. NASA Technical Memorandum 84351

" I

_I_ULA (_A:_A-'IM I'IC_- _3 _OD_ I_.L- Vc I-LY IT}f,_'A _H-_7_ MAChO.MAh_gIC.LZC AL OP_ER, N85- I003,_ '

1

VULtJ,'t_ 1 (NASA t 141'7 I,: dC ACV/_Y J,01 I

4 caCL 01(.. U_cLas 'i

G,3/0 5 29159 i

I _ 4"

1

I

I

A MathematicalSimulationModel ,I

of a CH-47B Helicopter

Jeanine M. Weber, Tung Y. Liu and William ChungI i

Volume I

August 1984
/

" Technical Memorandum 84351 ,{.

i

'i

"l

A Mathematical Simulation Model

' of a CH-47B Helicopter

JeanineM Weber, Ames Research Center, Moffett Field, California

TungY LiuandWilliamChung, Computer Sciences Corporation, Mountain View, California i

NSA

N;lh( )n;tl Aer_ )rlitl lhr :c,;;trod

:-}l.)ar:eA(lmmlrqr;_t_r)n

Ames Research Center

t,,/1()ff_,tt F_;;Irt (;,qhfr)rr,r,q rig():_r,

):
TABLE OF CONTENTS

Page

SUMMARY ..................................... l

NOMENCLATURE .................................. 1 I

i 4'

INTRODUCTION .................................. 2 _

i

MATHEMATICAL MODEL DESCRIPTION ......................... 3 i

Rotors ................................... 3 _

FuSelage Aerodynamics ........................... 13

Engine and Governor ............................ 16

Mechanical Controls ......................... 17

Stability Augmentation System ....................... 18

Electronic Control System ......................... 19

Slung Load ................................. 20

OPERATIONAL CONSIDERATIONS ........................... 24

CONCLUSIONS ................................... 24

APPENDIX A: FLAPPING AND CONING EQUATIONS ................... 25

APPENDIX B: INFLOW DYNAMICS SOLUTION ..................... 28

' REFERENCES ................................... 31

TABLES ..................................... 32

FIGURES ..................................... 95
,_ .f /

SUMMARY

I A nonlinear simulation model of the CH-47B helicopter, developed by the Boeing

Vertol Company (ref. I), has been adapted for use in the NASA Ames Research Center _

(ARC) simulation facility. The model represents the specific configuration of the ARC _i

variable stability CH-47B helicopter (fig. 1) and will be used in ground simulation I

research and to expedite and verify flight experiment design. _

Modeling of the helicopter uses a total force approach in six rigid body degrees

of freedom. Rotor dynamics are simulated using the Wheatley-Bailey equations,

including steady-state flapping dynamics. Also included in the model is the option

for simulation of external suspension, slung-load equations of motion.

Validation of the model (discussed in Volume II of this report) has been accomplished using static and dynamic data from the original Boeing Yertol mathematical

model and flight test data from references 2 and 3, as reproduced in reference 4. The

model is appropriate for use in real-time piloted simulation and is implemented on the

ARC Sigma IX computer where it may be operated with a digital cycle time of 0.03 sec.

NOMENCLATURE

AERO fuselage aerodynamics subroutine

ARC Ames Research Center

BV Boeing Vertol Company

c.g. center of gravity

CONTROL mechanical control system subroutine

DCPT differential collective pitch trim

ECS electronic control system

ENGINE engine and governor subroutine

N_ change in helicopter yawing moment per sideslip angle

" rpm revolutions per minute

ROTOR rotor dynamics subroutine

SAS stability augmentatio, system

SLING sling load dynamics subroutine
0

I_.

1

SNP shaft-normal-plane J

i

i' SNPW shaft-nornm]-plane-wind

q

V equivalent velocity _,

eq

INTRODUCTION _ _i

_: At Ames Research Center (ARC), the CH-47B provides a unique capability for generic , I

flight research in flight controls and displays for rotorcraft and VTOL aircraft. In _i

addition to the existing potential for variable-stability flight, a programmable disI play system and a variable force-feel system are being developed. The purpose of this

mathematical model development is to provide the capability for real-time simulation

_° and for the preliminary check-out of in-flight research experiments for the variablei stability CH-47B helicopter. _i

1

Subroutines that comprise the mathematical model describe the rotor systems,

fuselage aerodynamics, engine and governor, mechanical control system, the option for

either an electronic control system or the basic stability augmentation system (SAS),

and the option for externally suspended, slung-load dynamics. Forward and rear rotor

dynamics are simulated in a shaft-normal-plane-wind (SNPW) reference frame with the

Wheatley-Bailey (modified tip path plane) equations of references 5, 6, and 7. Steady

state flapping dynamic_ are represented with these equations; however, in-plane

motions are neglected. Forces and moments at the rotor hubs are then calculated as a

function of rotor aerodynamic conditions and dynamics, after which they are resolved

to the helicopter center of gravity. Six rigid-body forces and moments resulting

from fuselage aerodynamics are found from tabular data interpolated as a function of

fuselage angle of attack and sideslip angle.

Each engine is represented with nonlinear, second-order dynamics; left and right

engine models are identical, yet are modeled separately. The fuel control system and

gas generator are each modeled as a first-order system, the latter including a variable

time constant dependent upon power and power error. The engine governor, whose purpose is to regulate rotor rpm, is modeled as a linear, third-order system.

Modeling of the hardware from the cockpit controls to the swashplate comprises

tile mechanical controls subroutine. Included are upstream limiters on each control

input, first- and second-stage mixing, swashplate limits, and swiveling and pivoting

actuation dynamics (first order).

Stability augmentation in the form of longitudinal, lateral, and directional rate

damping is modeled. Additional features of the directional SAS include turn coordination and feedback of sideslip angle to obtain a stable yawing moment change with

" sideslip (NB).

The provision for an electronic control system (ECS) model has been included in

i this program. Although no specific ECS configuration has been documented in this

report, the information necessary to integrate such a subroutine into the simulation

model is discussed in the section concerning the ECS.

A mode] of an externally suspended, slung load has been developed and is available

for use with the helicopter simulation mode]. Three state variables, defining the

position ot the load and suspension cables relative to the helicopter, are represented

____ " "-'*" 2-_" _'a_k_*e".. _ °";*" _ " _ _ _e.._
with nonlinear, second-order equations of motion. Thus, the combined system (hell- ,q

copter and slung load), is represented with nine coupled, differential equations !i

_'% modeling the two rigid bodies.

i'' 6,

_ The specifications of the real-time simulation model are presented in this

I" report, organized by subroutine. Documentation of each subroutine is characterized I.

by an engineering explanation, input/output variable lists, and the definition of 11

! , computer mnemonics in terms of engineering variables. The subroutines are discussed q,

: in the following order: rotor dynamics (ROTOR), fuselage aerodynamics (AERO), engine _i

and governor (ENGINE), mechanical control system (CONTROl.), stability augmentation I

system (SAS), electronic control system (ECS) and slung-load dynamics (SLING). I

Operational considerations are discussed, including the specification of input

constants and other information necessary for a piloted simulation using a simulator

! cab and a visual display.

!_ Finally, in Volume II of this report, results of the ARC static and dynamic model

iE • validation are discussed. ARC static trim and stability derivative data are tabulated;

also, ARC dynamic data are compared with a Boeing Vertol Company (BV) model and CH-47

flight-test data from references 2 and 3 (reproduced in ref. 4).

MATHEMATICAL MODEL DESCRIPTION

Rotors

Wheatley-Bailey (modified tip-path plane) equations (refs. 5, 6, and 7) form the

basis for the simulation of the rotors in this mathematical model. In subroutine

ROTOR, total forces and moments resulting from each helicopter rotor are computed in

the SNPW reference frame. These are then transformed to the body reference frame at

the helicopter center of gravity (c.g.) for incorporation into the six degree-offreedom rigid-body equations (which are part of the established Ames simulation

facility and are known as subroutine SMART (refs. 8 and 9)). _

Figure 2 shows a signal flow diagram of the rotor subroutine (in terms of computer mnemonics), including variable inputs and outputs to and from other model subroutines. The equations are executed sequentially as indicated by the numbered

modules in the figure. Since the calculation of rotor hub forces and moments is

required for this model, it is necessary to perform transformations between the helicopter body and the SNPW reference frames. To do this, the position of the actual

rotor c.g. relative to the actual helicopter c.g. (fig. 3) is computed using equation (i),

SLFR,SLRR ;F,R ;F,Rx AXc.g ./12"

q

SDFR,SDRR dF,R = dF,R - AYc.g./12 (I) X

SHFR, SHRR hF,R hF,R AZc. g./12

where the positions oY the baseline rotor c.g. relative to the base]ine helicopter

c.g. are given by:

! 3
I

td d R O. 0 fc

_= 0 ft ' _ _= I,

" Fx x

hFx_ .49 ft_ •h R:_ 2.16 ft

The vector , Ilj

!p g°I

is the position in inches of the c.g. of the 3ctual helicopter relative to the baseline specifications. Baseline helicopter c.g. positions are

c'g_ = 1331.1n2n ]

ilggJ Ll1"2 inJ

and the sign conventions are as given in figure 4.

To compute forces and moments at the rotor hub, helicopter body-axis velocities

(from subroutine SMART, rigid-body dynamics model) are transformed from the body 0

reference frame to the rotor SNPW reference frame. Representation of the body axis

velocities at the rotor hubs is given in equation (2).

. .im a . i,

UFR1,URR1 1Fl,UR1 u ,, 0 -hF, R -dF, R pBI

VFRI,VRR1 v F = VBI + 0 qB (2) ;

l'VR1 hF'R _F,R

WFRI,WRRI w F w -_F 0 rBl

'WR I ;I dF,R ,R l

Body-axis velocities (at the rotor hub) are transformed (eq. (3)) from the body to

the SNP reference frame through shaft incidence angles iF,i R (fig. 5).

UFR2,URR2 cos ' 0 sin uF ,UR,

UF2'UR; IF'R iF'R 1

VFR2 ,VRR2 v = 0 I 0 (3)

F2 'VR2 VFl 'VR I

_ WFR2,WRR2 -sin ' 0 w F ,WRl

WF2 ,WR2 IF, R cos iF, R I

The rotor SNP may be considered an intermediate reference frame between the helicopter

_ and SNPW reference frames. body
' .s t

ORIGIN/,,L i:':.',' :,:, 11

/.ip,. OF POORQUJ,,,.,,,' t

"t

Rotor sideslip angle is defined by equation (4), 'i

BETAFR VF, R 2

' = arctan---- (4) _

BETAP.R BF,R uF ,R2

andl SNP translational velocities are effectively resolved (eqs. (5) and (6)) through i

• 8F,R into the SNPW reference frame, as shown in figure 6. Rotor-hub forces and I

moments are eventually computed in this frame, as indicated in the figure. _,

, UFR ,

I/ 2 (5) ,

URRUF'R= rU ,R + VF,R

WFR

WRR WF, R = WF,R2 (6)

Next, helicopter-body angular velocities (from SMART) are transformed (eqs. (7)

and (8)) to the SNPW reference lrame as shown in figure 6.

PFR p: cos _F' cos iF sin _F' cos _F' sin iF ,

F[ = ' ' ' sin iF (7)

QFR q -sin BF cos i F cos gF sin BF

RFR, rFl -sin iF 0 cos iF

I

! ! !

PRR[PR -cos BR cos iR -sin BR -cos BR sin PB

I ! l

QRRIqR = -sin 13R cos i R cos gR -sin gR sin i R qB (8)

RRRIr R sin iR 0 -cos iR r B

Rotor angular velocity is corrected for helicopter yaw rate in equation (9):

OMEGFR

!

f2F,R = _F,R rF,R (9) OMEGRR

i

and rotor tip speed is calculated based on this rpm in equation (]0):

VTIPFR

' VTIPRR VTiPF ,R = RBF,R :;F,R (]0)

Advance ratio and the free stream component of inflow ratio are calculated in equations (11) and (12):

5
ORIGINAL P_,_.. ',,

II

OF POOR QUe_LJJ"_ {'t

AMUFR UF, R -I

'_IF'R = RBF (_',R,. - rF R) (1]) ([ AMURR

,R '

,i

ALMPFR WF, R

X' = (12)

ALMPRR F,R RBF,R(_t_,R - rF,R) ' ]

Prior to their usage in computations (i,e., for flapping coefficients and rotor _'i

forces and moments), the pilot's control inputs are transformed to the SNPW reference

frame and corrected for control phasing angle (_p) and pitch-flap coupling (_3)' Thus, ]

it is unnecessary to make these corrections during the actual c reputation of these !

quantities (as noted in the flapping assumptions which follow). Longitudinal and

lateral cyclic pitch in the SNP reference frame (from subroutine CONTROL) are transformed to the SNPW reference frame in equations (13) and (14).

rA]I, A, iI

AICFRI = cos BF -sin 8 ICF (13)

BICFRI[B{c[ F2 in BF' cos B_]IB' FIIC

[A{cR'] [ ii R] I

AICRRI COS B_ S in _Rv! _C

= (]4)

BICRRI L-sin_R cos 8 _C

Although the pitch-flap coupling and control phasing angles are zero in the current i

configuration of the ARC CH-47B, the capability for these variations has been included

in the simu]ation model. The purpose of the control phasing angle, _p, is to offset

the lead of the blade relative to the pitch hinge, which was introduced by pitch-flap

(_3) coupling (fig. 7, taken from ref. lO). In equations (]5) and (16), rotor cyclic

pitch positions are transformed through control phasing angle, %p (fig. 8).

AICFR2 A[CF2 os _PF -sin _p _CFI

= (15)

B'

BICFR2LB' tin *PF cos _PFJ icrlJ

AICRR2 A'_CF2 'os _PR

= (16) ,

1

In equation (17), rotor cyclic and co]]ective positions are corrected for 63

(ref. i]).

,i

6

!
2

@RIGId'' ;'.... . ,]

OF POOR Q,;: ...... _'

AICFR,AICRR A,_ A[C aIF,R

"_F.R _,R2

' (17)

BICFR,BICRR B,_F.R = BzC + K bZF,R ,, _,R2 _F,R ,,

THOFR,THORR 00F,R 0'0F,R _ .a°F'R.

where K_F, R = -tan(63F,R)' 4,

Rotor degrees of freedom are limited to feathering and the computation of steady

• state flapping and coning coefficients. No in-plane (lead-lag) degree of freedom has

been considered. Flapping and coning coefficients are computed by solving a 3×3 linear H

system of algebraic equations, and are developed based upon the following simplifying

assumptions (ref. I):

I. Only the first harmonic terms are used. i

2. There is a uniform inflow, i

3. No reverse flow is considered.

4. Identical forms for the front and rear rotors are used. q

5. There are no pitch-flap coupling effects (the control inputs are corrected

in this regard).

6. There is a zero tip-loss factor.

7. There is a negligible hinge offset.

8. Rigid blades are used.

9. There are no compressibility effects.

I0. There is a constant rotor airfoil-section lift-curve slope.

Ii. The rotor airfoil-section drag varies only with rotor angle of attack.

Steady-state flapping and coning angles are found by solving equation (18) with

Cramer's Rule. (The derivation of these equations is given in appendix A.)

AF,R BF,R CF,I aOF,R 3F, R

DF, R EF, R FF,R, aZF,R = KF, R (18) J ,

GF,R HF,R IF,R IblF,R LF, R

where:

121F,R 3

= _ 2 K_F (I + U2

AF'R PaF,RCF,RRBF,R ,R F'R)

I W
g

_'W BF, R - 0

_'I CF'R = 2_F'RK_F,R

, Oi_lGtik_,L .........

2 Kg F R_F OF POOR Q_,.._,__:.

DF,R = - _ ,R

I

i

2

r I _F,R

EF,R = 4 8

FF,R = KB _+g F,

F,R

2

_f 4 UF,R

HF,R = -KB F,R

IF, R = 1.0

2_F, RB [C F 2

3 , _2 + 2X F - + 0 (1.2 + taF,R)

JF,R = 20°F,R (I + F,R ) ,R ,R 2 tWF, R

i. 2 , i +t -B' [! _ _R) I =- _F,R ICF,R2_4 +8 _F, KF,R 3 _F,R0°F,R +'2tF,RuF,R 28tWF,R

i _ 0aF,RCF,RRBF,R_F, R

Using Wheatley-Bailey theory (refs. 5-7), thrust, torque, side force, and drag at

the rotor hubs are computed. Expressions for thrust and torque follow the theory as

developed for a tandem rotor helicopter using the SNPW reference frame. Expressions

for rotor side force and drag were greatly simplified by BV during their development

because the simplified forms provided a better match with flight test data than did .,

the full theoretical expressions.
]

I

oRIGI_;_,L I ;, i'

OF pOOR Q_AL_i _

Mean rotor thrust is computed with equation (19).

CTFRI 2CT £_ 0tWF

F,R _, I F,R + 2 + 1 1I

CTRR1 aF,R°F,R 2 _ 00F'R _ ,R

i - BIC (19) I

" + _F,R F,R °F,R + _ ,R F, 4,

i

i

" In coefficient form, thrust is modified owing to limits on its maximum allowable value, ,

for rotor stall, and due to ground effect. Since the maximum allowable normalized J

thrust coefficient, 2CT/ao, is 1.0, a limit is imposed if the computed value is

greater than 1.0. As a function of advanced ratio, normalized thrust coefficient is

modified as shown in figure 9 for the effects of rotor stall. This is an empirica]

correction which was derived by BV to provide a better match of the model's dynamic 'i

response with wind-tunnel test data and is selected (along with a correction to rotor i

torque) with flag NSTALL in the simulation model. Thrust coefficient is computed as

shown in equation (20)

/ 2CT \a

CTFR - I F'R ] F'ROF'R

CTFR CTF,R \aF,R°F,_

(20) 2

and if longitudinal velocity is less than 40 knots (and if the ground-effect correction is selected with flag NGREFF), thrust is modified for ground effect as a function

of altitude and airspeed. Thrust is calculated in equation (2!) I

TF'R = CTF p_R_ __ + K T. (21) ,R BF,R _,R g.e.F, RLg.e.F,

where

K = 1 UF'R

U (Ug.e. = 40 knots)

geF,R ge

and Ti. g.e. is determined from figure i0 as a function of the rotor height to diameter

ratio (h/D)rotor.

9
I; OF p(.)Oi:_ (.',,: ..... "_

4,

_%. Mean aerodynamic torque required is found from equation (22)

2C

'1

CQFRI

6F'R a_F R + 0.25 IC aIF,R - 3a_l,'R ;

QF,R = I_F, R .25 _lF, R .65 aF,R 'F,R ' "

CQRRI aF,R°F,R ' i

F,R :" 2 alF,

1

Qb CFR)) ) (00F' R) '

(ItwF _

AI {iF., R 2 - XF,R \ 3 R ,

+ a0F,R _ ,_. + l

----_- 1F,R 2 \2aF, R XF,R -- + 4

+ 8- ,R - • ,R - a2LF,R - b_F, (22) '_

As a function of rotor thrust and advance ratio, the torque coefficient is modified

for rotor s_:all (flag NSTALL) as shown in figure 11. AJso, an empirical correction

is made to the torque coefficient to attain a better match with flight-test data.

This correction, the effects of which are shown in figure 12, is calculated as a function of adva'_ce ratio and thrust coefficient (flag NTRQCR). Including the two

corrections, the aerodynamic torque coefficient is:

/2C0 \

CQFR C = [

' "F,R ' } aF,R:rF,R + _,C + ,',,C (23)

CQRR QF,R \aF,R°F,R/ 2 QF,RR.s. QF,R

and the rotor torque required is

QAERFR

QAERRR QAE_, R = CQF ,R p_R_ F ,R_2 (24

Rotor sideforce is calculated with equati_-: s (25) - (27).

CYFRI 2CYF'R = 2CTF'R blF,R + _F __ [_ (blF ' AICF,R) - _F,Ra°F,R ]

CYRRI aF,ROF,R aF,RC_F,R ,R IF,R i R -

+ 2i(a°F,R _F,RBI'(,F,R - I'50°F'R - 3_F'R - _tWF,R I)

+ _ XF, R _IF,R - A 1 + _ a0F, R ICF, R

CF ,R

_. CYFR _ [_ F,R / aV'R°t:'R (26)

, CYR, CYF,R _aF. R_; i R/ 2 ,a

lO
e

Q

/

YFR

O_ _ _ (27)

YRR YF,R = CYF, R RBF, R F,g '

A quadratic form is assumed for blade-profile drag (eq. (28)) and the normalizeddrag (H-force) coefficient is calculated as An equation (29). "i

, DELFR _,

DELRR _F,R = _°F,R + 9_IF,RC_ F ,R (28) _i

I

CHFRI % 6F,R_F,R

2C ,R + (29)

. CHRRI aF,R_F,R = CTF,RalF'R 2aF,R

! Equations (30) and (31) show the calculations for rotor drag coefficient and !i-force,

respectively.

CHFR (2CHF, R _,aF,ROF, R

HFR

CHF _ >2

HF, R = p_RR Q_ _ (31) HRR ,R -F,R ....

Rolling and pitching moments at the rotor hub resulting i:rom aerodynamic forces

are found as a function of steady-state flapping angles (eqs. (32) and (33)).

AMHBFR

I 2

AMHBRR MhubF,R = _ eF'RbF'RMWF,R _F'RaIF'R (32)

ALHBFR

l bF _2 (33)

ALHBRR LhubF,R = _ eF,R 'RMWF,R F'RbIF'R

Inflow ratio dynamics, which are modeled using the ARC local linearization program LOLIN (ref. 12), are first order and depend upon thrust, advance ratio, and an

empirically derived rotor-on-rotor interference algorithm.

iF I WF CTF RF R

= F _FRBF + 2 + ----_.-- 2 (34) • 21/7 + 2"I/ R +

iR = 'IRI{' R 'RRB RwR + 2_,_CTR+ IR,,,2)&F j+DFFRC--T_ + 2,_ (35)
!

OF POOR QO_,d..ii"i" t,

i Referring to equations (34) and (35), rotor-on-rotor interference parameters DFR F

I (rear on forward) and (forward on rear) are calculated as sho_m in equation (36) DFFR

P

!" BDFFR

!, = d'. (L- Isin BFUSJ ) + Isin ] (36) "

BDFRF DFFR (RF) _FR (RF) CF a _FUS "

where dFF R and FR F are found depending upon whether the helicopter is in forward ' I4'

or rearward flight, in figures 13 and 1/, and CF2 is found in _:igure 15. A more _i

bi detailed description of the LOLIN approach to solving,_ equations (34) and (35) and an

explanation of the differences between this approach and the one used originally by _

BV, is given in appendix B.

r, Finally, rotor forces and moments at each rotor hub are transformed to the helicopter c.g. These forces and moments form a portion of the total forces and moments

acting on the rigid body (helicopter) and are integrated in SMART to give the trans- 'i

lational and rotational states, i

In equations (37) and (38), forces at each rotor hub are transformed from the

SNPW to the helicopter body reference frame.

XAEPFR X\E_ _ -cos _'F cos iF -sin _F cos iF sin i H_[ 'h I

= ! ! I

YAERFR YAE_: -sin $F cos _F 0 YF. (37)

ZAERI_ ZAER._ -cos _ sin iF -sin _ sin iF -co," i F TFj

! !

XAERRR ["AERq -cos _R cos iR sin BR cos iR sin iR R|

= ' ' 0 (38)

YAERRR "AEP_I -sin BR -cos BR RI

ZAERRR AER_ -cos _R' sin iR sin BR' sin iR -cos iR

Re

J ..I

Tota! moments at the helicopter c.g. due to the rotors have contributions from

two sources: (|) moments at the helicopter c.g. resulting from forces at the rotor

hub and (2) moments at the hub transformed to the c.g. Equation (39) shows the computation of the first contribution, equations (40) and (41) show the computation of

the Jecond contribution, and equation (42) gives the summation of moments from each of

the two sources.

ALFRI,ALRRI "I.;,ER F'- ,F 0 hF, R d F,R " "X"AERF, '

AMFR 1,AMRR 1 MIERF ,R = "hF'R 0 - _'F,R YAERF, R (39)

' -d 0 ZAE

ANFR 1,ANRR 1 NAERF,R F,R _'F,R ,RF, R,

12
/ I_ r i

OF po0_ _'u,',,.-_"_' '

/

i

,l

'_, ALFR2 ""LAERFI cos BF'cos iF -sin B_ cos iF -sin il; _'hub,p']

AMFR2 _'AER. sin 6F' cos 8F' 0 I]_ub_ (40) ,

! ,!

ANFR2 _AER. cos BF sin iF -sin _F sin iF cos iF _!GOVF i

4'

it! " " t !

ALRR2 AERR -cos 8R cos iR -sin 8R cos iR sin il ID'_ub_"

!"AEP_ ' ' 0 I, 

AMRR2 = -sin BR cos BR "'hub_ (41) ,

ANRR2 I.AERR -cos _ sin iN -sin 8_ si_ iR -cos iR _;GOV.. R

ALARFR, ALARRR LAERF,_ LAERF ,i; ,AERF'

= ' 4- M" (42)

AMARFR, AMARRR MAERF,R MAERF, R AERF, R

T ! L_f!

ANARFR, ANARRR NAERF,R- NAERF, R .AERF,R

Total rotor forces and moments,

[XAERFR,XAERRR 1 _,M_ARFR \LARRI_1

'IYAERFR,YAERRR_ and _ AMARFR,AMARRR t

kZAERFR, ZAERRR_ [ANARFR ,ANARRI_j

are passed to the AERO subroutine for summation with the fuselage quantities calculated therein; aerodynamic forces and moments (rotor + fuselage) are transferred to

SMART as inputs

FAY and II'AN p

LFAZJ LTANJ

Table I is a list of the ROTOR subroutine variables together with constants and

conversion factors. Included is each variable, its FORTRAN mnemonic, units, common

location, if applicable, and physical description. Table 2 is a list of the variables

transferred between ROTOR and other subroutines.

, Fuselage Aerodynamics

Tabular data from rotor-off wind-tunnel tests provides the basis for fuselage

aerodynamic forces and moments. These are represented in the helicopter body reference frame and are normalized by fuselage dynamic pressure. The data are obtained

from the function tables by linear interpolation on fuselage angle of attack and

sideslip angle (fips. 16-21).

13

k_ = ............ _
r _iL _,, i

I'

!,% To calculate fuselage angle of attack, rotor downwash velocity at the fuselage is ':

computed with an _mpirical expression, and is used to modify vertical velocity

(eq. (43))

(%_ - %F)_FRB %,

F

' = wB - (43)

WBPR wB 1 + DFR F i

Using tile vertical velocity at the fuselage, w_, fuselage angle of attack is calcu- _'

lated from equation (44). 41

_j

ALPHFS _FUS = arctan (44) \uB/

Fuselage sideslip angle is computed in equation (45), which is somewhat simplified

:" from the helicopter sideslip angle computed in SMART. '_J 

L

i BETAFS BFU S = arctan (45)

Fuselage dynamic pressure, used to normalize force and moment entries in the function

tables, is found using equation (46).

SQFS qFUS = _i p(u_ + VB2 + w_2) (46)

Q

From the function tables, the resulting forces and moments are: (D/q)FUS,

(Y/q)FUS, (L/q)FU S, (_/q)FUS' (M/q)FUS, (N/q)FUS" These quantities are then corrected

for differences in the equivalent "flat-plate area" between the actual helicopter and

the model used in the wind-tunnel tests from which the data were obtained. This

correction accounts for additional sources of drag (i.e., rotor hubs, rotor blades,

landing gear) that were not included in the wind-tunnel model.

Correction terms to be applied to the fuselage forces are calculated as shown in

equations (47)-(49), where Ale is the difference in flat-plate area; fuselage forces

are calculated in equations (50)-(52).

A(_IFus = Ale2(tan 2 1/2 (47) [I + (tan _FUS) BFUS ) ]

A Y = Afe tan BFUS

FUS 2(tan )2 1/2 (48) .

[i + (tan aFUS) BFUS ]

L_ '_ = Ale tan _FUS

2(tan 2 I_ (49) \qJFUS [I + (tan aFUS) BFUS ) ]

XAERFS XFU S [q(o) FUS

= -qFUS + A\qlFUS J (50)

14
7

OF pO0,.: .....

YAERFS YFUS qFUS fi FUS

+ _I=_ (52) +

ZAERFS ZFUS =-qFUS _ FUS _q]= r

To make the corrections necessary for differences in c.g. position between the actual _[

" helicopter and the wind-tunnel model, this moment arm is computed as in equation (53). ,,,J

. SLCFS V ] _ I_X . g.

d c d

SDCFS = - 'Yc. g. / 1 (5 3) ?US

SHCFS IAZ c /1

?US 'g"

is the baseline model e.g. offset (fig. 22), which I'

Idcxl has the constant numerical value of ft " Yc. is

the position (in inches) of the c.g. of the actual helicopter relative to its baseline

(fig. 4). i

Using equation (54), fuselage moments are adjusted for this difference in c.g.

position,

ALARFS LFU S "(_/q IF1S 0 h d XFU _

CFUS cFU_

AMARFS MFU S = (:!/q)FUS qFUS + -hCFus 0 -£cFU S YFUS (54)

ANARFS NFU S (N/q)FU S -d _ 0 "

• cFU S cFU S _+FUS

If the helicopter is in rearward flight, the signs on XFU S, MFU S, and NFU S are

reversed to account for the aerodynamic differences at this flight condition.

• Total aerodynamic forces and moments include rotor and fuselage contributions,

which are summed at the end of the subroutine (eqs. (55) and (56)) and passed to

SMART.

FAX XFU; FkAER.. IAER

FAY YAERO I = YFU ; + ;_ R[ "-.

.AER F + ,.AERR[ (55)

FAZ ZAEROI ZFU ;]' ZAERF :'AERRJ

15

I
TALLAERO 1 LFUS _.ER F LAERR i!

TAM MAERO I = MFU S + I_ER_ + LAER_ (56) _i

I

TAN NAERO ] NFU S t.AER_ LAER." i

4_

Table 3 gives the definition of the variables, constants, and conversion factors d'

of the AERO subroutine. Table 4 lists input/output variables to and from other subroutines, together with required input data.

Engine and Governor

; Power is supplied to the rotor system by two Lycoming T-55-L7C turbine engines

mounted on the aft pylon. Although the representations are identical mathematically, '

i each engine is modeled separately. The block diagram in figure 23 illustrates =.,e

modeling method for the left engine, including the governor and forward rotor-shaft

dynamics. Nonlinear functions are shown in more detail in figures 24-30.

As shown in figure 23, trimming of the engine by zeroing _, is done while in

initial condition (I.C.) mode by setting flag ISTEADY after the rigid-body states have

been trimmed. Pilot inputs, shown on the left side of the diagram, include: positions

of the collective stick (_c is fed forward into the engine to compensate for rpm

.... droop); N l lever (compressor speed); and beep trim switches (torque may be adjusted

i on engine individually, or engine torque rotor rpm may adjusted on

the left and be

both engines simultaneously). Changes in beep trimmer and collective positions modify

the fuel control actuator (N2) command. The fuel control mechanism is modeled as a

first-order system, with friction in the response represented by a deadband and by

hysteresis. Unlimited commanded power is calculated, as showal in figure 31, as the

difference between equivalent rotor rpm (NR) and the fuel control actuator position

(NR&). The term NR provides the intercept of the unlimited commanded power curve,

and_the slope of the_curve (M) is an empirically derived constant between engine fuel

flow and engine power. Feedback of NR(_ ) in the unlimited, commanded power calculation represents the governing loop of the engine, where engine power is modified to

I regulate variations in rotor rpm. i

As sho_ in figures 23 and 31, the topping power level of the engine is a function of NR(_ ) and the compressor speed (Nl). Three positions, STOP, GROUND, and FLY

I_ are available on the N I lever; actuator motion between the positions is at a constant rate of 0.8 in./sec. Unlimited commanded power is then topped as a function of

rotor rpm and compressor speed.

Gas generator dynamics are modeled as a Sirst-order lag with a tim,_ constant and

internal limiter, both of which are variable. The gas generator dynamics time constal,t is a function of power output, modified as a function of power error. The

variable internal limiter adjusts for the engine, which powers down six times

:.. faster th_n it powers up, and is a function of power output.

The engine governor and rotor shaft dynamics, modeled as a third-order system

(fig. 23), regulate rotor rpm. Inputs to the governor and shaft dynamics model are

power available from each engine and power required for the accessories (hydraulic

systems, transmission losses, etc.). As shown in the figure, this system is driven by

the difference between resistive torque (damping plus spring torque) and rotor torque

16

)
l

required. Rotor acceleration is the dlfference between shaft resistive torque and

engine torque available. Engine euLputs: ro_,r rnm (OMEGA), spring torque

QGOVRJ ,j

and rotor rpm uncorrected for helicopter yaw rate

i

OMEGPRJ

are passed to the ROTOR subroutine. I

Table 5 is a list of variables computed in the ENGINE subroutine, together with

constants and conversion factors, and table 6 has ENGINE subroutine input/output

variables, and logical flags.

i

'I

Mechanical Controls J

The purpose of the CONTROL subroutine is to represent the mechanical hardware

between the cockpit controls and the rotor swashplate. A block diagram of the subroutine logic is shown in figure 32. Mechanical control system inputs are lateral

cyclic (6Ap), collective (_Cp), longitudinal stick (6Bp), and directional (6Rp) cockpit control positions. The SAS and ECS actuator inputs from the respective subroutines, and selected with the flags shown in the figure, augment the appropriate

cockpit control positions. Longitudinal cyclic position is also augmented by the

differential-collective-pitch-trim (DCPT) actuator which (although this capability

has been disconnected in the ARC helicopter) may be selected in the simulation model

by setting flag IDCPT. The purpose of the DCPT actuator is to artificially provide a

stable longitudinal stick position gradient with airspeed (fig. 33). To accomplish

this, as a function of airspeed, the DCPT actuator automatically introduces a positive

pitching moment (fig. 34), requiring the pilot to move the longitudinal stick forward

to maintain trim (ref. 13).

After control-stop limiting (downstream of cockpit control-position limiting,

which is not included in the diagram), control positions are converted from inches to

degrees of equivalent swashplate, resulting in OAF,R , @CF,R , @BF,R, and @RF,R.

First-stage control mixing (longitudinal and vertical, lateral and directional) is

followed by cumulative lateral stop limiting (of the authority of differential lateral

and combined lateral inputs). Results of (vertical and lateral) second-stage mixing,

@FSP' @FPP' @RSP' AND @RPP are limited at the swashplate prior to driving the swiveling and pivoting upper-boost actuators. (In order that the swashplates move smoothly

and not bind up, each is driven by a combination of swiveling and pivoting motions.

Swashplate displacement is the sum of the two inputs.) The actuation dynamics are

• modeled as first-order lags, the outputs of which, @_F,R and A'ICF,R, may be interpreted to be collective and lateral cyclic pitch _ng]es represented in helicopter

body axes, respectively.

As described in reference 4, longitudinal cyclic pitch angle is scheduled with

equivalent airspeed (fig. 34); actuation dynamics are modeled as a first-order lag.

17

L ................. .......... -_'__:_i_!"_ "_'_''_'_ _ °'_ ..... _,
Mechanlcal control-system outputs are rotor hub col]active and cyclic positions

fA1CFRC, AICRR_}

BICFRC, BICRRC _ ',

TIIOFRC, THORRC I

which are passed to the ROTOR subroutine. Table 7 is a summary of the variables used

in the CONTROL subroutine; table 8 gives subroutine input/output variables and logical flags. !

i

Stability Augmentation System

The basic augmentation of the CH-47B helicopter is modeled in the SAS subroutine.

Rate damping only is implemented in longitudinal and lateral axes (figs. 35 and 36);

the directional axis has turn coordination and N_{ stabilization in addition to rate

damping (fig. 37). Figures 38 and 39 show the directional SAS nonlinearities in

detail.

The longitudinal SAS consists of pitch-rate feedback through cascaded first-order

lag, lead-lag, and washout filters. The lateral SAS is comprised of a single firstorder lag applied to roll rate. In the N_ stabi]ization portion of the directional

SAS, sideslip angle is calculated using the pressure difference between the static

ports located on the nose of the aircraft. In an appendix to reference 4 it was

determined that this pressure difference may be represented as in equation (57)

APlstatic = (1.1)(4)sin(2y)sin(2_)q (57)

port

where _ = the angle between longitudi,la] axis and the static port line (52 °) and

= the dynamic pressure (= (I/2)_V2q)._ The portion of the yaw SAS rudder input cal- q

culated to zero sideslip angle is given in equation (58) where KAP6R is a velocitydependent gain whose purpose is to wash out this rudder input at high speeds (fig. 38).

QK in. pedal_

= (kp in. H20) _ "in. H2Ol (58)

DRBYAW _RB _

P6 R

equiwdent /

pedal

Directional SAS yaw damping uses simp]e filtering with, at Veq = 40 knots, a change

from a first-order lag in cascade with a lead-lag to a first-order lag in cascade with

a washout filter applied to yaw rate. Turn coordination is implemented with a fi:storder lag on helicopter roll rate. Computation of the SAS filtering outputs uses

subroutine FACT/UPDATE, designed to solve ordinary differential equations (ref. 14).

Augmentation in any or all of the three axes may be selected with switches

located in the CONTROL subroutine, Fl_,gs RSASQ, RSASP, and RSASR _elect the longitudlnal, lateral, and directional SAS inputs, respectively.

SAS effectiveness may be demonstrated using dynamic response and stabilityderivative data. Figures 40-42 show SAS off and on responses for each of the longitudinal, lateral, and directional axes in hover. Figures 43-45 and 46-48 give similar

results -_or Veq = 75 and 130 knots, respectively. More complete static and dynamic i

i 18

I

I
model data may be found in volume 11 of this report, which gives the validation

results. Included therein are static trim and stability derivative data as well as a

summary of dynamic check results.

Table 9 is a list of the SAS subroutine variables together with constants and

conversion factors. Included is each variable, its FORTRAN mnemonic, its units, its

common location if applicable, and its physical description. Table I0 is a list of :d

the variables transferred between SAS and other subroutines. I

4'

Electronic Control System I

Using the ECS of the CH-47B, a researcher may either implement an experimental

control system or, by designing explicit model-following laws, exercise the helicopter's variable-stability capability. The ECS subroutine is a model of this system;

subroutine inputs are the research pilot's cockpit control positions and the outputs

are ECS signals sent to the mechanical controls subroutine, CONTROL. No specific ECS

is documented in this report. It is anticipated that a particular ECS design will be

developed along with an individual experiment, and will be documented at that time.

However, during model validation, some simple procedures were developed which aid in

properly linking the ECS to the rest of the model. A discussion of these follows.

Prior to engaging the ECS (with flag IECSCON in subroutine CONTROL), the helicopter is tri_ned using the basic airframe and mechanical control system• In this

case, the SAS must be turned off before trimming, since SAS inputs alter the cockpit

control positions for trim.

When the ECS is engaged the helicopter is flown by the research pilot; therefore,

in the simulation the safety pilot's inputs to the mechanical control system are

disconnected as the ECS is turned on (see the CONTROL schematic, fig. 32). To avoid

destroying the trimmed condition of the helicopter when the safety pilot's controls

are disconnected, each trim cockpit control position is used as a bias which is added

to the appropriate ECS input (which is zero at trim, by definition); this is shown in

equations (59)-(62).

DLATTOT = DLATECS + DATOTIC (59)

DLONTOT = DLONECS + DBTOTIC (60)

DYAWTOT = DYAWECS + DRTOTIC (61)

DCOLTOT = DCOLECS + DCTr'rlC (62)

where

• "DATOTI_ _DLATP_

DBTOTIC = iDLONP _

DRTOTiC |!DYAWP ]

_DCTOT] (_ k_COLI'_ trim

Table 11 gives the ECS subroutine input/output variable definition

19

b

mP
I

Slung Load

Subroutine SLING models a baseline, externally suspended load in three degrees of

freedom. This is accomplished by introducing three new state variables, each defined

as a relative displacement of the load and helicopter body reference frames. Additionally, terms which represent the effect of the slung load motion on the helicopter

response are computed and passed to subroutine SMART. Simulation of the slung-load '

dynamics is optional and may be selected with flag ISLING. I

4"

Figure 49 (taken from ref. i) illustrates the geometry of the slung load, its _i

attachment, and position relative to the helicopter. The baseline load data, which I

are included in the simulation model, is a "MIL-VAN" weighing 7500 lb. It is sus- _

pended ol. cables from tandem attachment points on the fuselage equally spaced about

the helicop, er c.g. It has been assumed that these attachment points may transmit no

moments between the load and the helicopter. Referring to the figure: _L, IL, and

_L are defined to be the longitudinal and lateral cable sway anglem ond the lateral

differential cable angle, respectively. '

To compute slung-load aerodynamic quantities, velocities in the helicopter body

reference frame at the slung-load c.g. are computed via equations (63)-(_5).

USL uSL = u B + (LL + RL)q B + LL_ L (63)

VSL Vse = v B - (ee + RL)P B - Leil (64)

WSL wSL = w B (65

Slung-load dynamic pressure, sideslip angle, and angle o_ attack, respectively.

are computed in equations (66)-(68).

I 2 _ + 2 I/2

SQSL qSL = _ P(uSL + vSL wSL) (66

arctan(VSL_ - _L (67)

BETSL 6SL = \"SL/

= arctanf"SL_ + (68)

ALFSL aSL \uSL ] @SL

Slung-load drag, sideforce, and yawing moment, respectively, are found from figures 50-52 as a functicn of load angle of attack and sideslip angle. These data,

normalized in the simulation model by load dynamic pressure, are taken from windtunnel tests. Prior to their use in the cable angle calculations, the load aerodynamic quantities arp ........_ _¢,_c _he hellcopter body reference frame, as in equations (69)-(7 I).

cos 'JL + sin v (69) "

XAERSL XAE_ = -qSL SL q- SL

2O

W
7

! oRIGINAL I"I',':*.... : QUmt',,' :

J o_poo_ !j

t YAERSL YAERL qSl, SI, c°s VL - q

!'r, ANARSL NAERI_ = qSL SL (7]) '

i Using and as inputs, suspension-cable angular accelerations

XAERL, "_mh _ NAERL

I

are computed with the nonlinear second-order differential] equations (72)-(74), from ,,

reference i.

AMULPD XAE_ _B LL+_ '\%_L mLL L LI L L

I rBv____B B •

_ rBiL + LL _ % .![ LL_ (sin @ + sin IaL) - K_p (72)

t

I! where

_t

'_!il [(mLg)2 + XAEP 2 _ ]I/2

!' _ = mLg

_,

ALMLDD _L- mLLL + I--_L- LL PB- ---2 LL rBqB mLLL qB';L LL

rBu B

• -- - -_- (sin $ + sin K_,_L (73)

+ rB_*L + LL LL XL) -

NAER L mLga L

COS COS --

ANULDD 5L - Jh _B 4JLL L @ SvL K66 L (74)

(During model validation, the value of K¢ was changed from the original value of

+1.8 to -0.03 to matcb BV dynamic-response data.)

Integratit,n results in cable angular velocities as in equations (75)-(77):

"_L = IUL dt (75)

AMULD

ALMLD _L = I_L at (76)

ANULD "['L = ;5I, dt (77)

21
OF PGOF( QUALIY'_'

and cable positions as in equations (78)-(80):

AMUI. I_L= f_L dt (78) ',

ALML _L = •F_L dt (79) !

ANUL _L = f{_L dt

(80)

At a straight and level flight condition, values of _L, _L, and VL may be found

by solving equations (72), (73), and ('74) at steady state. Resulting trim values _re

given in equations (81)-(83).

=sin_ [si n +

ALMLIC _L_ = -# (82)

i.C.

ANULIC _ = 0 (83)

LI.C.

where I.C. represents the initial flight condition. By selecting flag ISLTRM,

initial values of the slung-load states are computed at the same time that _he helicopter is being trimmed.

In the original BV simulation model, the helicopter and slung load were modeled

together as a coupled nine degree-of-freedom system. However, since subroutine SMART

i was from aesigned the original. to handleEquations only six(84)-(89) degrees ofare freedom, the nine thedegree-of-freedom ARC model is somewhat helicopter modified

I! equations of motion in the helicopter body reference frame (ref. l), where the underlined terms are those which arise specifically from the slung load.

XAERO mL JL

6B = MH qBWB - g sin 0 + rBvB - MHH (qBWB - _g sin uL) LLMH rBPB (84)

YAERO mL JL mL

+B - M H + g sin ¢ cos O + PBWB - rBu B + MHH PBWB LLMH (rBqB + qB_L) - _ g sin %L

(85)

ZAERO mL(L L + RL)

WB - (_ + MH) + g cos ¢ cos O + qBUB - PBVB + (_, + MH) (q_ + p_)

MLL L

+ (_, + MH ) (PB_i,+ qB_e ) (86)

22

) i, I II - ....... "-- - . .Oh _ ,liJ_i_i_!
_ o'

)'

I

OF POL:,;; QUALfi'_' I

I ( -yIxx) RLJL mLgRL KLp L (87)

. XZ (r_ - p_) + -Izz '"

"_ qB MAER-----_O lyy + "i---- YY ly rBPB 51yy rBPB __I/X____

I I_z) IZZ) i

PB = LAEROIzz + NAEROIxz . + PBqBIxz(Ixx _ lyy + + rBqB[l_(lyy _. - - 1xz2 ]

+ /(rBqB + qBCL ) + 4L----_Ixz cos _ cos @VL + h,g_,IzzX], (Ixxlz, -

i ¢ (8a)

r_ _B = _NAEROIxx + LAEROIxz + PBqB (12XX - IXXIyy + 12xz) + rBqB[Ixz(lyy - Ixx - l_z)] k

mLga_ cos 0 cos + xz 12

+ 4L----_-- Ixx _VL LL (rBqB + qB_L ) + mLqRLIxz l] Ixx Izz - x:c)

(8_)

The underlined portions of the above equations are designated as the slung-load

contributions to the helicopter body reference frame accelerations and are given in

equations (90)- (95) •

-mL - JL

UBDS fl - (qBWB sin pL) (90)

B s MH - KLg LLM H rBPB

-mL JL mL

VBDS " = --

VBs MH PBWB LLMH (rBqB + qBVL ) _ g sin IL (91)

WBDS " = '_(LL + _') mLLL

WBS (mL + MH) (qB + PB) + (mL + M_) (PBiL + qB_e ) (92)

-SJL mLgR L _

QBDS qBS - LLlyy rBP B +--f---yyKL_ L (93)

PBDS • = (qBrB qBVL. ) 4---LV xz pB S t\ LL + + mLga_ I co,_ , cos @vI

L}/ - ) (94)

+ mLgRLlzzk (IxxTzz 12xz

fmLga_ RLJLI

• FBDS r =] _7 1 cos @ cos _vL + xz (rBqB + qB_e )

BS % _ xx LL

+ mLgRLlxzl]_ /(Ixx Izz - 12)xz (95) J/

These contributions are added directly to the helicopter body reference frame

acceleration calculations in SMART. By executing SMART immediate]y prior to SLINC,,

the states are calculated in the same order as in the origlna] BV mode_.

23
" _ ..... _ - _ _7_77 -7-_-_........_ ......... _ ...... .......

I Table 12 gives the SLING subroutine variable definition; table 13 is a list of

subroutine input/output varlab]es and logical flags. i

OPERATIONAL CONSIDERATIONS ,,

i

Rea]-tlme piloted simulation using a simulator cab and visual display requires

the constant input informatien described in table 14, I

Additionally, in order that a pilot may land the helicopter model, a simple gear _

model has been devised. The landing gear subroutine is nct actually executed; rather,

subroutine BLAND has been modified so that tile ground is contacted artificially (i.e.,

the gear reaction force is prescribed to be equal to the aircraft weight) and no

! reactive moments are calculated).

i

i. CONCLUSIONS 'I

i

I A mathematical simulation model of the ARC CH-_7B helicopter has been purchased

from the Boeing Vertol Company and implemented on the ARC Sigma IX computer.

Volume I of this report includes engineering explanations of each model subroutine;

also given are the appropriate assumptions and simplifications necessary to ensure

the validity of a particular experiment.

Volume II of this report gives a comparison among ARC and BV model dynamic

response data and flight test data, together with ARC static-trim and stabilityderivative data. Successful validation of the ARC model has been completed against

BV model data. As with all mathematical models of physical systems, however, this

model is not a perfect replication of the CH-47B helicopter. This is particularly

true with a quasi-steady rotor dynamics mc_el, the type implemented herein. To represent specific aspects of the helicopter response more closely and to meet the needs

of a particular simulation experiment, it may be desirable to modify the model

described in this report.
OR|GINAL P,_"..... ."

b' OF POOR QU_LF_I

i,

i,

_ APPENDIX A: FLAPPING AND CONING EQUATIONS ,

Using Wheatley-Bailey theory (refs. 6 and 7), flapping and coning angles are .,

computed in the shaft-normal-plane-wind reference frame. Due to pitch-flap (-oupling '

(63), the solution for coning and flapping angles (a0,al,bl) is coup]ed with the

definition of swashplate cyclic and collective pitch ang]es (Alc,Blc,O0) , as shown in _j

equations (AI)-(A7). Additionally, coning ang]e is a function of r6tor thrust, I

defined in equation (AI). q,

" AORRF ao/'0aCRB /_I_L" (2CI"2/'-'0° _@tw _2_° ,I"

= - - (A2) ii

AIRR al i - (_2/2) + _-- + 2 (paCRB_!)/IF,R i

BIFR 4pa0 16PF,R[I - (_2/2)]

B2RR bl = + A1 c - (A3)

311 + (U2/2)] (pacR_)/IF, R"

where

AICFR

AICRR A1c = A_c 2 + KBal (A4)

BICFR

BICRR BIc = B{c 2 + K_bl (A5)

THOFR

THORR @o = @_ + KBao (A6)

CTRRI -_o = 2 + -3- + _ + _Lk2- + -_-) - <A7)

The purpose of this appendix is to provide the algebraic steps necessary to

aecouple these equations, eventually resulting in the mode] equation (18). F, IIo_TIn_,

is the step by step decoupling of the equations, reproduced from reference 4.

1. Substituting for (2CT/ao) in the a 0 equation:

_12___F, pacR_ R )( { 1 O0 0tw Ff)0 _)B:,]} 00 Otw T_2;0) So = _ +-_ + -_-+ U[U_ + - +'_ + 5 (A8)

/psc_ \/ 400 00 @tw 2 j_o_

a° = _I_F_R)VI +-3--+ @tw + 2_200 + _20tw - 2_,B]c +-6- +---_5 - 2-) (A9)

4
OF POOR k:'tJ.:..L:, '/ :I.,

2. Substitutln_ for O o and Bzc:

a = - (A::)

C'--_-_ pacRB/ o (0'0 + Kgao) " + 2 _2 2p :c' 2 + KBb : + 2: + + p;

[I2IF'R (_ + 3 )] (2_,K f_) "

aOl....-$ K_ 7._ + a:(O.0)+ b: 4'i

:_acRB

I

A B C _i

0 6 = :)_ + : p: - 2_B_ + 2>,+ + _ (AI2) •c 2 tw

J

3. After defining coefficient-_",qs indicated above, the equation has the form:

Aa 0 + Ba I + Cb: = J (A13)

4. Rearranging the a I equation:

tw :c Blc 16qF,R[I + (_2/2)][(I/4) - (P2/8)]

a: = T + --_ + 2 8 4 (_acR'_3!)/IF,Rn

(A14)

5. Substituting for L'o al:d B:,::

al = (r'_0+ Ki3a0) -_- - ' + KBb +

_Otw ]6qF,R[I + (D2/2)][(I/4) - (U2/8)]

.... (AID)

+ + 2 (pacR_2)/IF, R

ao _ + a: . 8 _ ---

D E

2PO'0 (I 3 2) p>, _Otw ]6qF R[I + (_212)][(i/4) - (_218)1

.... (AI6)

:3 B:c 2 : "+"--'_-- + 7- + 2 (_?acR_f_)/I.F,R

K

26

I,.__............... • -. •,w_._/" _- -
6. The definition of the above coefficients results in the form of equation (A|7):

Da0 + Ea I + Fb I = K (AI7) I,

7. Substituting for A1c in the b I equation:

J

lj

4_a0 16p F [1 - (_2/2)] ]

bl = + A' + KBal - ,R (AIS)

311 + (H2/2)] ic2 (pacR_)/iF, R I

i

-4_ 16PF,R[I _ (_2/2)] lj

a0 + al(-K B) + bl(l O) = A' - (A19)

311 + (_2/2)] " ic2 (pacR_)/IF, R

H I L 'i

i

8. After the above definitions, the equation has the form:

Ga 0 + Ha I + Ib I = L (A20)

As discussed in the text, equations (A13), (A17), and (A20), which are the same as the

text matrix equation (18), are solved for a 0, a I, and b I.

27

l

i
_'-_,_I, _ .... "_ r ............

ORIGI!": ! •

APPENDIX B: INFLOW DYNAMICS SOLUTION

In the original version of the model (developed by Boeing Vertol Company) from q

which this model was adapted, the inflow ratio was modeled by the equation (BI)

expression, including a flrst-order lag (ref. I). Past cycle values of CTF,R, )`F,R,

and _F,R were used, so no iteration on the current value of _F,R was performed i

using this implementation, q,

. , F,R FRF (FR) TR,F 1

ii ALAMFR ALAMRR AF ,R : )`F,R - (_,R + )2F, R )I/2 + 2(_R,F2 + )`R,F)2 1/ '%F,RS + (BI) _,

where

WF,R _ WF,R

XF'R = RBF ,R(_F,R - rF,R) RBF,RfiF,R

as defined in model equation (12).

A more exact real-time solution was obtained Oy Boris Voh, who represented the

above as a differentia] equation and solved it using a local linearization method

implemented as subroutine LOLIN (ref. 12). Following is the solution method, using

the forward rotor equation as an example:

[ ][]

DFRFCTR I (B2)

WF CTF + )`Fs I

_2 2 i/2 + (B3) 'F ( F + )`F) 2(>R

w F CTF DFRFCTR

Z)`F WF + - (B4)

T)`F_F + _F- RBF_F RBF_F 2(_12F+ )`_)i/2 2(_ + )`_)I/2

. DFRFCTR

WF WF CTF ]

i,F = RBFP'F T)`1F "F RBFI2F + 2(_F + X_)l/2 + 2_. 77R * AR) J (B5)

Following are the definitions necessary for the application of LOLIN to this problem:

2_
ORIC'. _ '!

OF.Pu._,,.._ ...... _ .,(

LOLIN Fngineering

Description definition definition

n

ql

Nonlinear function FN

Partial derivative of nonlinear FT '_1"

function with respect to time _'

"_iF _iv

Jacobian of system FS

?iR _i_,,

?_F ?kR

Be

System state vector SI ,

[:'ii_.

where

"'l<J

is defined above in equation (B5), the time derivative of the function,

and the four elements of the Jacobian may be calculated as in equations (B6)-(B9):

?iF I ] + i/2 - 2,3/:: (B6)

DF] _)XF 1 FTR(_DFRF/_)_R) a°DFRF d"J_L R _]

where

?DFRF (I Isin BFU S )AdeN F

_---R--= &I-(lR/UR)-O.mD]p R

29
.]

_C /_F a(_DFF R D_FRCTF_F 1

:°_ _IR I TF 3DFFR

2 8()J_ + %F) 2(_F ^F ) j "

where

3DFFR _ [I - Isin _FUS I]Ad_FR ,.]

eb 3%F AI-(%FIIJR)- 0"251i F

3iR = i Ii + aR°R _ CTRtR .]

Using LOLIN, equations (BI) may be solved with a Newton-Raphson numerical technique in equations (BIO) and BII),

3_,F . 3._R [

n+l n "8iF Di; In (BIO)

_l F 31 R

det

D1F 3.\ R

ALAMRR %R = %R +

n+l n 'JiF D_F" In (Ell)

3t F S_R

det

[)IF 3_ R

o)_. ,.;,...L P:':-:.<

30

_
REFERENCES

I. Cogan, C.; GaJkowski, B. J.; and Garnett, Jr., T. S.: Full Flight Envelope Math

Model for 347/HLH Contro] System Analysis -- Control Document• Boeing Company,

Vertol Division, report _ _01-10148-1, 1972 _

• 

2. Yamakawa, G.; and Miller, L. G.: Airworthiness and Qualification Test, Phase D, 4

CH-47B. USAASTA #66-23, 1970.

3. Albion, N.; Leet, J. R.; and Mollenkof, A.: Ground Based Flight Simulation of _

CH-47C Helicopter. Boeing Company, Vertol Division, report D8-2418-I, 1969.

4. Hackett, W. E.; Garnett, T. S.; and Borek, B. V.: Mathematical Model of the

CH-47B Helicopter Capable of Real Time Simulation of the Full Flight Envelope.

NASA CR-166458, 1983.

5. Hennessy, J. P.: Charts and Equations for the Rapid Calculation of Rotor Thrust

and Flapping Coefficients• Boeing Company, Vertol Division, report 15-A-13,

1949.

6. Wheatley, J. B.: An Aerodynamic Analysis of the Autogiro Rotor with a Comparison

Between Calculated and Experimental Results. NASA TR-487, 1934.

7. Bailey, F. J., Jr.: A Simplified Theoretical Method of Determining the Characteristics of a Lifting Rotor in Forward Flight NACA TR-716, 1941

8. McFarland, R. E.: A Standard Kinematic Model for Flight Simulation at Ames.

NASA CSCR-2, 1973.

9. Sinacori, J. B.; Stapleford, Robert L.; Jewel!, Wayne F.; and Lehman, John M.:

Researcher's Guide to the NASA Ames Flight Simulator for Advanced Aircraft

(FSAA). NASA CR-2875, 1977.

i0. Radford, R. C.: The Longitudinal Stability of the CH-47A Helicopter with the

Forward Rotor Delta-Three -- Results of Flight Test Program. Boeing Company,

Vertol Division, report I14-AD-006, ]967.

Ii. Bramwell, A. R. S.: Helicopter Dynamics. John Wiley and Sons, Inc., New York,

1976.

12. Voh, B.: "LOLIN/LOLIN2," NASA Ames Program Specification (NAPS), no. 215, 1982.

13. Davis, J. M.: Stability and Control Analysis, CH-47B/CH-47C. Boeing Company,

Vertol Division, report I14-AD-603, 1966.

14. McFarland, R. E.; and Rockkind, A. B.: FACT/UPDATE, NASA Ames Program Specification (NAPS), no. 194, 1977.



35
:36





I I I I I I _ "_l

_-_ I I __II I I .,13_

I I _ "_I I I I ,--th
43



47

I

49

__0
5O
51


i

TABLE 2.- ROTOR SUBROUTINE VARIABLE DEFINITION.

Input variables Output variables

Common Subroutine Common Subroutine of

Variable location of origin Variable location destination

AICFRC CH(39) CONTROL ALARFR CH(52) AERO iI

ALCRRCCH 38) I CH(53) I

BICFRC CH(37) AMARFR CH(54) 4,

BICRRC CH(36) AMARRR CH(55) 7

HCG A(176) SMART ANARFR CH(56)

OMEGPF CH(II5) ENGINE ANARRR CH(57)

OMEGPR CH(II6) ENGINE QAERFR CH(64) ENGINE

PB A(37) S_IART QAERRR CH(65) ENGINE

QB A(38) SMART TMGN01 CH(100) AERO

QGOVFR CH(257) ENGINE TMGN05 CH(I04)

QGOVRR CH(258) ENGINE TMGN06 CH(105) 'i

RB A (39) SMART XAERFR CH (72)

SBETFS CH(50) AERO XAERRR CH(75)

THOFRC CH(42) CONTROL YAERFR CH(73)

THORRC CH(43) CONTROL Y,_ERRR CH(76)

UB A(58) SMART ZAERFR CH(74)

VB A(59) SMART ZAERIRR CH(77)

WB A(60) SMART

Logical flags Required input data

Common Description

Flag location Common Function Variable location

NGREFF ICH(7) Ground effect correction DXCG CH(68) Position of actual

of thrust off/on (0/i) DYCG CH(69) helicopter c.g.

NSTALL ICH(5) Rotor stall modificati:,n DZCG CH(70) relative to its

of thrust and torque reference (fig. 30)

off/on (0/i)

NTRQCR ICH(6) Empirical correction [

of rotor torque

off/on (0/]) I

,I

54
L_




i

i TABLE 4.- AERO SUBROUTINE TRANSFER VARIABLES, INPUT DATA AND

i LOGICAL FLAGS

I

It_ut variables Output variables _,

Common Subroutine Common Subroutine of

Variable Variable

location of origin location destination

ALARFR SH(52) ROTOR BETAFS CH(59) SAS

ALARRR SH(53) i FAX A(136) SMART

AMARFR SH(54) FAY A(137)

AMARRR CH(55) FAZ A(138)

ANARFR CH(56) I TAL A(155) ANARRR CH(57) _' TAM A(156) _r _

TEMA gH(92) I S_IART TAN A(157)

TMGNOI CH(100) ROTOR

TMGNO5 SH(104) ROTOR

UB A(58) SMART

VB A(59) SMART

WB A(60) SMART

XAERFR CH(72) ROTOR

XAERRR CH(75) '

YAERFR CH(73)

YAERRR 8H(76)

ZAERFR CH(74) ,

ZAERRR CH(77) _r

Required Input Data

Common

Variable location Description

DXCG CH(68) Position of actual

DYCG CH(69) helicopter c.g. relative

DZCG CH(70) to its reference (fig. 30).



u_

I= I I I I I g I II

_,._

0

•_I ,_

C 0 0 0 0 0 _ _ _ _ ,-.1
65
66
,q

d

TABLE 6.- ENGINE SUBROUTINE TRANSFER VARIABLES.

Input variables Output variables I

Variable Common Subroutine Common Subroutine of _'

location of origin Variable !p_a _on _dj2t_na fO_ - _'1

DCOLTOT CH(210) CONTROL OMEGPF CH(II5) ROTOR

OMEGPR CH(II6) ROTOR _

IBEEPI Simulator cab

IBEEPI2 Simulator cab QGOVFR CH(257) ROTOR

QAERFR QGOVRR CH(258) ROTOR CH(64) ROTOR 'i

QAERRR I CH(65) ROTOR ,i

Logical flags

Common

Flag location Function

ISTEADY ICH(4) Zeros _ after rigid bod

states have been trimmed

off/on (0/i)
68

70
71

73



11

TABLE 8.- CONTROL SUBROUTINE TRANSFER VARIABLES

Input variables Output variables ]

Common Subroutine of Common Subroutine of

Variable Variable

location origin location destination L

DCOLECS CH(275) ECS AICFRC CH(39) ROTOR

DCOLP CH(206) Simulator cab AICRRC CH(38) ROTOR

DLATECS CH(272) ECS BICFRC CH(37) ROTOR

DLATP CH(203) Simulator cab BICRRC CH(36) ROTOR

DLATSAS CH(17) SAS THOFRC CH(42) ROTOR

DLONECS CH(273) ECS THORRC CH(43) ROTOR

DLONP CH(204) Simulator cab

DLONSAS CH(18) SAS

DYAWECS CH(274) ECS

DYAWP CH(205) Simulator cab

DYAWSA_ CH(19) SAS

1AND IA(29) Simulator cab

IANU IA(30) Simulator cab

ILWD IA(33) Simulator _-_ab

IRWD IA(34) Simulator c_b

VEQ A(75) SMART

Logical flags t

Common

Flag location Function

IDCPT ICH(3) Differential collective pitch

trim off/on (0/i)

IECSCON ICH(2) Electronic control system off/on (0/i)

IMHIS --- Simulator cab off/on (0/i)

RSASP CH(282) Lateral SAS off/on (O/i)

RSASQ CH(283) Longitudinal SAS off/on (0/i)

RSASR CH(284) Directional SAS off/on (0/I)
I

< < < < < < < o <

o o o o o o o _ _ o

o o o o o o o _ _ o '

•_ 0 ._ 0 ._ 0 ._ 0 _ ._ 0 ,_ 0 ,_ 0 _ _ _ ._ 0

0

o _

_ o _

Y

L

;2_

bn

_ ._ I I !

_ --_ I I I

_o

J

78

C C_C

0 0

_= ._ .-.

U

8O
.I,,J

o

_ o

o_
82

.._ ............................._ -_.._Jl_a_'" -_,.'_'-._ ...... -_,i

f TABLE lO.- SAS SUBROUTINE TRANSFER VARIABLES

b i

! Input variables Output variables

Variable Common Subroutine Variable Common Subroutine of '1

: location of origin location destination 4,

BETAFS CH(59) AERO DLATSAS CH(17) CONTROL _

I SQFS CH(IlO) AERO DLONSAS CH(I8) CONTROL

PB A(37) SMART DYAWSAS CH(19) CONTROL

QB A(38)

RB A(39)

VEQ A(75)

QBAR A(178)

i

I

TABLE II.- ECS SUBROUTINE TRANSFER VARIABLES.

r

Input variables , Output variables

Common Subroutine of t Common TSubroutine of

,.,Variable location origin ii Variable location I destination ,....

DCOLP CH(206) Simulator cab l DCOLECS CH(275) CONTROL

DLATP CH(203) Simulator cab l DLATECS CH(272) CONTROL

DLONP CH(204) Simulator cab IDLONECS CH(273) CONTROL

DYAWP CH(205) Simulator cab IDYAWECS CH(274) CONTROL

84
C0

C

--i

85

,i

)
_0

_> .,_

0 0

_ 0

8a

...... --_-:' -.--" :_I_,_,I_" _-_-o.__ ." _ _ _ ____._


c-_ cN

i

_D

•_ll(D

_.._ll

W


"FABLE 13.- SLING SUBROUTINE TRANSFER VARIABLES, INPUT DATA AND

LOGICAL _ ^r,e

[

Input variables t Output variables

Con_non Subroutine [ Common Subroutine of J

Varlablc Location of oriKi/!_ I Variable locat_on destination I

CPHI A([i) SMART r]TBDS CH( 251 ) SMART "

CTHT A(13) QBDS CH(252) _'

PB A(37) RBDS CH(253)

PBD A(55) UBDS CH(248)

PHIR A(4) VBDS CH(249)

QB A(38) WBDS CH(250)

QBD A(56)

RB A(39)

RBD A(57)

RHO2 ¢,H(IOI)

SPHI A(lO)

STHT A(12)

UB A(58)

UBD A(413)

VB A(59)

VBD A(414)

WB A(60)

XlXX A(II6)

XIXZ A(II9)

XIYY A(II7)

XIZZ A(II8) i

XMASS A(130)

!

Required Input Data ]

Variable location Common Desc rip tion ]

BJSL CH(266) Moment of inertia of slung load about '

load verti,'a] axis

BLSL CH(267) Average cable length below attachment

point

BRSL CH(268) Vertical distance between hook attachment point and aircraft c.g.

SASL CH(297) Cable separation distance

SMSLIC Slung load mass

THESL CH(269) Angle between load x-axis and helicopter x-axis

WGHTSL ,S lunz_l_q__ad 'weight _, ,

Logical Flags

_Flag [ Cormnon location Function

ISLING ISLTRM I ICH(1) ICH(8) Slung Slung load load subroutine trim in straight option level off/onflight (0/i)off/on

I (Oil)

92
t

i

F

!.

[ TABLE 14.- REQUIRED INPUT DATA FOR OPEItATIONAI. S[MUI,AT|ONS

Comnlon Units Physical description I Variable location

DXCG CH(68) in. Position of actual helicopter ¢

DYCG CH(69) in. c.g. relative to its refer-

_ DZCG CH(70) in. ence (fig. 30)

WAITIC A(242) Ibf Helicopter weight

XIXXIC A(243) slug-ft 2 Helicopter moments and prodXIYYIC A(244) slug-ft 2 uct of inertia

XIZZIC A(245) slug-ft 2

i XIXZIC A(246) slug.-ft2

i XP A(171) ft Position of pilot, in heliYP A(172) £t copter body axes, relative

• ZP A(173) ft to c.g. of aircraft

!

93
.t

l! ORIGINAL PAGE 19 *,'

OF POOR QUALI'W

Figure i.- CH-47B helicopter.

...._;XG P;',L_t*I"-...... ,,v"_, ,"_ _,,'w
ORIGINAL pAGE IS

OF pOOR QUALITY

r'_R'OM- INGIN| I (FROM 5)

r 7 ENG.NEOOOVFRL! _"'T' II ",T"R' f !

TO A|RO TORQUE QGOVRR I ICf"" _IlIICIIIITRR; ITO AERO I ,

I ! AVAILABLE I / L __1 i

L_.... J ------I------J ' --1 _

t .... l ........i

I,-FRI I'COMPUTERO;''_'R'I R] I,. COMPTUOTA TE L A'FR=_LRANSFORMROTO__ORMROTOR -1 [ -i

IO_H AERODYNAMIC I AMPRI ROTOR MOMEN

"IS_AMFR2 HUB MOMENTS 10 AERODYNAMIC FORCES 1.3_ tOM

IsN.; MOMEDUNT/ELASNFR,'JHEL,COPTL.R''= ERBOD I !"EL'YCIOPTERSOI _::_DCIOPTERBoD_IS"'"l [ >_

FROM 1; _1 TO HUB FORCES[ LI REFERENCE FRAME) !_ J REFERENCE FRkME I I REFERENCE FRAME / IYER' I - |

, :!ii -- [iL_!i i_Ni_ill !NMLi_il--[ _N_ii_ l_l_i_ii]--ii_N_ _ iLi_i [i_Nii_] I I_NTli_D:tUpGciNASH!FEiOTRO __.F_ O2t

A # -I I liii'F. VAIRRRI I 'i_!t ]

• .T, . / s,..WRIIIS,N0_..I IZ'RFRI'/ZA"RRII ' / . EoM

X.*_K"_[-RI/IX.*-_-"B-RI / ICOSI_RtlIcOSmRI I . _/ _"',_

• AIIMPM i | 1• AIKMIIIq / / I i / uplq IZASRFRI IZA[RRRI / -- I ......... _ I 1

JSlnlF cOStF. ImIR, COl;R I _...... ] l--'--'',.':L--_ I C COMR

(-- J ICOSIFR! tuuamrRI I COEl_

"_ sin,cos i F sin,col iR I Cl

/ I co_

[, COMPUTE I "'AMFR : _ F4. COMPUTE' I__IMWFR ROTOR BLADE Y!

..... . / ROTOR/ROTOR _ INFLOW RATIO J | A. ROTOR HUB I - BMWRR MASS MOMENT I c' COUl_

_ROM.. / | INTERFERENCE AL[_'_MRR ALAMFR , AL&MRR I | PITCHING MOMENT I c|

_m..,___,...,''R I / PARAMETER I ..................... - ......... I .... I AMHBFR , AMHBRR I SBFR NUMBER OF COMI_

PIICLI(,_,_,,IPI_: I ,.-- / "REVERSE _ _ _../rn -- , _ _:

LONGITUDINAL _.. uo _ _"N'TIONS FOR _ _1_ | B. ROTOR hUB I SBRR BLAD.S PER HUB HE

VELOCIT" ,UUDY / ,I R_ARWARO I BDFRF I CTRR / ROLLING M _MENT

REFERENc. E f--.-_-.._.- (_uBROUTINE I IFROM 13) | SEFR FLAPPING HINGE e. COM_

FRAME' I I FLIGHT). " I BDFFR LOLINCALLED) I ......... I ALHRFR , ALHBRR I_- "'RR OFFSET (_

,' --'--., ,o,,,.,O,,R_ _ L_____-.,..-_ "= rA,C'R "1

' * " T |B I CFR / COMJ T AEER!I [A,RR', LT.OFRj TORS

/ [RIFR] I letnRJ I IAICRFI"v] Q_

(FROM 12) -TAN ("3) B I CRRt __

FRO-MT---- ] . I , I [TNORR[

SMART FROM: ,,. KBETF KBETR ,

.........., /o./ .TRANSFORMA,,...... RFRA, M ,...OMP E UTE I I

_.,_r_.n | iRnJ ANGULAR RATES TO ........ I A. ROTOR ANGULAR _. I

......... I ' _ SHAFT NORMAL PLANE I ' ! F'!! R / I VELOCITY CORRECTED T [

VELOCITIES I WIND REFERENCE FRAME L--'-- T'---J I FOR HELICOPTER ' _ ROTOR

oLoLooLoLoL GPiPF___ OMEGFR, OME G

OMEGPF YAW RATE. RR

(BODY I (THSHAFT IROUGH _ , YAW RATE. I 11. CORRECT , _[ }

REFERENCE CONTROL INPUTS , CHORD"

FRAME) I INCIDENCE AND ROTOR FOR PITCH-FLAP

C__..... .._ SIDESLIP ANGLES.) OMEGPR b ROTOR TIP SPEED IU FRI COUPLING AI FR

PFR I PRR VTIPFR , VTIPRR (FROM 4) BIFR

QFR IQRRt ROTOR RBFR C. ROTOR ADVANCE URR AICRF AICRR AIRR

/RFRI IRRR BLADE _ RATIO BICFR b ICRR/ BIRR

RADIUS RBRR AMUFR , AMURR WRR THOFR , THORRI I

/T SRIETRR AIR RHO D. INFLOW RATIO (FROM 7)

SBETFRIcBETFR / CBETRR DENSITY _ (FREESTREAM COMPONENT). [AICFR21t[AICRR21 l

(FROM 5) ALMPFR , ALMPRR |BICFR2J|[BICRR2J |THOFRC {

RFR _--- / TNORRC '.

RRR

3, COMPUTE VELOCITY 5. COMPUTE ROTOR 9. TRANSFORM CYCL"C'_ 10. TRANSFORM I

IN R_TOR SHAFT [UFR21 SIDESLIP ANGLES PITCH INPUTS INTO I CO%ITROL INPUTS (FROM 6)

COSINEsSINES AND COISNIF IFRRS (RESOLvEDNOR PLANEMAL IWFR2 I FR21 |I|v SIETAFR , B|TARR [ClISTFRJ[SB|TFIR PLANESHAFT WINDNORMAL iI _[AICFR1] BICFRIj I PHASINGTHROUGH ANGLE.CONTROL THROUGH SHAFT ;, _, AND THEIR SINES _ REFERENCE FRAME. L._

oSHAFT : : i '

INCIDENCE ANGLE) [URR2.; - AND COSINES INCIDENCE Is..,R_ [I [A.C,R,[*_!

ANGLES, [UFR2] {URR=] lYnn=/ ISOZTrR1[CRWTFR]SB|TRR

,.,. oo.,.. I ......Ji

/VFR2/ /VRR21 LWRR2J SBSTRRJ,tCBITRR [ClIETRRJ |BICFRII ,Lmm '_CFR2J,IB CRR2 I

twFn,J4WRR'J [ " _

4, IL' :

I __ ,___JL_ ....

SUPRa! URn1] _ r ,-HUM:

I [pal jvF._ VRRt| 4 COMPUTvEr, -,.... i :_NTROL SP;:P=R} PHPRR1 I

[WFRI IWRRtJ IN PC,OR SHAki ; CYCL;" PITCH CPHPFRJ I =CPUPRR! _._

FROM: NORMAL PLANE _ _'L'L_-" CONTROL PHASING

SMHELICOPT ART ER COMPUTF VELOCITY REFERENCE FRAME I[#,CPRCI IAICRRCh ANGLES AND THEIR 1 COMPUTE I (r_ESOI.VEO THROUGH

ANGULAR AT ROTOR HUB, _ ROTOR S j[BiCFRCJ,IBICRRCII SINES AND POSITION O(1| IDESLIF -

VELOCITY I COMPENSATING FOR J COSINES ROTOR HUB

AIRFRAME ANGULAR ANGLE.) L_ RELATIVE TO]

HELICOPTER| (INERTIAL REF I RATES, (BODY J-UF_R] [URR|

FANOvELOCITY RM) O_: [ !_Wi] REFERENCE *:,AME) SLFR} [W.RI,IWRRJ SLFR} ElL'

HELICOPTER UFRt URR1 SDFR/ SDFR ISOIIIJ

VFR1 / VRR_ SNFR] /S.F.] ,_SNq

C.O. (BODY _.lml_ [WFRt , /_RR1

REF FRM) [ SLRR] J

SO_RI i

J SHRRI

_ VECTOR SCALAR } cURRENT CYCLE VALCOMPUTER UE ----- _ "R_ SCALA VECTORR } PACYCLE ST COMPUTEp VALUE ]i

Figure 2.- Rotor signal flow dLagram.

...... ", F:(:l,:l)I N1

't F_k ..... ' "" ..... "_ 97
OF p()o:< (/...i,":,Lf'lF_

P,

(FROM 5)

.=,,,,llJ-'"-.. r 1 ROTOR P In;'" " '"

ICIIIITFlltl I ICIIIITRRI I TO A|RO! SOLIDITY

......... L L.....L SmeA_IIORR t

16 TRANSFORM ROTOR

AERODYNAMIC FORCES 13a COMPUTE ROTOR TNHUST COEFFICIENT THTWFR ROTOR

TO HELICOPTER BODY tNER OTFR , CTRR _ • BLADE

REFERENCE FRAME IVFR - LIMIT SUBJECT TO ITS MAXIMUM TNTWRR TWIST

(THROUGH SHAFT [TFR MODIFY FOR ROTOR STALL ',

(SUBROUTINE RSTALL CALLED) T

INCIDENCE AND ROTOR _ _ j

SIDESLIP ANGLES). - MODIFY DUE TO GROUND EFFECT

NRR, COMPUTE ROTOR THRUST ALAMFR

I

XAERFR 1 [ X&ERRR I YRR', TFR , TRR _ (CROM 15) 4l_

I Y AERFR Y&ERRR TRR, ALAMRR

IINIRRI [Z&£RFR , ZAERRR b. COMPUTE AVERAGE SECTION PROFILE ._,

_l¢OlilRRt DRAG COEFFICIENT

: A OELFR , DELRR RBFR ROTOR " * I

Bin IR, col iR IS IN|FR |IS INIFRt _ BLADE d

ICOSlFRIIICOSlFRI c COMPUTEcoEFFICIENTROTOR SIDEFORCE RBRR BAO_US li

sin.col iF J sin.cos IR CYFR , CVRR COMPUTE ROTOR S;DEFORCE

_j_ BMWFR ROTOR BLADE YFR , VRR RHO AIR

BMWRR MASS MOMENT d COMPUte ROTOR DRAG COEFFICIENT _1--- DENSITY

CHFR , CHRR

SBFR NUMBER OF COM_UTE ROTOR DRAG _'

SBRR BLADES PER HUB HER , HRR *i

IR ! SEFFI FLAPPING HIN¢;E e COMPUTE ROTOR TORQUE COEFFICIENT t"ql" OMEGFR (FROM l_ ""= ,i

SERR OFFSET CQFR , CQRR OMEGRR "., i

l

_A I CFR MODIFY FOR ROTOR STALL

IB I CFR I (SUBROUTINE RSTALL CALLED)

_AI RR ! ITNOFR COMPUTE TOqQUE REQUIRED MEAN AERODYNAMIC _ SAFR ROTOR

IBtRRi _ SARR

QAERFR QAERRR BLADE

' SECTION C L

_IDM 12) -TAN (,3)

I I 'TN°""! _ i

KqTFIKS _F-_ mTR Il ' AOER FAORRI AMUR.

[A,FRI|IAIRR I (FROMz)

{S_FRj|_SIRR I AMUFR

I 11.CORRECT ROTOR SCFR _ 12 COMPUTE ROTOR _,'- ROTOR BLADE

THTWFR

I CONTROL INPUTS I CHORD SCRR FLAPPING AND THTWRR TWIST

i I FOR PITCta'FLAP CONING EQUATIONS

I COUPLING } }_&_FR I BY DECOUPUNG

i I !n'rnJ THE 3 • 3 LINEAR ALAMFR

(FROM 4) I iAICRFI i AICRR) J_ IA1FIR) EQUATIoNsSYSTEM OF .,41,q_-ALAMRR (FROM 15)

:_1 I SlCFR]IBICRRII StaR1

I ITNOFR]'LTNORR/J _ ' O.EGFR *OFR AORB, (FROM 7) _ AIFR !AIRR RBFR ROTOR BLADE

OMEGRR IBtFR LBIRR _ RBRR RADIUS

AICFR211,AICRR21 t :--

.|CFR,I/_.R|CR'', _ J_ _'-_ "NO AtR DENSITY

SA;'R ROTOR BLADE

_PFR! SECTION C L

I 10'TRANSFORM ] QFRJ SARR '

'S INTO I CONTROL INPUTS / (FROM 6) PRR FIFR

llAL I fAICFR1] I THROUGH CONTROL

FRAME._ _ PHASING ANGLE. QRR ROTOR RLAUL

FIRR MOMENT OF INERTIA

¢_"_"_t_ I FA_!C"_R_!II AICFR2] AICRR2 i

_ [BIGIqR,J[ "ICFR2J, BICRR2 J THOFRC THORRC

r FROM: co_-'_)L-]

1 COLLECTIVE j

I PITCH

I THOFRC THORRC I

I FsPHpFnSPHPRR OXCG CN I LcP"_'_mI CP.PR. OVCO

OZCG DIFFERENCE BETWEEN

_,_ CONTROL PHASING BASELINE & ACTUAL

ANGLES AND THEIR 1 COMPUTE _ HELICOPTER C.G.

SINES AND POSITION OF POSITION

COSINES ROTOR HUB

I HELICOPTER RELATIVE TO CG iSLFRXl

I I$LFR SLRIql ISO_"xl

_. IIDFR I IORR {IHFRX I BASELINE

I,liNFIq I, IIHRIq I _ POSITION OF

ROTOR HUB RELATIVE

[ILRRXJ TO HELICOPTER C Q. ,. ISOn_Xl "

ppu ----_ SCALA1R ,SNnnX,

TER PAST COMPUTER

CYCLE VALUE

I _ VECTOR

' _ F__''_''Ir- i FOLDOUT '"""

k_r st_;n_l flow (tia_ram,

97 ",l:(:f;I)h"P,\(,;'GE BLANK NOT FIL,_,II,:I)
, , q

t" .... !'I

OF l '

I

i

hR

4'

IR ;

IF

dF

Figure 3.- Helicopter rotor center of gravity positions relative to rotorcraft

center of gravity (ref. i).

c-g.actual

AXcg _

• c.g. basei,ne

Figure 4.- Actual versus baseline helicopter center of gravity position.

PRECF-DI,NTC,P,,_r:r- ",r.ANr_ N_OT FILMF.D

99
Figure 5.- Reference frame transformation through shaft incidence angles.

T F

YF MhubF _ YR _= M..hubR TR

_, _'_ _'t "_ QAEROI=

""Z-.._F1

WF .WF

ZF2, ZF

ZF2, zR _

Figure 6.- Reference frame transformation through rotor sideslip angles.

100

,)
q

PITCH ARM ,J

.iX LEAD LAG ,,

C \ _/I/'.. r _z' HINGE

BLADE j

111" I PIAXIS TCH _I,

FORWARD

HUB _ _BLADE FLAP AXIS

WITHOUT PITCH-FLAP COUPLING

WITH PITCH-FLAP COUPLING

Figure 7.- Modificaticn of rotor swashplate arrangement for pitch-flap

coupling (ref. 11).

10l
i+ B' B'

, ICF1 ICF

_ /

/

/ \,,

1CF

\ /

\ /

\ /

\ /

_,=0 °

Figure 8.- Correction of cyclic pitch inputs for phasing angle, #PF"

F

L L02
i°. _',2_........

i'I OE l_'u_.,,_...... . _ ,,

!.

L,

• 0.25 < _ < 0.35

,_ INTERPOLATE i

,<

'. o .1 ,i

Yz o

u. ,07

I,u

I-- q

O

w

o

t J , .

0 .07 .1 .2 .216

CT/°I UNCORRECTED FOR ROTORSTALL

CT/O]UNCORRECTED_<0.216

<_0.25: CT/OICORRECTED = -3.572 (CT/o)2 + 1.5494 (CT/a} - 0.02095

/__>0.35: CT/O]CORRECTED = -2.737 (CT/a)2 + 1.2884 (CT/a) - 0.006776

0.25 <,u < 0.35: INTERPOLATE BETWEENVALUES

CT/°I UNCORRECTED > 0.21(;: CT/a ICORRECTED = CT/° IUNCORRECTED

Figure 9.- Rotor stall thrust coefficient correction (subroutine RSTALL).
411

i

' 1

I' OF P0_''. _ ......._t,+,+

_'r +,

+

+ + :

"+

t

J

I ,-_ I J _+ 0 1 10,000

i ' (h/D)ROTOR

L

Figure i0.- Altitude dependent term for thrust modification due to ground effect.

Figure Ii.- Rotor stall torque coefficient correction (subroutine RSTALL).

104
.... _"_-- .!, .i r / Eo=IJiP

! OF l-'o0,;,.,........ " " ,I

I

MODIFIED O..,j

t _ ,,,/,_CO

NMODIFIED Q '.

Q I ,

11 I

INCREASING/_ 4,

J

Veq

WHERE ACQF,R IS COMPUTED AS FOLLOWS:

IF ,u_<0.1: ACQF ' R = 0.000833 (0.088 - PF, R) + 0.01753 (C'FF,R - 0.0062)

IF0.1 <p_<0.2: ACQF ' R = 0.0002 (,U.F,R - 0.1)-0.00001 +0.01753 (CTF, R -0.0062)

IF 0.2 <,u _<0.3: ACQF ' R = 0.00042 (/_F, R - 0.2) + 0.000006 + 0.01753 (CTF ' R - 0.0062)

IF p > 0.3: ACQF ' R = 0.0016 (,UF,R - 0.3) + 0.000048 + 0.01753 (CTF ' R - 0.0062)

I F ACQF ' R < - 0.00001 : _CQF, R = - 0 000""

Figure 12.- Empirical correction of rotor torque coefficient

(in-line calculation).

1.80 d' (FORWARD FLIGHT)

FF R

d' (REARWARD FLIGHT) FRF

1.50 1.00

.50 __.,,_.,......__________ ___ -..<)..-.....

-XF/,UF (FORWARD FLIGHT)

-_R/PR (REARWARD FLIGHT)

0 .5 1.0 1.5 2.0 2.5 3.0 5.0 10.0 100.0 10,000.0

Figure 13.- Rotor-on--rotor interference terms: d'_ "forward flight) and F

and d_R F (rearward flight) FR

105
Q/ • •

!. 0 .5 1.0 1.5 2.0 2.5 3.0 5.0 10.0 100.0 10,000.0

[ Figure 14.- Rotor-on-rotor interference terms: d_, (forward flight) and

I and d_FR (rearward flight).RF

2

r

-" 3 ' ' ' ,

II_ " 1 2 3 4

- ;_/_

!I -

Ii Figure i5.- Rotor on rotor interference term.
is i /r ,, ,f

/ /

ORIGINF_L p.!,..t._. ,._ 4'i

I OF pOOR QUALF(Y,

_-_

i (ft 2) ,,

_. 40 ."

_. _-- c_= -90 °

..... _ = _20°

--.-- _ = _10°

• "_%_ ''''''' C_= 0 4;

,/, , t _

' 20 .;. ,, \\-..

r_Io" .. ..

,.'.._:._ ._"3,,,,.

il -20 , , ' , , ' , ,

-90-75 -50 -25 0 25 50 75 90

/3,deg

t (ft2)

30

/ r%% _,.._._ -- r-O

./_,,, _ .'_"

.j.,_,, ,_,\..... --'--_=o-0o ,u

20 /,'/ "_'¢\ ....... c_= 20°

o,oo

_:-Io"

,,j -"........... ,

"!

I, Y - . .,X

_4-" I" : "-. "_"-.\

_" i" : " _._

i 0 ....

-10 ' ' _ J _ ' _ J

-90 -75 -50 -25 0 25 50 75 90

/3,deg

Figure 16.- Fuselage drag data (table: FDOQT).

107
'J" _ 1 _

(ft 21

600 ,,,_ _

,fo.._':...... \ _ _

400 t_.-.... .".', -, _, 90° ,_ ---- c_=- I

--_ "... _% ..... _ = -IU ° q,

_ "._' _ --'-- c_= -10

"_ "':' '4 ....... 0° "_

200 _. "._..,,_

-200 _

-400 ',:,x".. ....

_. *%'° °'_S S

%% _* SS

% •

-600 I J , i I J _/" _ ,P

-90 -75 -50 -25 0 25 50 75 90

3, deg

(ft21

600

= 90°

o_= 20°

400 --.-- c_= 10°

_ ",_._, ....... o_= 5°

"_. "_'_ -- o_= 0°

200

>'T_ o

-200 ,_.

-400

-600 1 L L __ i l L _ L a

-90 -75 -50 -25 0 25 50 75 90

3, deg

Figure 17.- Fuselage sldeforce data (table: FYOQT).

]08 ) ;
• J

o f

i

i'}

i ',

[r OF F'_..,

L/ (ft2 ' '_ '

_, 200 "

l ---- o_= -90

_ ....._ = -20"

• --'--cx -- -10" '1

.,''',,. ..,.'... ...,,, _ = 0 °

/ ,. -- ...\,

• ,:." ",

= / ,/.." "-',,, x. : u. -200 /

_ //.. %

. ,,,,

l° o•• •

",,X, -400 _'

-600 I , , , i , , ,

-90 -75 -50 -25 0 25 50 75 90

/3,deg

(ft 2

200 ..

• ,*•••,o ••°°•

• ,° ,•

..'" j._'_.,, "'...'" ../'""_ "...

• / _-" _ ",, "-.I s,," _ -_. "_ .

•""/,," / ""-- x ",".,". i

<,> ."/;" i \ "','.'..

u .. / \ ,,', ". ,,.

• I/

..'/,,/ \ ,_.... 200 -z">" I \ ,,,,,

,_" / ---<_: ', 'k.. / 0o "'.

..... --'-- oo__== 510° ° _._..... _

-400 ...... _ = 20°

l _ a = 90°

-600 i , i __L i c._____j

-90-75 -50 -25 0 25 50 75 90

/3,deg

Figure 18.- Fuselage lift data (table: LTOQT).

IO9

,)
OF PO0:_ _,,. ,.! ....

(ft 3)

100,

---- _x= -90 °

..... _ = _20°

--.-- _ = _10°

O9

it.

,o /

_ "11

-90-75 -50 -25 0 25 50 75 90

_, deg

(ft 3)

100 _ = 90°

c_= 20°

_= 10°

_= 5°

_.o /

J L_

-5o v,,_, ,(/

_-'...... %, ,'_

-100 --- i , L I............. ,

-90 -75 -50 -25 0 25 50 75 90

13,deg

Figure ]9.- Fuselage rolling moment data (tab]e: FLOQT).

i_ 110

b
_,...... 4i

(ft3) _"_'_ __ "

tl,

-250 _'i

-5qo I "\ /l ,i

:_ -7_0 --- _ =

_cr I cx=-10° I _ = _20_'

-1000 _ _ = -90°

-1250 l

-1500 L J ; L- L j_.__..i_..____--L------J

-90 -75 -50 -25 0 25 50 75 90

(3,deg

(ft 3) i'

2000

....... _=90 °

/'\. __.-- (_= 20'_

15oo / -..\ .... _--_o' :

\

1ooo / \

/ \

/ ,, "\

It. / I _ •

_E_ / / ,, x

, , '\\

500 ./,, / \ __.._...._

./ ._ %%% •

0 --_= L'_-- "--_ _- : " _-_ _

-500 _._.._;__.......,_._x_._.L_ t _ ___L.-.---_

-90-75 -50 -25 0 25 50 75 90 /j, deg

Figure 20.-- Fuselage pitching moment data (table: FMOQT).

111 ,!
.... : r , -7::7.

i (ft3)

i"_ 400

i' .\

I' [ • _I

_. 200 /' \ i \

, ,,,_ /I I-:_-',l._/, ...\.. 4a

/ ....... _ = _90°

; -200 "\'.-- ..... ._-J __.__ _ = _20°

i J .... 0°

_' -400 ...... = = i = J , i ,, J 'i'

_ -90-75 -50 -25 0 25 50 75 90 .i

!: /3.deg

L (ft 3)

ii ,oo ---- _=90 °

i o<=20°

-.- 50 / _ ....... _ =

/s _ __ _ = 0 o

,,............. .,. ....?..<.,,,

zT_ v"A

_.ooo° I= ool of° ** =oolJ.

_ _ ..... _ I _

-50 _-

100 i _ i , _ = = .j

-90 -75 -50 -25 0 25 50 75 90

_,deg

Figure 2[.- Fuselage yawing moment data (table: FNOQT).

C.g. actual

C/ " .

'g'model

c_

Figure 22.- Actual helicopter versus wind

tunnel mode| center of gravity.

112

l
ORiC:i(;',L !,

OF POOR Qu_:_{i_

_RLI.P] BEEP TRIMMER

(LEF I ENGINf MOTOR & L IMITS

()NIY) _ FULL CONTROL SYSTEM

'1() t:C2 [ 44_- "] N2 LEVER ANGLE

Bf.EP TNIMME R

-f%-7_.J /-L_t.OU...EEPER

0C) '.) _1.. INGO3L

IBQTH ENGINES) "FEP ?IIC,

I

N2 ERROR

1 N2 LEVER DEADBAND ACTUATOR FT- COMM ACTUATOR (t C 1,5 75 r-T-] .... "-'l N 0 ARM 7["_"-_--'-m N2Lt:VER r_

(7 "--_--" EN2 COMMANDANGLE.._ N2 ,N a, I /I 2"r r---5,ec-_, *10 POSI,ION .... 17'5'5/-I-ANGLE" N

o _--J j__' =ool _ ,,,Q,.v:.. T L______ ?N, :0 I__.______.... J I-- L_

,=T=.ovL 1

_oo..,20o _ I *' 09 -,',u,.

EN_,TNER,LOOP M _ = " "-- ='''' I

20 FUEL CONTROL

Sc BIAS N2 LEVER ANGLE L, MOTOR & LIMITS _

DCQIAS

1 _7-,.;f:::l THROUG. ,,_

L "c

.o, ! 2','

o°o_,o, - "'"°lk "_'° I ,..uo,

21.91

NR o

ENG14L

DAMPING

GAS (JENERATOR BOVK2 

i

TORQUE _

:M_-_"_- _'-"_:_ p=_//_, __, AVA.LA_LEr .rl_\__A . TORQUE.OV..,....

LOw=. ""PE" / ,.,,;;_l_,,,

_-- ] XOBLOiNV

ENGINE)

•EN_'_u-_ 7LI_ 100 IIVAmAB LIMITSPOLEWER _.ovR, - 1%JRB .

o._ooo - _,,_.._o..==

Tf3ROUE

(FROM REAR

POWlr RT ROTOR )

I, E27T

!_,NR

OMEGA ACCESSORY ft Ib

POWER _19,000 _c _

TOPPING REQUIRED _ ,'

t/_-_RE E

TPL_ POWER _"J_"-" OMIGRFI Pace

ENGINE APR

GROUND ANGLE " r__

CONDI LEVTEION R _5_,,_-,--_)% ENGL¥t "v L i 0h1 J ENG20L -- = L_ GAS TIMEGENERA CONSTANTORT

PE RCENT TOPPING --- P_ i _

POWER 400 , 3000

o3 _ _owT

" .u,,

OMEGA _ ;

_ra_d/1_:) _Pwr MOQIFIE R

DAY TOPPING PWR )

1500, • 15OO

GOVERNORE_EDSACK_OOP

Figure 23.- Engine, governor, and shaft dynami(_ block diagram.

FOLDOUT FRAME - ..=,..., -;,,..,... o.11), .ac" -- i;
F /r,/

I'

(_'. |

FUEl. CON I ROE ,%YSf_M

i

N 2 ERROR ' '

• ACTUATOR

DkADBAND COMM ACTUATOR 15 75

(_C t 7___-- t N2 LEVER _ ...... 1

• r _'----'_ er _ _ O POSITION p (/b //_ ANGLE (,,2) R,.., | i

r- J-_--_ -io ACT,EL_ . .. _ q

[ L-----'-_I | "2., oo o_ -....

=,auL I _,

-;!?" , I °•'

FUEL CONTROL I ;;

MOTOR & LIMITS I *" 

_

N:_ _!

jf'_

J

ENG14L ,i

OAMPING _"

TORQUE r_ -,_

BOVK2 I

b_ -=-==! SPRING I

TORQUE _ V-_ [ '_':F _ {

RESISTIV t GO. T

POW ERLL'I-_ L HP REQUIRED

GOVK I GAENFR

"=-'_ UPPER 1/_ "2Ref

j LIM 1/OMEGA TORQUERJ '_---_. 5:'

1t ENGINE) E(_"PF

_F_ VARIABLE POWE R

: - _ [_ i00 pj Ch_OVP" _ I"ITURB i', -

I_NG27L LIMITS

TORQUE

0 "" 3000 IFROM REAR

POWERT ROTOR) XITURBI

i E27T

ACCESSORY 99 f)O0 ft Ib

POWER

TOPPING REQUIRED sec 1/!_RE F

POWER Pacc OMEGRIrl

APR

TIME CONSTANT

V_ 7s-g-3

__ TAUPWRL

40_. 3Cu_

_WT

TAUPT

_Pw_MODIFIER

10

1500. .1500

GOVERNOR FEEOBACK LOOP

¥ernor, and shaft dynamics block diagram.
" l

t

t'% ,1 ̧

60 _

i- 50 9.1 !

Z_ 40 llI

_. Ill

; =i

_'_20

;. zN

10 V

i i i i I i l i

0 1 2 3 4 5 6 7 8 9

6CTOT. deg(DCOLTOT)

Figure 24.- Computation of N2_ C as a function of 6CTOT .

30 '"i

,It

' ¢3

Z

IJJ

..I 20 _

L_

Z

ll:

Z

0 | __ l l I I l I l I

10 20 30 40 50 60 70 80 90

_2, deg(ENG13L ENG13R)

Figure 25.- Determination of fuel control actuator position, NR_.

i--r ", ,° "I , , ,.,[,_G PAGE P,LANK NOT FIL,_IEI)

115

)'

i
I:

'" ORIL_(_qALPP,'2_i"'_

OF POOR QUALiI,,/

lq

1.0

.75

L_

.5o _

-- .25

• o. , ! I I

F,-

0 1000 2000 3000

PL, R (POWERLPOWERR)

Figure 26.- Power dynamics time constant (table: POWT, TAUPT).

200O

1500

z

1000

Z

W

50O

I ! I

0 1000 2000 3000

PL, R (POWERL POWERR)

Figure 27.- Variable power limits (table: POWERT, E27T).

116

L .......... ' _ ._ _ : -_:-__-:_" : "I_'_2"_" °'_ ...... _._,
O'

O;.... ,.....

% OF POOR Q_,.',

_ 1.0

9[ _

•8 _

.7

o

N

_ .6

Z

_ ..j .5

0

r_ .4 ,:

U.I

.3

.2

.1

0 .1 .2 .4 .5 .6 .7 .8 .9 1.0

N1,% (ENGLV1LENGLVIR)

Figure 28.- N z lever topping power correction term (table: ENGVLT, E2OT).

IOF

, , , ,

t- -1500 -500 500 1500

PERL, R

Figure 29.- T modifier (in-line calculation).

pwr .
ORI_!N/_£ _"_ ' 1 OF PO0_ Q,.;;.Lii,_? '

-t

w

.75

2 /

N .50

O .25

- /

I// I I 1 )

0 10 20 25 30

_} rad/soc

Figure 30.- Percent topping power (table: OMEGAT, POMEGT).

T

m" TOPPING "

IJJ t

POWER

O(3.

C3

z

< \

O

o

a

.,,.I

Z I ,_

N R NR N R

Cmin. ¢ NRCmax.

N R, rad/sec

PCOMMANDED = M (N R

(UNLIMITED) -NR¢)

M = 955 HP/rad/sec

Figure 31.- Unlimited commanded power calculation.

]18
UPPEI_

CUMULAT,VE S,,ASP'..ATE%C

,.c.co. _A..AL LA..ALSTOPS ,'OSI,ILOIM,TS N STICK r ,.,,_.--_ ] +4_._]/-- F--"

1 LIMITER 'HTRYF THTFIP

_Ap O m,

- TFI

DLATP AlCAF + / -16,5 J ON|PT2

THTRYFUL _ THTFSPUL '

0 THTRYFLL J THTFSPLI. (FO_

• O DLATUL RC

o _ IEC$CON ty RSASPOi.-TU. A,CA. sw,v

hAEcs hAsAs _TF = 7.85"

DLATECS DLATSAS THTTF

S;'ICK +

IECSCON LIMITER

_Cp 0 1 _) : ._ _) tJFPP ' 

DCOLP 0 _ THTOCF i + [_-_1.65 I L__

0 y OCOLTOT THTFPPUL THTFPPLL TI (FOR

IECSCON O _ d 1 .OCOCl,.k COLUL THTOCR PIVCRO

_C!cs [ _.or- /-- -

_ v r / , 60 /

DCOLECS n VkEt' ? "_t_l,:_i" J 1-20_

'_BDcP) 1 i LONGrrUDINAL CYC

TF"M SCHEDULE

Veq _ _(in)_

IDCPT 0 ,,_)5DCPT BDC P LONGITUDINAL I

IECSCON 0,_ "r STIC K

5Bp O _: I_ I- [______.J THTBF

DLON'P"_0 _ /" '_BToT -I. THTOBF DLONTOT] _ t

0 /' _ £ I -e.RO" de9 /BR _: : _.++? ('RSP _'1 "-'/1165

O A01 I OAO DL_- I"1_1 THTBR I+ THTLCR THTRSP

I I DLONLL THTOBR I " '

=' THTRSPUL T

BECS ,yIECSCON hB(SAS _RSASQ UTR = 7.85 THTTR THTRSPLL (REAl:

DLONEC$ DLONSAS ROOT COLLECTIVE SWI_

I WITH _C FULL DOWN

IlrCSC_;_ PEDAL

1 _

OVAWp o-_"-'-" ' + I +4e3e/--I r---

,_'v r_ ] ...__3.60, ' iOYAWTOT_ "RR ; _X,/THTRYR, _ HTI _ YTN I I "rRP

o

O, (_11 10 O O,&WUL _ THTRR _ -L__,___T; j.Rpp ij//T,.. t lECSCON OYAWLL AICRR - . _:1 ;.65_J L__

y RSASR THTRYRUL THTRPPUL T

_ THTRYRLL _ -_ TF'.tRPPLL

FIRST STAGE SECON _ _:_AGE (REAl=

5Ri_cs 5R_;AS MIXING MIXING PIV( DVAWS-S owwecs

" v_ _- _._L__--_--

(kt._ 6o_2o

FOLDOUT FRAME

,tlRure 32.- ,Mechat_[c;_l control sy£tem £chemat[{.:,

_Jl'_LJ: ,';. , " ' "j I I_

OF POOR QUALiiY

L_ .............. "
- r ....................... I

d

UPPER BOOST

I,ATIVE SWASH PLATE ACTUATION

bL STOPS POSITION LIMITS DYNAMICS

__3 . =+,;_s___/__._....!_ "_L__. "OF' I"°, I

-- -- =- j T.OF.¢, 2'

-- __]TH'IrRYF -- _ T.rFSl=I/ I I _FSSP+1ITHilS, p0 OTHOF.C ¢ <,=n o.-p:= _+ /-'-11's" J I__J ("',) / THTmUL TFS,

-- ,.,,.,L- (FORWARD

ROTORI---- " ]

,,,s_ 5 "EPP S_,VEL,NG/ ,__) "i

_I'F ,

)'/ THTLCF y

_3 : " _AICFRC l

THTFPP v THTFI_PD DAICFRC _ (tad) - . HALF (deg)

THTFPPUL TFPP

THTFPPLL (FORWARD ROTOR i i

PIVOTING)

-, 13.O: 2-r .,--ve---- :1rLcFS+ 11 ,l'c ,B, .,

;-- ............ : _ - : _ -BICFRC,

-1. DBICFRCN DBICFRC / (rad) _ I

(deg)

LONGITUDINAL CYCLIC TLCF

TRIM SCHEDULE
_ D.C.P. AUGMENTED

J I _LONGITUDINAL CYCLIC

1 POSITION GRADIENT

FORWARD 1 11"_ (STABLE)

. _BDcP r

AFT _ NATURAL LONGITUDINAL " I

jCYCLIC POSITION

I I ___. GRADI ENT j (UNSTABLE)

0 50 100 150 200

AIRSPEED ,;

(knots) i

Figure 33.- Longitudinal cyclic position gradient stabilization with

differential collective pitch trim.

2.35 /,E)

2.0 --

krL

o

E3

.E

Q.

O 1.0

n_

I I t

0 50 100 150 200

Veq, knots

VEQ

Figure 34.- Longitudinal cyclic differential collective pitch input

(table : VDCP, DCPTT).

;'!,'I':(:I'U)INt; PA(;E BLANK NOT FILMED-

.I

121
t

Kq?B_ r2 = 2.0 sec LONGITUDINAL SAS r I = 0.37 sec r3 = 3.6 sec r4 = 20 sec ACTUATOR LIMITS

+16,0 in. EQUIV. STICK 1 r 2 s+ 1 r4s 8BsAS I

rad/secPITCH RATE r 1 s + 1 r 3 s+ 1 r4 s + 1 DLOI_$A$ "

in. "J_

GKQDB T1 T2, T3 T4 -1.7 *-_ 1.7

ALONLIM

Figure 35.- Longitudinal stability augmentation system.

KP_A r5 = 0.05 sec ACTUATOR LATERAL LIMITS SAS

p_._B+4.0in rad/s.ecEQUIV. ROLL RATE ST:CK PBG r5s1 + 1' 1I-_/I-1"01DLATSAS 8AsAs in.

GKPDS T5 -1.0 _ 1.0

ALATLIM

Figure 36.- Lateral stability augmentation system.

[22
]

OF F'Ot.,,i _, ......

I } s,','r,c,,oR'," •

=1.1 ( )=in[2×52°1 PRESSURE DIFFERENCE

PRESSURE = :. ----- QBAR 1

CK q,

SIOESLIP SAS

SAS PORT

ACTUATOR d!

_JRti in. DYNAMICS i

flFUSELAGE

BETAF$ [

DRB-YAW I rR5 s + 1 ' DRBYAWI: ..._i i[;.

-1.57,, +1.57 TR5 ' 'J

(rad) -1.7in. " +1.7

DBYXT

_VE _ in._EDAL DBYAWT ';,,

K_p 8r in, H20

• 8R/3

VEQ I GKDPDR •

VEL! DBYAW

VEQ$ST

GKDPT

SIDESLIP SAS

DIRECTIONAL SAS

ACTUATOR LIMITS

TR6- 3.2 _c _ .6__

PBP " 15'77in'EQUIV'PEDAL l = " 111 8RPs+I _- _--=-- 1 __ _RSAS-_ rad/sec ROLL RATE PB1 TR6 DPYAW DYAWSAS

GKPDR TR6 -1.68

-1.68 ,. 1.68

TURN CO-ORDINATION ADIRLIM

rR3 - 1.6 sec

rR4 = 3.2 sec DRYAW ,8R r

Veq < 40kn._ r R44S+1 1 _

r I'''nEOU,VPAEDAL LE1N___rR1 T =

'1_°_ I2""(""'R3'IO. +11<,W_

R-B I r_ _rRlS+l_"_ _ rR2=3-2sec Wl_

L __z__

GKRDR TR1 r R s

Veq ?_40knots { rR2s+ 1 IDRYA

TR2

RATE DAMPING

Figure 37.- Directional stability augmentation system.

'I

123

t
_. ORIC.iN#.L _"'..

.5 OF POOR QL,;.,'.....,

e_ .4

,.r .3 L.

c_

m .2 0,.

¢ya. .1

v

l I l J

0 60 1O0 146 200

Veq, knots

Figure 38.- Velocity dependent sideslip SAS gain (table: VEQSST, GKDPT).

q3. .952 L/J

_ o[//_ /I/'

-.952

-1.7(_ L. 1 J

-1.7 -.68 0 .68 1.7

6R_ I UNLIMITED

Figure 39.- Sideslip SAS actuator limits.

124 '_

P

I
:w d

. 1}_

_ Oi:_ i._,

+1!

IN

J

t -1 -._--.I A A I I I 1 I I I I J .-L--J__.L I I l i I I., I I L J

+1

.i L.

ff

-1 I l I I I I I t I 1 I I _J__t I I I I I ; I I I I t

+25

•_ 0- °

_ -

-25 _ i ; i i J i i i i i 1 i _- i i i i i i l J J i i J l

+5-

C

,_ 0

--------r'_,

-5 -- I J I l I l I I I I I I I , I I I 1 I 1 I i I I I 1

0 ,5 10 0 5 10

t, sec t, sec

SAS OFF SAS ON

6B = 0.25 in. X 1 s_ PULSE 6B = 1 in. × 1 s_ PULSE

Mq =-1.1 Mq = -1.1

-.....

Figure 40.- Longitudinal axis dynamic response SAS OFF and ON;

hover, weight = 33,000 lb, nominal c.g. position.

125
+11

'i

#,

,Q" 4 j

- !

-I I I ! _..... i _ J . I ] l I i i I i i i i i J

! +.5

i

Q.

-.5 J l J J I - 2_ _.1 _ L I I I I I I l 1 I I J i

p i

-50 II lilllillllllt

+5

.E

_5 1 J I 1 I I 1 1 I I 1 I I 1 I I 1 I 1 1 1 ! I 1 I I

0 5 10 0 5 10

t, $ec t, sec

SAS OFF SAS ON

,5A = 0.25 in. × 1 $ec PULSE 8A = 1 in. X 1 secPULSE

Lp = -1.28 Lp = -2.16

Figure 41.- Lateral axis dynamic response, SAS OFF and On;

hover, weight = 33,000 ]b, nomlnal e.g. position,

12_
' 7.7/.... ,_r_!l,

.i

ORIGIN,e,{L-q:;:.. ,, .. Ii

orPoorQu,,Lkg+ '*

+.5r- _

_ 0 ..__r__

ql

-.5 I 1 t J i t _ 1 I I I I l F I l I ! _ _ I I L I 41

+.5

L.

L,.

r -

_,5 L i l i I I , , , i l l = i , l , _ = = t l l l i i I

+100

_-

_-

-100 t t t l _ t J a I i t l I ¢ t t t t t l I 1 1 t _ I

+5[

.£

-5 l t I t J t l l i i 1 L 1 LI I | t t t l t t I 1 I t

0 5 10 0 5 10

t, sec t, sec

SAS OFF SAS ON

6R = 0.25 in. X 1 secPULSE _R = 1 in. × 1 sec PULSE

N r = -0.09 N_ = 0.0001 Nr = -0.32 N_ = 0.0001

Figure 42.- Directional axis dynamic response SAS OFF and On;

hover, weight = 33,000 Ib, nominal c.g. position.

t27

U
i i

_ L.... '

+1 r OF i_J<,_ L .,.'., ; , le I

1

_IL_ l I i I 1 1 I I I I ,,1 d l i I 1 1 I I I 1 1 I i i

li

+1-

_ ,

-1 I I I I I I 1 I I I 1 l i i i I I i I I 1 I I I 1 I i

+25

= /

"_ 0 °

_ -

__25 I I I I I I 1 -1 1 1 I I I I I I I I I I I I I I I I

+5 -

e-

"_ 0 _

r - V'I

L -

F -5 l J J l l i I I I l I I I i I 1 i I 1 I 1 I I I I J

0 5 10 0 5 10

t, sec t, sec

SAS OFF SAS ON

6B = 0.25 in. X 1 secPULSE 68 = 1 in. X 1 sec PULSE

Mq = -1.63 Mq = -1.63

Figure 43.- Longitudinal axis dynamic response SAS OFF and On;

Veq = 75 knots, weight = 33,000 ]b, nomlna! c.g. position.

128

,),

i -- - m ....... =... h • --. .... . . . -- , -- • .mdid_
Figure 44.- Lateral axis dynamic response SAS OFF and ON;

Veq = 75 knots, weight = 33,000 Ib, nominal c.g. position•

129

..)
,.;i<_t.P_!_'hYL AGEIll .1

PoorQuAuw ,l

+.5-__ j

-

IN -

_ o -.-¢-% _

-

k. '1

- 1

-,5 1 J I 1 I I I I I I I 1 J , t 1 t I I I I 1 I 1 I J. i _:

i

i

-_ o _

-.5 1 I I 1 t I I l I I I I I I t I I I I I t I I I 1 I

+100

-- !

-100 IIIllllllllll IllJllilllllt

+5 -

'--

': 0 __l-I

cl:

-5 I 1 1 1 t I i 1 I i t I I 1 t : __], I I 1 I I t t i I

0 5 10 0 5 10

t, $ec t,sec

SAS OFF SAS ON

6R = 0.25 in. × 1 secPULSE 8R = 1 in. × 1 $ecPULSE

Nr = -0.062 N/3= 0.148 N r = -0.062 N/3= 1.38

Figure 45.- Directlonal axis dynamlc response SAS OFF and ON;

Veq = 75 knots, weight = 33,000 Ib, nominal c.g. position.

J

130 J
e

; q Oi: _,_ Q3ALITY .t

"_ +1 -

.ff

-1 J t t I I I I t l t J I I l l t I I 1 I | I I I 1 I _i

+1

!,

i . ¢J

i ,

_ L

o" ,i

I

-1 1 i l I i 1 l i 1 l i i i _L._J__I 1 t I I I 1 I I I t

+25

-o 0 J

I

-25 L i t 1 i i _ i _ , , 1 1 i i 1 i 1 1 i t ] i j

+5 ;

e-

,_ O_

c,O

- ___r-!

-5 [ I t I I 1 I I I I 1 ] __ 1 1 I 1 I I I I I I 1 1 I

0 5 10 0 5 10

t, sec t, sec

SAS OFF SAS ON

6B = 0.25 in. X 1 secPULSE _B = 1 in, × 1 secPULSE

Mq = -1.68 Mq = -1.68

Figure 46.- Longitudinal axis dynaml_- response SAS OFF and ON;

Veq 130 knots, weight = 33,000 ]b, nominal c.g. position.
a) 4

i _Jl(IL_ll',<_., ., _-;r<f.._- ....

• ,

OF POOR QUALi_Y

' lJ

+1

, E

IN

_ -

°Q" --

-1 I 1 I I I I I 1 1 -J 1 I J l 1 I I I_ I I i ! I I I I t_

,D

i --

-1 ' I I I I I I I 1 I I I I 1 I 1 I I I I 1 1 I I I 1 I

+50 -

o -

r

-50 1 l i J I L I I _J___L__L _ I I 1 I I I 1 I J I i J i

k

._=

a: 0 _'J'--_

oO

--5 l l I l I l I I J I i I I fI I l i 1 I I I i I I I J

0 5 10 0 5 10

t, sec t, sec

SAS OFF SAS ON

6A = 0.25 in. X 1 sec PULSE _A = 1 in. X 1 secPULSE

Lp = -0.93 Lp = -1.83

Figure 47.- Lateral axis dynamic response SAS OFF and ON;

V = 130 knots, weight = 33,000 Ib, nominal c.g. position.

eq

1 '32
Figure 48.- Directional axis dynamic response SAS OFF and ON;

V = 130 knots, weight = 33,000 ]b, nominal c.g. position.

eq
I

_Q W

1 ORIGINAL PAGE I,_.) ,

_% OF POOR QUALI'Ii_

i

XBOOy

TI

I

ql

0SL LONGITUDINAL GEOMETRY

ZLOAD

'_BOOY

LATER,_L GEOMETRY

XBODY

XLOAD

ZLOAD

i ZBODY

DIRECTIONAL GEOMETRY

YBODY

YLOAD

Figure 49.- Slung load geometry (fig. 6.1 of ref. I).

i 1'34 1

......................... _._,!
_l_i_ _ _"_=m_IZWJ-_- - "_"7 - I

' ' 7:7

. ]I

OF PO0_ I_t;;,i...__V "

70:..... ;::-:;_:,_..

--40J _e, = 0°

_ 20 _SL=2o_..__ / °

-- 10 . . _SL = 10°_--____ _'o I

10 20 30 40 50 60 70 80 90

/_SL,deg g

Figure 50.- Slung load drag force (table: SLDQT). .

-50 \ ___....J_ _ _ 1,,o

I \ x\ _ __._--------- SL Uo

-100 "_ -'---°_SL= 20

..I

-150_ "_

-200 ---:-_._ ....

0 10 20 30 40 50 60 70 80 90

_SL' deg

Figure 51,- Slung load side force (table: SLYQT).

100 ""-

/\

5°i \\

-50

._l -100

z -15o

-250 o_SL= 0°

-300

0 10 20 30 40 50 60 70 80 90

_,SL deg

Figure 52.- Slung-load yawing moment (table: SI,N(_T).

,I

1_5