A Mathematical Model for Vertical Attitude Takeoff and Landing (VATOL) Aircraft Simulation: Model Description Application - Volume 1

utility o f VATLAS. These functions enab;e the VATLAS user to impose open 'loop time varying inputs (e.g. steps, doublets, etc.) on each cockpit controller and/or specify pilot controlled (closed loop) stationkeeping and transitions.

Section 3 . 0 details the VATLAS application to the Vought SF-121 VAT& airplane depicted in figures 1-2 and 1-3. This application is the development o f a baseline flight control sjstem for the SF-121 beginning with a definition of the basic airplane data and proceeding through actuator input specification and trim characteristics evalution to specification and evaluation o f the baseline system gains and control laws.

Coxlusions and recommendations established during the model development and application are incorporated in Section 4.0.

_ - Figure 1-2. SF-121 Series Superfly VATOL F i g h t e r b

t

c, C

B

0, 0) c L L

& j I

i I I

- $ ..- 1 f

m

c

I r 2.0 V A T a SlntrLATION FIATH MODEL This chapter provides background and d e t a i l s f o r the s i x component models o f the VAT& simulation math model. The component models and applicable r e p o r t sections are as follows:

o Aerodynamic Forces and Moments - Section 2.2

o Propulsion System Model i n c l u d i n g dynamics, forces and moments, and RCS (Reaction Ccintrol System) i n t e r a c t i o n s - Section 2.3.

:: Inlet 9 3 ~ F e c e s 2nd Moments - Section 2.4

o RCS Forces and Moments - Section 2.5

o C o r i o l i s Forces and Moments - Section 2.6

o Actuation System - Section 2.7

o F l i g h t Control System - Section 2.8

The model discussions are preceded by a d e s c r i p t i o n i n Section 2.1 o f the primary axis s y s t e m used i n the simulation.

Since VAT& airplanes r o u t i n e l y maneuver a t p i t c h angles approaching 90 degrees where the standard Euler angle transformation has B s i n g u l a r i t y , the airplane equations o f motions were formulated with d i r e c t i o n cosines.

This formulation and other possible a l t e r n a t i v e s t o avoid the s i n g u l a r i t y are Section 2.10 d e t a i l s the pseudo-pilot functions discussed i n Section 2.9.

which were incorporated i n t o VATLAS t o simulate p i l o t c o n t r o l o f the a i r c r a f t .

2 . 1 Primary Axis Systems Four primary axis systems are employed in the VAT& simulation math model. These !nclride a North oriented inertial or earth axis system, the vehicle-referenced body axis system, the wind axis system, and the stability axis system. The relation between earth axes (XI, YI, Z l ) and body axes ( A e , YB, Z e ) is depicted in figure 2-1. The orientation of the body axes with respect to earth axes is determined by an ordered rotation through

the standard Euler angles - first, yaw (Iy) around the 2: axis, then pitch

(e) around the Y1 axis, and finally roll (6) around the X B axis. Aircraft

Cg position reg) is measured in earth axes and has components Xe, Ye, and 2 , along the XI, Y , and ZI axes respectively. Similarly, aircraft cg velocity r ) is measured in earth axes and has components e . 6 +cg In the body axis system, aircraft velocity has Xe, Ye, anJ 2 , .

components u, v, and w along the XB, Ye, and ZB axes respectively.

e . .

Xe, Ye, Ze and u, v, w are related by the Euler transformation matrix:

cos 0 c a s p cos o sin$) - sin o

;:I = [ i n 6 sin o c o s p s i n p s i n o sin 4 sin o cos I [

-sinqcos d +cos(1cos 4 c o s f ~ o s sin e s i n S c o s 6 sin o cos 4 cos o + s i n v s i n 6 -cosS)sin 6 d21 d22 d23 where the d i j t s are direction cosines.

The body axis system is oriented in the aircraft as follows (figure 2-2): The origin i s at the aircraft cg. The X a axis is parallel t o the fuselage reference line and positive forward. The YB axis is perpendicular to the aircraft plane of symmetry and is positive to the right.

The Zg axis i s in the plane of symmetry, perpendicular to the X B and Y B axes, and positSve downward. This orientation remains fixed in the aircraft for all time. Locations of aircraft features o f interest (e.g. engine inlets Figure 2-1. Systems o f Inertial and Vehicle Body Axes Figure 2-2. Relation o f A i r c r a f t Coordinates t o Vehicle Body Axes and e x i t s , l i f t i n g surface centers o f pressure) i n the body a x i s system are expressed i n a i r c r a f t coordinates - fuselage s t a t i o n (FS), b u t t l i n e (BL), and w a t e r l i n e (WL). The d i r e c t i o n s of increasing a i r c r a f t coordinates are i n d i c a t e d on f i g u r e 2-2.

U n l i k e the body a x i s system, t h e wind and s t a b i l i t y systems do n o t maintain f i x e d o r i e n t a t i o n t o the a i r c r a f t . The r e l a t i o n s between wind, s t a b i l i t y , and body axes are depicted i n f i g u r e 2-3. The X wind a x i s ( X u always p o i n t s i n t o the r e l a t i v e wind. Note t h a t i f angle of attack (a) and s i d e s l i p angle ( 6 ) are both zero, the wind, s t a b i l i t y , and body a x i s systems are coincident. S i m i l a r l y i f a - 0 and B # 0, the body and s t a b i l i t y axes are coincident and, i f a # 0 and 6 I 0, the s t a b i l i t y and wind axes are coincident.

The VATOL math model uses several a x i s systems o f convenience f o r f o r c e and moment producing elements of the a i r c r a f t . These systems are introduced as required i n the model development. Examples include the i n l e t and C o r i o l i s force and m m n t a x i s systems. Regardless o f the a x i s system adopted f o r a component model, a l l forces and moments are resolved e v e n t u a l l y i n t o body axes.

RUE F i g u r e 2-3. Systems of Wind, Stability, and Vehicle Body Axes 2.2 Aerodynam:cs Model Operating with the guideline t o produce an e a s i l y modified model, the NASA c o n t r a c t requirement t o produce a componentized aerodynamics model, and the f a c t t h a t VAT& a i r c r a f t w i l l experience l a r g e angles of attack and sideslip; Clark's model (reference ( a ) ) was adopted as a base f o r the VATLAS aerodynamics model. This model "builds" the t o t a l a i r p l a n e aerodynamics from fuselage and l i f t i n g surface c o n t r i b u t i o n s i.e., i t i s componentized. The model provides continuous aerodynamics functions f o r a l l a ' s and 6 ' s

i.e., -180 a - < 180 degrees and -90 5 8 - < 90 degrees. The model i s based on

DATCOM (reference ( b ) ) techniques and thus requires o n l y a modicum o f data (e.g. l i f t i n g surrace geometry, l i n e a r l i f t curve slopes, s t a l l angles, e t c ) t o completely model airplane aerodynamics i.e., i t i s e a s i l y modified t o I n r e c o g n i t i o n o f the l i m i t a t i o n s o f represent a range o f VATOL concepts.

OATCOM i n p r e d i c t i n a aerodynamic c h a r a c t e r i s t i c s a t high a ' s and B'S, the reader i s reminded that, i n terminal operations, l a r g e U ' S and 8 ' s are encountered o n l y a t low speeds where aerodynamics do not a f f e c t s i g n i f i c a n t l y the a i r c r a f t f l y i n g q u a l i t i e s .

Adapting C l a r k ' s model t o current purposes was guided by a self-imposed reqrrirement tc? o b t a i n reasonable f i t s o f the publ ished Vought SF-121 aerodynamics data i n reference ( c ) . Obviously these publ ished data could have been loaded d i r e c t l y i n t o the math model, but a t the s a c r i f i c e o f o v e r a l l VATGL model f l e x i b i l i t y and timeliness. The strength o f ? l a r k ' s approach i s i t s inherent a b i l i t y t o produce consistent aerodynamic estimates f o r a i r c r a f t concepts n o t y e t possessing wind tunnel data bases.

The procedure o u t l i n e d below was followed i n applying and eventually modifying Clark's model f o r VATOL simulation: 1. Model parameter data were developed f o r the SF-121 e i t h e r from the data i n reference ( c ) o r from DATCOM. DATCOM was used i f the data could not be extracted from reference (c).

C l a r k ' s model as published was applied t o the SF-121 using the 2.

model parameter data determined i n step 1.

3. Calculated and published SF-121 data were compared t o i n d i c a t e what model m o d i f i c a t i o n s might be necessary t o improve i t s p r e d i c t i v e c a p a b i l i t y .

The candidate modei m o d i f i c a t i o n s were made, evaluated, and 4.

incorporated as required.

Equations f o r t h e aerodynamics mo.'cl sjhich evolved from t h i s procedure are given i n Section 2.0.1 o f Volume 11 of t h i s r e p o r t . Model parameter data f o r the St-121 are given i n Section 3.3 of Volume 1 1 . Results of the published and c a l c u l a t e d SF-121 aerodynamics data comparisons and t h e m o d i f i c a t i o n s made t o Clark's model t o produce t h e VATLAS model are presented and discussed i n the next section.

2.2.1 Data Comparison and Aero Model M o d i f i c a t i o n s Figures 2-4 through 2-10 compare the published SF-121 data (reference ( c ) ) with t h e " i n i t i a l " and " f i n a l " aero models. The SF-121 data are a composite o f r e s u l t s from various Vought and NASA wind tunnel t e s t s on s i m i l a r configurations. The " i n i t i a l aero rrtodel" r e s u l t s represent C l a r k ' s model applied t o model parameter data developed from references ( b ) and ( c ) . The " f i n a l aero model" r e s u l t s represent a modified version o f Clark's model applied t o the i n i t i a l aero model parameter data base augmented by the a d d i t i o n a l data required by the modifications.

Comparison w i t h SF-121 data of the r e s u l t s o f applying the i n i t i a l model t o the SF-121 l e d t o the f o l l o w i n g observations: Predicted and SF-121 l i f t c o e f f i c i e n t ( f i g u r e 2-4) data are i n 1.

good agreement f o r a l l a - < 90 degrees.

2. Predicted atid SF-121 drag c o e f f i c i e n t ( f i g u r e 2-5) are i n good agreement below a = 50 degrees. Predicted drag c o e f f i c i e n t s are considerably higher than SF-121 data f o r a > 50 degrees.

3 . For a < 20 t o 30 degrees, the model provides reasonable p r e d i c t i o n s o f SF-121 p i t c h moment c o e f f i c i e n t ( f i g u r e 2-6) data. For a > 30 degrees the model p r e d i c t i o n s and data have - 1 -... ~ .- _ .

h n c U C .

opposite trends; the model p r e d i c t s an increasing (unstable) p i t c h moment as a increases w h i l e the data show a decreasing ( s t a b l e ) p i t c h moment with increasing a . The apparent cause and r e s o l u t i o n o f t h i s discrepancy are discussed i n t h e next paragraph.

4. Predicted and Sf-121 C1 and CY ( f i g u r e 2-7) data are i n reasonable agreement'for all'a - < 90 degrees.

5. o. "cted and SF-121 Cn ( f i g u r e 2-7) data are i n good agreement f o r a < 20 t o % degrees. For a > 25 t o 30 degrees, SF-121 data are considerabley mor2 negative than the model t h e pred i c t i ons .

Below a = 25 degrees, the predicted and SF-121 rudder d e r f v a t i v e s 6.

( f i g u r e 2-8) are i n reasonable agreement. The Cla p r e d i c t i o n r i s reasonable t o a a 90 degrees. Cn, and Cya predictions are not good i n the a = 36 t o 60 dggrees rancje; t h e data f a l l o f f f a s t e r than t h e predictions. Beyond a = 60 degrees, the and Cya pr e d i c t i o n s are reasonable; data and p r e d i c t i o n s i n d i c a t e small values o f the derivatives.

7. SF-121 e l a data ( f i g u r e 2-9) are reasonably predicted f o r

a < 30 degFees. A t high a, the data i n d i c a t e a i l e r o n reversal which is not predicted by the model.

8 . SF-121 Cnd data ( f i g u r e 2-9) i n d i c a t e a proverse yaw f8r a < 15 t o 20 degrees which i s not predicted by t h e tendency model. The data t r e n d toward adverse yaw w i t h increasing a ( f o r a < 35 degrees) i s predicted by the madel. With the exception o f more itdverse yaw displayea by the data f o r a = 55 t o 70 degrees, the model p r e d i c t i o n s and data have reasonable agreement f o r a > 35 degrees.

The r e s u l t o f most concern from tlld i n i t i a l aero model &valuation is Based on the poor p r e d i c t i o n o f p i t c h moment c o e f f i c i e n t f o r a > 30 degrees.

the good agreement i n l i f t c o e f f i c i e n t data and predictions, i t i s obvious t h a t soms, i f not a l l , the p i t c h moment discrepancies could be resolved bj' allowing an a f t s h i f t o f the center o f pressure (cp) o f the aerodynamic C l a r k ' s model has no p r o v i s i o n f o r a cp s h i f t components w i t h increasing a.

c

t

i

- + c, !

Q I t L Y .r .

h i cu .C I L L , ... .

I-..

i c .. ._.

, . .

h n 0, Y L .

c a V c- I .

V e a I b I Y n n L m c L Q) U .......

1 ' . .

-._ - - .

' 1

__- .e- -~.- -

-1- . . . .

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

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

U Q) L m -C c n a a .... , ........

m Q) > -c c, Q > .C L a J a E L

'rJ

_. .+' u l N

= t '* a

h

. . . . . .

w i t h a. Section 4.1.4.3 i n D A T C O W describes a model f o r t h e cp s h i f t o f l i f t i n g surfaces. This model was appended t o Clark's basic equations.

Equations were a l s o added t o a l l o w t h e cp o f t h e fuselage t o change w i t h a.

This fuselage cp s h i f t i s n o t covered i n DATCW b u t was added t o conpensate f o r r e s i d u a l p i t c h moment discrep' iec, between model and data a f t e r t h e e f f e c t o f l i f t i c g surface q . s h i f t s are included. I n t h e absence o f a data base, t h e fuselage cp s h i f t would n o t be inrglemented. Figure 2-10 presents the data comparison obtained w i t h the f i n a l p i t c h moment model i.e., Clark's model modified t o include cp s h i f t s w i t h a f o r both fuselasge and l i f t i n g surfaces. The agreement between p i t c h moment c o e f f i c i e n t data and p r e d i c t i o n i s riow almost as good as t h a t f o r t h e lift c o e f f i c i e n t .

Examination o f the d i f f e r e n c e between drag c o e f f i c i e n t data and a > 50 degrees l e d t o a m o d i f i c a t i o n i n the c a l c u l a t i o n o f h i g h p r e d i c t i o n f o r a l i f t i n g surface drag. C l a r k ' s high a drag mode1 f a i r s l i f t i n g surface drag c o e f f i c i e n t t o 1.2 a t a P 90 degrees. This l i m i t i n g value o f drag c o e f f i c i e n t i s based on the reference area o f the surface. It seems reasonable that, i n consonance with other c a l c u l a t i o n s i n C l a r k ' s model t h e l i m i t drag should be based on exposed surface r a t h e r than reference area. This m o d i f i c a t i o n (i.c.

m u l t i p l y 1.2 times the r a t i o o f exposed area t o reference area i n the high a drag equation) was made i n Clark's model and produced the much improved high a drag c o e f f i c i e n t p r e d i c t i o n shown i n f i g u r e 2-5.

The differences between Cn6 and Cy3, pr e d i c t i o n s and data i n the a = 30 t o 60 degrees range (figuFe 2-8) are a t t r i b u t e d t o a gradual, and eventually t o t a l , l o s s o f v e r t i c a l t a i l effectiveness due t o masking by the wing and fuselage ( r e f e r t o SF-121 3-view on f i g u r e 1-3). Since Clark's model has no p r o v i s i o n f o r t h i s phenomenon, i t was incorporated i n a t a b l e format o f v e r t i c a l t a i l effectiveness as a function o f a. The t a b l e was q u a n t i f i e d using C y a data which, u n l i k e other side force derivatives, have m l y a v e r t i c a l t a i l c o n t r i b u t i o n . For a i r c r a f t not possessing a data base, reasonable estimates o f v e r t i c a l t a i l effectiveness can be made by s c u t i n i z i n g r e l a t i v e l o c a t i o n s o f the v e r t i c a l t a i l and other aerodynamic c o n t r i b u t o r s o f the a i r c r a f t as a f u n c t i o n o f a. The much improved p r e d i c t i o n s o f C 6r and cn6 w i t h the modified model are shown on f i g u r e 2-8.

Note t h a t the predictqon of C l a i s o n l y s l i g h t l y affected by t h i s modification.

r rc .

P I cu The m o d i f i c a t i o n o f v e r t i c a l t a i l effectiveness a l s o affects t h e s i d e s l i p d e r i v a t i v e s . The dashed curves f o r C n and C1 on f i g u r e 2-7 8 8 r e f l e c t t h i s m o d i f i c a t i o n . The Cy dashed curve includes t h i s p l u s another m o d i f i c a t i o n t o be discussed below. The C 1 p r e d i c t i o n i s improved a t h i g h a w i t h l i t t l e change i n t h e alreadg good low a p r e d i c t i o n .

The Cn p r e d i c t i o n i s improved o n l y i n t h a t , l i k e t h e data with increasing B

a, the a i r c r a f t does n o t r e a c q u i r e a p o s i t i v e cn once i t becomes

negative. To P r e d i c t t h e l a r g e C n shown by t h e data f o r a > 30 degrees would r e q u i r e m o d i f i c a t i o n s t o the'model which are h i g h l y c o n f i g u r a t i o n s p e c i f i c and are thus beyond the scope o f intended model application. The r e q u i r e d changes were n o t made f o r the SF-121 appl i c a t i o n reported herein.

The other m o d i f i c a t i o n r e f l e c t e d i n the dashed C curve on yB f i g u r e 2-7 is the a d d i t i o n of a Cy term i n the wing c o n t r i b u t i o n 'C'Z

t o cy . Calculations o f Cy with o n l y t h e v e r t i c a l t a i l effectiveness

m o d i f f c a t i o n showed a degraeed predicton c a p a b i l i t y from t h a t o f the basic Clark model, This i n d i c a t e d a need f o r f u r t h e r model refinement. Examination of unpublished wing-body c y data f o r t h e SF-121 j u s t i f i e d the i n c l u s i o n ' B of a C term i n the model and allowed i t s value t o be estimated.

Section 5.1.1.1 o f DATCOM has a methodology L~ determine i t s value i n the absence o f data. The term was incorporated i n t o the aero model and C y was recalculated. AS i n d i c a t e d by the dashed C y curve on f i g u r e 2-7 !he model p r e d i c t i o n c a p a b i l i t y has n o t been enhancea s i g n i f i c a n t l y Jver t h a t o f t h e basic Clark model. The modified model i s , however, consistent w i t h DATCOM methodology and the v e r t i c a l t a i l e f f e c t i v e n e s s change w i t h a.

S i m i l a r t o s i d e s l i p d e r i v a t i v e s , the h i g h l y configuration s p e c i f i c nature o f high a l a t e r a l c o n t r o l d e r i v a t i v e s o f p l a i n flapped elevons (used on the SF-121) precludes r e 1 i a b l e predictions. Thus the p r e d i c t i o n of C l a r k ' s model for Cnd and Claa ( f i g u r e 2-9) cannot be improved without data.

a The " f i n a l aero model" was used t o generate a l l S i - 1 2 1 aero data f o r t h e a p p l i c a t i o n described i n Section 3.0 o f t h i s volume. The major discrepancies remaining between data and model predictions are high a C ,

and C l a . It is postulated that the effects of thece discrepancies on

aircraft flying qualities will be minimal because, in SF-121 terminal operations, high a ' s are encountered only at low airspeeds and low dynamic pressures. To prove this contention is beyond the scope of the contract.

The modifications to the "initial aero model" to produce the "final aero model" are reiterated below: 1. Incwporation of DATCOM method to calculate cp shift of lifting surface as a function of a. Also a fuselage cp shift has been incorporated to fine tune the pitch moment coefficient prediction if supporting data are available.

The a = 90 degrees lifting surface drag coefficient (= 1.2) has 2.

been referenced to exposed surface area.

3. A table to incorporate vertical tail effectiveness as a function of a has been made available.

4. A c y

term has been added in the wing contribution to %, L sideforce cal cul at ions.

The equations for the final model in Section 2.0.1 of Volume I 1 are given while model parameter data for the SF-121 are given in Section 3 . 3 o f the same volume.

2. : . 2 Aerodynamic Rotary Derivatives The aero model calculates rotary derivatives. Reference (c) has no rotary derivative data for the Sf-121, thus a comparison of model predictions For completeness, a sampling of calculated SF-121 and data is not possible.

b rotary derivatives is given in figures 2-11 through 2-13. These were, of course, used in the SF-121 application described in Section 3 . 0 o f this volume.

* _ ~ ..

. ..

. - 1 I

:--1 . - +----

Figure 2-11. Sf-121 P i t c h Rate Derivatives Calculated by Aero Model

- 7 -

I.L - -

\MI

, - . . . . , .

. < Figure 2-12. SF-121 R o l l Rate D e r i v a t i v e s Calculated by Aero Model Flgure 2-13. SF-121 Yaw Rate D e r f v a t l v e s Calculated by Aero Model 2 . 3 Propulsion System Model The basic propulsion system model f o r VATOL s i m u l a t i o n has s i x primary d i s t i nglc i sh i ng features: o Thrust d e f l e c t i o n i n two d i r e c t i o n s v i a a gimballed nozzle a r r a ngemen t o Engine i n s t a l l a t i o n angle

o Nonlinear dynamics - time constant and r a t e l i m i t s vary w i t h t h r u s t

1eve1 o Continuously modulated afterburner which can be l i t a t any t h r o t t l e s e t t i n g o RCS bleed c a p a b i l i t y o One o r two engines The model i s presented as t h r e e submodels: The r e l a t i o n s for r e s o l v i n g i n d i v i d u a l engine t h r u s t s i n t o body a x i s forces and moments are developed i n Section 2.3.1. The engine performance and dynamics model i s discussed i n Section 2.3.2. The modeling o f R C S e f f e c t s on engine performance i s discussed i n Section 2.3.3.

Lata f o r the Sf-121 a i r p l a n e propulsion system are provided i n Section 3 . 4 o f Volume 11. The Sf-121 uses two scaled MFTF-2800-25-1 engines whose performance and $iysical c h a r a c t e r i s t i c s are described i n reference (d). The c h a r a c t e r i s t i c s o f these Ilpaper" engines were developed by Vought from a P r a t t and Whitney parametric c y c l e analysis computer program and are believed t o be a t t a i n a b l e f o r a 1995 I O C ( 1 n i t ; a l Operational C a p a b i l i t y ) .

The engine dynamics t i m e constant and r a t e l i m i t s data are t h e same as used i n the core engine model o f the reference ( c ) study.

2.3.1 D i r e c t Thrust Forces and Moments Model Figure 2-14 depicts the geometry f o r r e s o l v i n g the t h r u s t o f one engine i n t o body a x i s forces and moments. The t h r u s t i s assumed t o a c t a t the center o f the nozzle e x i t face p a r a l l e l t o the nozzzle c e n t e r l i n e . To L rc .

d c I cu determine t h e d i r e c t t h r u s t forces and moments r e q u i r e s t h a t the a i r c r a f t coordinates o f the t h r u s t a p p l i c a t i o n p o i n t and the t h r u s t components i n the body a x i s system are known. The t h r u s t a p p l i c a t i o n p o i n t coordinates w i l l be develor d f i r s t .

The VATOL sinlulation model provides f o r nozzle r o t a t i o n ( i . e . t h r u s t d e f l e c t i o n ) i n two d i r e c t i o n s about the swivel p o i n t m d f o r an engine The nozzlc r o t a i o n s i n s t a l l a t i o n angle (a ) r e l a t i v e t o the XB axis.

Y

provide yaw (yT) and p i t c h (eT) t h r u s t d e f l e c t i o n s . Since the nozzle

swivel p o i n t remains f i x e d i n the body a x i s system, it i s convenient and necessary t o determine the a i r c r a f t coordinates ( A F S , , , A B L ~ ~ , bWLSW)of the t h r u s t applicaton p o i n t r e l a t i v e t o the swivel p o i n t . A l l three angles - a,,, qT, @T - and the nozzle l k n g t h ( I N o z ) influence these coordinates.

S t a r t i n g w i t h the engine and nozzle c e n t e r l i n e coincident and p a r a l l e l t o the X B axis, the f o l l o w i n g rotdt.,n sequence o r i e n t s the no7zle r e l a t i v e t o the body axis system (see f i g u r e 2-14). F i r s t r o t a t e by a about the Y s w a x i s Y

which i s P a r a l l e l t o the yB axis, then r o t a t e ? b y Y T about the Z

swl

axis, and f i n a l l y , r o t a t e by 9 about the Y s w

axis. The r e l a t i o n which

describes t h i s sequence and defines A F S ~ ~ , bBtSw, and AWL^^ i s as

follows: The coordinates o f the t h r u s t a p p l i c a t i o n p o i n t are thus defined as: To complete the development, the bod;( a x i s components o f t h r u s t must This r e s o l u t i o n i s e s s e n t i a l l y the same as t h a t o f equation be determined.

(2.1) except t h a t the sense of vT r o t a t i o n

s reversed t o r e f l e c t t h e sign reversal between the d i r e c t i o n of increasing W L and t h a t of t h e ZB axis: where AXT, A Y ~ , bZT are the body axis components o f d i r e c t t h r u s t TcoR i s gross t h r u s t corrected for RCS i n t e r a c t i o n s as described i n Section 2 . 3 . 3 and f l o w t u r n i n g e f f e c t s as described below.

The eqbctions f o r the flow t u r n i n g c o r r e c t i o n t o t h r u s t are as follows:

TCOS TAk?L K A F T ( 2 *4 1

(2.5) K KA AFT + K~ FT2 A~~ FT1

k n t cos -' [cos eT cosY(T]

(2.6) where i s gross t h r u s t corrected f o r RCS i n t e r a c t i o n s only

' APPL

KA and KA are constants.

FT1 FT2 AFT i s the geometric t h r u s t turnincl angle defined as the angle between the engine c e n t e r l ine and nozzle c e n t e r l ine.

Equation; (2.1) through ' ; , . I , are the basic r e l a t i o n s f o r the d i r e c t t h r u s t forces and moments model. They are expanded i n f u l l i n Section 2.0.2 o f Volume 11.

2.3.2 Engine Performance and Dynamics Model The engine performance and dynamics model i s depicted i n f i g u r e 2-15.

Engine performance i s represented by the f o l l o w i n g model parameters: 1. F G i s the gross t h r u s t l e v e l a t i d l e t h r o t t l e and i s a fu&ion of Mach number (M,,,).

i s t h e gross t h r u s t l e v e l a t maximum rpm a t minimum

2* F$p

af rburner s e t t i n g and i s a function of MN.

There i s an assumption here t h a t the t h r u s t a t maximurn rpm w i t h no a f t e r - burner i s the same as the t h r g s t a t maximum rpm a t minimum afterburner; a c t u a l l y there i s a f i n i t e b u t g e n e r a l l y n e g l i g i b l e d i f f e r e n c e between these two t h r u s t levels.

3 . F i s the gross t h r u s t l e v e l a t maximum rpm a t maximum %AX afterburner s e t t i n g and i s a function o f MN.

4 . -h, i s maximum engine rpm.

MAX FRpM i s f r a c t i o n a l engine rpm and i s a f u n c t i o n o f f r a c t i o n a l 5 .

non-afterburning t h r u s t l e v e l (TF 1 . TF, a model dynamic parameter, i s the t h r u s t produced by changing spool rpm normal ized t o F , 0 %i N - 6 .

mMAX i s the i n l e t mass f l o w r a t e when T F = 1 and i s a function of MN.

I n l e t mass f l o w r a t e i s assumed t o be a function of T F only; thus, by inference, i n l e t mass flow r a t e i s not a f u n c t i o n o f afterburner s e t t i n g .

7 .

KBT adjusts the commanded t h r u s t l e v e l (T,) f o r the reference RCS blee’ ( B R E F ) l e v e l . Thus when model output t h r u s t (To) i s adjusted f o r actual bleed ( F D ) l e v e l and T D = B R E F , t n e t h r u s t applied t o the a i r c r a f t w i l l equal T c . The use o f t h i s parameter assumes t h a t engine c o n t r o l s w i l l be able t o compensate f o r known reference RCS bleed. If the c o n t r o l s a r e n o t t h i s sophisticated then kBT can be set t o 1.0.

These p a r z i e t e r s are q u a n t i f i e d f r o m steady s t a t e engine data. D a t a f o r the SF-121 engines, which are scaled versions of the MFTF-2800-25-1 engines described i n reference ( d ) , are provided i n Section 3.4 o f Voluine I I .

I- (

p.. iI’

v) c i N The engine dynamics model f o r non-afterburning t h r u s t (output i s TF) i n d i c a t e d on f i g u r e 2-15 i s nonlinear and was defined by P r a t t and Whitney f o r use by Vought i n p r e l i m i n a r y Type A V/STOL a i r p l a n e design studies. For the c u r r e n t a p p l i c a t i o n a model of afterburner t h r u s t dynamics (output i s TAB) has been placed i n p a r a l l e l with t h e basic model. The afterburner can be l i t according t o the l o g i c i n d i c a t e d i n the figure.

With the afterburner lit t h e more r a p i d afterburner t h r u s t response w i l l enhance the s'ower non-afterburning t h r u s t response which i s influenced by the engine spool i n e r t i a . The equations i n d i c a t e d by f i g u r e 2-15 are expanded t o f u l l d e t a i l i n Section 2.1 of Volume 11.

The engine dynamics model i s p a r t i c u l a r l y s u i t e d f o r parametric v a r i a t i o n s t o e s t a b l i s h propulsion system requirements and c o n t r o l system i n t e r f a c e . I t i s also computationally e f f i c i e n t f o r real-time simulation.

The a p p l i c a t i o n and v a l i d i t y o f the non-afterburning t h r u s t model ( i n essence, the spool dynamics model) has been demonstrated i n the simulator studies of references ( e ) and ( f ) . Thus, as a baseline, the same values used i n reference (e) f o r the nonlinear t i m e constant ( T E N G ) and r a t e l i m i t s b b and T ) of the non-afterburning t h r u s t model used i n ( TFMAX FM N reference ( e ) kave been adopted f o r the analyses presented herein. I n l i e u o f d e f i n i t i v e data, the time constant o f the afterburner t h r u s t model (TAB) has a t 0.05 sec been set t o simulate the dynamics o f f u e l d e l i v e r y t o the afterburner. S i m i l a r l y the afterburner t h r u s t r a t e l i m i t s ( T A B and e M A X T ) have Seen set high ( = 20.) t o simulate a non-rate l i m i t e d ABM a f t e r h r n e r . i i l s o T~~ a t 0,001; has been set a t 0.10 and TAB t h i s establishes t h a t Pke afterburner w i l l be l i t whe8' exceeds ?!

T ~ ( I ) by 0.10 C l o y o f F G ) o r when T F exceeds 1. The Grrrner M W i l l main l i t u n t i l T A E [ ~ ) has droppehN;c 0.001 (O.l%of FG ) and M I N i s not more than 0.10 l a r g e r than T F ( I ) .

2 . 3 . 3 RZS E f f e c t s on Engine Performance The RCS-propulsion system inter-actions model i s depicted on f i g u r e 2-16.

Model 'nputs are T F ana the output t h r u s t (To) of the engine performance and dynamics model.

To i s t o be c o t r e r t e d f o r R C S effects.

T

Model outputs are the corrected t h r u s t (TAppL) applied t o the a i r c r a f t and the r a t i o o f RCS bleed a i r c u r r e n t l y a v a i l a b l e t o the max m u m avai 1ab1e (%). The maximum RCS bleed a i r i s a v a i l a b l e when the i n e t mass f l o w r a t e i s maximum which occurs when T F = 1. AS w i l l be shown i n Section 2.5, the RCS model applies m u l t i p l i c a t i v e factors t o scale down the maximum RCS

c a p a b i l i t y ; Kr;l i s one o f these factors. The data f o r I$, f o r the SF-121

were taken from reference (d).

Corrected t h r u s t (TAppL) i s %med by m u l t i p l y i n g To by a correc- t i o n factor (K'BT) which i s based on actual bleed ( K D ) and F

. The

%AX f i r s t step t o determine K ' B T i s t o c a l c u l a t e the bleed a v a i l a b l e ( B A V ~ ) a t t h e c u r r e n t uncorrected t h r u s t l e v e l .

BAVL i s then compared w i t h R C S bleed RCS model.

required (BREg) which i s generated by the If BREQ 2 BAVL then i s s e t equal t o BAVL; thus i n t h i s case K ' B T w i l l be s e t by To and the RCS i s saturated.

If, on the other hand, BREQ < BAvl ti,en r D i s s e t equal t o 6 R ~ Q ; thus K ' B T w i l l be s e t by RCS requirements and excess RCS c a p a b i l i t y proportional t o (BAVL - BRE9) i s available.

Note a l s o t h a t if BREQ = BREF ( t h e reference bleed) then K ' B T w i l l equal KBT ( f i y i r e 2-16) and TwpL w i l l equal commanded t h r u s t (Tc). The data t o define KBT for the SF-121 were a l s o taken from reference (d).

The r e l a t i o n s and l o g i c indicated by f i g u r e 2-16 are expanded t o f u l l d e t a i l i n Section 2.1 o f Volume 11.

2.4 I n l e t Ram Forces and Moments Model The development of the i n l e t ram forces and moments model i s presented i n two steps. F i r s t t h e r e l a t i v e l y simple, standard model i s given. This model i s phenomenologically c o r r e c t b u t lacks experimental and/or t h e o r e t i c a l guidance t o d e f i n e the ram f o r c e a p p l i c a t i o n p o i n t . This aspect o f the model . s normally l e f t t o user whim. A recent Vought contracted e f f o r t (reference ( g ) ) , undertaken t o remedy t h i s s i t u a t i o n , r e s u l t e d i n a s e r i e s o f i n l e t f o r c e arid moment design c h a r t s intended f o r p r e l i m i n a r y design appl i c a t i o n . Tne standard model was expanded and modified t o incorporate This i s the second step o f the model development.

these r e s u l t s .

2.4.1 The Standard Model Figure 2-17 d e p i c t s the geometry of the standard ram forces and The forces and moments have moments nodel i n the a i r c r a f t plane of symnetry.

c o n t r i b u t i o n s from t w o sources: 1. The forces and moments imposed on the i n l e t by the captured stream o f a i r which enters it.

2. The a d d i t i o n a l forces and moments imposed on the i n l e t when, because o f a i r c r a f t r o t a t i o n , it moves r e l a t i v e t o the captured stream o f a i r .

The model o f the flr.st c o n t r i b u t i o n assumes a ram force (F&M ) paral.lel

b u t opposite t o the r e l a t i v e airspeed vector (TA) a c t i n g a t an a p p l i c a t i o n The r a m f o r c e i s defined 2s p o i n t ( A P ) .

rc m -

n - m v

FRAMo I A

where hI i s the i n l e t mass f l o w r a t e determined by the propulsion system

-

model and VA has the components U ~ S , vAs, and w A s along the X B ,

Y B , and t g axes, r e s p e c t i v e l y . Thus the body a x i s components o f 'iRAMo

a r e J

d -

\

\

4 1 (2.4.1) A n t i c i p a t i n g t h e modifications t o t h e standard model t o incorporate t h e recent Vought r e s u l t s , an a l t e r n a t e formulation O f A X

b y R , and

RO ,

AZ i s now introduced. The angles AT URN^ and BTURN are require!

RO f o r t h i s purpose ( f i g u r e 2-18). ATURN, i s defined as the geometric i n l e t

f l o w t u r n i n g angle and i s equal t o t h e angle yA makes with t h e i n l e t

c e n t e r l i n e .

qURN i s defined as t h e angle between t h e iiA-engine

c e n t e r l i n e plane and t h e a i r c r a f t plane o f symmetry.

Using ATURN ,

B T U 8 N c and t h e ram f o r c e magnitude (i.e. IFRAM I

= h i l V ~ l =

iIb ), equations (2.4.1) can be r e c a s t as

( 2 . 4 . 2 ) where As noted above, guidance on where t o place AP i s lacking.

It i s g e n e r a l l y agreed t h a t i t should l i e on the c e n t e r l i n e o f the engine.

There i; no agreement, however, i n where it should l i e r e l a t i v e t o the i n l e t face.

I t has Seen placed by various researchers fro11 XAppL = 0. upstream t o iAppL I D I N and beyond. Since information now e x i s t s t o q u a n t i f y X A P p L (reference ( g ) ) , t h e d e r i v a t i o n o f t h e standard moa21 continues w i t h XAppL unspecified. The moments about the a i r c r a f t cg due t o FRAMo are v) W

-

0, E P cn c .r E L

r

I - I

J

P

'F f - r I l cn

b

% - 1 -

a J -Q

z"

H i I if -

I

E rd

\F I \ u

(u

-

t Y rc / c

\

I N (2.4.3)

I [Ro ' I N - "R0 Z I N ]

AxR, Z I N - AzRo ( ' I N + 'APPL)

AyRo ( X I N + 'APPL) - "R0 ' I N

-

where M~~ i s t h e moment vector of FMM

r ~ p ?s the vector l o c a t i o n o f the ! P r e l a t i v e t o t h e cg.

'IN, YIN, 2 1 ~ are the coordinates o f the i n l e t i n a i r c r a f t body axes,

NRAM, are the components o f flRM

LRAM 9 MRAM * a1on8 the a ? r c r a f t body axes , The second c o n t r i b u t i o n t o the i n l e t !=am forces o r i g i n a t e s i n the v e l o c l t y , produced by a i r c r a f t r o t a t i o n , o f the i n l e t r e l a t i v e t o the incoming stream o f a i r . The d e f i n l n g r e l a t i o n i s (2.4.4) where

A Y R , bZRI are t h e body a x i s components o f FRAM

A X R

p , 6: r d e the body a x i s r o l l , p i t c h , and yaw r a t e s &nd are a l s o the

components o f GA.

I)

F~~~ acts a t the i n l e t face, The momerits due t o FRAM are thus

I def lied as

- -

-

L ~ ~ ~ I lZRI ' I N *'RI ' I N

- -

( 2 . 4 . 5 ) %AMI

LXRl ' I N - * ' R I ' I N

RAM I "RI ' I N - "RI ' I N

- -

-

where

-

L R A I . ~ , M R A M ~ , N R A M ~ are the body a x i s components o f MRAM I Combining the two c o n t r i b u t i o n s represented by equations 2.4.2 through 2.4.5 gives the standard model form f o r t h e body a x i s forces and moments produced by i n l e t ram e f f e c t s : (2.4.6) Recall t h a t the standard model makes the f o l l o w i n g assumptions about the r a m f o r c e (PRAM,):

1. IFRAM! i s equal t o hI V , (where = l V ~ l ) f o r a l l values

-

2.

FRAM, a c t s p a r a l l e l and opposite t o y~

Vought's recent e f f o r t s (reference ( 9 ) ) t o applg sophisticated i n l e t modeling techniqltes t o determine the ram f o r c e a p p l i c a t i o n p o i n t determined t h a t not o n l y the a p p l i c a t i o n p o i n t b u t a l s o the actual i n l e t f l o w t u r n i n g angle and

magnitude of t h e ram force vary w i t h ATURN , r a t i o o f ambient airspeed t o

i n l e t a i r speed ( v e / v I ) , and i n l e t geometry. The next s e c t i o n w i l l describe the m o d i f i c a t i o n and expansion o f the standard model t o incorporate these e f f e c t s .

2.4.2 Expansion and M o d i f i c a t i o n o f the Standard Model A b r i e f synopsis o f the work perfcrmed by Vought i n reference ( 9 ) i s required as background for the development i n t h i s section: Under c o n t r a c t t o Naval A i r Development Center, Vought has developed a computerized p r e d i c t i c q t i method for propulsive induced forces and moments i n t r a n s i t i o n and STOL f l i g h t . This method i s basea on Vought's V/STOL A i r c r a f t Propulsive E f f e c t s (VAPE) program. One o f the '/APE options provides f o r the c a l c u l a t i o n o f i n l e t forces and moments. This o p t i o n combines a h i g h l y modified Stockman i n l e t f l o w model w i t h a program which i n t e g r a t e s the i n l e t pressures determined by t o produce i n l e t forces and moments. A r b i t r a r y axisymmetfmic the i n l e t model i n l e t geometries are accepted by the proyam. The bulk o f the program a p p l i c a t i o n s i n reference (9) i s t o the NASA QCSEE GE2 i n l e t , Being a subsonic i n l e t , i t has r e l a t i v e l y t h i c k l i p s . To determine the e f f e c t s o f t h i n n e r supersonic l i p s , a l i m i t e d program a p p l i c a t i o n was made t o a t h i n l i p p e d configuration. The f o r c e and moment d i f f e r e n c e s were minor a t low

values O f b / v I ( < 0.3 t o 0.4) and n e g l i g i b l e a t higher values of

v ~ / v ~ . Model r e s u l t s designated f o r p r e l i m i n a r y design a p p l i c a t i o n can oe presented as the d i f f e r e n c e between the geometric and e f f e c t i v e flow t u r n i n g angles (AATURN), t h e ram effectiveness f a c t o r {R,,,), and normalized ( t o equivalent i n l e t diameter) ram moment a r m ( X A p P L / O I N ) as functions o f ATURN, and b/ VI ( f i g u r e s 2-19 t o 2-21 ) .

NOTE: Figure 2-19. E f f e c t of Velocity R a t i o and Geomet, -low Turning Anqle on I n l e t b n e n t 4t-z Figure 2-20. E f f e c t o f Velozlty Rat13 and Geometric Fiow Turning Angle on the Difference

Between Effective and j ' m c r i c Fiow Turnfng Angle (qmN)

I . .. . . A - .- .-..

Ftgure 2-21. € f f e c t o f V e l o c i t y R a t i o and Geometric Flow Tur3ing Angle on Ram Effectiveness Factor ( R M ) There i s no p r o v i s i o n i n the Vought VAPE program f o r rectangular i n l e t s , thus data equivalent t o t h a t o f f i g u r e s 2-19 t o 2-21 cannot be generated f o r rectangular i n l e t s . For a p p l i c a t i o n o f the VATOL simlrlation model, i t i s assumed t h a t the data f o r a x i s y m e t r i c i n l e t s can be appiied t o rectangular i n l e t s by r e p l a c i n g them w i t h equivalent c i r c u l a r i n l e t s . The equivalent c i r c u l a r i n l e t s have the same area as the rectangular i n l e t s ; the i n l e t diameter (DIN) specified i n t h e s i m u l a t i o n model i s the diameter o f the equivalent c i r c u l a r i n l e t . The v a l i d i t y Gf t h i s approximation cannot be r e a d i l y assessed. It 'i believed thak t h e i n l e t forces and moments c a l c u l a t e d by the s i m u l a t i o n model w i l l provide reasonable estimates o f actual ram effects and w i l l c e r t a i n l y be adequate f o r comparing i n l e t ram e f f e c t s on various VATOL a i r c r a f t concepts.

I n t r o d u c i n g the data and terminology o f =igures 2-19 t o 2-21 i n t o the standard model (equation (2.4.6)) gives the f o l l o w i n g s e t o f equations: (2.4.7) (2.4.8) (2.4.9) [2.4.10) (2.4.11j (2.4.12) *TURN = %AN,, + "TURN (2.4.13) (2.4.14) (2.4.15) (2.4.16) where ATURN i s the e f f e c t i v e i n l e t flow t u r n i n g angle FRAM i s the e f f e c t i v e magnitude o f f i e ram force Equations (2.4.7) through 2.4.18) are t h e basic r e l a t i o n s o f the VATOL simulation i n l e t ram forces and moments model. Jhe functional r e l a t i o n s by equations indicated (2.4.8) through (2.4.10) a r e the data of f i g u r e s 2-19 t o 2-21 extrapolated as indicated t o (\LIVI) = 0 ana ATURN = 0 and 180 degrees. The d e t a i l e d equations a c t u a l l y programmed i n t h g VATOL math model are given i n Section 2.0.3 o f Volume 11. These V o l u r i I 1 equations include the e f f e c t of engine tilt angle i o y ) which was not intrcduced here f o r reasons o f b r e v i t y and c l a r i t y .

5 1 2.5 Reaction Control System Forces and Moments The features of the RCS forces and moments model are as f o l l o w s : o Up t o t e n j e t s l o c a t a b l e anywhere i n t h e a i r p l a n e and a t any angle r e l a t i v e t o a i r c r a f t axes.

o J e t s can be s p e c i f i e d as demand o r continuous bleed. Demand bleed j e t s can be f u r t h e r specified t o demand more bleed than t h e RCS reference bleed.

o Jets t h r u s t i n one d i r e c t i o n only.

o The bleed r e q u i r e d by the RCS i s monitored and l i m i t e d , i f necessary, by the bleed a v a i l a b l e from the engines.

o Continuous j e t forces f o l l o w RCS actuator outputs w i t h no lag.

Demand j e t forces are lagged r e l a t i v e t o actuator outputs t o simulate bleed f l o w dynamics.

The model i s presented i n three sections: the procedure f o r l o c a t i n g and s p e c i f y i n g the type of j e t i s described i n Section 2.5.1, c a l c u l a t i o n o f i n d i v i d u a l j e t forces i s developed i n Section 2.5.2, r e s o l u t i o n o f j e t forces i n t o boay a x i s forces ana noments i s developed i n Section 2.5.3. Data f o r t h e SF-121 RCS are presented i n Section 3 . 6 of Volume I 1 w h i l e d e t a i l e d equations are given i n Section 2.0.4 o f the same volume.

t s RCS modeling i s t o c a l c u l a t e an i d e a l f o r c e The o v e r a l l approach demanded a t each j e t based on an i d e a l maximum. This maximum i s based on the maximum i n l e t mass f l o w r a t e of the engines. The i d e a l force i s then corrected f o r actual i n l e t mass f l o w r a t e , bleed a v a i l a b l e f o r the RCS, and demand f o r t h r u s t a t the other j e t s . This modeling 2pproach has evolved p r i m a r i l y from the author's experience w i t h the math model and background data o f the VAK-191B a i r p l a n e (reference ( h ) ) . The procedure f o r l o c a t i n g j e t s i s $ based on reference ( a ) .

1 RCS Jet Parameters 2.E The pataneters involved i n l o c a t i n g o r o r i e n t i n g R C S j e t s are The a p p l i c a t i o n p o i n t (i.e. l o c a t i o n ) of a j e t force cted i n f i g u r e 2-22.

deP

P

I 4 m c, a J L rc i s defined i n a i r p l a n e coordinates. The o r i e n t a t i o n i s defined by the ordered r o t a t i o n r e q u i r e d t o a l i g n a j e t force i n i t i a l l y along t h e p o s i t i v e X B a x i s w i t h i t s f i n a l i n s t a l l e d f o r c e d i r e c t i o n . The ordered r o t a t i o n proceeds as follows: f i r s t , r o t a t e around t h e ZB a x i s by the j e t yaw angle (YJET), then, r o t a t e t h e r o t a t e d Y a x i s by the j e t p i t c h angle (‘JET), F i v e parameters are therefore associated with the l o c a t i o n and o r i e n t a t i o n of each j e t : 0 Fuselage S t a t i o n (FSjET), B u t t L i n e (BLJET), and Waterline ( ~ L J E T ) o f the f o r c e appl i c a t i o n p o i n t .

o J e t yaw and p i t c h angles (pJET and ‘JET)

Three more parameters are r e q u i r e d t o completely s p e c i f y each j e t .

-

These are m, the demand parameter, BLDM, the bleed more parameter, and

A demand bleed j e t i s designated , t h e maximum f o r c e o f the j e t .

FRCS by s k i n g 1.; f o r a continuous bleed j e t , = 0. I f the j e t i s dem 1 bleed, then must be specified; i f P 1. the RCS bleed can be inct eased beyond the reference l e v e l if the a d d i t i o n a l bleeo c a p a b i l i t y i s required and available; i f m M t O., RCS bleed cannot exceed the reference The SF-121 has l e v e l . (m can be set t o 0.0 f o r continuous bleed j e t s ) .

t w c RCS demand bleed j e t s f o r r o l l c o n t r o l and has a 3.5greference bleed

- -

Therefore DMD = BLDM .I l e v e l (which i s the bleed r e q u i r e d f o r non-RCS “ses).

1. f o r bath Sf-121 RCS j e t s .

The maximum f o r c e of the j e t i s the t h r u s t produced i f the j e t area i s maximum an’ bleed required i s ess than b eed available, the engine i s f l o w r a t e , and there i s no t h r u s t l o s s due operating w i t h maximum i n l e t mass t o other operating j e t s . c o r the SF-121, FRCS o f each j e t was set a t MX 1500 l b .

2.5.2 C a l c u l a t i o n o f I n d i v i d u a l R C S J e t forces f i g u r e 2-23 o u t l i n e s the c a l c u l a t i o n of i n d i v i d u a l j e t forces. The inputs t o the process are the i n d i v i d u a l normalized j e t areas (bRCs(1)), ? . ~ 5 e are processed by the standard demand bleed o r continuous bleed f o r c e

t

%

- - - 1 m (u I (u shaping functions t o produce comnanded forces. The demand bleed shaping f u n c t i o n i s as follows: The continuous bleed shaping f u n c t i o n i s 3 s follows: Continuous bleed j e t s are assumed t o a c t i n pairs. The t o t a l j e t f l o w area i s constarit f o r these j e t pairs; d i f f e r e n t i a l c o n t r o l forces are produced by increasing one j e t area a t the same r a t e as the other i s decreased. Thus when 0, the j e t areas are equal and both j e t s command FRCS ( I ) .

~ R C S ( I ) M When 6~~-(1) .I 1.0, the one j e t area i s double i t s value a t sRcsfI) = 0, and comnands 2 FRCS ( I ) w h i l e the other j e t area i s zero and comnands MX zero force.

The demand j e t comnanded force takes throe paths ( f i g u r e 2-23): one path determines whether more bleed should be allowed t o handle t h e a d d i t i o n a l RCS f o r c e requ,rement. This a d d i t i o n a l bleed, i f any, i s r e f l e c t e d i n the v a r i a b l e A F R ~ ~

. The second path combines the force i n t o the comanded

M force summati01 !FRCS When a l l j e t s have been processed, FRCS ).

8UM represents the t o t a l x i t f l o w area o f the RCS. The t h i r d path adj@ the cumnanded j e t f o r c e f o r various thrust-loss c o n t r i b u t o r s (such as a v a i l a b l e bleed l e s s than required and l e s s than maximum i n l e t mass f l o w r a t e ) before applying i t t o the a i r c r a f t . The continuous j e t commanded f o r c e i s a l s o combined i n t o FRCS and adjusted f o r t h r u s t losses before being apol i e d SUM t o the airplane.

Bleed required by the RCS (BREQ) i s generated from the sum o f the R C S f o r c e required a t the reference bleed l e v e l (FRCs ) and MXO PO. A F R c s ~ ~ ~ . Note t h a t if the RCS i s t o t a l l y demand bleed, F RCSMX 0 BREQ i s compared w i t h bleed s v a i l a b l e ( B A V L ) t o e s t a b l i s h t h e actual RCS Bleed a v a i l a b l e i s generated by t h e propulsion system bleed l e v e l (G).

model. The r e l a t i o n between RCS f o r c e and engine b l e e d denoted by f R C S i s a f u n c t i o n o f t h e engine i n s t a l l a t i o n and bleed c a p a b i l i t y . The var?able Fxc-~~ represents t h e t o t a l RCS force a v a i l a b l e and i s l e s s than o r equal

. K ; i s generated by t h e propulsion system model and i s t h e

t o FRCS r a t i o o?"!ctual i n l e t mass flow r a t e t o t h e maximum a v a i l a b l e . Thus t h e r e l a t i o n f o r a d j u s t i n g the i n d i v i d u a l j e t command forces t o the force applied t o the a i r c r a f t can be shown t o be: This r e l a t i o n assumes each j e t i s a f f e c t e d p r o p o r t i o n a l l y the same by i n l e t mass flow r a t e s and bleed c a p a b i l i t y .

FRCS ( I ) i s processed by the RCS f o r c e dynamics t o incorporate the e f f e c t s o f demand o r continuous bleeding on the f o r c e applied t o the a i r c r a f t . Continuous bleed j e t s are assumed t o nave no l a g and FRCS ( I ) Demand bleed j e t s are a s s d d t o have i s applied immediately t o the a i r c r a f t .

f i r s t order l a g dynamics t o represent t h e delay between j e t area changes and t h e appropriate f o r c e changes. Thus, f o r demand bleed j e t s , FRCS ( I ) i s sent through J f i r s t order l a g before being applied t o the aircraCt.

2.5.3 Resolution o f RCS Forces i n t o Body Axis Forces and Moments Body a x i s R C S forces are the summation over the number o f j e t s o f t h e body a x i s components o f the i n d i v i d u a l j e t f o r c c s (FRCS ( I ) ) : A n 1-1 I =1 5 7 JET JET where 'RCS, YRCS, LRCS are the t o t a l body a x i s RCS forces A X R C S ( I ) , A Y R c s ( I ) , A Z R C S ( I ) are the body a x i s RCS forces due t o j e t I "JET i s the number o f RCS j e t s .

Body a x i s moments are the sumnation o f the moments produced by each j e t : 1-1 where LRcs, MRCS, NRCS are the t o t a l body axis RCS moments

XJETII), Y d E T ( I ) , ZJET(I) are the body a x i s components of

the p o s i t i o n vector between the a i r c r a f t cg and the a p p l i c a t i e n p o i n t o f j e t I.

2.6 C o r i o l i s Forces and b m e n t s Forces and moments are generated when the a i c r a f t r o t a t e s and produces a change i n the d i r e c t i o n o f the mass flow passing through t h e propulsion system. These f o r c e s and moments are due t o the C o r i o l i s ..I w a c c e l e r a t i o n imposed on t h e a i r c r a f t - aco,<m(rA x V ) wherer' i s t h e a i r c r a f t r o t a t i o n vector and m y i s proportional t p the mass f l o w r a t e .

Although C o r i o l i s forces and moments are n o t l a r g e i n magnitude and are g e n e r a l l y n o t i n f l u e n t i a l c o n t r i b u t o r s t o a i r c r a f t dynamics, a mode: o f the e f f e c t was incorporated f o r completeness i n the VATOL simulation.

The model i s derived from t h e s t r a i g h t through propulsion system representaion shown i n f i g u r e 2-24. T h i s i s an assumption i n t h a t t h e f l o w through actual propulsion systems may have several t u r n s t o t r a v e r s e before e x i t i n g . The model also assumes t h a t the amount o f mass w i t h i n the propulsion system i s proportional t o the i n l e t mass f l o w r 3 t e , thus the e f f e c t o f f u e l mass flow added w i t h i n the propulsion system i s neglected. This i s reasonable since f u e l mass f l o w r a r e l y exceeds 10%of the i n l e t mass f l o w and i s t y p i c a l l y 5%or less.

The development o f the Cor;olis f o r c e and moment model equations i s based on reference ( i ) and proceeds from the d e f i n ' t i o n s o f C o r i o l i s moment (2.6.1) (2.6.2)

Sp i s the i n t e g r a t i o n v a r i a b l e which moves along the

propulsion system center1 ine ( f i g u r e 2-24) i.e. along the Xg axis.

i L l D K T is tht length along the centerline from inlet face to exit plane with no nozzle deflection.

O A F is the mass f l o w rate through the propulsion system

m R is the vector from the aircraft cg to point% In terms of propulsion system and aircraft variables, the vector quantities in equations (2.6.1) and (2.6.2) can be written as (2.6.3)

-

-

- 7

(C .6.4) uA = ( p cos u y -r sin a ) 1 + qj + (r COS u + p s l r i u )k Y Y Y 9 -.

where 7, J , k are uait vectors along the propulsion system X D , YD, Z D

axes.

Suostituting equations (2.6.3) through (2.6.5) into equations (2.6.1) and 2.6.2) gives: (2.6.6) (2.6.7) and moment equatic,is whict reswl: when equstions (2.6.6) The Coriolis Qorc, and (2.6.7) are integrated are detailed i n Secton 2.0.5 o f Volume 1 1 .

. .; L ~ I .ctuation System Model The VATOL simulation models for the actuation and f 1 ight control systems are perceived to in'vface as shown in figure 2-25. The purpose of the flight control system (FCS) model is to combine cockpit controller and v t i o n sensor inputs through various control laws to generate control comnands for the aircraft degrees of freedom. These control comnands direct the applicat'on of body axis control moments and forces to the airplane. The act. ?ti IC s y s i m d e l converts the control comnands into commands for the actuators of the control force and moment generators and provides dynamic models , ; r the actuators. The propulsion system is shown on figure 2-25 because one of its functions 4s to serve as the actuator for thrust comnands.

The four FCS submodels - roll, pitch, yaw, and heave control systems -

are justified and presented in Section 2 . 8 . The actuation system actuator input submodel is discussed in Section 2 . 7 . 1 while the actuator dynamics sub- ,node1 is discussed in Section 2 . 7 . 2 .

2 . 7 . 1 Actuator Input Model The VATOL simulation model has remained generic to this point: Insofar as a proposed configuration has no more than four lifting surfaces (i.e. left and right wing halves, horizontal stabilizing surface, and vertical stabilizing surface), one fuselage, ten RCS jets, and two jet engines with the capability to deflect thrust in two directions, it can be simulated without changing the force and m0mer.t models for any arrangement of these components.

The futility o f maintaining generality in the actuator input model a n d the need for this model to be more configuration specific become apparent in the following discussion: The VATOL force and moment models accept inputs fvom twenty eight control force a n d moment generators. As a minimum, the actuator i n p u t model, to maintain generality, must provide paths from each FCS control comnand to each actuator. Generally the gains in these paths mr;st be programed as functions of aircraft state or control variables to accommodate controls blending ar,d/or nonlinear gearings for optimum flying qualities during transition. Crossfeeds between actuator inputs are also generally r e q u i r e d t o minimize c o n t r o l couplings. A n actuator i n p u t model which provides a p r i o r i f o r a l l these contingencies would be so l a r g e as t o preclude r e a l time manned simulation. In a p r a c t i c a l application, o n l y a small p o r t i o n o f the general model would ever be required and s p e c i f i c a t i o n o f t h a t p o r t i o n would be guided by a c o n t r o l system analysis o f the simulated a i r c r a f t concept. Thus, the actuator i n p u t model i s constrained t o be more c o n f i g u r a t i o n s p e c i f i c than any o f the other s i m u l a t i o n component models and must be developed by o f f 1 i n e analyses.

The development of the 9 - 1 2 1 actuator i n p u t model i s described i n Section 3.5 o f t h i s volume. The model i s depicted i n f i g u r e 3-2 and d e t a i l e d by the equations o f Section 2.2.1 of Volume 11.

2.7.2 Generic Actuator Dynamics Mae1 With the exception o f propulsion system t h r u s t dynamics, the dynamics o f a l l actuators i n the VATOL simulation model are represented by the p o s i t i o n and r a t e l i m i t e d f i r s t order model shown I n f i g u r e 2-26. The p o s i t i o n and r a t e l i m i t s and t i m e constants f o r the SF-121 actuators are specified i n Section 3.7.2 o f Volume 11. The model equations aro d e t a i l e d i n Section 2.2.2 o f Volume 11.

2.8 F l i g h t Control System b d e l As indicated by f i g u r e 2-25, the FCS Illode1 has four submodels. These are the mil, pitch, yaw and heave* contr-!? system models and correspond t o the f o u r degrees o f freedom which normally r e q u i r e some l e v e l o f automatic c o n t r o l or au-ntation i n VATOL airplanes, The r o l l , pitch, and yaw degrees o f freedom are augmented i n a l l flight regimes while heave i s augmented o n l y i n the low speed (hover) regime. Surge and sway c o n t r o l a t a l l speeds and high speed heave c o n t r o l are not modeled because these are t o t a l l y manual modes u t i l i z i n g t h r o t t l e comnands and/or a i r c r a f t a t t i t u d e as the means t o generate c o n t r o l forces. Generic r o l l , pitch, yaw, and heave c o n t r o l systems are depittec' on f i g u r e s 2-27 through 2-30 and are discussed i n Sections 2.8.1 through 2.8.4 The FCS model receives inputs ( f i g u r e 2-25) from three conventional cockpit c o n t r o l l e r s - pedals, control s t i c k with r i g h t - l e f t and fore-aft degrees o f freedom, and manual t h r o t t l e s - plus one additional c o n t r o l l e r f o r heave. The pedals and both control s t i c k degrees of freedom can be t r i e d .

Motion variables assumed available f o r FCS control law formulation include body axis r o l l , pitch, and yaw r a t e s (p, q, r ) , s t a b i l i t y a x l s yaw and r o l l

rates (rs and ps), airspeed ( V A ) , Euler angles (e, # , c y ) , a i r c r a f t

l a t e r a l and normal accelerations a t the Cg (n and nL ), and heave yC9 cg r a t e (Ze) +As used herein, heave, surge, and sway degrees o f freedom are referenced t o

earth axes; heave i s motfon along the z I a x i s , surge i s motion along the

X I axis, and sway i s along the V I axis.

The FCS submodels are similar in several respects: All feature the option to switch control laws and cockpit controller function as a function of

the control system switch (Cssw) value. The value of CSsw is determined

by vA; CSsW = 0 . for high speeds, = 1 . for hover. Most of the system

gains are P r o g t m a b l e as functions of v ~ . The forward loops can he set u p

as proportional or proportional-plus - integral controllers. The cockpit

controller comnands can be input through pure or shaped (by a lag filter) gains (for rate or attitude command systems) or through proportional-plus- integral arrangements (for rate comnand-attitude hold or acceleration comnand-rate hold systems).

Most o f the feedbacks provided for the various FCS submodels are fairly conventional: For example, body and stability axis roll rates (p and Ps) and Euler roll angle ( 9 ) are available in the roll control system; body and stability axis Yaw rates (r and rs) and Euler roll and yaw angles ( 6 a n d v ) are available in the yaw control system; body axis pitch rate (9) and Euler pitch angle (e) are available in the pitch control system; heave rate e (Ze) is used in the heave control system. Several unconventional feedbacks have also been provided: For example, to avoid the high sensitivity of 8 and to aircraft rotations when e > 80 to 85 degrees and provide a feedback proportional to attitude, the integrals of roll and yaw rates (pINT a n d ~ I N T ) have been made available in the roll and yaw control system. Also to avoid problems with the range of e (-90 < e < 90 degrees) and provide a feedback proportional to pitch attitude, the integral of pitch rate (qINT) has been made available in the pitch control system.

T w o areas of concern in VATOL terminal operations which will be studied extensively via manned simulation are cockpit controller function switching and control mode switching. Cockpit controller function switching is required to avoid pilot confusion with VATOL concepts which rotate the cockpit as the aircraft approaches hover. The requirement for control mode

switching should be obvious - the aircraft flies differently in aerodynamic

force - supported flight t h a n it does in thrust - supported flight. As

specified in the FCS model, both cockpit controller function switching a n d control mode switching are controlled by the control system switch (CSsw).

It 4s asumed t h a t the f u n c t i o n and mode switchings occur s h u l t a n e o u s l y and t h a t Cssw changes from 0 t o 1 o r v i c e versa i n one sample p e r i o d o r one computer t i m e frame. Logic i s provided f o r r e i n i t i a l i z i n g any i n p u t o r feedback i n t e g r a t o r s when CSSW changes value. This helps t o avoid l a r g e s w i t c h i n g t r a n s i e n t s , p a r t i c u l a r l y when s w i t c h i n g between Euler angle and i n t e g r a t e d r a t e feedbacks. T h i s s w i t c h i n g scenario i s rudimentary and should provide a *worst case" s t a r t i n g p o i n t . Many s w i t c h i n g f u n c t i o n s w i l l be explored i n e v o l v i n g VATOL design guidelines; each o f these w i l l r e q u i r e r e p r o g r a m i n g of the s i m u l a t i o n model .

2.8.1 R o l l Control System Model The r o l l c o n t r o l system model i s depicted on figu-c 2-27. Table 2-1 gives the parameter values r e q u i r e d t o implement several common combinations Feedback v a r i a b l e o f r o l l c o n t r o l system types and forward loop c o n t r o l l e r s .

s 2 l e c t i o n i s c o n t r o l l e d by the t h r e e s e l e c t o r gains; Y, f o r r o l l r a t e , PB K , f o r 4, and K f o r PINT; which are f u n c t i o n s of CSsw and 3P g e n e r a l l y assume values of 0. o r 1.. Those gains which can assume any value are i n d i c a t e d i n Table 2-1 as being C 0. The exact values o f these gains must be established by o f f - 1 i n e c o n t r o l system analyses.

Figure 2-27 represents t h e r o l l c o n t r o l system f o r a VATCL a i r p l a n e i n which the c o c k p i t r o t a t e s as hover i s approachec. c o c k p i t c o n t r o l of r o l l i s switched from l a t e r a l s t i c k t o pedals and r o l l t r i m f c n c t i o n switches from l a t e r a l s t i c k t r i m c o n t r o l l e r t o pedal t r i m c o n t r o l l e r . This f e a t u r e can be eliminated from t h e model by removing the CSsw dependence from the c o c k p i t c o n t r o l 1er i n p u t s t o the system.

Equations f o r the r o l l c o n t r o l system model are given i n Section 2.3.2 o f Volume 11. Parameter values f o r the SF-121 r o l l c o n t r o l system are given i n Section 3.8.2 of Volume 11. These parameter values were established by the c o n t r o l system analyses described i n Section 3.7 of t h i s volume.

'T

..

u ; t f s s

s s

L u u Y Q L d d n VI

-

S U

- c

d d U * - a C W -0 u n Q -0 c W c d d k I N * L W VI W c c

-4 VI -

m 2, 0 U c

-

4 U C C Q

. . V

0 0 * * U VI a n h VI Q

-

Q d d U E 0 c * * U U W a

-

Q n I c L h U d d E W h n VI Q u S v) c .- c n U . .

c 4 L 0 0 0 V VI '.-a W u S U n U o!

s

-

c u

-

a w

!

C

-

. c -

rn n VI B U

I

n d a * z c e e 2.8.2 P i t c h Control System Model The p i t c h c o n t r o l system model i s depicted on f i g u r e 2-28. Table 2-2 gives t h e parameter values r e q u i r e d t o implement several c m o n combinations Feedback v a r i a b l e o f p i t c h c o n t r o l system types and forward loop c o n t r o l l e r s .

s e l e c t i o n i s c o n t r o l l e d by t h e two s e l e c t o r gains; K f q f o r qINT and K , f o r 0; which are functions Of CSSW and g e n e r a l l y assume values o f 0. o r 1..

Those gains which can assume any value are i n d i c a t e d i n Table 2-2 as being f 0.

The exact values of these gains must be established by o f f - l i n e c o n t r o l system yses.

ana Equations f o r the p i t c h c o n t r o l system model are given i n Section Parameter values f o r the SF-121 p i t c h c o n t r o l system are 2.3 3 o f Volume 11.

given i n Section 3.8.3 o f Volume 11. These parameter values were established by the c o n t r o l system analyses described i n Section 3.7 o f t h i s volume.

2.8.3 Yaw Control System Model The yaw c o n t r o l system model i s depicted on f i g u r e 2-29. Table 2-3 gives t h z parameter values r e q u i r e d t o implement several common combinations o f yaw c o n t r o l system types and forward loop c o n t r o l l e r s . Feedback v a r i a b l e s e l e c t i o n i s c o n t r o l l e d by the f o u r s e l e c t o r gains; ' 6 , f o r 8 , K r B S

f o r yaw r a t e , ~9 f o r

and KJ' f o r r I N T ; Nhich a r e f u n c t i o n s o f csSw

and g e n e r a l l y assume values o f 0. o r 1. Those gains which can assume any value are i n d i c a t e d i n Table 21-3 as being f 0. The exact values of these gains must be established by o f f - l i n e c o n t r o l system analyses.

Figure 2-29 represents the yaw c o n t r o l system f o r a VATOL a i r p l a n e i n c o c k p i t c o n t r o l o f ycw i s which the c o c k p i t r o t a t e s as hover i s approached: switched from pedals t o l a t e r a l s t i c k and the yaw t r i m f u n c t i o n switches from This f e a t u r e can be pedal t r i m c o n t r o l l e r t o l a t e r a l s t i c k t r i m c o n t r o l l e r .

eliminated f r o m the model by removing the CSsw dependence from the c o c k p i t c o n t r o l l e r i n p u t s t o the system.

7 1 Y J

+ y ---+-lilq L+

f

d I I . .

- 0 I 1 0 0 X Y % h

T

.C C . .

0 - . .

-0

fi

u . + .r .- . .

. . . . . .

0.- 0- 0- 0- c _ - F I

-

d d d D - 4 L - N - c d d d 3 -N .(L I d d d

4 4

't

t l ~ c Y s: 3

+t

u ( 0 ' .

d I d I d

Y O -

& - Z 6 d Y L d d 0 d o d Y 'I 'I E 1 . * 1 .

I

$ *

w o > - -.. 'I 'I - I) -4 ~~

-

u o 0 0 x - . . '.. -L 7 5 The 'lateral a c c e l e r a t i o n (n ) t o FCS yaw c o n t r o l command ((YAW) feedback was added t o decouple Yc? coupled r o l l - s p i r a l W e which (See Section 3.7 appeared i n the SF-121 i n the speed range o f 60 t o 200 k t .

i n t h i s volume). The feedback can be removed simply by zeroing t h e l a t e r a l (Ka ).

acceleration g a i n Y Equations f o r t h e yaw c o n t r o l system model are given in Section 2.3.4 Parameter values f o r the SF-121 yaw c o n t r o l system are given i n o f Volume 11.

These parameter values were established by the Section 3.8.4 o f Volume 11.

c o n t r o l system analyses described in Section 3.7 of t h i s volume.

2.8.4 Heave Control System Model The heave c o n t r o l system model is depicted on f i g u r e 2-39. It receives i n p u t r a t e comnands from the heave r a t e c o c k p i t c o n t r o l l e r , compares these i n p u t s w i t h a heave r a t e feedback, and adjusts t h r u s t t o reduce the e r r o r according t o a ~ r o ~ o r t i o n a l ( K 1 0.) o r proportional p l u s ze I i n t e g r a l ( K 4 0.)

forward loop c o n t r o l law. The heave c o n t r o l system z e l operates o n l y a t low

speed ( c s s ~ 1.). The e r r o r gain ( K z ) and e r r o r

e i n t e g r a l gain ( K z ) must be determined by o f f - l i n e c o n t r o l system e I analyses.

Equations for the heave c o n t r o l system model are given i n Section 2.3.5 o f Volume 1 1 . Parameter values f o r the SF-121 heave c o n t r o l system are given i n Section 3.8.5 of Volume 11. These parameter values were established by the c o n t r o l system analyses described i n Section 3.7 o f t h i s volume.

L c, E u a m 7 7 2.9 Relative W i e n t a t i o n o f A i r c r a f t Body Axes and I n e r t i a l Axes Host simulations i n v o l v i n g v e h i c l e dynamics r e q u i r e a transformation t o define the o r i e n t a t i o n o f a s e t o f vehicle-fixed body axes r e l a t i v e t o an earth-fixed o r i n e r t i a l a x i s system. There are two basic formulations o f t h i s transformation: Euler r a t e equations and d i r e c t i o n cosines. Because o f t h e i r s i m p l i c i t y and almost universal a p p l i c a b i l i t y , the Euler r a t e equations are used for most a i r c r a f t simulations.

Their one drawback i s a s i n g u l a r i t y a t o .I 90 degrees. Ev?n i n a i r c r - f t simulations, such as a i r t o a i r combat, where r a p i d l a r g e angle maneuvers are involved, t h e Euler r a t e equations are used by introducing approximate continuous forms o f the equations whm o i s close t o 90 degrees. These approximations work w e l l and have t o l e r a b l y small e r r o r s as long as o = 90 degrees occurs o n l y momentarily. It would be impossible t o t r i m the a i r c r a f t a t o = 90 degrees w i t h the approximations present. VATOC a i r c r a f t r o u t i n e l y maneuver f o r long periods w i t h o close t o 90 degrees. I n a d d i t i o n they must be t r i e d near 90 degrees f o r i n i t i a t i n g hover analyses.

For these reasons, the d i r e c t i o n cosines formula:’-’l was adopted f o r the VATOL simulation math model since it i s continuous everywhere. Because nine ( v i c e three Euler r a t e equations) equations are involved, a s l i g h t l y increased computation load i s imposed on the simulation computer. Reference (j) q u a n t i f i e d t h i s increase t o be 0 . 0 4 m i l l i s e c o n d per i n t e g r a t i o n using an Adams 2nd order i n t e g r a t i o n algorithm; the Euler r a t e equations usdo 7G milliseconds per i n t e g r a t i o n w h i l e the d i r e c t i o n cosines used 0.74 In r e a l time manned simulation a c t i v i t i e s t o date using t h i s milliseconds.

VAT& model and requdring a frame time o f approximately 50 milliseconds, t h i s increased load has not been noticed. Neither has i t noticeab:y increased expected r u r times i n applications of VATLAS t o generate dynamic check cases f o r the manned simulation.

A l t e r n a t i v e s t o the d i r e c t i o n cosines formulation which have not been explored are as follows:

RoLated I n e r t i a l Axis System - Choose an i n e r t i a l a x i s system i n

1.

which the XI and 21 axes a r e r o t a t e d r e l a t i v e t o the standard i n e r t i a l system i n which the 21 axis i s aligned w i t h g r a v i t y .

The Euler r a t e s and angles would then be applied t o the r o t a t e d For example, f i g u r e 2-31 shons that, with t h e a x i s system.

i n e r t i a l a x i s system r o t a t e d 45 degrees, VATOL hover occurs a t ' R = 45 degrees (where g~ i s p i t c h angle referenced t o the r o t a t e d axes) and the s i n g u l a r i t y w i l l n o t occur u n t i l t h e a i r c r a f t r o t a t e s another 45 degrees off the v e r t i c a l . S i m i l a r l y , s t r a i g h t and l e v e l f l i g h t i n the r o t a t e d axes w i l l occur w i t h QR = - 4 5 degrees.

2. 9\ aternions - Computational speed and universal a p p l i c a b i l i t y are

A l i m i t e d i n v e s t i g a t i o n by c i t e d as advantages o f quaternions.

Vought o f these claims ( r e f (j)) found t h a t quaternions are s l i g h t l y f a s t e r than both Euler r a t e equations and d i r e c t i o n cosines (0.66 m i l l i s e c o n d s per i t e r a t i o n vs 0.70 milliseconds f o r Euler r a t e equations and 0.74 milliseconds f o r d i r e c t i o n cosines) and are continuous everywhere. This speed improvement i s "down i n the noise" o f r e a l time manned simulations which operate i n the 40 t o 60 m i l l i s e c o n d range.

The equations f o r the d i r e c t i o n cosine formulation are d e t a i l e d 3long w i t h the a i r c r a f t equations o f motion i n Section 2.4 o f Volume 11. This formula' ;un incorporates r e l a t i o n s developed i n reference ( k ) which maintain the orthonormality of the transformation by c o r r e c t i n g the d i r e c t i o n cosines f o r i n t e g r a t i o n e r r o r s .

Figure 2-31. R e l a t i o n o f Standard and Rotated I n e r t i a l A x i s Systems

ao

2 . 1 0 Pseudo-Pi lot Functions To effectively apply the VAT& simulation model in an off-line mode required the incorporation of pilot-like (or pseudo-pilot) logic and inputs into VATLAS. These pseudo-pilot options include: 1. Apply open-loop inputs to any combination of cockpit controllers using data tables.

2 . Equations for pilot-flown transition 3 . Equations f o r pilot-flown stationkeeping The table input functions can be applied in parallel with pilot-flown transitions or stationkeeping. Since the pseudo-pilot functions are not required for the VATOL manned simulation, they are not detailed in Volume 11.

Instead they will be presented here.

2 . 1 0 . 1 Open-Loop Cockpit Controller Inputs The equations for the open loop cockpit controller inputs are quite simple: 6~~~~~~ = fpp2(t) where the fpp's are user defined tables ~ L N ~ T K i s f o r e - a f t motion of the c o n t r o l s t i c k 6LATgK i s l e f t - r i g h t motion of t h e c o n t r o l s t i c k 4 p ~ ~ i s pedals n o t i o n i s heave r a t e comanded by the heave r a t e c o n t r o l l e r z ' C ~ T ~ U T i s t h r o t t l e motion b d i n a r i l y the i n p u t functions are arranged t o be steps, doublets, pulses, and other t e s t inputs but, because o f t h e i r t a b l e i n p u t format, can be made completely random. VATLAS i s arranged so t h a t i n p u t s can be applied t o any I n addition, the input: can be and a l l o f the c o n t r o l l e r s simultaneously.

d i f f e r e n t f o r each c o n t r o l l e r since each c o n t r o l l e r has i t s own function table.

2.10.2 Pseudo-Pilot T r a n s i t i o n Equations The p i l o t - f l o w n t r a n s i t i o n equations r e q u i r e tables o f t r i m p i t c h angles and t h r o t t l e s e t t i n g s as a f u n c t i o n o f ground speed. Thus an analysis of t r a n s i t i o n t r i m s i s required before t h e pseudo-piiot can "fly" the t r a n s i t i o n . The equations assume t h a t the p i t c h c o n t r o l system i s r a t e comnand-attitude hold a t high speeds (CSsw .I 0.) and a t t i t u d e command a t l o w speeds (CSsW I 1.) The equations are given below:

6 - ic - (ec2 - ec ) / A T

where Ve i s i n e r t i a l speed Ve i s r a t e o f change o f i n e r t i a l speed i s estimated i n e r t i a l speed a t the next update assuming VeEST Ve i s constant AT i s the time between updates 0 . .

u, v, w are t h e r a t e s of rhange o f the body a x i s components o f i n e r t i a1 speed i z the t r i m p i t c h angle a t speed Ve e C 1 e i s the t r i m p i t c h angle a t speed Ve c2 E ST eC i s the p i t c h r a t e required over thx next AT seconds t o reach e a t t h e next update c2 i s +he value o f the i n p u t i n t e g r a t o r when CSsw changes TRMfrom 0. t o 1.0 (i.e. when the p i t c h c o n t r o l system switches from r a t e command-att i tude hold t o a t t i t u d e command).

To i p i t i a t e a t r a n s i t i o n dTHROI. i s retarded below t r i m t o s t a r t a deceleration, then as the speed decreases t o 80 t o 100 k t , the t h r o t t l e i s advanced t o the proper t r i m s e t t i n g , These t h r o t t l e changes are c o n t r o l l e d by the values i n fpp (V,). When CSsW changes t o 1.0, the heave c o n t r o l system i s engaged and adjusts the t h r u s t l e v e l t o maintain the preset heave r a t e (normally = 0 ft/sec.). A sample pilot-flown t r a n s i t i o n i s shown i n f i g u r e 3-32 and discussed i n Section 3.8.9.

2 . 1 0 . 3 Pseudo-Pilot Stationkeeping Equati,.is The development of the stationkeeping control equations assumed that the aircraft pitch and yaw control systems are attitude hold and that the heave rate comnand system was operative. It also assumed that the three inertial position loops are closed by the pilot who has both inertial rate and position available. The stationkeeping control laws are depicted in figure 2-32. The pseudo-pilot’s goal is to maintain aircraft position at Xe = Ye = 0 and Ze at some desired altitude. Since ~ L N G S T K controls pitch attitude which in turn controls fore-aft motion along the Z body axis (recall e 2 90 degrees while stationkeeping) and ~ L A T S T K controls yaw attitude which in turn controls right-left motion along the Y body axis, the X , and ye rate and position data are resolved into the body axis system. Longitudinal and lateral stick commands are then made proportional to Z and Y body axis errors respectively. Similarly, the heave rate comnands are made proportional to heave and hedve rate errors or, equivalently (with e = 90 degrees), X body axis position and rate. By reference to figure 2-32, the pilot-flown stationkeeping equations can be written as follows: t t t

4 * %NGSTK = K ‘es Z, s

5 * 6~~~~~~ a K Y Figure 2-32. Stationkeeping Control Laws where

'e , Ye , Ze are t h e e r r o r q u a n t i t i e s along t h e X, Y, Z

S boay axds assuming e = 90 degrees. ihe p o s i t i o n c o n t r i b u t i o n s (i.e. jwdt, {vdt, fudt) i n the expressions a t t h e f a r r i g h t o f equations 1, 2, and are exact o n l y if d13, d23, d12, and dz2 are constants (i.e. t h e r e l a t i v e o r i e n t a t i o n o f the body and i n e r t i a l axes does n o t change).

Ku, Kv, K , , , are the r a t e feedback gains and must be determined by o f f - l i n e c o n t r o l system analyses.

are t h e e r r o r gains and must a l s o 8 K zeS be determined by o f f - l i n e c o n t r o l system analyses.

A sample p i l o t - f l o w n t u r n over a spot i n a 35 k t wind a t a commanded 20 degreeslsec t u r n r a t e i s shown i n f i g u r e 3-33 and discussed i n Section 3.8.10. This maneuver combined t h e pseudo-pilot stationkeeping equations w i t h an open loop pedal input.

3.0 APPLICATION OF VATLAS TO THE VOUGHT SF-121 AIRPLANE This s e c t i o n describes the a p p l i c a t i o n o f VATLAS t o develop and demonstrate a FCS for terminal operations of the Vought SF-121 airplane, The general FCS design procedure depicted on f i g u r e 3-1 was followed f o r t h i s appl i c a t i o n . I n 8 primary outputs of t h i s i t e r a t i v e process are s p e c i f i c a t i o n o f actuator i n p u t s and FCS laws and gains. Requirod i n p u t s include a i r c r a f t data, operational conditions, d e s i r e d FCS configuration, and i n p u t s f o r Also r e q u i r e d are an i n i t i a l s e t o f actuatilr i n p u t t e s t i n g FCS performance.

Specifications and FCS laws and gains. Each step i n the ;rocewre (denoted b; the blocks i n f i g u r e 3-1) i s discussed i n d e t a i l below. C a l cions are performed by VATLAS, which i s used t o generate 6DOF n o n l i n e i q l ~ s and response time h i s t o r i e s t o t e s t inputs, and LINA, Vought's li analysis r o u t i n e .

The purpose o f t h i s VATLAS a p p l i c a t i o n t o the SF-121 was t o develop a baseline FCS which would enable a p i l o t t o perform t r a n s i t i o n and hover f l i g h t tasks i n a moving base s i m u l a t i o n of the airplane. This FCS i s t o be capable of t r i m i n g the a i r c r a f t anywhere i n the t r a n s i t i o n c o r r i d o r and o f meeting the maneuver requirements of MIL-F-83300 and A W D 577. There ? r e no requirements t h a t t h i s FCS be optimized w i t h regard t o p i l o t workload, augmentation l e v e l required t o accomplish terminal operations, r i d e q u a l i t i e s , and s i m i l a r items which can be considered when d e f i n i n g a baseline FCS b u t can not be completely evaluated without simulator studies and f l i g h t t e s t s .

n

L

3.1 SF-i21 Airplane Data The data required by VATLAS t o d e l an a i r p l a n e have been discussed i n Secton 2.0 of t h i s volume. Requisite SF-121 data have been incorporated i n V o l u e I 1 o f t h i s r e p o r t as follows:

M a s s Properties Data - Section 3.1

o

6eometry Data - Section 3.2

o

Aerodynamic Oata - Section 3.3

o

o Propulsion System Data - Section 3.4

I n l e t Ram forces and nolnents Data - Section 3.5

o

Reaction Control System Data - Section 3.6

o

o Actuation System Data - Section 3.7

The mass properties data i n Volume I 1 represent o n l y one SF-121 loading -

design mission stores (2 Sidewinder afid 2 Sparrow m i s s i l e s and gun plus 400 rounds o f m u n i t i o n ) , gear down, 1000 lb. f u e l . This i s a landing c o n d i t i o n and served as the loading f o r the baseline FCS design. Tables 3-1 through 3-4, taken f r o m reference (c), provide more extensive mass properties data f o r design mission stores on and o f f and gear up and gear down.

SF-121 c o n t r o l system data are given i n Section 3.8 o f Volume 11. These data are outputs o f the FCS design procedure; they were n o t required o r available a t i n i t i a t i o n p f the design process described herein.

(3 v) w I

*

N 00, h v) h N c c N v) r - 1 1 c c m c m a 0 0 h h h h c d m (u c m I I h m In OI

s m

0 QI rg m m 0 F m

s

?

m d m m cu 0,

m 6

m Q) 03 I C - - - - . . . .

o 0 c ; o o d ‘ d d

0 0 0 0 0 0 8 0 0

* U * * U U b b d . . . .

n n n n n n - c - c 7 - 0 h

b n *

9 P

0, cr) m h h c cu, h cp m L n VI m m m m 0 h v) c

- u) 0

h 0 a 'u, 4 0 c e (v (u m m v) m c 0, h m e n h, .)

rn In 0 m c'1 c

i g 0

c c c h.

c 0 c

6 d

0 0 h v) v) 0 c N cu I I I h

3 -

c vi 3 .

v) h (0 v) v) v) c c v) Qo cu h v) c e m N

b. . 9

. ?

F c 0 0 0

€i 0

0 0 0 0

c c 7 -

0 e c 0 0 W

. . . c‘f

. .

m m a) a0 a) a0 m c e F c c F c c c N m ln

9 . . s

. .

c c c c c c -

0 0 0 0 0 0 0 d

U U * d * e

W e . . . .

a n n n n a n w e e r e L 3.2 SF-121 Operational Conditions As s t a t e d above, t h e baseline FCS development was t o consider o n l y terminal operations of the SF-121. Terminal Operations i n c l u d e approach t o t r a n s i t i o n , t r a n s i t i o n or reconversion, and hover flight conditions. It i s assurned t h a t these operations occur a t l o w a l t i t u d e i n a speed range of 0 t o 200 k t . A t 200 k t , t h e S-121 c r u i s e s i n aerodynamically supported (convectional) f l i g h t a t a S 9 . 5 degrees w h i l e a t hover the a i r p l a n e i s f u l l y t h r u s t supported a t a 90 deg. The s p e c i f i c operational c o n d i t i o n s selected f o r l i n e a r analysis and design of t h e baseline FCS were VA I 0, io, 40, 60, 80, 120, and 200 k t . i n l e v e l f l i g h t a t Vt ( V e r t i c a l Landing) weight and i n e r t i a s . The c l o s e l y spaced c o n d i t i o n s a t VA I 40, 60, and 80 k t ernphasite t h a t p o r t i o n o f t h e SF-121 t r a n s i t i o n where the a i r c r a f t t r i m c h a r a c t e r i s t i c s change most r a p i d l y w i t h speed. (See Section 3 . 6 for the SF-121 t r i m data.)

Landing was considered more c r i t i c a l t o the design since M. t r i m t h r u s t (thus c o n t r o l power) i s lower than VTO ( V e r t i c a l Takeoff) t h r u s t and V L i s a more demanding p i l o t i n g task than VTO.

Another operational c o n d i t i o n imposed by the NASA-Ames S.01 simulator l i m i t a t i o n on c o c k p i t p i t c h angle b u t c e r t a i n l y w i t h i n the realm of VATOL p o s s i b i l i t i e s was that, i n hover, t h e c o c k p i t c e n t e r l i n e w i l l be approximately perpendicular t o the fuselage c e n t e r l i n e ; i.e. the p i l o t looks out the a i r p l a n e Z body a x i s during hover. This c o c k p i t ( p i l o t ) o r i e n t a t i o n i s s i m i l a r t o t h a t o f the Ynutcrackern a i r c r a f t concept. To maintain harmony between c o c k p i t c o n t r o l l e r inputs and p i l o t - perceived a i r c r a f t motions, the baseline FCS has t o provide f o r swapping pedals and l a t e r a l s t i c k functions during t r a n s i t Ion. Thus, l a t e r a l s t i c k always comnands c o c k p i t r o l l and pedals always comnand eockpit yaw.

3.3 Basel i n e FCS Configuration Selection It was i t m e d i a t e l y obvious t h a t a t l e a s t two modes were r e q u i r e d f o r the SF-121 base1i n e FCS configuration; one mode for hover o r thrust-supported

f 1 i g h t and one for conventional o r aerodynamically-supported flight . A switch

p o i n t o r blending r e g i o n between these modes has t o be established. Sections 3 . 6 and 3.7 d e t a i l the development o f t h i s mode chqnging.

The next step i n FCS c o n f i g u r a t i o n s e l e c t i o n was t o consider how c o n t r o l forces and moments are produced f o r t h e SF-121 airplane. Table 3-5 sumnarizes t h i s information f o r each o f the a i r p l a n e s i x degrees o f freedom and f o r hover and conventional f l i g h t modes. The t a b l e s p e c i f i e s the primary f o r c e o r moment generator and c o c k p i t c o n t r o l l e r , i f available, f o r each degree o f freedom. Tne c o c k p i t heave c o n t r o l l e r i n hover f l i g h t i s a separate c o n t r o l l e r if closed l o o r heave o r heave r a t e c o n t r o l i s adopted; otherwise i t i s the t h r o t t l e . With the exception o f the r o l e reversal o f pedals and l e f t - r i g h t s t i c k motion and the possible a d d i t i o n of a heave c o n t r o l l e r i n hover f l i g h t , the functions of the c o c k p i t c o n t r o l l e r s are f a i r l y standard.

The dual-mode requirement f o r t h e FCS and s i m i l a r i t y i n number and func- t i o n o f the cockpit c o n t r o l l e r s l e d t o adoption f o r the SF-121 of the augmen- t a t i o n l e v e l s and functions o f the baseline FCS o f the l i f t l c r u i s e fan V/STOL airplane studied i n reference (e). The s e l e c t i o n o f these l e v e l s and func- t i o n s f o r the l i f t / c r u i s e fan airplane FCS was based on an extensive founda- t i o n o f analysis, simulaticn, ano f l i g h t t e s t i n g o f terminal operations o f V/STOL airplanes. These l e v e l s and functions were demonstrated i n reference (e) t o be adequate f o r launch and recovery operations on a DD963 type ship.

There was no reason t o doubt t h s t t h e same FCS concept would s u f f i c e as a baseline FCS f o r terminal operations the SF-121 airplane.

The SF-121 baseiine FCS c o n f i g u r a t i o n i s summarized by degrees o f freedom controlled, system type, cockpit c o n t r o l l e r , and f l i g h t mode i n Table 3-6.

The only d e v i a t i o n from the l i f t / c r u i s e fan V/STOL baseline FCS i s the s u b s t i t u t i o n of a r a t e comnatid-attitude h o l d system f o r an a t t i t u d e comnand system i n the p i t c h a x i s f o r the conventional f l i g h t mode. The p i t c h angle changes required during VAT& t r a n s i t i o n are l a r g e ( 5 0 4 0 degrees). With an

-

Y

k

v) LL W Q

x

x

m"

Y L bib I I I W tii!

w w a a I u t ; ; t ,

a

* n

z - X C W

-I- -

a W

v) 2

3 w a W C

L s

a = 0 W w o c ( C L x u

k

U c3 u S L

I LE

E i

m e

- I g z

d r a

a - x a t t i t u d e comnand system l i m i t e d t o 15 o r 20 degrees p i t c h comnand a u t h o r i t y for the s t i c k , the p i l o t has t o spend considerable time on the t r i m button t o keep t h e s t i c k i n a desirable range o f t r a v e l . The r a t e command-attitude h o l d system eliminates the requirement f o r t r i m b u t t o n inputs and maintains the a t t i t u d e s t a b i l i t y supplied by the a t t i t u d e comnand system.

3.4 Test Cases t o Evaluate FCS Performance The t e s t cases selected t o demonstrate and evaluate FCS performance are as f o l 1 ows: o Steps, doublets, and/or pulses imposed on various c o c k p i t c o n t r o l l e r s i n both hover and conventional modes and i n the mode switching f l ' . i h t regime.

o Pseudo-pilot flown t r a n s i t i o n Pseudo-pilot flown t u r n over a spot i n a 35 k t wind o Since these runs w i l l be produced by the f u l l nonlinear simulation program (VATLAS), they should h i g h l i g h t any problems due t o actuator p o s i t i o n o r r a t e l i m i t s , nonlinear aerodynamics, t h r u s t dynamics, kinematic coupling, and s i m i l a r n o n l i n e a r i t i e s . The pseudo-pilot t r a n s i t i o n and stationkeeping runs w i l l i n d i c a t e p o t e n t i a l p i l o t i n g problems i n attempting t o perform t r a n s i t i o n and hover tasks.

3.5 Actuator I n p u t S p e c i f i c a t i o n

The SF-121 has fourteen actuators which are t o be l i n k e d with f o u r FCS

variables. The FCS v a r i a b l e s are comnanded t h r u s t and r o l l , p i t c h , and yaw c o n t r o l c m a n d s . The r o l l , p i t c h , and yaw comnands are normalized such t h a t - +1. comnands a l l a v a i l a b l e c o n t r o l power i n t h e appropriate d i r e c t i o n . The f o w t a e n actuators are as follows: o L e f t and r i g h t wing t r a i l i n g edge f l a p s (elevons) o Vert c a l s t a b i l i z e r c o n t r o l surface (rudder) o L e f t and r i g h t engines p i t c h t h r u s t d e f l e c t i o n o L e f t and r i g h t engines yaw t h r u s t d e f l e c t i o n L e f t and r i g h t engines t h r u s t (1.e. propulsion system) o o L e f t and r i g h t wing t i p RCS j e t s o Canard t r a i l i n g edge f l a p o L e f t and r i g h t wing leading edge f l a p s The i n p u t s t o the l e f t and ( * i g h t wing l e a d i n g edge f l a p actuators and t o the t r a i l i n g edge f l a p o f the canard are s p e c i f i e d i n reference ( c ) t o be Inputs f o r each of the o t h e r actuators except f u n c t i o n s o f angle o f attack.

t h e propulsion system were formed by m u l t i p l y i n g the appropriate normal i r e d r o l l , p i t c h , o r yaw comnand by the maximum d e f l e c t i o n c o n t r o l l e d by t h a t actuator. For example, the normalized p i t c h c o n t r o l ( 6 ~ 1 7 ~ ~ ) was l i n k e d t o the r i g h t and l e f t wing elevon actuators (which are the primary generator o f p i t c h c o n t r o l power d u r i n g conventional f l i s h t ) and t o the l e f t and rqght engines p i t c h t h r u s t d e f l e c t i o n a c t u t a t o r s (which are the primary generator o f p i t c h c o n t r o l power d u r i n g hover f l i g h t ) . A l l actuators were assumed t o be d r i v e n f u l l time. The gains f o r the elevon actuator i n p u t s were 25 degrees, the maximum symnetric elevon d e f l e c t i o n , and the gains f o r the p i t c h t h r u s t 15 degrees, the maximum p i t c h t h r u s t d e f l e c t i o n .

d e f l e c t i o n actuators were The actuator inputs a r e deplcted i n f i g u r e 3-2. This arrangement i s the i n i t i a l and, as w i l l be shown, the o n l y actuator i q p u t s p e c i f i c a t i o n required.

Note t h a t , i n a d d i t i o n t o the b a s i c l i n k s , the arrangement a n t i c i p a t e s use o f d i f f e r e n t i a l l e f t - r i g h t p i t c h t h r u s t d e f l e c t i o n f o r r o l l c o n t r o l (gain

n

Figure 3-2. SF-121 Actuator Input j p e c i f i c a t i o n

KeTbr) and a crossfeed o f roll c o n t r o l t o rudder ( g a i n K, br) and

Yaw t h r u s t d e f l e c t i o n ( g a i n 6r). As w i l l be shown, t h k e a d d i t i o n s were not required. The r i n p u t gains a r e s p e c i f i e d i n Section 3.7.1 o f Volume 11.

1 02 3.6 Trin C h a r a c t e r i s t i c s Evaluation (hce t h e actuator i n p u t s were specified, t h e a i r p l a n e could be trimmi using FCS c o n t r o l variables. Two types o f t r i m were c a l c u l a t e d by VATLAS: hover t r i m s i n a 35 k t wind whose d i r e c t i o n v a r i e d fror head wind t o t a i l wind and t r a n s i t i o n trims. T r a n s i t i o n t r i m s assumed s t r a i g h t (6 I 0) and l e v e l (y I 0) flight and were c a l c u l a t e d for t h r e e d e c e l e r a t i o n l e v e l s ( V A 0, 4.1, -0.2 9) along the f l i g h t path for a speed range of 0 t o 200 k t . The primary t r a n s i t i o n t r i m v a r i a b l e s - ? i t c h angle, t h r u s t l e v e l , and normal .ed p i t c h c o n t r o l (bplTCH) - are shown on f i g u r e 3-3. S i m i l a r l y t h e primary t r i m variables - p i t c h and bank angles, t h r u s t l e v e l , angles o f a t t a c k hover and s i d e s l i p , and normalized r o l l , p i t c h , and yaw c o n t r o l s - are shown on f i g u r e 3 4 0 Figures 3-3 and 3-4 i n d i c a t e t h a t t h e SF-121 has s u f f i c i e n t c o n t r o l power f o r t r i m i n 35 k t winds and along reasonable reference t r a j e c t o r i e s i n t h e airplane's t r a n s i t i o n c o r r i d o r . The maximum percentage use o f a v a i l a b l e p i t c h c o n t r o l power t o t r i m i s 74Xwhich occurs a t 80 k t i n a 0.29 d e c e l e r a t i n g t r ? n s i t i o n . The maxinum percentage use o f a v a i l a b l e r o l l c o n t r o l power t o t r i m i s 9Xwhich occurs i n a 35 k t crosswind (hIND = -90 degrees) w h i l e 35 k t wind o r i e n t e d 75 deg t h a t f o r yaw c o n t r o l power i s 17Xwhich occurs i n a t o p o r t o r starboard.

Figure 3-5 compares pitch, r o l l , and yaw c o n t r o l power a v a i l a b l e w i t h t r i m ( f o r a 0.29 decelerating t r a n s i t i o n ) and f l y i n g q u a l i t i e s s p e c i f i c a t i o n requirements. because 0 - the r o t a t e d SF-121 c o c k p i t i n hover t h e f l y i n g q u a l i t i e s r o l l (yaw) c m t r o l power requirements are compared w i t h Sf-121 yaw ( r o l l ) c o n t r o l power. AGAR0 577 requirements are assumed t o be applicable f r o m C t o 35 k t , which i s the range f o r hover and l o w speed f l i g h t s p e c i f i e d i n MIL-F43300. The AGARD 577 requirements i n d i c a t e d on f i g u r e 3-5 show the c o n t r o l power range designated t o be t y p i c a l f o r a t t i t u d e s t a b i l i z e d V/STOL a i r c r a f t f v maneuvering, t r i m , and gust r e g u l a t i o n functions. The c o n t r o l power a v a i l a b l e f o r maneuvering and gust r e g u l a t i o n i s a l s o compared w i t h t h e f l y i n g qual.,ties requirements on f i g u r e 3-5. As can be seen the SF-121 has adequate c o n t r o l power f o r meeting the t r i m and maneuvering s p e c i f i c a t i o n requirements w i t h some margin l e f t f o r gust r e g u l a t i o n .

1 03 Figure 3-3. SF-121 Trim Requlremnts for Level Fllght D e c d e r a t i o n s (Sheet 1 o f 2 ) Figure 3-3. Y-121 T r i m Requirements for Level F l i g h t Decelerations (Sheet 2 o f 2 ) . ..

.- I ..

; . I . ' . ; , . - . . ; , . . _. _ . . . . . _ . _ _ * - . _ _ . . _ _ 1. _ _ _ . - . . . - . - . , Figure 3-4. SF-121 T r i m Requirements for Stationkeeping I n a 35 kt Witid (Sheet 1 of 4) - , I Figure 34. SF-121 Trim Requiremints for Stationkeeping i n a 35 k t Wind (Sheet 2 of 4 ) 1 07 . ..

I F l y r e 3-4. SF-121 Trim Requirements for Stationkeeping i n a 35 k t Yind (Sheet 3 of 4 )

- WIUC

Figure 3-4. 9-121 Trim Requirements for Stationkeeping in a 35 k t Wind (Sheet 4 of 4) The r e s u l t s o f t h e t r i m c h a r a c t e r i s t i c s e v a l u a t i o n have shown t h a t t h e SF-121 has s u f f i c i e n t c o n t r o l power and t h a t the actuator i n p u t s p e c i f i c a t i o n of Section 3.5 i s adequate. Thus no i t e r a t i o n s were r e q u i r e d o f t h e actuator 3-1.

i n p u t s p e c i f i c a t i o n design loop shown i n f i g u r e A more comprehensive t r i m analysis might have i n d i c a t e d a nonlinear blending o f the elevon and p i t c h t h r u s t deflections i s b e t t e r than the l i n e a r blending which has been adopted. For example, the elevon could be programed t o provide a l l t h e t r i m c o n t r o l power t o as low speeds as possible. This would save t h r u s t d e f l e c t i o n f o r the maneuvering and gust r e g u l a t i o n functions.

Another r e s u l t o f the t r i m c h a r a c t e r i s t i c s e v a l u a t i o n was t h e s e l e c t i o n o f 60 k t as the switch p o i n t between t h e hover and conventional modes o f the FCS. To o b t a i n t h i s r e s u l t the t r a n s i t i o n t r i m data o f f i g u r e s 3 3 and 3-4 were examined using t h e f o l l o w i n g c r i t e r i a : More than 50%of the a i r c r a f t weight supported by t h r u s t (i.e.

o t r a n s i t i o n more than SOfJ,complete) This occurs a t approximately 65 k t .

Since surge and sway c o n t r o l i n hover are g e n e r i c a l l y t h e same f o r o the SF-121, s i m i l a r c a p a b i l i t i e s and c h a r a c t e r i s t i c s are d e s i r a b l e i n t h e p a i r e d p i t c h l s u r g e and yawlsway degrees o f freedom. Thus it was decided t h a t p i t c h c o n t r o l margin and yaw c o n t r o l power should be approximately equal a t and below the switch p o i n t . As shown by f i g u r e 3-5 t h i s c r i t e r i o n i s f i r s t met near 60 k t when the two c o n t r o l powers equal 0.7 radlsec'.

The f i n a l r e s u l t o f the t r i m c h a r a c t e r i s t i c s e v a l u a t i o n was the p r o v i s i o n o f dimensional s t a b i l i t y d e r i v a t i v e s f o r developing t h e FCS laws and gains.

These d e r i v a t i v e s are an important by-product o f VATLAS t r i m c a l c u l a t i o n s ; they are automatically generated a t each t r i m p o i n t . Tables 3-7 and 3-8 sumnarize SF-121 d e r i v a t i v e s a t t h e speeds selected f o r FCS development. The d e r l v a t i v e s are based on a t r a n s i t i o n t r i m along an unaccelerated s t r a i g h t and l e v e l f l i g h t path.

Figure 3-5. Comparison of SF-121 Control Power With, Flying Qualities Specification Requirements 1 1 1 h I m W -.I m U I- U U 0 u H U H \ \ a n c, *r L c c c I -cI \ 'r N N N N V u U Y u Y Ln H \ ?1 \ H \ \ U ci U Y rc rc + c 1 I I 1 t Q t a N cf N N c m N % S $ Z 0 - m h m ? ? ? ' ? ? " i O O O d O O m 1 1 1 1 . . . . . * .

o o o j d d d o o p ' o o o " ; I I N I I I I m

--

L n N . . .

rl d d d d o w m I l l N U V V Y 0) a J m m m

\ - .- 0

m U V 5 73 5 a L .

L L L

\ - . cu

N N u N U V U a J m a J aJ 01

-

m m m

\ - 1

v m U 5 m 0 +8 L L L L I I b e l I v ) I I I I I V a 2 L a c z t w L n L o w 0 -1 2 2 L 2 - 1 * + - >

3.7 S p e c i f l c a t l o n o f Baseline FCS LIWS and b l n s

Linear analysis, supported by LINA, was applied t o q u a n t i f y the baseline FCS configuraton described i n Section 3.3 and fable 3-6. Design analyses were p e r f o r d a t each of the speeds s p e c i f i e d i n fables 3-7 and 3-8. The f i r s t step i n these analyses was t o c a l c u l a t e t h e unaugmented o r bare airframe transfer functlons using the otabll i t y d e r i v a t i v e s i n the tables. These airframe functions are given i n Tables 3-9, 3-10, and 3-11.

.

Longitudinal ( p l t c h and heave) FCS development w i l l be discussed i n Section 3.7.1 followed by l a t e r a l d i r e c t i o n a l ( r o l l and yaw) development i n Section 3.7.2. Discussion of the hover FCS design d e t a i l s are focused on the

VA I 10 k t case while c o n u m t l o n a l FCS d e t a i l s are focused on the VA 120

k t case. The FCS f o r other speeds d i f f e r s only i n gain f r o m the

representattve 10 and 120 k t cases.

Before the baseline FCS configuration (Table 3-6) could be quantified, several issues having general a p p l i c a b i l i t y t o the design process had t o be resolved. These were: How should FCS gains be scheduled o M a t a t t i t u d e signal should be fedback f o r a t t i t u d e s t a b i l i z a t i o n i n o t h e hover mode Whet are desirable bandwidths for the a t t i t u d e s t a b i l i z a t i o n and o heave r a t e loob.

The f i r s t issue was resolved i n favor of gain scheduling as j f u n c t i o n of airspeed. P i t c h angle scheduling was considered but q u i c k l y eliminated; a wide range o f p i t c h a t t i t u d e s can be attained a t any speed, thus a high probabil I t y o f incompatible FCS gains e x i s t s w i t h possibly disastrous consequences.

The issue o f a t t i t u d e feedback signals for hover stems from t h e discon- t i n u i t y a t o = 90 degrees i n the Euler angle transformation. I f the a i r c r a f t body axes are aligned w i t h standard North-oriented i n e r t i a l axes a t

e = 6 I 3/= 0 deg. then 6 and p m u s t change by 180 degrees t o maintain the

._ .

n n c CI m W 0 N v) "i c

-

I Y Y Q,

-

h n c c N v) I c Q!

Y h N m m I I Y 0 Y A

- n

d I Y N n 0 N N Y v Y m u) "i "i d

"

c V z LL CL W n n h m 0 h b.

N h I co ! - Y '9 A m I v m 8

--

'9 h .

m m 0 . a I Y ' 3

-

cum I O I m

-

X?

h 2 0 W

P

v N Y II L n m N v) m '9 * I VI 'U u) c, n 0 W L n L ru W n 7J Ln L c- co Ln h Y c1 c, L ?

4) v) m I N 7 Y

nu) -

In- n v) l n .

c I

s .a

Y (u '3 8

i

1 4 ) I x,d Y I n * CI

0 i

8 " Y Y * " u) h CS m N 2 m . .

* I 0 7 I - J m -U m I I X V u 0 L c, t, a Q. w n a J Q .

.x 0 w w *N W t 2 z n OI (0 n

=

I Y A

s

OD h m '3

'4 -

(u I Y I h

$

c Y E + L- Qo

8'

M C I 0 . c I c, V n A cn c (u CQ n a c Y cc 0: c h (D m L Y c c, 0 ) n 0 cn 0 " * m 0 cc v) a L r

-

(D

q

L L I cc W c, I Y L It h In 0 0 L) Y .c E . c c a 4 PI

.g c

cn n VI X 1 3 0, V >

-

U

.e -

- .

u l U 1 hU I c, W e L cn A cn cn h . c Q,

c I

c

_ I n 0

c u 0 0 .C n cn I c Y c5 I I c n * c

- f

m m 0 h m d t 9 ?

c ' f I d i

VI

t 3

cu I .r I C Y I u c, (u cn d t , L .L.

Q W t L I.- Y ..

Q) S I V V L L . I ? 4 .e? ,o

= L

-

c n r . ,

I

! I > t U c m '9, ,3

I

n 0, 0 n 0 m c -.

0 1

-

I- u) N '9 r ) .-( m * cv I '9 & Y) N W ?

-

0 .- =z v)(v y!

..

W consistency of the transformation as the a i r c r a f t X8 a x i s ~ o e s through v e r t i c a l . These l a r g e angle changes would be irposed i n t h e appropriate feedback paths and produce c o c k p i t motions which are d i s o r i e n t i n g t o the p i l o t : For example, t o slow dorm i n surge the p i l o t simply p u l l s back on t h e s t i c k t o bring t h e a i r c r a f t nose through v e r t i c a l . He doesn't conaand o r expect c o c k p i t r o l l o r yaw motions d u r i n g t h i s mneuver. U i t h Euler angle feedbacks based on t h e standard North-oriented i n e r t i a l axes the p i l o t w i l l experience u n c m n d e d c o c k p i t yaw and r o l l motions which ( i f c o n t r o l i s n ' t l o s t and/or the p i l o t doesn't punch o u t ) w i l l place him i n the o r i e n t a t i o n he expects. Analysis o f t h i s problem indicated t h a t uncomanded cockpit motions could be avoided i n hover by feeding back the i n t e g r a l s o f body a x i s r o l l , p i t c h , and yaw r a t e s as a t t i t u d e feedbacks. (Rlso, the r o t a t e d i n e r t i a l a x i s system discussed i n Section 2.9 could be applied.) Thus the a t t i t u d e feedback issue was resolved as follows: feedback the i n t e g r a l s o f body r a t e s i n t h e FCS hover d e and standard Euler angles i n the FCS conventional mode. I n the body r a t e i n t e g r a t o r s must be i n i t i a l i z e d t o equal Euler angles addition, upon switching t o hover mode. S i m i l a r l y , upon switching t o conventional mode, the t r i m systems must be r e i n i t i a l i z e d t o avoid d i s c o n t i n u i t i e s i n a t t i t u d e feedbacks.

Desired a t t i t u d e loop bandwidth was set a t 3.0 radlsec. This s e l e c t i o n was based on experimental evidence (references (1) and (m)) t h a t p i l o t s s t r i v e for closed loop bandwidths o f approximately 3.0 radlsec when they manually close the loop. This provides adequate separation between the f l i g h t path and o f the a i r c r a f t and allows the p i l o t t o a t t a i n reasonable e t t i t u d e modes manual closures o f the f l i g h t path c o n t r o l loops. I n a d d i t i o n t o reducing p i l o t workload, a 3.0 radlsec a t t i t u d e bandwidth a l s o provides good r e g u l a t i o n against distrubances.

Desired heave r a t e bandwidth was set a t 1.5 radlsec. S i m i l a r t o the a t t i t u d e bandwidth selection, t h i s r a t e bandwidth allows the p i l o t t o e a s i l y close the manual heave p o s i t i o n loop i n the desired bandwidth range o f 0.7 t o 1.0 rad/sec.

An issue o f lesser importance t o quantifying t h e baseline FCS was t h e

s p e c i f i c a t i o n o f parameter values f o r the p i l o t i n p u t shaping networks i n t h e r a t e conmand-attitude h o l d and a t t i t u d e ccmand systems. Even thou# these parameter values w i l l be established v i a the p i i o t e d s i m u l * t o r studies, i n i t i a l yguessm values are r e q u i r e d a t t h i s p o i n t i n the design process.

Therefore the f i r s t order l a g i n t h e a t t i t u d e comnand system i n p u t shaping network was s e t a t 4.0 radlsec i n accordance with Vought experience w h i l e t h e breakpoint o f the lead term i n the r a t e c m a n d - a t t i t u d e h o l d systems i n p u t shaping network was s e t a t 3.0 radlsec which was used i n reference (e). Also i n accTtdance w i t h reference (e) i n p u t c m a n d a u t h o r i t y was set t o - +I5 deg.

f o r the a t t i t u d e comnand systems and - +20 deglsec f o r t h e r a t e conrPand-attitude hold s y s t m s .

3.7.1 Longitudinal FCS Oevelopnrent The bascline c o n f i g u r a t i o n f o r t h e p i t c h c o n t r o l system i s shown i n f i g u r e 3-6. The values adopted f o r many o f the generic p i t c h c o n t r o l system parameters are evident i n a comparison of f i g u r e s 2-28 and 3-6. The baseline heave c o n t r o l system i s e s s e n t i a l l y the same as the generic system shown i n f i g u r e 2-30. % s t features of these cortfigurations have already been The functional descriptions which follow discussed i n Sections 3.3 and 3.7.

are intended as a review b u t provide a d d i t i o n a l d e t a i l s where required.

The forward path o f the p i t c h FCS consists of a s t r a i g h t gain ( K ) and qe

a p a r a l l e l i n t e g r a t o r ( g a i n - K

) t h a t provides automatic t r i m and qeI 1 boosts the low frequency gain o f the loop.

i s programed as a func- Kq t i o n o f airspeed. The feedbacks i n the hover &ode include p i t c h r a t e through a gain ( K I n t h e ) i n p a r a l l e l w i t h the i n t e g r a l of p i t c h r a t e (qINf).

qq conventional mode the feedbacks include p i t c h r a t e through Kq i n p a r a l l e l w i t h p i t c h angle (e). The p i t c h FCS has t w o p i l o t inputs, the l o n g i t u d i n a l s t i c k t r i m button ( 6 ) and l o n g i t u d i n a l s t i c k d e f l e c t i o n ( 6 L N ~ ~ ~ K ) .

“BUT I n the hover mode, ~ L N ~ T K i s i n p u t through a gain (k. ) and f i r s t order 4 C shaping network (time constant =TpIrCH). I n the conventional mode, ~ L N G S T K i s input through Kq and a p a r a l l e l i n t e g r a t o r ( g a i n = K C qcl ); 12c TpITcH i s zeroed. Thus, ~ L ~ S T K cannands are p r o p o r t i o n a l t o the i n t e g r a l of P i t c h r a t e (qINT ) i n t h e hover mode and t o p i t c h r a t e (q) i n the canventional mode. ‘Logic for i n i t i a l i z i n g t h e p i t c h r a t e i n t e g r a t o r , manual t r i m i n t e g r a t o r , and p i t c h i n p u t i n t e g r a t o r a t the FCS mode switch p o i n t i s based on t h a t indicated on f i g u r e 2-28.

The heave FCS i s operative o n l y i n the hover mode. I n conventional mode I n hover mode he the p i l o t c o n t r o l s t h r u s t d i r e c t l y w i t h manual t h r o t t l e .

normally c o n t r o l s heave (and thus t h r u s t ) through h i s heave r a t e c m a n d lever. Manual t h r o t t l e i s a v a i l a b l e d u r i n g hover but i t s use would l i k e l y be l i m i t e d t o emergency conditions r e q u i r i n g sudden l a r g e changes i n t h r u s t .

S i m i l a r t o t h e p i t c h FCS, t h e forward path o f the heave FCS has a s t r a i g h t

gain ( x z ) i n p a r a l l e l with an i n t e g r a t o r ( g a i n = K ) for automatic

0 Z e I t r i m acd low frequency gain boost. The feedback i s heave r a t e which i s compared w i t h the heave r a t e comnand l e v e r inputs t o form the forward path e r r o r signal. It w i l l be demonstrated i n Section 3.8 t h a t t h e performance o f both modes o f the p i t c h and heave FCS laws and gains developed here i s adequate. Thus there was no need t o i t e r a t e the l a w s and gains loop o f the FCS design procedure ( f i g u r e 3-1). Complete s p e c i f i c a t i o n of the SF-121 baseline p i t c h and heave FCS gains i s given i n Sections 3.8.3 and 3.8.5, respectively, of Volume 11.

3.7.1.1 Hover Mode System Analysis A r o o t locus sketch o f the p i t c h FCS hover mode loop closure a t Y A = 10 k t as a function of K The zero a t s = -0.2 = i s shown i n f i g u r e 3-7.

qe -K and p o l e a t t h e o r i g i n r e s u l t from t h e forward path compensation.

qeI1 The zero a t s = -2.0 = r e s u l t s from the p i t c h r a t e feedback gain

and was placed t o e f f e c t a good closed loop damping r a t i o (0.7 - 0.8) a t the

desired system bandwidth (approximately 3.0 rad/sec). With the except ion o f t h e elevon and p i t c h t h r u s t d e f l e c t i o n actuators both having poles a t s = -20, the other open loop poles and zeros are those o f the unaugmented a i r p l a n e

~INT/~PITC- t r a n s f e r function. As can be seen, the selected Kq

( = 10lrad) provides dominant closed loop r o o t s which appear t o frovide a larger than desired system bandwidth. As indicated by the closed loop J 23 frequency response ( f i g u r e 3-9). t h i s i s n o t t h e case. The q I I m / q 1 , equivalent closed loop bandwidth i s 2.8 radlsec which i s s l i g h t l y l e s s than des i r e d .

A root locus sketch of the heave FCS loop closure a t VA 10 k t with t h e p i t c h FCS hover mode loop closed i s shown i n f i g u r e 3-8. The forward path

gain (Kz ) v a r i e s along t h e locus. The zero a t s - -0.2 = -Kz and

e eI pole a t t h e o r i g i n r e s u l t from the forward path canpensation. The p o l e a t s = -5.0 represents t h e t h r u s t dynamics a t t h e t r i m t h r u s t s e t t i n g . The remalning

'open \oopm p o l e a t s =

i s the o n l y one of t h e i e / 6 " ~ ~ v ~ ) q 1 ~ , - q +

transfer f u n c t i o n poles n o t e f f e c t i v e l y cancelled by zeros. The designation, 0 e Z e / 6 ~ ~ ~ ~ I q 1 ~ , q + 6PITCH, i n d i c a t e s the HEAVE t r a n s f e r f u n c t i o n which r e s u l t s when the p i t c h FCS loop i s closed (id?. q I N T and q are fedback selected (- 500 l b l f t l s e c ) provides a

t o PITCH). The value of K

' e heave r a t e loop bandwidth of 1.41 radlsec which i s acceptably close t o t h e desired 1.5 radlsec bandwidth. This i s demonstrated by the closed loop a e frequency response i n f i g u r e 3-10.

2 / Z e 3.7.1.2 Conventional Mode System Analysis A r o o t locus sketch o f the p i t c h FCS conventional mode loop closure a t VA = 120 k t as a f u n c t i o n of K i s shown i n f i g u r e 3-11. The zero a t q,

s = -0.2 = xq and p o l e a t t k e o r i g i n r e s u l t from t h e forward path

e , , compettcation. The zero a t S = -2.0 = -1/K r e s u l t s from the p i t c h r a t e q9 a closed loop bandwidth o f feedback gain and was placed t o o b t a i n approximately 3.0 radlsec. With t h e exception o f the elevon and p i t c h t h r u s t d e f l e c t i o n actuators both having poles a t s = -20, the other open loop poles and zeros are those of the unaugmented airplane O/~PITCH transfer function.

Note the unstable s h o r t period pole which arises from the s t a t i c i n s t a b i l i t y designed i n t o t h e SF-121. AS confirmed by the e/ec frequency response ( f i 3 u r e 3-12), the selected K ( = 7.lrad) provides a 3.15 radlsec a t t i t u d e Qe bandwidth. The olec frequency response does not include the e f f e c t s o f the l o n g i t u d i n a l s t i c k shaping network [(s + 3.33)/s] which makes the conventional mode p i t c h FCS a r a t e connand-attitude hold system.

k

x

e 3

, Ilr

*

I I

a w ~

K

t

e

-I I 1 29 3.7.2 L a t e r a l FCS Develoynent Baseline c o n f i g u r a t i o n s for t h e r o l l and yaw c o n t r o l systems are shrwn i n f i g u r e s 3-13 and 3-14 r e s p e c t i v e l y . The values adopted f o r many o f t h e generic r o l l and yaw c o n t r o l system parameters are evident i n comparisons o f f i g u r e 2-27 and 3-13 and of f i g u r e s 2-29 and 3-14. Many features o f these c o n f i g u r a t i o n s have been discussed i n Sectlons 3.3 and 3.7, The f u n c t i o n a l d e s c r i p t i o n s which follow are intended as a review b u t provide a d d i t i o n a l d e t a i 1 s where required.

The forward path o f the r o l l FCS c o n s i s t s o f a s t r a i g h t g a i n (K ) and P a p a r a l l e l i n t e g r a t o r (gain = K ) that provides automatic t r i m an% peIl boosts the low frequency gain of the loop. K i s p r o g r a m d a s a p ?

f u n c t i o n of airspeed w h i l e K i r 1 function o f c o n t r o l system mode.

peI The feedbacks i n the hover mode i n c l u d e body a x i s r n l l r a t e through a gain (KP ) i n p a r a l l e l w i t h t h e i n t e g r a l of body a x i s r o ? l r a t e (PINT).

I n P the conventional mode the r o l l FCS feedbacks are s t a b i l i t y a x i s r o l l r a t e through Kp i n p a r a l l e l w i t h r o l l angle ( 9 ) .

P The forward path o f the yaw FCS i s i d e n t i c a l i n function t o t h a t o f the r o l l F c s except the gains are K r and Kr , S i m i l a r t o the r o l l e eI1 FCS, Kr i s programmed as a f u n c t i o n o f airspeed w h i l e Kr i s a e e,, I & f u n c t i o n o f c o n t r o l system mode!, The feedbacks i n the hover mode i n c l u d e body a x i s yaw r a t e through a gain (Kr ) i n p a r a l l e l w i t h t h e i n t e g r a i o f body r a x i s yaw r a t e kI& The feedbacks i n the conventional mode r e f l e c t r e - quirements imposed by the bare airframe l a t e r a l c h a r a c t e r i s t i c s of the SF-121 (Table 3-10)!, The a i r p l a n e has a coupled r o l l - s p i r a l mode and an inadequate r e l a t i o n between t h e numerator of the r s / 6 y a w t r a n s f e r f u n c t i o n and the Dutch r o l l mode. The coupled r o l l - s p i r a l mode i s decoupled by a l a t e r a l ac- c e b l a t i o n ( a ) t o 6 feedback through a gain (Ka ). The l a t t e r Y Yaw c h a r a c t e r i s t i c makes pure rs feedback i n e f f e c t i v e a i a yaw damper and r e -

s u l t e d i n the adoption of a pseudo - d ($ - (g/VA) 4 - r s ) t o 6yaw feed-

A The use o f B as a yaw damper as w e l l as a t u r n coordinator i s described back, i n reference ( e ) .

d I[

!“kl

‘7 - I r-

t t

W 5’

.

The l a t e r a l F C S has four p i l o t c o n t r o l l e r i n p u t s - l a t e r a l s t i c k t r i m b u t t o n (6p ), pedal t r i m ( 6 ), l a t e r a l s t i c k d e f l e c t i o n BUT ‘BUT 6PED). The r o l e s of these i n p u t s are a ( ~ L A T S T K ) , and pedal d e f l e c t i o n f u n c t i o n o f F C S mode: I n t h e hover mode, the r o l l F C S receives i n p u t s from while the yaw F C S r e c e i v e s i n p u t s from 6LATSTK and

PED and 6r

BUT

In t h e conventional mode, the c o n t r o l l e r r o l e s are reversed -

pBuf become become yaw F C S i n p u t s and 6LATSTK and

PED and 6r

r o l l F C S i n l ! k . The r o l l F C S i s r a t e comnand-attitude%ld i n both modes.

Thus, 6pEO i n hover and 6l-ATSTK i n conventional are i n t e r f a c e d with t h e F C S through a gain (KP ) and a p a r a l l e l i n t e g r a t o r ( g a i n = r o l l C ). The yaw F C S i n conventional mode i s a pseudo-; comnand system.

Kpc* The pedals are thus i n t e r f a c e d with t h e yaw F C S through a gain (Kr ) and C i n p u t f i l t e r ( t i m e constant = vyAw). Note that, except f o r d e l i b e r a t e s i d e s l i p s , the p i l o t should n o t have t o use pedals i n the coventional mode.

In hover mode the Yaw Fcs is a ‘INTc comnand system; 6LATSTK i s i n t e r f a c e d through Kr and the i n p u t f i 1t e r .

C Logic f o r i n i t i a l i z i n g the yaw and r o l l r a t e i n t e g r a t o r s and the t r i m i n p u t s a t the FCS mode switch p o i n t i s based on t h a t i n d i c a t e d on f i g u r e s 2-27 This l o g i c helps t o smooth the mode change t r a n s i e n t s . and 2-29. I t s effectiveness i s demonstrated i n Section 3.8.

It w i l l a l s o be shown i n Section 3.8 t h a t the performance o f both modes o f the yaw and r o l l FCS laws and gains developed here i s adequate. Thus there was no need t o i t e r a t e the laws and gains l ~ o p of the FCS design procedure ( f i g u r e 3-1). Complete s p e c i f i c a t i o n o f the SF-121 b a s e l i n e yaw and r o l l FCS gains i s given i n Sections 3.8.2 and 3.8.4, r e s p e c t i v e l y , o f Volume 11.

3.7.2.1 Hover Mode System Analysis A r o o t locus sketch o f the yaw FCS hover mode loop closure a t VA = 10 k t i s shown i n f i g u r e 3-15. The forward path gain (K,. ) v a r i e s along the ‘ e locus. The zero a t s = -0.9 = - K r and one o f the poles a t the o r i g i n e I 1

i

d

d

w

D

d gr

t

X 8 )

a r i s e from t h e forward path compensation. The zero a t s = -2.0 = - l / K r

r e s u l t s from t h e body a x i s yaw r a t e feedback 3nd was placed t o provide hood

loop closure properties. The actuator p o l e a t s - -20. represents t h e

dynamics o f t h e rudder and yaw t h r u s t d e f l e c t i o n actuators. The remaining open l o o p poles and zeros are those of the unagumented a i r p l a n e ~ I N T / ~ ~ M t r a n s f e r function. The selected closed l o o p g a i n (Kr = 13/rad) i n c d i n a t i o n with the r o l l FCS loop c l o s u r e (depicted f n f i g u r e 3-16) i s demonstrated by the rINT/rINT frequency respwc-2 ( f i g u r e 3-17) t o produce an a t t i t u d e bandwidth'of 3.24 radisec.

The r o o t locus o f the r o l l FCS hover mode c l o s u r e a t VA = 10 k t with t h e yaw FCS loop closed i s shown i n f i g u r e 3-16. E q u i v a l e n t l y t o the yaw loop, the r o l l l o o p forward path g a i n (Kp ) v a r i e s along t h e locus; the zero a t s = -0.8 = -K and the p o l e a t t8e o r i g i n a r i s e from the forward path p e I 1 compensation; and the zero a t s = -2.0 = - l / K p r e s u l t s from t h e body a x i s The remaining "open loop"Ppoles and zeros are those o f r o l l r a t e feedback.

t r a n s f e r f u n c t i o n which do not the PIN+R&L( I NT lr + 6~ AW Actuator dynamics are n o t i n d i c a t e d i n the e f f e c t i v e l y cancel each other.

The selected closed loop gain locus sketch due t o t h e i r n e g l i g i b l e influence.

( K = 6 / r a d ) i s demonstrated by the PINT/PINT frequency response Pe ( f i g u r e 3-18) t o produce an a t t i t u d e Oandwidth'of 3.32 rad/sec. This frequency response p l o t does n o t include the e f f e c t s o f the pedals shaping

network [ i s + 3.33)/s] which makes the hover mode r o l l FCS a r a t e

comnand-attitude h o l d system.

3.7.2.2 Conventional Mode System Analysis As mentioned above, the SF-121 has a coupled r o l l - s p i r a l mode a t the airspeeds considered i n t h i s FCS development. T r a d i t i o n a l design guidelines f o r l a t e r a l c o n t r o l l a w development ( a l s o the f l y i n g q u a ? i t i e s s p e c i f i c a t i o n ) p r o h i b i t t h i s coupling. The f i r s t task i n the l a t e r a l FCS conventional mode development t h e r e f o r e was t o decouple the r o l l and s p i r a l modes. This was ar-omplished by a l a t e r a l a c c e l e r a t i o n ( a ) t o YAW feedback.

Figure 3-19 Y h c I m . .

- 3 ' 2

*04 i

f i g u r e 3-19. Root Locus o f Lateral Acceleration t o dYAw Loop Closure ( V A s 120 k t ) shows a r o o t locus sketch of t h i s 100P Closure a t VA 120 k t . The l a t e r a l acceleration gain (Ka ) v a r i e s along t h e locus. Note t h e formatdon o f the decoupled e q u i v a l e i t r o l l and s p i r a l modes and the c h a r a c t e r i s t i c decrease i n Dutch r o l l damping which accompanies l a t e r a l acceleration feedback.

Also mentioned above was t h e a p p l i c a t i o n of psuedo-8 (8. = (g/vA) 6 - rs)

feedback f o r increasing Dutch r o l l damping and p r o v i d i n g t u r n coordination.

T r a d i t i o n a l l y these functions are provided by a washed o u t s t a b i l i t y a x i s yaw r a t e feedback. The effectiveness o f t h i s feedback depends on the r e l a t i v e l o c a t i o n of the complex zeros of the r s / 6 y ~ t r a n s f e r f u n c t i o n numerator and the Dutch r o l l mode poles. If these zeros and poles are near the j, a x i s o r i n the r i g h t h a l f plane o r the frequency of the zeros i s greater than 0.4 t o 0.5 t h a t o f the poles, the yaw r a t e feedback w i l l be i n e f f e c t i v e . Both these d e t r a c t i n g conditions are displayed by the SF-121. Reference ( e ) develops and demonstrates how pseudo-; feedback i s an appropriate s u b s t i t u t e f o r washed out yaw r a t e .

A Figure 3-20 provides a r o o t locus sketch of the 6 t o 6yAw loop closure a t 120 k t w i t h the a t o 6yAw loop closed.

The forward path gain (Kr ) Y e The Zero a t S = -0.2 = -Kr v a r i e s along t h e locus.

and the pole a t eI1 the o r i g i n are contributed by the forward path compensation. The remaining open loop zeros are the zeros of the f / d y A w t r a n s f e r f u n c t i o n w h i l e the remaining poles are the equivalent l a t e r a l d i r e c t i o n a l modes created by the ay t o 6 y ~ w loop closure. Note t h a t the h t c h r o l l damping i s increased and t h a t an unstable low frequency mode i s developed by t h i s closure. The I unstable mode w i l l be s t a b i ' i i z e d by the r o l l FCS loop closure. As i s cc\ demonstrated i n f i g u r e 3-22, the gain selected f o r 6 loop closure (Kr = l . l / r a d / s e c ) i n combination w i t h the r o l l FCS loop closure (sketched O n f i g u r e 3-21) produces a body a x i s l a t e r a l v e l o c i t y ( v

v ~ 6 ) t o pedal (or $1

frequency response which i s s i m i l a r t o t h a t of an unaugnented a i r p l a n e having uncoupled r o l l and s p i r a l modes and a w e l l damped Dutch r o l l made.

The f i n a l l a t e r a l conventional mode loop closurc, the r o l l FCS, i s depicted by the r o o t locus sketch of figure 3-21 for VA , = 120 k t . The N o t e :

x

e

Figure 3-20. Root LOCUS o f Pseudo-; t o 6yAw LOOP Closure With a , , t o 6 y ~ ~ Loop Closed ( V A = 120 k t ) w Y I I

b

8'0 X e t 1 / I

U

" 3 I

fOrward Path g a i n (KP ) v a r i e s along t h e locus. The zero a t s = -0.2 -

-K and t h e p o l e a ! the o r i g i n are c o n t r i b u t e d by the forward path peI1 compensation. The zero a t s = -3.0 = - 1 / K res:;its from t h e s t a b i l i t y pP a x i s r o l l r a t e feedback ?no was placed t o e f f e c t a reasonable loop closure.

The actuator p o l e a t s = -20 represents the elevon a c t z a t o r s dynamics. The

e f f e c t s of t h e dynamics o f the RCS and i t s actuators are n e g l i g i b l e t o t h i s loop closure. The remaining "open loop" poles and zeros are those o f the

~ / ~ R o L J , , 9 + 6 y ~ i t r a n s f e r function. As i s demonstrated by the

919, freqgency reponse ( f i g u r e 3-23), the gain selected f o r r o l l FCS loop closure (K = 4/rad) produces an a t t i t u d e bandwidth o f 2.7, radlsec which Pe i s s l i g h t l y l e s s than the desired 3.0 radlsec. This frequency response p l o t does n o t i n c l u d e t h e e f f e c t s o f the l a t e r a l s t i c k i n p u t shaping network [(s + 3.33)/s] which makes the conventional mode r o l l FCS a r a t e comnand-attitude h o l d system.

3.8 FCS Performance Evaluation The c o n t r o l laws and gains established by the analyses described i n Section 3.7 were incorporated i n t o VATLAS. Nonlinear time reponses t o various cockpit c o n t r o l l e r inputs and pseudo-pilot flown scenarios were then calculated t o evaluate the FCS performance. Ten cases selected f o r evaluation and demonstration of t h i s performance are as follows: 1. LC j i t u d i n a l sticlr doublet a t VA I 120 k t connMnding 10 deg/sec p i t c h r a t e f o r 0.7 sec followed by -10 deglsec f o r 0.7 sec ( f i g u r e 3-24) L a t e r a l s t i c k pulse a t VA = 120 k t cotmanding 20 deg/sec r o l l r a t e 2.

f o r 1.4 sec ( f i g u r e 3-25)

3. Pedal step a t VA 120 i c t conmanding 4 deglsec o f pseudo i ( f i g u r e

3-26 1

4. Longitudinal s t i c k doublet a t v~

10 k t comnanding 10 deg of QINT for 0.7 sec followed by -10 deg f o r 0.7 sec ( f i g u r e 3-27) L a t e r a l s t i c k doublet a t VA = 10 k t commanding 10 deg o f 'IHT f o r 5 .

0.7 sec followed by -10 deg f o r 0.7 sec ( f i g u r e 3-28) 6. Pedal pulse a t VA = 10 k t -,manding 20 deglsec r o l l r a t e for 1.4 sec ( f i g u r e 3-29) 7 . Heav r a t e c o n t r o l l e r doublet a t VA 10 k t comnanding -10 f t / s e c heave r a t e f o r 3.0 sec followed by 10 ft/seC for 3.0 sec ( f i g u r e 3-30) Mode switching transient. A i r c r a f t trimned i n a 0.lg decelerating 8.

0.5 m i l e t u r n a t vA

62 k t , then simultaneous l o n g i t u d i n a l and l a t e r a l s t i c k pulses o f 0.7 sec durat'on comnanding 10 deg/sec p i t c h arid r o l l rate: are i n p u t 0.3 sec i n t o the run ( f i g u r e 3-31) Psuedo-pilot flown t r a n s i t i o n i n i t i a t e d a t VA = 200 k t ( f i g u r e 3-32) 9.

Pseudo-pilot flown t u r n over a spot (i.e. stationkeeping) i n a 35 k t 10.

wir,d ( f i g u r e 3-33) Each case i s discussed i n some d e t a i l i n Sections 3.8.1 t o 3.8.10.

The doublet, step, and pulse inputs f o r cases 1 t o 7 were g i v t n s u f f i c i e n t mag. i t u d d t o induce c o n t r o l sys,an s a t u r a t i o n and/or exercise other s i g n i f i - cant system n o n l i n e a r i t i e s . As such they simulate f a i r l y vigorous p i l o t use of the SF-121 and i t s c o n t r o l system. Other than the f a c t t h a t 0.7 sec i s approximately t w i c e the time constant o f the a t t i t u d e loops there i s no r a t i o n a l e f o r s e l e c t i n g m u l t i p l e s o f 0.7 sec for pulse and doublet lengths.

S i m i l a r l y 3.0 sec f o r the heave r a t e doublet i n p u t i s approximately t o u r times the time constant of the heave r a t e loop. Case 8 demonstrates the system c a p a b i l i t y t o maintain c o n t r o l i n tire presence o f l a r g e simultaneous a t the mode switch speed. Cases 9 and 10 demonstrate m u l t i - a x i s p i l o t i n p u t s the c a p a b i l i t i e s o f t h e VATLAS pseudo-pilot l o g i c and the c o n t r o l system f o r two operational scena-'r)s f o r the a i - c r a f t .

3.8.1 Case 1 - Longitudinal S t i c k Doublet a t VA = 120 kt.

The p i t c h r a t e response i s e s s e n t i a l l y l i n e a r u n t i l the doublet reverses a t 1 .O sec ( f i g u r e 3-24). The 1 inear response o\.a-shoots i t s commanded value This i s consistent with the p i t c h loop o f 10 deglsec by approximately 20% frequency response ( f i g u r e 3-12) which i n d i c a t e s t h a t :he system i s less than c r i t i c a l l y damped (i.e. i t has a 2.5 db peak which i n d i c a t e s a damping r a t i o o f approximatzly 0.4). A t 1.0 sec the symnetrical elevon comnand becomes saturated due t o the normalized p i t c h c o n t r o l becoming < -1.0. From t h i s p o i n t on the response i s nonlinear. The r e s u l t i n g response i s s t a b l e and complete; the doublet maneuver w i t h considerable lag. Coupling i n t o the l a t e r a l degrees o f freedom i s minimal.

3.8.2 Case 2 - L a t e r a l S t i c k Pulse a t VA = 120 k t

The l a t e r a l s t i c k puls.: comnands a f a i r l y r a p i d e n t r y t o a 28 deg banked turn. A stescy s t a t e t u r n r a t e of approximately 4 deglsec i s generated by i n d i c a t e t h a t the t h i s iiawuvei.. The t i m e h i s t o r y traces shown on f i g u r e 3-25 28 degree r - ~ l l angle i s a t t a i n e d w i t h no overshoot b u t reduces a degree o r so when the l a t e r a l s t i c k cornnard i s released due t o the overshoot i n the r o l l r a t e response. Approximately 4 deg o f 6 (adverse yaw) and -0.159 l a t e r a l a c c e l e r a t i o n are generated d u r i n g the t u r n e n t r y . These are r a p i d l y d r i v e n t o system when the near zero (thus coorLinating the t u r n : oy the yaw c o n t r o l desirzd r o l l angle i s a t t a i n e d and held.

T

c T

. -

A E (c a f ?

n O D b J N r U +--------.I 0. 2. b . 8 . e. I O . 12. I b . 18.

T I R E .SEC T I R E .SEC F i w 2.24. Longitudinal Stick bublrt k m r c a t kh 120 kt ( M e e t 7 of 3 ) I u b u a c4 J 120 k t (YHlt 3 of 3 ) Longttuoinrl Stick Doublet ReSDonsc a t VA F l g m 3-24.

*

0 j /

- T E!

'y n!

0 bf-

c S o

0. 2. 1. a. 8 . 10. 12. 1). 16 -

IIAE.8EC F I g u n 3-25. L a t e r a l S t i c . %lrc Resmw 4 : V , I 120 tt (Sheet 1 of 3 ) O y!

N W

4a

L

a

0, ? 1 U W n O W N 0 . 2. 4 . e. 10. 12. 1 4 .

T I nE .sEc LLTERLL S T I C R PULSE LT VR=120 Kf F t p 3-25. l a t e r a l Stick Pulse Respanse a t VA 120 k t (Hrt 3 O f 3 ) IS3 Coupling i n t o the l o n g i t u d i n a l degrees of freedom i s apparent and was anticipated. The steady s t a t e p i t c h r a t e i s required by t h e kinematics o f the steady turn. The reduced (from t r i m ) steady s t a t e p i t c h angle is due t o the pit;' c o n t r o l system e r r o r r e t u r n i n g t o zero a t steady state; since both p i t c h r a t e and p i t c h angle are fed back and steady s t a t e p i t c h r a t e is non zero w i t h a p o s i t i v e value, steady s t a t e p i t c h angle must reduce t o keep the p t ch c o n t r o l system e r r o r zero. Increased p i t c h angle during t u r n e n t r y s caused by the loss of elevon effectiveness a t l a r g e deflections; t u r n e n t r y requires increased l e f t elevon d e f l e c t i o n and reduced r i g h t elevon deflection thus producing a nose up moment. A nose down moment i s produced when the d i f f e r e n t i a l elevon d e f l e c t i o n is removed upon a t t a i n i n g the desired r o l l angle.

Overall, there are no apparent s t a b i l i t y o r c o n t r o l problems o r unantici- pated motions i n the a i r c r a f t response t o the l a t e r a l s t i c k pulse.

3 . 8 . 3 Case 3 - Pedal Step a t VA = 120 k t

The pedal step comnands the a i r c r a f t t o perform a wings l e v e l ( 4 = 0) skidding ( 6 f 0) t u r n (r f 0). The pedal step on figure 3-76 i s l a b e l l e d as a

pseudo-; command input. This i s consistent w i t h $ feedback o f the yaw control

system. Since the a t t i t u d e hold feature o f the r o l l control system keeps wings level, the yaw control system feedback becomes yaw r a t e and the pedal becomes a yaw r a t e c o n t r o l l e r .

The 6 response shows the effects Of the two "shelf" V/6, frequency response ( f i g u r e 3-22). The magnitude of the frequency response has a steady s t a t e l e v e l ( " s h e l f " ) o f 57 db which extends t o approximately 0.02 radlsec, then the response drops t o another "shelf" o f 42 db which extends t o approximately 1.0 radlsec where the response s t a r t s i t s c h a r a c t e r i s t i c drop off t o -oodb. Thus the 6 time response should and does demonstrate two d i s t i n c t modes; a shoi t term response wherein 6 reaches approximately -4 deg i n 2.5 sec superposed on a long term response which appears as a d r i f t . The yaw r a t e response has a s i m i l a r bimodal response.

e

V ?

a - i l e L w 9, h 3.

W Y f P 0. 2 . b . a. I. I O * 12. LI. 16.

TlIlEtSEC

F i g - n 3-26. PIdri Step Uespmrc st Vk - 120 kt (%et 1 of 31

* ! i l d I - - V - 0 . 2 . 4 . 6. flnt.5fC 8 . 10. 12. 1 4 . 18. 4

Figure C26. Pedal Stro f!ewonrr a t VA - 120 k t (Wet 2 o f 3 )

1% t i v e ..

g d Z 2

a

A Another i n t e r e s t i n g aspect o f f i g u r e 3-26 i s the e f f e c t o f decreased elevon effectiveness a t l a r g e d e f l e c t i o n s which was discussed i n Section . . 8 . 2 . As 8 increases, t h e r o l l moment r e q u i r e d t o maintain wings l e v e l increases because of t h e a i r c r a f t d i h e d r a l e f f e c t (C1 ). This i s seen i n

t h e ROLL trace. The p i t c h up due t o t h e elevon effectiveness loss must be

countered by i n c r e x e d nose down p i t c h moment as shown by the 6 p 1 ~ c ~ trace.

Note t h a t the a i r c r a f t i s n e a r l y out o f nose d w n p i t c h c o n t r o l ( d P r T C H % -1.0) and running out o f negative toll c o n t r o l a t the end o f t h e 15 sec time h i s t o r y .

A short time more and t h e a i r c r a f t would be i n c o n t r o l saturated s i t u a t i o n .

3-26 demnstrates a 6 l i m i t a t i o n i n the t r a n s i t i o n region o f Thus f i g u r e f l i g h t ; a n o t uncomnon c h a r a c t e r i s t i c o f V/STOL a i r c r a f t .

3.8.4 Case 4 - Longitudinal S t i c k Doublet a t VA 10 k t

The l o n g i t u d i n a l s t i c k doublet comnands the a i r c r a f t t o p i t c h through v e r t i c a l tnen down through triq and then r e t u r n t o t r i m .

Since i s c o n t r o l l e d by D i t c h a t t i t u d e (qrNT) t h e i n t e n t o f t h i s maneuver i s t o decrease Xe then increase i t beyond t r i m Xe a?d then r e t u r n it t o near t r i m . Figure 3-27 shows t h a t the desired p i t c h m a .aJvcr i s performed with

some s a t u r a t i o n of t h e p i t c h controls; )6plfCHI exceeds 1.0 and 1 5 1 i s

l i m i t e d t o 15 deg. The desired e f f e c t on Xe i s not ob;ained and h e r e i n l i e s t h e aost d i s t i n g u i s h i r i g f l y i n g q u a l i t i e s c h a r d c t e r i s t i c o f hover c o n t r o l o f the SF-121. (The c h a r a c t e r i s t i c i s indigenous t o any VATOL a i r c r a f t employins a f t end t h r u s t d e f l e c t i o n f o r moment c o n t r o l . ) Xe i n i t i a l l y inc-eases

*- -

before proceeding t o f l l l o w the desired response: i.e. the Xe anLa likewise, nz response t o p i t c h a t t i t u d e are i n i t i a l l y i n the wrong d i r e c t i o n . f 8 e reason f o r t h i s i s t h a t t d i x r e a s e p i t c h angle t h e t h r u s t must d e f l e c t forward ( i n a dire.-.:ion t o increase X e ) i n i i i a l l y t o produce a nose up p i t c h mcment. This i s a nonainimum phase c o n t r o l c h a r a c t e r i s t i c and e i s i n d i c a t e d d u r i n g c o n t r o l system analysis by zeros o f the X t / , 3 L N ~ ~ T K transfer f u n c t i o n l y i i l g i n the r i g h t h a l f o f Lhe s-plane. Thus the SF-121 has the p o t e n t i a l f o r i . l s t a b i l i t y and PI0 ( p i l o t induced o s c i l l a t i o n s ) if the p i l o t aggressively pursues p o s i t i o n c ' n t r o l o f the airplane. The a d d i t i o n b f p i t c h HCS j e t s a c t i n g as a f o r c e couple would e l I .,nate *.his tende-cy and ailow p i t c h t h r u s t I e f l e c t i o n t o be used d s a d i r e c t f o r c e c o n t r o l .

8 & i L U (Y

c - 3

T

8. 6 , IO. 12. 14. 16 TIRE .SEC

Figure 3-27, Longltudlnrl S t i c k Doublet I)rlpanre &t VA - IO k t (Hnt 2 of 3)

L .

T t ) ( c . ~ C Flgure 3-27. Lonqltvdinal S t i c k Doublet Rcrponsc a t VA I 10 k t (Sheet 3 of 3 ) the l o n g i t u d i n a l s t i c k doublet response a l s o demonstrates t h a t there i s a modicum o f l a t e r a l coupling b u t f a i r l y s i g n i f i c a n t through a n t i c i p a t e d heave coupling. Thrust d e f l e c t i o n reduces the v e r t i c a l t h r u s t component and t h e a i r c r a f t begins t o s i n k (ze > 0). the heave c o n t r o l system provides e appropriate t h r u s t c o r r e c t i o n s t o d r i v e t h e heave r a t e back t o t r i m (Ze I 0). Note t h a t the a i r c r a f t w i l l s i n k f o r p i t c h c o n t r o l inputs i n e i t h e r d i r e c t i o n from t r i m . Should i t prove annoying t h e heave coupling can be a l l e v i a t e d by a crossfeed from 6PITCH t o t h r u s t cmmnd.

3.8.5 Case 5 - L a t e r a l S t i c k Doublet a t VA I 10 k t

The l a t e r a l s t i c k doublet response 1s the l a t e r a l dual o f the l o n g i t u d i n a l s t i c k doublet response. The f o l l o w i n g verbal and spnbology replacements inserted i n Section 3.8.4 w i l l make the discussion generally applicable as w e l l t o the time t r a c e o f f i g u r e 3-28: P o 'e p i t c h 1 i n Sectioq 3.8.4 w i t h Rep1ace &PITCH ~ L A T S T K n

.'

c ycg The l a t e r a l response d i f f e r s as a dual from the l o n g i t u d i n a l response only i n t h a t ye, and subsequently 6, do not r e t u r n t o zero ( t r i m ) a t the end of the e m m m e r whereas 'e, t h e l o n g i t u d i n a l dual, does. The d i f f e r e n c e stems from the fact t h a t the fuselage t i l t s t o the r i g h t f a r t h e r and longer than it does t o the l e f t during t h e maneuver ( L e . r I N T i s p o s i t i v e for a longer t i m e than i t i s negative and a t t a i n s l a r g e r p o s i t i v e magnitudes). Since Ye i s proportional t o the integral of rlNT it should, and does, have a p o s i t i v e Since the a i r c r a f t i s now moving o b l i q u e l y value a t the end o f the maneuver.

through t h e a i r mass, i t also has a steady s t a t e 8 .

O W E A ?

Et TIRE .3LC Figure 3-28. L 4 t r a l Stick Ooublet P a w n s @ a t VA I 10 k t (Sheet I o f 3 ) 1 U ! ?

I 0 . e. I O . 19. 14. 16.

T ?

c) l T ~ ~ L . S E C

Figure 3-28. L a t e r a l Sttck Doublet Rcwonrr a t VA - IO k t (mt 3 of 3 )

WY ~

3.8.6 Case 6 - Pedal Pulse a t V4 10 k t

The pedal pulse coarnands the a i r p l a n e t o r o t a t e 28 deg around the Xs a x i s a t a r a t e o f approximately 20 deglsec. This maneuver appears t o t h e p i l o t as a c o c k p i t yaw t o the l e f t . As indicated by f i g u r e 3-29, the maneuver i s performed with no c o n t r o l saturation, n e g l i g i b l e coupling i n t h e yaw degree o f freedom, and noticeable, b u t expected, coupling i n the heave, surge, and p i t c h degrees o f freedom. The r o l l c o n t r o l power f o r t h i s maneuver i s provided by t h e RCS j e t s . The RCS has a demand bleed arrangement and thus, when r o l l c o n t r o l power i s required, t h r u s t w i l l decrease. I n a d d i t i o n t h e RCS j e t s are located a f t o f the cg and t h r u s t along t h e a i r p l a n e p o s i t i v e XB a x i s such t h a t a nose up moment and small p o s i t i v e surge f o r c e (negative The reduction i n t h r u s t produces a decrease i n nz ) are generated.

> 0). The 2 , i s corrected by t h e nxcg and establishes a sink r a t e (Ze hegge c o n t r o l system. S i m i l a r l y the p i t c h moment e f f e c t s are cancelled by t h e p i t c h c o n t r o l system. The surge force i s not c o n t r o l l e d and the airplane d r i f t s t o a s l i g h t l y higher airspeed f o l l o w i n g completion o f the maneuver.

Note t h a t the d i r e c t i o n o f heave, surge, and p i t c h coupling i s the same regardless o f the d i r e c t i o n o f r o l l con+rol power application.

I n general, the l o n g i t u d i n a l coupling displayed by the pedal pulse response i s t y p i c a ? o f RCS - equipped airplanes. Should it prove annoying, the c u l p r i t can be eliminated o r a l l e v i a t e d by one o r more o f the following modifications: 1. A l l e v i a t e p i t c h coupling by r e l o c a t i n g the RCS j e t s nearer t h e cg or by a t o PITCH crossfeed.

Eliminate heave coupling by a continuous b 2. eed RCS but a t the expense o f reduced t h r u s t capabi 1 ity.

A l l e v i a t e heave coupling by a crossfeed of 3. 6 ~ a ~ t o t h r u s t command.

3.8.7 Case 7 - Heave Rate C o n t r o l l e r Doublet a t VA = 10 k t

The heave r a t e c o n t r o l l e r doublet commands the airplane t o e s t a b l i s h a 10 e f t l s e c r a t e of C l i m b (Ze I -10 f t l s e c ) followed by a 10 f t l s e c sink r a t e ?

0 . 2. 4. 1. 10. 12.

figure 3-29, Pedal Pulse hsponsr a t VA I 10 k t (Sheat 1 o f 3 ) I67 e

i

s

0 - t 4 . e. 0 . IO. 12. t 4 . t o .

0, P ’ 1t)rL.SLC figure 3-29. Ped11 Pulre krponrc a t V I 10 k t (Sheet 3 of 3 ) e ( 2 , I 1 0 ftlsec) and return to trim (figure 3-30). The mast significant feature of this response i s the thrust dynamics shown by the trace o f the thrust before (B4) correction for RCS coupling. Since time constant increases

and the deceleration limit decreases as thrust level decreases the thrust

response is slower when, at the same trim speed, establishing a sink rate, arresting a climb, or changing from climb to sink than it i s when establishing a climb, arresting a sink, or changing from sink to climb.

Coupling into the lateral degrees of freedom was negligible during the maneuver and not worth showing in the traces. Coupling into the surge and pitch degrees of freedom is small but noticeable; the appropriate tracc ; have been included. Overall, the response is smooth, stable, and essentially single degree of freedom.

3 . 8 . 8 Case 8 - Mode Switching Transient

To investigate the transients which occur at the switch at 60 kt airspeed from conventional t o hover FCS modes, the airplane was trimmed at 62 kt in a 0.5 mi radius right turn while decelerating at 0 . l g along a constant altitude flight path. At 0 . 3 sec into the time history the stick was deflected aft and right to impose simultaneous 10 deglsec positive pitch and roll rate commands on the airplane. These stick commands were held for 0 . 7 sec and released and should increase airplane pitch and roll angles by approximately 7 degrees The traces for this maneuver are shown in figure 3-31.

each.

The 6 and e traces show that the desired maneuver was performed and nct cancelled or altered by changing FCS modes. Control saturation is displayed

only by PITCH. It exceeds -1.0 for a short time following the release of

the stick input. The mode switch occurs approximately 1 . 3 sec into the run.

It is marked by rapid changes in ROLL, 6yAw, 6pITCH. ny , and

thrust comnand (i.e. the heave control system is activat68) with those in The pilot will YAW, nyc , and thrust command being fairly large.

likely notice the n , which reverses from -.OS9 to .05g, and 6 y W ,

YC ! !

which commands a yaw 8cceleration step approximately -0.5 rad/sec to be applied to the airplane, since these are unexpected accelerations. He will Io N TINE .tEC HEAVE RATE COMTROLLLR OOUBLET vA=io K T

F l g m 3-30. L a v e Rate Controllr hublet Response rt VA - 10 k t (SMCt 1 of 2 )

in

I

i

t fi PP U E - 4 'p n?

-I c c t " .

A 0 a c Q U c Mote: Airplane t r i m a t 62 k t i n a 0.5 m i radius r i g h t turn *hllc decelcratlng a t 0.19 along a constant a l t i t u d e f l i h t path.

t 4 - L +

t

* - ?

a P

s

also n o t i c e the t h r u s t increase t o a r r e s t the sink r a t e established by the s t i d t inputs. P i l o t e d simulation studies should determine whether these switch t r a n s i e n t e f f e c t s are annoying. For n o w it sufficies t o say t h a t the transients are stable, controllable, and, w i t h the few exceptions noted above, r e l a t i v e l y smooth and Fredictable.

3.8.9 Case 9 - PseudWPilot F l o m T r a n s i t i o n

The pseudo-pilot flown t r a n s i t i o n ( f i g u r e 3-32) demonstrates the capabili- t i e s o f the pseudo-pilot t r a n s i t i o n equations d e t a i l e d i n Section 2.10.2 and provide f u r t h e r substantiation o f the s t a b i l i t y and c o n t r o l l a b i l i t y o f the airplane through the mode switch region. The t r a i l s i t i o n i s i n i t i a t e d by Psuedo-pilot's l o n g i t u d i n a l s t i c k cGmnands r e t a r d i n g the t h r o t t l e t o i d l e .

are b a s i c a l l y open loop i n t h a t they are calculated w i t h the a i d o f a t a b l e o f t r i m p i t c h angles v s airspeed. The s t i c k camands are i n i t i a l l y proportional t o p i t c h r a t e and become proportional t o p i t c h angle a t the mode switch Psuedo-pilot's t h r o t t l e v a r i a t i o n s are s i m i l a r l y open loop being point.

determined from a t a b l e o f t r i m t h r o t t l e settings vs airspeed. Even though pseudo-pilot has no inputs t o the r o l l o r yaw control systems, the t r a n s i t i o n i s w e l l behaved l a t e r a l l y . It can thus be i n f e r r e d t h a t the baseline FCS w i l l enable the t r a n s i t i o n t o be flown w i t h l o w p i l o t workload.

The mode switch, which occurs approximately 56 sec i n t o the t r a n s i t i o n , i s accompanied by noticeable r a p i d changes i n 6PITCH, 6 y ~ u , 6RmL, and

. The change i n "ITCH i s expected because o f the change o f command

ny f u @ t i o n o f the l o n g i t u d i n a l s t i c k w h i l e those i n iJYAw, "RL, and

ny are unerpected. Thrust command, and consequently, nx , a l s o

chgige r a p i d l y , not unexpectedly, because the heave c ~ n t r o ~ ~ s y s t e m has been activated and imnediately attempts t o a r r e s t the 10 f t l s e c sink r a t e which has developed. As discussed i n Section 3.8.8 any annoyance r e l a t e d t o these switch t r a n s i e n t e f f e c t s can best be judged during a p i l o t e d simultion.

3.8.10 Case 10 - Pseudo-Pilot Flown Turn Over a Spot i n a 35 kt Wind

The pseudo-pilot flown t u r n over a spot i n a 35 k t wind ( f i g u r e 3-33) laws demonstrates the c a p a b i l i t y o f the pseudo-pilot stationkeeping control t 1.

P

v I 0. 10. t o . 30. 40 60. 80. 00.

?

m

t

C .

c a Ed

-

f

E?

Y o x h 0 1 w -.

3 4

Fipurr 3-32. PseUdpPIlot F l o w Transition (Sheet 2 o f 3 )

f 1

f

i . 0

0 -

a

b d c o

a"*

i ,, Note: Airplane t r i m e d I n I hover 6 u i I n 4 35 k t head wind.

ef

t .

0 4 I figure 3-33. Pscudo-Pilot F l m Tu-n Over 4 Spot I n 4 35 k t Wind (Sheet 1 o f 5 ) w I t. 8 . I O . 18. 20.

ffgun 3-33. Pseudo-Pilot F l a n Turn Over I Spot i n I 35 k t Wind (Sheet 2 of 5 ) i l i l S t C Fjgure 3-33. PseudoStlot F l o w Turn Over a Spot In a 35 k t Wind (Sheet 3 of 5 ) P f !

z:

-

?

I IRE I SL c F I g w 3-33, P w u d o S I l o t F l a n Turn her 1 Spot I n 4 35 k t rllnd (Shaet 4 of 5 ) f & y!

I

T

1 I I 08LC Figure 3-33. Pseudo-Pilot F l o w Turn her I Spot i n I 35 r t Yind (Sheet 5 of 5) P r i o r t o c a l c u l a t i n g the t i m e h i s t o r y of the turn, a depicted i n f i g u r e 2-32.

l i n e a r ana?ysis was performed o f p i l o t x l o s e d m i t i o n loops i n a headwind t o e s t a b l i s h t h e pseudo-pilot stationkeeping gains. Because o f the non-mininum phase c h a r a c t e r i s t i c s o f surge and sway c o n t r o l of t h e airplane, t h e gains had t o be chosen c a r e f u l l y t o avoid p o s i t i o n loop i n s t a b i l i t y . The gains established by the analysis and used t o generate the traces o f f i g u r e 3-33 are as follows: IL IL -0.005 u n i t s 6L,,mKlft; 5.0 f t l f t l s e c ;

Kw

5.0 f t l f t l s e c ; K V = 2.0 f t / s e c / f t ; Ku = 0.

Kx The a i r p l a n e handling c h a r a c t e r i s t i c s are functions o f wind d i r e c t i o n but, as noted, pseudo-pilot gains were established o n l y f o r headwind conditions.

For t h i s reason plus the f a c t t h a t wind d i r e c t i o n changed f a i r l y r a p i d l y during the t u r n it was expected t h a t pseudo-pilot would have a d i f f i c u l t task t o maintain xe and Ye a t the desired Xe = Y e = 0 reference point.

This was indeed the s i t u a t i o n . I n the t i m e of one complete t u r n (approxi- mately 18 sec), the airplane had d r i f t e d i n Xe from 10 ft forward t o 3 ft a f t o f the reference and was c o r r e c t i n g back towards the reference w h i l e i n ye it had d r i f t e d from 10 ft l e f t t o 40 ft r i g h t of the reference and was not yet c o r r e c t i n g back towards the reference. Psuedo-pilot had the s t i c k

properly placed - forward and l e f t - a t the completion o f the t u r n f o r

c w r e c t i n g both situations. Because there was no wind component along the

ze axis, pseudo-pilot d i d an e x c e l l e n t job, maintaining 2 , w i t h i n 1.5 f t

of the Ze = -100 ft reference.

P i l o t e d simulation studies w i l l be beneficial t o evaluate the airplane and control system performance demonstrated here. A t t h i s p o i n t it can only be concluded t h a t turns over a spot a t f a i r l y high t u r n r a t e s are c o n t r o l l a b l e w i t h modest c o n t r o l power usage and have predictable performance.

i $5

Ihe roll rate and e ~ a ~ traces o f figure 3-33 demonstrate unexpected

m a 1 1 one cycle oscillations at 5 and 14 seconds into the maneuver. These are postulated t o be related to the high a and large 6 flow conditions which occur at these ties. Time was not available to study completely this anomaly.

Fortunately it does not detract from the overall utility of the test case but should be studied further to assess its root cause.

3 . 8 . 1 1 SUnDRary of Results of Performance Evaluation of the FCS performance The following results are the most significant evaluation: 1 . No stability or controllability problems were actually encountered in the test cases. The following potential problems, however, were indicated: Sideslip limitation due to roll and/or pitch control power a) limitations at V A = 120 kts.

(Case 3) Potential PI0 situation due to inherent non-minimum phase b) control characteristics when the pilot attempts tight horizontal plane position control in hover. (Cases 4 and 5) 2. There are noticeable uncomnanded mode switching transients particularly in the lateral degrees of freedom. (Cases 8 and 9) 3. There is noticeable coupling into the longitudinal degrees of freedom when the RCS is used. (Case 6) 4. The pseudo-pilot transition and stationkeeping control logic works.

(Cases 9 and 10) 5. An unexpected oscillation in roll rate occurs under conditions of high a, large 6, and relatively high steady state roll rate. Time was not available to determine the root cause of this peculiarity.

The fact that its effect is minor and occurs under seemingly unique conditions place it among items recomnended for future study. (Case 10) The conclusion dram from the FCS performance evaluation 1s that the baseline

FCS provides an adequate starting point for piloted S h l a t h studies and

that, consquently, the design does not have t o be iterated throug)r the performance loop of the FCS design procedure (figure 3-1)* 4.0 COWCLUSIONS AND RECOmENDATIONS The f o l l o w i n g conclusions are supported b y the d e v e l o m n t s and analyses descr ibed herein: 1. A u s e f u l c a p a b i l i t y has been developed f o r conducting both p i l o t e d and non-piloted sfmulatiens of t h e terminal operations o f VATOL airplanes. This simulation c a p a b i l i t y can be, but i s not r e s t r i c t e d t o being, applied a t conceptual design phases where relat’-!ely few

c o n f i g u r a t i o n - s p e c i f i c data are available. It w i l l h ghl i g h t

handling q u a l i t i e s c h a r a c t e r i s t i c s which are indigenous t o the various designs.

The aerodynamics math model i s deterministic, functions with DATCW -

2.

gh angle o f type data, and can adequately represent the low speed h attack, l a r g e s i d e s l i p aerodynamic c h a r a c t e r i s t i c s of VATOL airplanes.

3. The Vought SF-121 airplane, as modeled herein, has adequate c o n t r o l power for meeting the t r i m and maneuvering requirements o f the MIL-F-83300 and AGAR0 577 f l y i n g q u a l i t i e s s p e c i f i c a t i o n s w i t h some r e s i d u a l f o r gust regulation.

4. The baseline FCS developed f o r t h e SF-121 provides an adequate s t a r t i n g p o i n t for p i l o t e d simulation studies.

s t c o f the SF-121 5 . The most d i s t i n g u i s h i n g f l y i n g q u a l i t i e s character airplane (ar,d s i m i l a r l y t h r u s t deflected c o n t r o l l e d VATOL airplanes) i s a strong non-minimum phase c o n t r o l c h a r a c t e r i s t i c ( i .e. i n i t i a l acceleration i n wrong d i r e c t i o n ) which w i l l become apparent when tne i n hover.

p i l o t attempts t i g h t h o r i z o n t a l plane p o s i t i o n control The developments and analyses herein have provided background f o r the f o l l o w i n g recomnendations f o r possible math model modifications and areas o f emphasis for p i l o t e d simulations: 1. Evaluate the use o f r o t a t e d i n e r t i a l a x i s system coupled w i t h Euler This angles t o o r i e n t the airplane body axes (Section 2.9).

a l t e r n a t i v e t o th2 d i r e c t i o n cosine formulation w i l l circumvent the s i n g u l a r i t y i n the standard Euler transformation a t e = 90 deg. and provide continuous a t t i t u d e references for a t t i t u d e c o n t r o l loops throughout the operating range o f VATOC airplanes. If t h e approach has merit, incorporate t h e appropriate r e l a t i o n s i n t o the math m o d ~ l .

Determine and correct, i f necessary, t h e mechanism for t h e small 2.

o s c i l l a t i o n i n r o l l r a t e which appears'to occur under conditions of simultaneous high angle o f a t t a c k rates, l a r g e s i d e s l i p s , and r e l a t i v e l y h i g h steady s t a t e r o l l r a t e s (Section 3.8.10).

P i l o t e d s i m u l a t i o n s t u d i e s should consider a t l e a s t the f o l l o w i n g 3.

issues regarding terminal fiper=tions o f VATOL airplanes: Non minimum phase c o n t r o l c h a r a c t e r i s t i c s and t h e i r impact o on p i l o t comfort, workload, and a b i l i t y t o e f f e c t precise p o s i t i o n c o n t r o l i n hover and on the need for a d d i t i o n a l moment c o n t r o l s (e.g. independent p i t c h and yaw RCS).

o Cockpit and/or p i l o t r o t a t i o n d u r i n g t r a n s i t i o n . F i r s t consider i t s necessity. If required, then consider whether switching o f c o c k p i t c o n t r o l l e r r o l e s and p i l o t l c o c k p i t angle c o n t r o l should be automatic o r manual functions.

T r a n s i t i o n c o n t r o l system considerations - c o n t r o l system o

type ( r a t e command, r a t e comnand/attltude hold, a t t i t u d e c m a n d , e t c ) , automatic o r manual mode switching, mode blending, annoyance l e v e l o f uncomnanded motions d u r i n g mode switching, c o p k i t c o n t r o l l e r a u t h o r i t i e s and s e n s i t i v i t i e s , p i l o t i n p u t command shaping requirements, system bandwidths, gust r e g u l a t i o n c a p a b i l i t i e b .

5.0 REFERENCES

Clark, Jr. J.Y., Low-Speed V/STOL S t a b i l i t y and Control Prediction -

Volunw I : h d e l Description and Validation, NADC Report 76323-30, 11 January 1977.

A n o n p u s , USAF S t a b i l i t y and Control DATCOM, A i r Force F l i g h t Dynamics Laboratory, U.S. A i r Force, October 1960 (April 1978 Revision).

Driggers, Herbert H., Study o f Aerodynamic Technology for V/STOL Fighter/ Attack A i r c r a f t , NASA CR-152132, Hay 1978.

Bender, 0. D . , V/STOL Type B Engine Data: Engine HFTF-2800-25-1 for VATOL Concept, Vought Report D I R 2-53200/70IR-105, 30 November 1977.

Stapleford, R. L., Clement, W. F., Booth G . C. Fortenbaugh, R. L., F l i g h t Control /Flying Q u a l i t i e s Investigation f o r L i f t Cruise Fan V/STOL: Volume I. Analytical Development, Volume 11, P i l o t e d Simulation, Volume 111.

Simulator Model, NADC Report 77143-30, August 1979.

Heimbold, Richard L., Y i , C . James, M i l l e r , Ronald J., F l i g h t Propulsion Control Coupling and Dynamic I n t e r a c t i o n Investigation, Phase 111, AFFDL- TR-77-41, June 1977.

Beatty, T. D., Kress, S . S . , Prediction Methodology f o r Propulsive Induced Forces and Moments o f V/STOL A i r c r E f t i n Transition/STOL f l i g h t , NADC Report NADC-77229-30, July 1979.

Fortenbaugh, R. Schonowski, J., USN/FMOD FRG VAK-191B J o i n t F1 i g h t Test Program: Volume 9, F1 i g h t Controls and Hydraulics, NAVAIR-9R-76, August 1976.

Vetter, H. C., "Effect of a Turbojet Engine on the Dynamic S t d b i l i t y o f

an A i r c r a f t " , Journal o f the Aeronautical Sciences , Volume 20, November

1953, pp 797-798.

(j) Hillman, 6. Y., New Subroutines for Use i n Off-Line S i m l a t i o n , Vought Report 2-53362/3AV&75, 9 May 1973.

(k) Bihrle, Jr., W i l l i a m and Heylaan, Arthur C., The Spin Behavior o f A i r c r a f t , GAEC Report No. 394-68-1, December 1967.

P. and Smith, R. E.: A n I n f l i g h t I n v e s t i g a t i o n t o Develop ( 1 ) Neal, T.

Control System Design C r i t e r i a for Fighter Airplanes, AFFDL-TR-7CL74, Volume I and Volume 11, June 1970.

(m) Chalk, C. R . , DiFranco, 0. A., Lebacqr, 3. V., Neal, T. P., Revisions t o MIL-F-87856 (ASG) Proposed by Cornel 1 Aeronautical Laboratory Under Contract F33615-71-C-1254, AFFDL-TR-72-41, A p r i l 1973.