e r f a c e is presented f o r comparison of predominant response frequenc ie s w i t h t h e a n a l y t i c a l r e s u l t s s i n c e t h e f l i g h t data had a z e r o s h i f t . The comparison i n d i c a t e s t h a t t h e predominant modes c o n t r i b u t i n g t o both t h e expe r i - mental and a n a l y t i c a l a c c e l e r a t i o n r e sponses were t h e first and n i n t h symmetric modes, however, a t t h e d i f f e r e n t modal f r e q u e n c i e s p rev ious ly d i scussed . S ince t h i s l and ing impact was symmetric, i t would be u n l i k e l y t h a t any s i g n i f i c a n t asymmetric re sponses would be p r e s e n t i n t h e spanwise d i r e c t i o n on t h e a i r p l a n e . The data presented i n f i g u r e 6 i n d i c a t e t h a t the FATOLA program can adequa te ly p r e d i c t t he s i g n i f i c a n t l o a d s and r e sponses f o r a f lex ib le -body a i r p l a n e du r ing a symmetric touchdown.

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I

Flexible-Body YF-12A Airp lane - Asymmetric Touchdown

A s i n d i c a t e d i n a p rev ious s e c t i o n , t h e a v a i l a b l e modal d a t a used t o r ep re - s e n t t h e a i r p l a n e f l e x i b i l i t y were l i m i t e d t o symmetric modes i n the spanwise d i r e c t i o n . u a t i o n of FATOLA.

However, an asymmetric touchdown of t h e YF-12A w a s selected f o r eva l -

F igu re 7 p r e s e n t s comparisons of a n a l y t i c a l and f l i g h t test t i m e h i s t o r i e s of e l e v a t o r and a i l e r o n c o n t r o l d e f l e c t i o n s , p i t c h a t t i t u d e , p i t c h rate, ro l l . rate, a n g l e of attack, ground speed , s t r u t s t r o k e s , a x i a l s t r u t f o r c e s , and nor- m a l body a c c e l e r a t i o n s f o r the asymmetric l a n d i n g impact and r o l l o u t of t h e YF-12A research a i r p l a n e . The data of f i g u r e 7 were ob ta ined w i t h t he f l e x i b l e - body o p t i o n of FATOLA i n approximate ly 1800 decimal seconds of c e n t r a l p rocess ing u n i t time w i t h 115K o c t a l words of s t o r a g e on a Con t ro l Data 6600 series d i g i t a l computer.

E leva to r d e f l e c t i o n s . - E l e v a t o r c o n t r o l d e f l e c t i o n s and t h e a n a l y t i c a l programmed v a r i a t i o n s are shown i n f i g u r e 7 ( a ) . moment c o e f f i c i . e n t w i t h e l e v a t o r d e f l e c t i o n s noted i n t h e symmetric touchdown a l s o r e q u i r e d a r e d u c t i o n of 110 pe rcen t of the a v a i l a b l e aerodynamic c o e f f i c i e n t on e l e v a t o r d e f l e c t i o n s t o ach ieve good c o r r e l a t i o n w i t h f l i g h t data d u r i n g t h i s asymmetric s imula t ion .

The s e n s i t i v i t y o f t h e p i t ch ing -

Ai le ron d e f l e c t i o n s . - S ince t h e YF-12A a i r p l a n e had a r o l l ang le of 1.2O t o the r i g h t a t touchdown, c o n s i d e r a b l e a i l e r o n c o n t r o l d e f l e c t i o n s were i n i t i a t e d by the p i l o t dur ing t h e asymmetric l and ing f o r r o l l c o n t r o l . s e n t s t h e exper imenta l a i l e r o n d e f l e c t i o n and the a n a l y t i c a l i n p u t s of the a i le - ron c o n t r o l .

F igu re 7 ( b ) pre-

P i t c h a t t i t u d e . - A comparison of the exper imenta l and a n a l y t i c a l p i t c h a t t i - t u d e time h i s t o r i e s are p resen ted i n f i g u r e 7 ( c ) f o r t h e asymmetric impact and r o l l o u t of the YF-12A a i r p l a n e . Good agreement i s shown between the a n a l y t i c a l r e s u l t s and t h e f l i g h t test data t o beyond nose gear impact which occurred a t approximate ly 6.5 sec.

P i t c h rate.- Presented i n f i g u r e 7 ( d ) is a comparison of t h e computed and f l i g h t t e s t time h i s t o r i e s of the p i t c h ra te response f o r t h e YF-12A a i r p l a n e . The f i g u r e i n d i c a t e s t h a t t h e magnitudes and t r e n d s of t h e a n a l y t i c a l and f l i g h t tes t time h i s t o r i e s are i n good agreement throughout t h e i n i t i a l 10 sec of the asymmetric l and ing and r o l l o u t . The g e n e r a l v a r i a t i o n s i n t h e p i t c h rate ref lect the p i l o t ' s use of t h e e l e v a t o r s t o c o n t r o l t h e p i t c h rate p r i o r t o nose gear impact whereas the higher f r e q u e n c i e s are re sponses of t h e p i t c h rate s e n s o r t o s t r u c t u r a l i n p u t s noted p rev ious ly .

Roll rate.- A comparison of t he exper imenta l and a n a l y t i c a l r o l l rate of t h e The data i n d i c a t e t h a t t h e c o r r e l a - YF-12A a i r p l a n e is p resen ted i n f i g u r e 7 ( e ) .

t i o n between exper imenta l and a n a l y t i c a l r o l l rate i s good d u r i n g t h e i n i t i a l phase of the impact. Beyond approximate ly 2 sec, t he o s c i l l a t i o n s of r o l l rate are ou t of phase w i t h t h e exper imenta l data bu t the peak v a l u e s agree w e l l . The d i f f e r e n c e s i n phase o f a n a l y t i c a l r e s u l t s may be a t t r i b u t e d t o the absence o f an t i symmetr ic modes i n t h e f l e x i b i l i t y r e p r e s e n t a t i o n i n t h e spanwise d i r e c t i o n .

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Angle o f attack.- Comparisons between the f l i g h t data and a n a l y t i c a l a n g l e The a n a l y t i c a l a n g l e of at tack shows a of at tack are p resen ted i n f i g u r e 7 ( f ) .

smooth decrease as the a i r p l a n e p i t c h e s over d u r i n g t h e l a n d i n g as would be expec ted . The expe r imen ta l data, however, are errat ic and are suspec t especially beyond approximate ly 3.0 sec.

Ground speed.- During t h e first 10.0 sec of t h e asymmetric touchdown and r o l l o u t , the a i r p l a n e t r a v e r s e d approximate ly 792 m (2600 f t ) o f runway 22 a t the Edwards A i r Force Base. (See f ig . 4.) I n f i g u r e 7 ( g ) t h e comparison of t he computed and exper imenta l ground speed i n d i c a t e s good agreement throughout t h e time h i s t o r y . S i n c e t h e d r a g . p a r a c h u t e was n o t deployed d u r i n g t h i s par t of the r o l l o u t , the decrease of the a i r p l a n e ground speed i s the r e s u l t of a l l o t h e r drag f o r c e s opposing t h e forward motion of t h e a i r p l a n e .

S t r u t s t r o k e s . - A comparison between t h e a n a l y t i c a l and exper imenta l main gear and nose gear s t r u t s t r o k e s could no t be made because of a l o s s of t h e s t r u t s t r o k e data channe l s f o r t h i s p a r t i c u l a r f l i g h t . However, f i g u r e 7 ( h ) p r e s e n t s t he a n a l y t i c a l s t r o k e s f o r completeness of data p r e s e n t a t i o n . The data i n d i c a t e t h a t t h e main gear s t r u t s t r o k e s , i n t h e l a t t e r p a r t of t h e time h i s t o r i e s , were o s c i l l a t i n g s l i g h t l y about a l e v e l of approximate ly 0.26 m (0.85 f t ) . gear s t r u t s t r o k e was st i l l t r a n s i e n t du r ing t h e t i m e h i s t o r y presented .

The nose

Axial s t r u t f o r c e s . - Comparisons of t he exper imenta l and a n a l y t i c a l a x i a l s t r u t f o r c e s which r e s u l t e d du r ing t h e asymmetric l a n d i n g impact and r o l l o u t of t h e YF-12A a i r p l a n e are p resen ted i n f i g u r e s 7 ( i ) t o 7 ( k ) . A s i n d i c a t e d i n t h e f i g u r e s , t he o v e r a l l shapes and magnitudes of a l l three a n a l y t i c a l a x i a l - f o r c e time h i s t o r i e s agree w e l l w i t h t h e f l i g h t data time h i s t o r i e s . A t approximate ly 3 .3 sec, however, and from 7.5 t o 10.0 sec, t h e a n a l y t i c a l r i g h t main a x i a l s t r u t f o r c e s ( f ig . 7 ( i ) ) were somewhat h igher t h a n t h e f l i g h t data. I n f i g u r e 7 ( j ) , the l e f t main gear f o r c e w a s lower a t approximate ly 3.5 sec. O s c i l l a t i o n s of t h e a n a l y t i c a l f o r c e s i n t h e main gears are o u t of phase wi th t h e f l i g h t data i n t h e l a t te r stage of t h e time h i s t o r i e s .

D i f f e r e n c e s i n t h e magnitude and phas ing of t h e a n a l y t i c a l and f l i g h t data time h i s t o r i e s ( f o r bo th r i g h t and l e f t main gears) might be a t t r i b u t e d t o t he absence of spanwise an t i symmetr ic modes. If ant i symmetr ic degrees of freedom had been inc luded i n t he a n a l y s i s , i t is be l i eved t h a t t h e o v e r p r e d i c t i o n of the r i g h t gear and t h e unde rp red ic t ion of t h e l e f t gear s t r u t f o r c e s would both have been s u b s t a n t i a l l y reduced.

I n f i g u r e 7 ( k ) t h e a n a l y t i c a l and exper imenta l nose gear a x i a l s t r u t f o r c e time h i s t o r i e s are i n ve ry good agreement. S ince t h e nose gear i s on the v e h i c l e p l ane of symmetry, t h e an t i symmetr ic spanwise motions would n o t be expected t o a p p r e c i a b l y affect the r e s u l t s f o r t h e nose gear. For t h i s l and ing , t h e a i r p l a n e remained c l o s e t o t h e measured track of runway roughness and better agreement between the nose gear a x i a l f o r c e s w a s i n d i c a t e d as compared w i t h t h e symmetric touchdown d i scussed p rev ious ly .

Normal body a c c e l e r a t i o n s . - Comparisons of f l i g h t test and a n a l y t i c a l normal a c c e l e r a t i o n s a t t h e c e n t e r of g r a v i t y , c o c k p i t , and l e f t main gear-body i n t e r - face are shown i n f i g u r e s 7 ( 1 ) , 7(m), and 7 ( n ) , r e s p e c t i v e l y , f o r t he asymmetric l a n d i n g of t h e YF'-12A a i r p l a n e . I n f i g u r e s 7 ( 1 ) and 7(m), t h e same impor tan t

12

I

p o i n t s of s i m i l a r i t y noted i n t h e symmetric touchdown ( f ig s . 6 ( n ) t o 6 ( p ) ) are a l s o ev iden t i n t h e s e comparisons. For i n s t a n c e , i n f i g u r e 7 ( 1 ) a t t h e c e n t e r o f g r a v i t y , bo th t h e f l i g h t t e s t and a n a l y t i c a l a c c e l e r a t i o n r e sponse f r e q u e n c i e s ( expe r imen ta l ly a t 3.4 Hz and 23 Hz and a n a l y t i c a l l y a t 2 .5 Hz and 18 Hz, respec- t i v e l y ) which correspond t o t h e first and n i n t h symmetric modes are t h e predomi- nan t c o n t r i b u t i o n s t o t h e responses .

A t t h e c o c k p i t ( f i g . 7 ( m ) ) , t h e predominant exper imenta l a c c e l e r a t i o n response f r e q u e n c i e s correspond t o t h e first mode (3 .4 Hz) and t h e e i g h t symmet- r i c mode (15 Hz). For t h e a n a l y t i c a l a c c e l e r a t i o n s , t h e predominant r e sponses were t h e first and n i n t h a n a l y t i c a l modes. S ince t h e c e n t e r of g r a v i t y and cock- p i t p o s i t i o n s are i n t h e p lane of symmetry of t h e * a i r p l a n e , t h e asymmetric land- i n g and t h e absence of an t i symmetr ic spanwise modes would n o t be expected t o a p p r e c i a b l y affect t h e r e s u l t s f o r t h e s e v e h i c l e l o c a t i o n s . On t h e o t h e r hand, p o s s i b l e d i f f e r e n c e s between t h e f l i g h t t e s t and a n a l y t i c a l r e sponses could be expected f o r the l e f t main gear and body i n t e r f a c e comparison shown i n fig- u r e 7 ( n ) . Indeed, t h e a n a l y t i c a l r e s u l t s i n d i c a t e t h a t t h e predominant r e sponse f r equenc ie s of 2.5 Hz and 18.0 Hz correspond t o t h e first and n i n t h symmetric modes whereas t h e exper imenta l response f r e q u e n c i e s of 4.3 Hz and 29.0 Hz cor re - spond t o t h e first and s i x t h exper imenta l an t i symmetr ic modes of t h e a i r p l a n e .

The comparisons of t h e exper imenta l and a n a l y t i c a l data f o r t h e asymmetric touchdown of t h e YF-12A a i r p l a n e i n d i c a t e t h a t t he FATOLA program can adequa te ly describe t h e s i g n i f i c a n t a i r p l a n e l o a d s and r e sponses . The use of more a c c u r a t e modal data i n c l u d i n g an t i symmetr ic modes should improve s i g n i f i c a n t l y t h e accel- e r a t i o n c o r r e l a t i o n s f o r an asymmetric touchdown case.

F l e x i b i l i t y Effects

An impor tan t effect t h a t t h e a v a i l a b l e f l e x i b i l i t y data have i n a l t e r i n g the l o a d i n g behavior on t h e YE'-12A a i r p l a n e i s shown by t h e comparison i n f ig- u r e 8 of t h e a n a l y t i c a l r igid-body and f lex ib le -body nose gear a x i a l s t r u t f o r c e s . major peaks between 6.5 and 10 sec i n t h e time h i s t o r y . metric f l e x i b i l i t y s i g n i f i c a n t l y al tered the load p a t t e r n t o on ly one complete unloading and f o u r major peaks wi th s l i g h t l y h ighe r magnitude of f o r c e s t h a n t h e rigid-body f o r c e s . For t h e f lex ib le -body o p t i o n , t h e nose gear c o n t a c t occur red approximately 0 .3 sec la te r than t h e rigid-body o p t i o n r e s u l t s . A s i n d i c a t e d i n f i g u r e 7 ( k ) , bo th t h e magnitudes and load p a t t e r n of t h e f l e x i b l e data are i n good agreement wi th t h e exper imenta l f o r c e behavior . airframe f l e x i b i l i t y can be impor tan t i n load p r e d i c t i o n . f i g u r e 8 were from a computer run which r e q u i r e d 600 decimal seconds of c e n t r a l p rocess ing u n i t t i m e w i th 115K o c t a l words of s t o r a g e on a Con t ro l Data 6600 series d i g i t a l computer.

The rigid-body data i n d i c a t e t h r e e n e a r l y complete unloadings wi th s i x The i n t r o d u c t i o n of sym-

These r e s u l t s i n d i c a t e t h a t The rigid-body data i n

CONCLUDING REMARKS

A F l e x i b l e Aircraft Take-off and Landing Analys is computer program (FATOLA) is used-in an exper imenta i and-ana ly t i ca l c o r r e l a t i o n s t u d y o f v e h i c l e l a n d i n g behavior t o demonst ra te t h e rigid-body and f lex ib le -body o p t i o n s of t h e program

13

and t o v a l i d a t e t h e a n a l y s i s . Modi f ica t ions t o t h e program t o improve the analy- t ical s imula t ion c a p a b i l i t i e s of t h e FATOLA program are d iscussed .

Based on c o r r e l a t i o n s between a n a l y t i c a l and experimental d a t a f o r both t h e X-24B v e h i c l e and t h e YF-12A a i r p l a n e , o v e r a l l agreement between t h e a n a l y t i c a l and f l i g h t test d a t a i s good. For the YF-12A a i r p l a n e , airframe f l e x i b i l i t y i s impor tan t f o r nose gear loading . a c c e l e r a t i o n magnitudes and f l i g h t d a t a f o r t h e YF-12A; however, similar modes appear i n t h e a n a l y t i c a l resu l t s and t h e f l i g h t d a t a . The use of more a c c u r a t e symmetric and ant isymmetr ic modes and f r equenc ie s would l i k e l y improve t h e accel- e r a t i o n c o r r e l a t i o n s . The p resen t c o r r e l a t i o n s i n d i c a t e , however, t h a t t h e FATOLA program is a v e r s a t i l e and v a l i d a n a l y t i c a l t o o l f o r t h e s tudy of a i r c r a f t l anding dynamics.

D i f f e rences are ev iden t between a n a l y t i c a l

Langley Research Center Nat iona l Aeronaut ics and Space Adminis t ra t ion Hampton, VA 23665 September 7 , 1977

14

APPENDIX

PROGRAMMING CHANGES

Th i s appendix p r e s e n t s t h e changes i n t h e FATOLA program t o improve t h e a n a l y t i c a l s imula t ion c a p a b i l i t i e s .

S t r u t Axial F r i c t i o n

Three mod i f i ca t ions were made t o improve t h e s t r u t a x i a l f r i c t i o n f o r c e s i m - u l a t i o n . To accomplish t h e first two m o d i f i c a t i o n s , t h e fo l lowing s t a t e m e n t s were i n s e r t e d i n t h e LGEA3C s u b r o u t i n e of FATOLA:

COMMON/NORMFF/SLENI (51, SLEN2(5) COMMON/TEMPRES/GAMA , PATM DIMENSION IFRI ( 5 ) DATA ( I F R I ( I ) , I = 1 , 5 ) / 0 , 0 , 0 , 0 , 0 / IF(SD1(1,I).EQ.O.O.AND.IFRI(I).EQ.1)IFRI(I)=O IF(SDl( I,I).LE.O.5.AND.IFRI(I).EQ.0)2,3

GO TO 4

IFRI(1) = 1

2 HYPTAN = 1 .O

3 HYPTAN = ABS (TANH(4.O*SDI(l,I)))

4 FF ( I) = MUS ( I) *SQRT( FDX( I) *FDX ( I)+FDY ( I) *FDY ( I) ) FF(1) = FF(I)*(l.O+2.O*((SLEN2(I)-S(1,I))/

(SLENl(I>+S(l,I))))*HYPTAN

The two COMMON statements a l low t h e new i n p u t v a r i a b l e s t o be passed i n t o s u b r o u t i n e LGEA3C. The D I M E N S I O N s ta tement s i z e s t h e f r i c t i o n i n d i c a t o r s I F R I ( I ) , and t h e DATA s t a t emen t i n i t i a l i z e s t h e i n d i c a t o r s t o ze ro . statements and HYPTAN = 1.0 a l low t h e f u l l f r i c t i o n f o r c e t o be used u n t i l t h e s t r u t v e l o c i t y S D l ( 1 , I ) of any s t r u t d rops below 0.152 m / s ( 0 .5 f t / s e c ) ( a r b i - t r a r i l y chosen) a f te r t h e i n i t i a l s t r o k i n g . When t h e s t r u t v e l o c i t y becomes less t h a n 0.152 m / s (0.5 f t / s ec ) , t h e f r i c t i o n f o r c e is t r a n s i t i o n e d through z e r o a long t h e hyperbol ic tangent f u n c t i o n

The two IF

HYPTAN = ABS (TANH ( 4 . 0 * S D I ( l , I ) ) ) .

The o r i g i n a l s t r u t a x i a l f r i c t i o n f o r c e equa t ion (statement numbered 4) was modi- f i e d t o a form of equa t ion ( 4 ) i n reference 10 t o i n c l u d e t h e moment effects on t h e ax ia l f r i c t i o n . The expres s ion i s

FF ( I) = FF ( I) *( 1 .0+2.0*( (SLEN2 ( I ) -S( 1 , I ) ) / (SLENI ( I) +S( 1 , I ) ) ) )

where

SLEN2(I) a r r a y of d i s t a n c e s between hub and lower b e a r i n g f o r f u l l y extended gear

15

APPENDIX

SLENl(1) array of distances between upper and lower bearing for fully extended gear

S(1,I) strut strokes for each gear

The third modification was to change the statement

TMP(2) = 0.0

in the subroutine LGEAR1 to

TMP(2) = 1.0

which allows the friction force to be effective at all times.

Strut Air Pressure Equations

Revised strut air pressure equations were also inserted in the LGEA3C subroutine to replace the original equations. The revised equations are

P (I) = (PZERO(I)+PATM)*(VZERO(I)/(VZERO(I)+A2(I)*S2~l,I)-S(l,I)*A(I)))**GAMA-PATM

P2(I) = (P20(I)+PATM)*(V20(I)/TMP(I))**GAMA-PATM

where PATM (atmospheric pressure) has been included to convert gage pressure to absolute pressure and GAMA (y) has been added to allow variations in the compres- sion process.

Structural Damping

To incorporate structural damping in the flexible body simulation, the statement

COMMON/DAMPCOM/GDAMP(20)

and expression

were added to the subroutine FLEX1 of the FATOLA program. The COMMON statement makes available the necessary input variable GDAMP (modal damping) in the FLEX 1 subroutine. The second term of the expression

represents the modal damping force that has been added. As stated in reference 12, the equivalent viscous form of structural damping GDAMP(1G) can be approximated by

APPENDIX

where

jth generalized modal stiffness

structural damping in jth mode (usually based on experimental data)

jth vibration natural frequency

Kj j

gj

wj

Roll Autopilot and Control Response

To permit variations in r o l l control deflections to be simulated throughout the landing, the logic in the roll autopilot and control response sections were altered in the auxiliary computations routine of the program. For the r o l l autopilot the changes were

102 IF(IAP.EQ.4) GO TO 68 DELPD=O GO TO 103

68 IF(TR.LE.TST) GO TO 69 DELPDE = DELPI+DELA*(TR-TST) GO TO 103

GO TO 103 69 DELPI = DELPD

and in the control response

63 IF(IAP.EQ.4) GO TO 64

The changes given create, in the r o l l autopilot, a special branch for the landing impact and rollout phase (IAP = 4 ) to allow the aileron deflections to be initialized and programmed by inputs of DELPD (initial input aileron deflection), TST (time for staging), and DELA (aileron rate). The addition of statement 63 in the control response also switches the logic only for actual aileron deflection, used elsewhere in the program, to the desired value of 'aileron deflection (DELPDE) computed in the r o l l autopilot.

IAP = 4 to set the

New Input Data

To make the new variables associated with the modifications to FATOLA available to the program subroutine where they are used, the programming changes presented below were added to the main program TOLA.

COMMON/NORMFF/SLEN1(5),SLEN2(5) COMMON/TEMPRES/GAMA,PATM COMMON/DAMPCOM/GDAMP(20) NAMELIST/BEGDATA/SLENI,SLEN2,GAMA,PATM,GDAMP READ ( 5,5002 ) SLEN 1 , SLEN2 READ(5.5003)GAMA, PATM

5002 FORMAT(5F10.0)

5003 FORMAT(2F10.0)

17

.. . . . ... . . . . .

APPENDIX

READ(5.5004)GDAMF'

WRITE(6,BEGDATA) 5004 FORMAT(8F10.0)

The common s t a t emen t s e s t a b l i s h l a b e l e d common b locks f o r t h e v a r i a b l e s i n NAMELIST. The READ and FORMAT s t a t emen t s i n i t i a t e t h e r ead ing of t h e new d a t a ca rds . The WRITE s ta tement i n i t i a t e s p r i n t i n g of t h e new i n p u t d a t a list p r i o r t o t h e read and p r i n t of t h e normally s p e c i f i e d FATOLA i n p u t da t a .

18

REFERENCES

1. DC-10 Landing Gear Modified. Aviat. Week & Space Technol. , vo l . 98, no. 12, Mar. 19, 1973, p. 181.

2 . Ropelewski, Robert R . : Airbus Test Tempo Quickening. Aviat . Week & Space Technol. , vo l . 98, no. 10, Mar. 5, 1973, PP. 32-35.

3. McGehee, John R . ; and Carden, Huey D.: A Mathematical Model of an Active NASA Control Landing Gear f o r Load Cont ro l During Impact and Roll-Out.

TN D-8080, 1976.

4. Lynch, Urban H . D. : Takeoff and Landing Analys is (TOLA) Computer Program. P a r t I - C a p a b i l i t i e s of t h e Takeoff and Landing Analys is Computer Program. AFFDL-TR-71-155, P t . 1 , U . S . A i r Force , Feb. 1972. (Avai lab le from DDC as AD 741 942.)

5. Lynch, Urban H . D. ; and Dueweke, John J.: Takeoff and Landing Analysis (TOLA) Computer Program. P a r t 11.- Problem Formulat ion. AFFDL-TR-71-155, P a r t 11, U . S . A i r Force, May 1974.

6 . Lynch, Urban H . D . ; and Dueweke, John J.: Takeoff and Landing Analys is Computer Program (TOLA). P a r t 111.- User's Manual. AFFDL-TR-71-155, P a r t 111, U.S. A i r Force , Apr. 1974.

7 . Young, Fay 0.; and Dueweke, John J.: Takeoff and Landing Analys is Computer Program (TOLA). P a r t I V : Programmer's Manual. AFFDL-TR-71-155, P a r t I V , U.S. A i r Force, Jan. 1975.

8. Dick, J. W . ; and Benda, B. J.: Addit ion of F l e x i b l e Body Option t o t h e TOLA Computer Program. P a r t I - F i n a l Report . NASA CR-132732-1, 1975.

9. Dick, 3 . W . ; and Benda, B. J.: Addit ion o f F l e x i b l e Body Option t o t h e TOLA Computer Program. P a r t I1 - User and Programmer Documentation. NASA CR-132732-2, 1975.

10. Milwitzky, Benjamin; and Cook, F r a n c i s E. : Analys is of Landing-Gear Behav- i o r . NACA Rep. 1154, 1953. (Supersedes NACA TN 2755.)

11. Wignot, Jack E . ; Durup, Paul C . ; and Gamon, Max A . : Design Formulation and Analysis of an Active Landing Gear. Volume I. Analys is . AFFDL-TR-71-80, Vol. I , U.S. A i r Force , Aug. 1971. (Avai lab le from DDC as AD 887 127L.)

12. Edinger , Lester D . ; Schenk, F rede r i ck L . ; and C u r t i s , Alan R . : Study of Load A l l e v i a t i o n and Mode Suppression (LAMS) on t h e YF-12A Airplane. NASA CR-2158, 1972.

13. Fung, Y. C. : An In t roduc t ion t o t h e Theory of A e r o e l a s t i c i t y . GALCIT Aeronau- t i ca l Series. John Wiley & Sons, Inc . , c.1955.

14. E tk in , Bernard: Dynamics of F l i g h t . John Wiley & Sons, Inc . , c.1959.

19

15. Kordes, E. E . ; and C u r t i s , A. R . : R e s u l t s of NASTRAN Modal Analyses and Ground Vib ra t ion Tests on t h e YF-12A Airp lane . SOC. Mech. Eng. Winter Annual Meeting (Houston, Texas) , Nov.-Dec. 1975.

Paper 75-WA/Aero 8 , h e r .

16. Wilson, Ronald J.; Cazier, Frank W . , Jr.; and Larson, Richard R . : R e s u l t s of Ground Vib ra t ion Tests on a YF-12 Airplane. NASA TM X-2880, 1973.

20

\ \ IMPACT RUNWAY STEERING

OPERATIONAL LOADS

WIND DRAG CHUTE BRAKING THRUST REVERSAL AERODYNAMIC

9 ASYMMETRIC IMPACT

INPUT LOADS FOR TOTAL VEHICLE RESPONSE ANALY S I S

’ VEHICLE DYNAMIC LOADS AND RESPONSES

CHARACTERISTICS

MODAL FREQUENC I ES @MODAL M A S S .MODAL DISPLACEMENTS .MODAL DAMPING

Figure 1.- General capabilities of the Flexible Aircraft - Take-off - and - Landing - Analysis (FATOLA) computer program.

Figure 2.- X-24B r e e n t r y r e sea rch veh ic l e .

* ^ , ,,,, _I, ,

L-77-279 Figure 3.- YF-12A research a i r p l a n e .

N W

Elevation Southwest of runway

m

-6.0

- 5.5

- 5.0

above end 22,

-4.5

-4.0

,

Location of YF-12A symmetric touchdown

Location of YF-12A asymmetric touchdown

z c

Delta elevation (roughness) above general runway slope

c

-

Runway slope = -0.07575' -. -

, I I

-20

-19

-18

-17

-16

-15

-14

7 I I I I I .2 .4 .6 .8 1.0 1.2 1.4

. -13

Elevation Southwest of runway

ft

Runway distance, km

I I I I I 1 I I I I .6 1 .o 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 416 x 103

Runway distance, ft

above end 22,

F igure 4.- C h a r a c t e r i s t i c s of a 1219-m (4000-ft) s e c t i o n of runway 22 a t Edwards A i r Force Base, Ca l i fo rn ia .

-1 8

-20

-22

Elevator deflection, -24

deg

-2 6

-28

-30

Nose gear touchdown - Flight test ---- Analytical input

Lift coefficient staged for flap effect of 16Odown lower elevon

(a ) El'evator d e f l e c t i o n .

F igure 5.- Analy t ica l r i g i d body and f l i g h t tes t d a t a f o r X-24B vehic le .

16

12

8

Pitch

deg attitude, 4

0

-4

-8

Flight test - - - - Analytical -

Nose gear touchdown

1 I I 0 .5 1 .o 1.5

I I I 1 2.0 2.5 3 .O 3.5

Time, sec

( b ) P i t c h a t t i t u d e .

F igure 5. - Continued.

I

0 -

-6

Pitch rate, deg/sec

-1 2

-24

Nose gear touchdown

I I I .5 1.0 1.5

1

I I I I I

I I

Flight test ---- Analytical

Time, sec

( c > P i t c h ra te .

F igure 5.- Continued.

16

12

8

4 Angle of attack,

deg

0

4

Nose gear touchdown

43 0 .5 1 .o 1.5

Flight test Andy t ical ----

\

~~

2.0 2.5 3 .O 3.5

Time, sec

(d) Angle of attack.

Figure 5.- Continued.

89

86

Ground speed, 83 m/sec

80

Nose gear touchdown

77 I I I I 0 .5 1.0 1.5

Flight test ---- Analytical

I I I 2.0 2.5 3.0

290

280

270

2 60

250 i

Ground s p e d , ft/sec

Time, sec

(e> Ground speed.


W 0

Strut stroke,

m

Nose gear touchdown

Flight test Andy t ical - 0 - -

1.2 1, 1.0 strut

ft .6 stroke,

.4

I I I l o 2.0 2.5 3 .O 3.5

Time, sec

(f) Right main gear s t r u t stroke.


.35 -

.30

.25

Strut .20 stroke, m

.15

.10

.05

0

Nose gear touchdown

- 1.2 Flight test -- - - Analytical

- 1.0

Strut

ft

1 .4

- .2

Time, sec

( g ) Left main gear s t r u t s t roke .

F igure 5. - Continued.

W N

.30

St rut stroke,

m

.25

.20

.15

- -

-

.10 - 005 I-

I I I I J 0 .5 1 .o 1.5

Flight test - - - - Analytical

Nose touch

~~~

2.0 2.5 3 .O 3.5

1.2

1.0

.8 St rut

stroke, ft

.6

.4

.2

0

Time, sec

( h ) Nose gear s t r u t stroke.


40

32

24 Axial strut force, kN 16

8

0

3 Nose gear Flight test - 10 x 10 touchdown - - - - Analytical

-

-

-

.5 1.0 1.5 Time, sec

I I I 2.0 2.5 3.0 3.5

8

Axial s t rut force,

lbf

6

4

2

0

(i) Right main gear a x i a l s t r u t force.

Figure 5. - Continued.

W W

40

32

Axial strut 24 force,

kN

Nose gear Flight test touchdown _---- Analytical

0 .5 1.0

IO x lo3

8

Axial.

force, 1 st rut

//-- lbf - 4 ------ \-4--

- 2

I I I , o 2 *o 2.5 3 .O 3.5

Time, sec

( j ) Left main gear axial strut force.


40 -

Axia strut force,

kN

32

24

16

8

0

Nose gear touchdown

Flight test Analytical - 8 x 1 0 3 --- - -

I

- 6

(k) Nose gear a x i a l strut force.

Figure 5.- Concluded.

w ul

w m i

2

-2

Elevator deflect ion,

deg

Drag parachute deployed

I

Flight test Analytical input

- - -- -

m t 7 Nose gear touchdown

I I I I 0 2 4 6 8 10 12 14 16 18 20

Time, sec

( a > Eleva tor d e f l e c t i o n .

F igu re 6.- Ana ly t i ca l f l e x i b l e body and f l i g h t - t e s t data f o r symmetric touchdown of YF-12A a i r p l a n e .

Pitch attitude,

deg

'Zir Drag parachute deployed

- Flight test ----- Analytic a1

Nose gea r touchdown

I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20

Time, sec

(b) Pi t ch a t t i t u d e .


w 03


0

Pitch rate, deg/sec

-2

Nose gear touchdown

-Flight test - - - -Analytical

A

-6 b I I I I I I I I I I 8 10 12 14 16 18 20 0 2 4 6

Time, sec

( c > P i t c h ra te .


Flight test - - - - Analytical -

2o r Nose gear touchdown

Drag arachute dep B oyed

12 - Angle of attack, deg

I I 0 2 4 6 8 10 12 14 16 18 20

Time, sec

( d ) Angle of attack.


ll0 r Drag parachute deployed

Ground speed, m/sec

70 - 60 :+

I

5O k i

F1 ight test _---- Analytic a1

3 60

3 20

280

Ground

- 200

I

40 L

I I I I I i I I I i120 0 2 4 6 8 10 12 14 16 18 20

Time, sec

( e ) Ground speed.


.35

.30

.25

.20 strut stroke,

m .15

.10

.05

0


I

- Flight test ---- Andy t ical Nose gear touchdown

I I 3 L

I

i\

- 1.2

I 2 4 6 8 10 12 14 16 18 20

Time, sec

( f ) Right main gear s t r u t s t roke.

..o

.8

Strut

ft .6 stroke,

.4

.2

0

Figure 6 . - Continued.

-t= N

i

I i I

.35

.30

.25

Strut stroke, .20

m

.15

.10

Flight test - ---- Analytical

Nose gear touchdown


I

1.2

1.0

.8 St rut

stroke, ft

.6

- .4

- .2

I I I 0 0 2 4 6 8 10 12 14 16 18 20

Time, sec

( g > Left main gear s t r u t s t r o k e .


Strut stroke,

m

.10

.05

- Flight test 1 *4 - - - - Analytical

Nose gear - .3 r Drag parachute touchdown I

_ - deployed

0 Time, sec

lH I i

12 14 16 18

-i O 2

Strut stroke,

ft

( h ) Nose gear strut stroke.


c' W

240r 200 r

i 160 1-

Axial strut force,

.-

kN 120 7

Axial strut force,

lbf 20

Flight test Nose gear - touchdown -- - - Analy tical

P

80

40

50 x lo3

- 1 l 0

I I I 10 0 2 4 6 8 10 12 14 16 18 20

Time, sec

(i) Right main gear a x i a l s t r u t fo rce .


200

3 -50 X 10 - Flight test Nose gear touchdown -0- -Analytical

I: -

Axial strut force,

kN

Time, sec

(j> Left main gear a x i a l s t r u t fo rce .


Axial strut force, lbf

80 - Flight test - - - - Analytical 16 x lo3

12

Axial strut

lbf 8 force,

- 4

0

60

Drag parachute

Axial strut

kN force, 40

20

0 2 4 6 8 10 12 14 16 18 20 Time, sec

(k) Nose gear a x i a l s t r u t f o r c e .


Drag parachute

kN force,

240 -

200 -

- Flight test - - - - - Analytical 3 - 50 X 10

160 - - 40

160 - - 30

Drag parachute

Ibf 120 - force,

- 20 80 -

- 10 40 -

r I I 0 0 2 4 6 8 10 12 14 16 18 20

Time, sec

(1) Drag parachute fo rce .



- Flight test Analytical - - - -

Nose gear ' 0 touchdown

Center-of -gravity longitudinal acceleration, -0 2

g units

-.4

-. 6

-.8 I1 I I I I I

I

0 2 4 6 8 10 12 14 16 18 20 Time, sec

(m) Longitudinal a c c e l e r a t i o n of cen te r of g r a v i t y .


G z (9th)

2.8

2.4

2.0

1.6 Center-of-gravity

normal acceleration,

g units 1.2

.a

-4

0

-. 4

2.0

1.6

Center- of -gravity normal

g units acceleration, 1.2

.8

.4

‘1‘ I

/


I I I

Flight test

-1 .2 sec

I Analytical

f = 2.5 Hz (1st)

1 I I I I 1 1 -u 0 1 2 3 4 5 6 7 8 9 10

Time, sec

(n) Normal acceleration of center of gravity. f denotes frequency.


49

2.4

2.0

Cockpit 1.6 nor mal

g units acceleration,

1.2

.8

.4

0

f = 3.4 Hz (1st) f 4 = 12 Hz (7th)

// Dr%p! rachute red

I 1

Flight test

Nose gear touchdown

1 I I ~- J -

Analytical I Drag Darachute

1.6

Cockpit 1.2 normal

acceleration, g units .8

.4

0 2 4 6 8 10 12 14 16 18 20 Time, sec

(0) Normal acceleration of cockpit. f denotes frequency.


50

Left main gear-body


g units

Left main gear-body


g units

2.5 I-

ll

f = 23 Hz (9th)

Flight test I

2*o M f = 18 Hz (9th) 1' 1,

Nose gear touchdown

I

t

-0 2 4 6 8 10 12 14 16 18 20 Time, sec

( p > Normal acce lera t ion of l e f t main gear body. f denotes frequency.

Figure 6.- Concluded.

Elevator deflection,

deg

- Flight test

I I I I I I I I I I I 1 2 3 4 5 6 7 8 9 10

-1 0 0

Time, sec

( a ) Elevator d e f l e c t i o n .

F igure 7.- Analy t ica l f lexible-body and f l i g h t t es t da ta f o r asymmetric touchdown of YF-12A a i r p l a n e .

4

3

2 Aileron

deflection, deg

1

0

-1

-2 0

A - Flight test - --. Analytical input

-w I

J

1 2 3 4 5 Time, sec

(b) Aileron deflection.

6 7 8 9 10


Pitch attitude,

deg

12

10

8

6

4

2

Flight test Analytical ----

-‘A 0 1 2 3 4 5 6 7 8 9 10

Time, sec

( c > P i t c h a t t i t u d e .

F i g u r e 7.- Cont inued .

2

1

0

Pitch

deg/ s ec rate, -1

-2

-3

4


1 I I 1 1 I . 1 2 3 4 5 6

Time, sec

( d ) P i t c h rate.

F i g u r e 7.- Cont inued.

I I I

i ; ‘I

1 7 8 9 10

Roll rate, deg/sec

6

4

2

0

-2

4

-6

-8

I

I I

1 1 \

Flight test - - Analytical _--

Nose gear touchdown

1

1 2 3 4 5 6 Time, sec

h 7 8 9 10

(e> Roll rate.


10 - Flight test -- - - Analytical

8

6

4 Angle of

attack, deg

2

0

-2

Time, sec

(f) Angle of a t tack .

F igu re 7.- Continued.

Ground speed, m/sec

t-

I-

.--

Flight test - - - - Analytical 1280 1275

Nose gear speed, ~ ft/sec

I260

I 7 5 L , I I I I I I I 1 I I 1245

0 1 2 3 4 5 6 7 8 9 10 Time, sec

(g> Ground speed.


.35

.30

.25

Strut .20 stroke, m

.15

Analytical Right main ----- Left main --- Nose gear

r Right main

I I i Nose gear 7 .10 - /

f I /

I i

.05 - / /, I I 1

0 1 2 3 4 5 6 7 a 9

Time, sec

( h ) S t r u t s t rokes.

..2

.O

,a

strut

ft ,6 stroke,

.4

.2

0 1

F i g u r e 7. - Continued.

m 0

240

200

160

Axial

force, kN

strut 120

80


Nose gear touchdown k

50 x lo3 1 - 40

Axial strut

Time, sec

(i) Right main gear a x i a l s t r u t force.

force, lbf - 20

- 10


240 r I

200 - Flight test ---- Analytical

-

Nose gear k touchdown

3 - 50 X 10

- 40 160 -

0 1 2 3 4 5 6 7 8 9 Time, sec

30 Axial strut force,

lbf 20

10

0 I

( j ) Left main gear axial strut force.


48 - - Flight tes t -- - - Analytical 40 -

16 - 8 -

Time, sec

Axial strut force,

kN

(k) Nose gear a x i a l s t r u t f o r c e .

X lo3

Axial strut force,

lbf

F i g u r e 7. - Continued.

m w

I

1.6 I- I r f 23.0 HZ I , 11 J I . /r f =: 3.4 Hz (faired) I . II I I

0 I I I I I I I I I I I Analytical Nose gear 1.6

Center- of- gravity 1.2 normal

acceleration, g units

.8

.4 0 1 2 3 4 5 6 7 8 9 10

Time, sec

(1) Normal a c c e l e r a t i o n of c e n t e r of g r a v i t y . f deno tes f requency .

F i g u r e 7.- Continued.

Cockpit normal

g units acceleration,

1.8

1.4

1 .o

.6

Cockpit normal


f = 3.4 Hz (faired) L f = 15.0 Hz

1*8[ 1.4

Nose gear Flight test touchdown

Nose gear Analytic a1 touchdown

f = 2.5 Hz (fair

0 1 2 3 4 5 6 7 8 9 10 Time, sec

(m> Normal acce le ra t ion of cockpi t . f denotes frequency.


Left main gear-body


g units

3.0

2.6

2.2

1.8

1.4

1.0

.6

.2

-. 2

-. 6

-1.0

1.6 2*oL Left

main gear-body normal


th) t)

Nose gear touchdown

I

Flight test

1 1

Analytical

!

I "

I l l I I I

Nose gear touchdown

f zz 2.5 Hz (1st) 1.2

.8

.4 0 1 2 3 4 5 6 7 8 9 10

Time, sec

( n > Normal a c c e l e r a t i o n of l e f t main gear-body i n t e r f a c e .

F igu re 7.- Concluded.

65

48

40

32

Axial

force, kN

strut 24

16

8

0

,io x lo3

Axial st rut force, lbf

7 8 9 10 Time,

6 7 8 9 10 sec

Figure 8.- Analy t ica l rigid-body and flexible-body nose gear a x i a l s t r u t f o r c e s f o r YF-12A a i r p l a n e .

2. Government Accession NO. - I " - - NASA TP-1025

4. Title and Subtitle VALIDATION OF A FLEXIBLE AIRCRAFT TAKE-OFF AND LANDING ANALYSIS (FATOLA)

.- . - - - - .- - . - 7. Author(s)

Huey D. Carden and John R . McGehee ~

9. Performing Organization Name and Address NASA Langley Research Cen te r Hampton, VA 23665

_ _ - - _ _ i

- __ . -

12. S nsoring A ncy Name and Address vationage Aeronau t i c s and Space Admin i s t r a t ion Washington, DC 20546

- __ - 15. Supplementary Notes

3. Recipient's Catalog No.

5. Report Date

6, Performing Organization Code

October 1977

.. . - - . .

8. Performing Organization Report No.

L-11704 ~- ..

743-01-12-03 10. Work Unit No.

~ . - ~~ - ~ ~

11. Contract or Grant No.

- . ~

13. Type of Report and Period Covered Techn ica l Paper

- - 14 Sponsoring Agency Code

__. _ _ - - -

16 Abstract

M o d i f i c a t i o n s t o improve t h e a n a l y t i c a l s i m u l a t i o n c a p a b i l i t i e s o f a m u l t i - degree-of-freedom _F lex ib le Aircraft Take-_off and Landing A n a l y s i s (FATOLA) computer program are d i s c u s s e d . The FATOLA program w a s used t o s i m u l a t e t h e l a n d i n g behav io r of a s t i f f - b o d y X-24B r e e n t r y r e s e a r c h v e h i c l e and of a f l ex ib l e -body s u p e r s o n i c c r u i s e YF-12A r e s e a r c h a i r p l a n e . The a n a l y t i c a l r e s u l t s were compared w i t h f l i g h t t e s t . d a t a , and c o r r e l a t i o n s o f v e h i c l e mot ions , a t t i t u d e s , f o r c e s , and a c c e l e r a t i o n s d u r i n g t h e l a n d i n g impact and r o l l o u t were good. Fo r t h e YF-12A a i r p l a n e , airframe f l e x i b i l i t y was found t o be impor t an t f o r nose gear l o a d i n g . Based upon t h e c o r r e - l a t i o n s t u d y p r e s e n t e d h e r e i n , t h e v e r s a t i l i t y and v a l i d i t y o f t h e FATOLA program f o r t h e s t u d y of l a n d i n g dynamics o f aircraft are confirmed.

- ~~ - 17. Key-Words (Suggested by Author(s))

F l e x i b l e a i r c ra f t Landing behav io r Landing a n a l y s i s Aircraft r e sponse

.~ ~ ~ ____ ~ - _ . . .

18. Distribution Statement

U n c l a s s i f i e d - Unlimited

S u b j e c t Category 05

19. Security Classif. (of this report1 20. Security Classif. (of this page)

- -- U n c l a s s i f i e d $4.50

-~ . . U n c l a s s i f i e d

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