D-Ai45 899 A MATHEMATICAL MODEL OF THE UH- HEL IUV

NATIONAL AERONUATICS AND SPACE ADNINISTRRTIOH MOFFETT

FIELD CA AMES RESEARCH CENTER K B HILBERT APR 84

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NASA Technical Memorandum 85890 USAAVSCOM T~chnical Memorandum 84-A-2

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A Mathematical Model of theUH-60 HelicopterKathryn B. Hilbert

April 1984a- l~~~llS LE C-- ,-4S

SEP 2 11984

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This document has bee= appmoedtot pub .isale and sae, itsdistribution is unlimited

United States AryAiation SystemsNational Aeronautics and CommandSpace Administration U9 21 046

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NASA Technical Memorandum 85890 USAAVSCOM Technical Memorandum 84-A-2

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A Mathematical Model of theUH-60 HelicopterKathryn B. Hilbert, Aeromechanics Laboratory,

U.S. Army Research and Technology Laboratories-AVSCOMAmes Research Center, Moffett Field, California

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NAMINational Aeronautics and United States ArmySpace Administration Ai ytmAmes Research CeffterComnMoffett Field. California 94035 St. Louis. Missouri 631201

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SYMSOL$

a blade lift-curve sl ope, per rd

ao blade coning angle measured fram hub plane in the hub-vind axes system. red

al longitudinal first-harmonic flapping coefficient measured fram the hub plane in

the wind-hub axes system, rod

ay lateral acceleration. m/sec (ft/secl)

* bi lateral first-harmonic flapping coefficient mesured from hub plane tn the wind-hub axes system, rod

C- rotor thrust coefficient, T/v(ORt)(R)8

D Drag force. N (lb)

H rotor force normal to shaft, positive dovmiind, I (Ib)

IHS incidence of horizontal stabilator, positive for leding edg. up. red

K tall rotor cant angle, rad

K. pitch-flap coupling ratio, tan 6

i fuselage rolling moment, X-s (ft-lb)

L fuselage lift. N (lb)

*00

M P rolling moment, pitching moment, and ywing moment, respectively, U-1 (ft-lb)

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p

q roll, pitch, and yaw rates in the body-c.g. es system, rad/sec

q dynamic pressure, cV, X/a' (lb/ft') :4I,, r .

Q torque, $-a (ft-lb) .

' iR rotor radius. a (ft)STA longitudinal location in the fuselage axes system, a (ft)

T thrust, X (lb) ....

j~d~~CONN

V'0a

V longitudinal* lateral, end vertical velocities to the body-.,. sysle of an*&.J rI/Sc (ti/seC)

v tall rotor Induced velocity at rotor di6k. esaec (ti/ec)

At. verticil location i the fuielage awe system. a (tt)

x1Y lossitudisa1 lateral, and vertical forces tis be bod,. , .. as *yst_. ,Ib)

zI

* StblliimS surface agle of attack, fed

d'%4 rptof sideslip angle, red

bl-d. Lock number. oac I'/l

* .quivoloat rotor blade profile drag coetficiest

lateral cyclic stick mmemst. positive to riot. Ce (to.)

cilleciii cmirol Iput, poitiw up. cS (is.)

Ivatitudial cyclic stick eSemte Positive aft. cm (10.)

I lpedal MOeV eto positive fight. CS (1i.)

l" ee-t Is

iuler pitch aegle. red

blede rot collective pitch. red

total bladle tist (root slam tip iscidsace). rad

*' Inflow ratio, I -T

rotor advance ratio,

*" € air density. bg/s1 (li*It')

rotor olildity raio, lise reuldlalk atae

I iuler toll eagle, red

r uler yM sile, ted

T .rotor agular velocity, radliec

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CW castito amm syst

C-2. congsv of pwticy

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f* W'O* fW*ItWp sinv**mIcS Swt* O.MuId Wa~it ariely W1,44-400001 feet40t PV*4WVted toe tfcto"Ce 2. T~be fe"I&e. folt*. am *vW~ oiq~tlfatewt* atief tm 00"0s t"-t dots Val" a twpuessio* alw#rtt ft*f- ).. VW*n aslontlo 10el Ifits & c*Vn to top"s *at* *ea 0 4.641l.0.t f"Ottle ef sweet'a owtwdhpmnt Wailabft

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ftaeIage forge and 80000 0009tow gives tiroeewo I star* gboy aire *peciic to

ghe U*60 boktqopser.

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The Induced volscity at the tail mow tat

The torge. as Ot all MOW& 9M hent ds ote o be calculate metog a troos-

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Fiaure 10 is a block diasrm of the UI-60 horizontal stabilator control system(raf. 2). This logic has ben incorporated in the generalized stability and controlausentation system of the math model. The stabilator logic also includes the provi-*Ion tor a fixed horizontal tail incidence that is to be specified by the pilot.

PITCH SIAS ACTUATOR

The M--0"s control system includes a pitch bias actuator (PMA), a variableLength control rod which cbasete the relationaship becveen longitudinal cyclic control.- wd ow4hplate tilt as a function of three flight parameters: pitch attitude, pitchr4to. and airspeed. The main purpoec of the PM is to Improve the apparent staticLonsttudtnal stability of the aircraft. A detailed description of the PRA is givenin Wrtwrente 2.

the PM was modeled directly from the block diagram shown in figure 11 (ref. 2).Cho atr~lwad toedbmk Is only active between 90 and 180 knots since below 80 knots.tho ott*pe.d Veedback for the stabilator perform the sme stability function. The;t ht *tttud& *d rate feedback is active throughout the entire speed range. As can

b or," rion the block diagram, the PA actuator authority is 152 of longitudinalv tult throw and ha a maxim rate limit on the actuator travel of 32 per sec.

tP, output u t O P "I s added to the total longitudinal cyclic control. The PBA* kt-: toatudefo ea al/e/o witch to Inactivate the PMA, if desired.

01-60 DuE PTION31 RMINTS

r*btv I list, the printer. required to model the UW-60 and the values used inth, mah . 'dol, Ibl table is Identical to table J-1 in reference I, except thattoot of ,O t qvitvd twol.e prmter have been ellainated because of the modifi-"-t oa to itm r1%olae aerdymdmsc model. The values listed for the UN-60 in1*bto te 061i*ed from tverewe 2.

tole " lit9 the m~er* feedtorwsrd, croeofeed, and feedback ins for the>L-AO wtrvl oy*to (see fin. 4 of re. 1). A detailed description of the four con--. o colov'i*q is gtve* I% referwece 2.

* r'1 ) lists O petmier that re required to model the two General Electric.?rA)--k.-O* e*Irme that pwmr the N-40 and the value that are used In the mathm,v.t. Thus vala.s to bawd am available TT00-CE-700 eaine data for the AN-6

tW40 Mn N U IIE STICS

Tal e & list* the flst cottol Ittlon, tag Ac. and 6.pe the lateral andv'ttlei "wlrities io 64" em, vS MW vl, &ad the uler pitch and roll angles,* d i. ftt theo -4 ttla d I* lowl flight at a variety of airspeeds.

'II

W-60 STASILITT DERIVATIVES

'~~b~U- *~-kI~fto-0 ao for the UH-60 math model are presented in.uIttj 46, A*) "gtv*gtvws were generated under the following conditions:

SWmet flisist

pmsch Ise actuator on

* wv~a..ual etabilator active

oftse/perr model off

, ' Di / 0 brB M 5.0 deg/sec

a is 66* A 0.1 in.

'I L6 ~ - 0.1 in.

J ko* o4M A6 c 0.1 in.

Ai6 -O0.1in.p

Put~ somoo *lability derivatives were obtained by considering.44sA oo 4ps" W .swmb~loi about a reference trim condition. The

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N36L VALIDATION4

F . -f tt~ meLftst% godl was accomplished by comparison of trim and~* tftq sete generated from the UH-60 math model with data that

~ ~'-~ otaw total force and moment math model of the UH-60, devel-P,* to*409ed Digital/optical Control System (ADOCS) program

OLa'm tI #* level flight trim characteristics and dimensional sta-

~ gsp~vot~ by the 1seing-Vertol UH-60 math model for comparison

to tables 4 through 10. These derivatives were generatedA* -ks w&A ta1 ie - h 90-60 derivatives were, but with significantly larger

t" m * #41tibIl M#Ph aircraft gross weight, and a faster main rotor

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rotational velocity. Figures 12 through 17 illustrate six of the more important UH-60stability derivatives vs airspeed. For these plots, the UH-60 data are shown as wellas the data generated from the Boeing-Vertol UH-60 math model.

CONCLUDING REMARKS

The mathematical model of a UH-60 helicopter described in this report was devel-oped for real-time piloted simulation. To date, this model has been used successfullyin two handling qualities simulation experiments on the six-degree-of-freedom VerticalMotion Simulator (VMS) at NASA Ames Research Center (refs. 5 and 6) in support of theADOCS program.

For these simulations, however, high levels of stability augmentation were addedto the baseline UH-60 math model, thus effectively masking many of the characteristics tof the basic aircraft. The baseline UH-60 model has not been evaluated in real-timepiloted simulations nor has it been validated with flight data to determine the accu-racy with which it models the actual aircraft dynamics and handling qualities. Inaddition, neither the analog and digital stability augmentation system (SAS) nor theflight path stabilization (FPS) system of the actual UH-60 helicopter is included inthe model.

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REFERENCES.1

1. Talbot, P. D.; Tinling, B. E.; Decker, W. A.; and Chen, R. T. N.: A MathematicalModel of a Single Main Rotor Helicopter for Piloted Simulation. NASATM-84281, September 1982.

2. Howlett, J. J.: UH-60A Black Hawk Engineering Simulation Program, Volumes Iand II. NASA CR-166309 and CR-166310, December 1981.

3. Systems Control, Inc.: SCI Model Structure Determination Program (OSR) User'sGuide. NASA CR-159084, November 1979.

4. Landis, K. H.; and Aiken, E. W.: An Assessment of Various Side-Stick Controller/

Stability and Control Augmentation Systems for Night Nap-of-the-Earth FlightUsing Piloted Simulation. Helicopter Handling Qualities. NASA CP-2219,April 1982.

4 5. Landis, K. H.; Dunford, P. J.; Aiken, E. W.; and Hilbert, K. B.: A PilotedSimulator Investigation of Side-Stick Controller/Stability and Control Augmen-tation System Requirements for Helicopter Visual Flight Tasks. AHS

* Paper A-83-39-59-4000, May 1983.

6. Landis, K. H.; Glusman, S. I.; Aiken, E. W.; and Hilbert, K. B.: An Investigationof Side-Stick Controller/Stability and Control Augmentation System Requirementsfor Helicopter Terrain Flight Under Reduced Visibility Conditions. AIAAPaper 84-0235, January 1984.

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,j: TABLE I.- UH-60 DESCRIPTION REQUIREMENTS

Description Algebraic Computer Units UH-60symbol mnemonic

Main rotor (MR) group

MR rotor radius RM_ ROTOR ft 26.83

MR chord cM CHORD ft 1.73

MR rotational speed S1 OMEGA rad/sec 27.0MR

Number of blades n BLADES N-D 4.0

MR Lock number YMR GAMMA N-D 8. 1936

MR hinge offset C EPSLN percent/100 .04659

MR flapping spring constant K AKBETA lb-ft/rad 0

MR pitch-flap coupling tangent K1 AKONE N-D 0of 63

MR blade twist 6tM R THETT rad -.3142

MR precone angle (required for aCMR AOP rad 0teetering rotor)

MR solidity a SIGMA N-D .08210 IMR lift curve slope aMR ASLOPE rad -1 5.73

MR maximum thrust Or CTM N-D .1846

MR longitudinal shaft tilt i CS rad .05236(positive forward) s

MR hub stationline STARH STAH in. 341.2

MR hub waterline WLH WLH in. 315.0

Tail rotor (TR) group

TR radius RR RTR ft 5.5

TR rotational speed TR OMTR rad/sec 124.62

TR Lock number YTR GAMATR V-D 3.3783

TR solidity aTR STR N-D .1875

TR pitch-flap coupling tangent KIT R FKITR N-D .7002of 63

- TR precone aOTR AOTR rad .01309

* TR blade twist 'tTR THETR rad -.3142

TR lift curve slope aTR ATR rad - 5.73

TR hub stationline STAin STATR in. 732.0

TR hub waterline WLTR WLTR in. 324.7

47.

.... TABLE 1.- CONTINUED

DescriptionAlgebraic Computer Units UN-ODescription symbol memonic

Aircraft mass and inertia

Aircraft weight W ic WAITIC lb 16400.0

Aircraft roll inertia ' XIXIC slug-ft2 5629.0Aircraft pitch inertia Iyy XIYYIC slugft2 40000.0

Aircraft yaw inertia Izz XIZZIC slug-ft2 37200.0

Aircraft cross product of inertia XIXZIC slug-ft2 1670.0

Center of gravity statlonline STAc.$. STACG in. 360.4

Center of gravity waterline WL c.. WLCG in. 247.2

Center of gravity buttline BLC.A. BLC in. 0

Fuselage (Fus)

Fus aerodynamic reference point STAACF STAACF in. 345.5stationline

Fus aerodynamic reference point WLACF WLACP in. 234.0waterline

Horizontal stabilizer (HS5)HS station STARS STARS In. 700.4

HS waterline 1EL. MRS in. 244.0

HS incidence angle i AIRS rad variableHS area SS SS ft, s.O

HS aspect ratio ARLN ASKS N-D 4.6

HS maxim lift curve slope CLmXHS CIS 14- 1.03

HS dynamic pressure ratio 3Sii N-D .4

Main rotor induced velocity effect KVMR XIKVR N-D 1.8% "% at HS

Vertical fin (VF)

2-. VF stationline STAVF STAVF in. 695.0

VF waterline vLVF in. 273.0

VF incidence angle 'VF AIFF red 0

* VF area SVF SF ft, 32.3

VF aspect ratio ARVF ARF N-D 1.92

VF sweep angle AF ALIF red .7156

VF maxium lift curve slope C1 CLMF N-D .89

VF dynamic pressure ratio nF VF N-D .651% V

Tail rotor induced velocity effect kVTR XKVTR N-D 1.0e ,.-E at VF

12

TABUI I .- CONC.UDO

Decription Al*ratc Cmputer uais UN-"symbol a ic

ControlsSe.shplate lateral cyclic pitcb CAI $ CAIS rad 0

for zero lateral cyclic stick

Swasbplate loitudinal cyclic Cats cats red 0* pitch for aero longitudinal

cyclic stick

Longitudinal cyclic control CIs ClI rad/li. .0"939sensitivity

Lateral cyclic control setsivtty CX (12 rdlis. .02?9:

Min rotor root collective pitch CS CS red .2286for zero collective stick

Main rotor collective control CS C6 rid/is. .02792sensitivity 4

* Tall rotor root collective pitch C, C7 rid .l74)for tero pedal position

Pedal sensitivity Ce CB rid/La. -.07714

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-IVWL FLIHIT TRIM CHARACTERISTICSk|tfC.-vITOL UH-60 MATH MODEL

fqwvalont airspeed, knots

UnitsI O. 40.0 60.0 100.0 140.0

L LIJ 0.$93& 0.3636 0.5149 -0.5356 -1.0539 in.

PW -,?920 -.7106 -.3199 -.1098 -.0917 in.

I-ODJ U$. 4.2440 3.8582 4.2054 5.6883 in.

40 -.1409 -.05631 -.1254 .0974 .1798 in.

0 0 13.165 9.4517 11.308 ft/sec

4k .0$01 6.5824 3.8820 4.8946 -13.840 ft/sec

t LL46 6. Q 5.5167 2.2425 1.6799 -3.3533 deg

" -. 60) -1.2929 0 0 0 deg

'4tt t4 4. I, AID Z-FORCE STABILITY DERIVATIVES

Wlg3~-VU~T0I 4UH-60 MATH MODEL

tqlvalet airspeed, knots, , - -Units

I t "@0 40.0 60.0 100.0 140.0

i ,i .cam -0.0274 -0.0201 -0.0422 -0.0517 1/sec

"- 11 -1.3039 -1.2532 -.7256 -.2927 ft/in./sec2

, 052) -.0693 -.0950 -. 1336 -.1749 1/sec

*Ot .4"s .9417 .9148 .9364 .9924 ft/in./sec2

62 -1) I.6140 -1.7968 -2.1322 -2.3677 ft/in./sec2

1-.S)i -.1332 -.0546 -.0158 -.0324 I/sec

*1* 17- .5395 -.6523 -.7658 -.8418 1/sec

t W - 2 -1.8678 -3.0911 -5.8800 -8.8178 ft/in./sec2

4. CAPS *32 -7.8250 -9.0061 -10.4761 -11.8225 ft/in./sec2

- i4a .1o 1 1.7228 2.5612 4.3935 6.3606 ft/in./sec2

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TABLE 13.- M-MOMENT STABILITY DERIVATIVESBOEING-VERTOL UH-60 MATH MODEL

-"" .. ,_ __ _ __ _ _

Engineering Equivalent airspeed, knots Unitssymbol 0.5 20.0 40.0 60.0 100.0 140.0

M 0.0005 0.0091 -0.0043 0.0040 0.0022 0.0019 rad/ft/sec

.0085 .0022 -.0006 .0011 -.0019 -.0068 rad/ft/sec

Mw .0021 .0122 .0050 .0072 .0082 .0113 rad/ft/sec

" q -.7674 -1.0262 -1.2832 -1.5541 -1.9808 -2.1616 I/sec

M .2938 .2859 .2567 .2379 .1797 .1937 1/secpMr -.0688 -.0595 -.1181 -.1149 -.0860 -.0750 I/sec

.e .3287 .3366 .3850 .4133 .4543 .4997 rad/in./sec2

M6 -.0051 .0042 .0134 .0128 .0397 .0585 rad/in./sec2

M6 -.0183 -.0352 .1574 .1362 .1294 .1418 rad/in./sec 2

4M6 .0411 -.0010 -.0499 -.0562 -.0881 -.1113 rad/in./sec2

TABLE 14.- L-MOHENT STABILITY DERIVATIVESBOEING-VERTOL UH-60 MATH MODEL

Engineering Equivalent airspeed, knotssymbol Unitssymbol 0.5 20.0 40.0 60.0 100.0 140.0

L -0.0260 -0.0250 -0.0267 -0.0258 -0.0304 -0.0343 rad/ft/sec

" L -1.7256 -1.8067 -1.5485 -1.4919 -1.3987 -1.4051 I/secq

L -3.3484 -3.5455 -3.7116 -3.7659 -3.6853 -3.3574 1/secpLr .2119 .3507 .4149 .4878 .6814 .8556 1/sec

L 1.3118 1.3297 1.3147 1.2866 1.2907 1.3128 rad/in./sec2

' L6 -.9313 -.8816 -.8968 -1.0035 -1.1990 -1.3063 rad/in./sec2

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TABLE 15.- N-MOMENT STABILITY DERIVATIVES

BOEING-VERTOL UH-60 MATH MODEL

Engineering Equivalent airspeed, knots Units' .'-'. symbolUnssymbol 0.5 20.0 40.0 60.0 100.0 140.0

N 0.0081 0.0108 0.0119 0.0141 0.0176 0.0195 rad/ft/secVNp -. 1856 .0322 .0251 -.0446 -.0706 -.0955 1/sec

N -.2879 -.3902 -.5142 -.6283 -.8389 -1.0394 1/secr

N6 .0266 -.0286 -.0268 -.0110 .0014 .0032 rad/in./sec2

N6a .0665 .0576 .0222 -.0191 -.0544 -.0041 rad/in./sec2

N5 p .7153 .6731 .6720 .7668 .9319 1.0023 rad/in./sec 2

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l-. NUwt NASA TM U5890 "a C10111" 11band USMVSCO4 TH-54-A-2 A*- ?977___________

'-C Til ~ill w' ille fka ow~

A MATHEMATICAL MODEL OF THE UH-6O HELICOPTER April IGAA.

Ka~thryn B. Hilbert *A-9646

OWUS40 rftDOW ldl014T-6292

% ~Ames Research Center and Aeromechanics Laboratory, of 01 -Gief%: U. S. Army Research and Technology Laboratories --* ~AVSCOM, Ames Research Center, Moffett Field, CA. 91.03 ____________

~WWAAPE M~A~WTechnical M emo randumNational Aeronautics and Space Administration, 4t *MvaWashington, D. C. 20546 and US Army Aviation System'b p~

~Coand.-St. Louis. MD. 63120 505-42-11I-.&4Vw.6tWV kae,,

Point of Contact: Kathryn B. Hilbert, MS 211-2, Moffett field, CA. 94035(415) 965-5272 or FT3 448-5272

I1 ADe.aet This report documents the revisions made to a ten-degree-of-freedom.full-flight envelope, generic helicopter mathematical model to represent theUH1-60 helicopter accurately. The major modifications to the model includefuselage aerodynamic force and moment equations specific to the 13-60, acanted tail rotor, a horizontal stabilator with variable incidence, and apitch bias actuator (PDA). In addition, this report presents a full eat ofparameters and numerical values which describe the helicopter configurationand physical characteristics.

Model validation was accomplished by comparison of trio and stabilityderivative data generated from the UN1-60 math model with data generatedfrom a similar total force and moment math model.

..

Helicopter Aerodynamics, 11-60, CatdUnlimited* tail rotor, Horizontal stabilizer,

Pitch bias actuator, Stability deriw' Subject category 06atives, Mathematical model, Simulator

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