+ All Categories
Home > Documents > UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

Date post: 02-Jun-2018
Category:
Upload: manitheaerialfighter
View: 228 times
Download: 0 times
Share this document with a friend
361
NASA CONfRACTOR REPORT 366309 . . 4 1 UIi-60A Black Hawk Engineering Simulation Program: Vol ume I - >lathematical Model J . . Ho~lc CONTRACT NAS2-10626 Dec entb e r 1 9 8 1 NASA i \ I I
Transcript
Page 1: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 1/360

N A S AC O N f R A C TO RREPORT 3 6 6 3 0 9

.

.

14

1

UIi-60A B l a c k Hawk E n g i n e e r i n g S i m u l a t i o n P r og r am :

Vol ume I - > l a t h e m a t i c a l Model

J . . H o ~ l c

CONTRACTNAS2-10626

Dec entbe r 1 98 1

NASA

\

I

Page 2: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 2/360

-.

NASA CONTRACTOR REPORT1 6 6 3 0 9

U H - 6 0 A B l a c k H a w k E n g i n e e r i ng S i m u l a t i o n P r o g r a m :Vo l u m e I - M a t h e m a t i c a l M o d e l

J . J . H o w l e t tU n i t e d T e c h n o l o g i e sS i k o r s k y A i r c r a f tS t r a t f o r d , C o n ne c t i c u t 0 6 6 0 2

P r e p a r e d f o rX m e s R e s e a r c h C e n t e ru n d e r C o n t r a c t Y U AS 2 -1 06 2 6

"A

Page 3: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 3/360

o o c u f i mNO. SER 70452

TABLEOF CONTENTS

Page Number

FORWARD

1 SUMMARY 1.1

2.1

3.1

4.1

5.1

2 I NTRODUCTI ON

3 OVERVI EWOF SI MULATI ON MODEL

4

5 SI MULATI ON f l ODULES MATHEMATI CAL DEFI NI TI ON

DESCRI PTI ON OF THE BLACK HAWK HELI COPTER

5. 1 Mai n Rot or Modul eFusel age Modul eEmpennage Modul eTai l Rot or Modul eFl i ght Cont r ol s Modul eEngi ne/ Fuel Cont r ol Modul eLandi ng I nt erf ace Modul eGr ound Ef f ect s Modul eGust Penet r at i on Modul eMot i on Modul e

5.25 . 35.45 . 55.65 . 75 . 85. 95. 10

6 DEFI NI TI ON OF THE BLACK HAWK COCKPI T 6.1

PRECEDINGPAGE BLANKNOT FILMED/

i vPAGO‘

.

Page 4: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 4/360

-

OOCUMENTN O . S E R 7 0 4 5 2

SUMMARY

A non-linear mathematical modelo f the UH-GOA BLACK HAWKhel icopter hasbeen developed under ContractFIAS2-10626. This mathematical model, whichis based on the Sikorsky General Helicopter (Gen Hel)F l i a h t DynamicsSimulation, provides theA r m y w f t h an engineering simulationf o r Performanceand Hand l ing Qu al i t ies evaluat ions .analysis mode w i t h eventual application t o real time pilot-in-the-loopsimulation,

:Th is mathematical model i s at o t a l systems defini t ion o f the aLACKHAWK

he1 icopter representeda t a uniform level o f sophist icat ion considerednecessary f o r Hand1i n g Qual i t i e s evaluation s. The model i sa t o t a l fo rce ,large angle representat joni n s ix r i g i d body degrees o f freedom. Rotorblade f l a p p i n g , l a g g i n g and hub rotat ional degrees of freedom are alsorepresented. In a d d i t i o n t o th e basic‘ he1 ic op te r m odules, support’vemodules have been definedf o r the landing interface, poweru n i t , grounde f f e c t s and gust penetrat ion.re levant t o pi lo t-i n- th e- lo op sim ulatio n i s pre sent ed. T his same model wasact iva ted on Sikorsky’s DEC POP K L l Ocomputer t o generate check casesf o ruse d u r i n g the validation o f the simulation a t NASA.

Volume I o f this report defines the mathematical modelusing a modularformat . The documentationo f each module i s se lf-co ntain edand includesa descript ion, mathematical defini t ionand i n p u t for the BLACKHAWK.

Volume I 1 provides backgroundand descriptive information supportivet oan understanding o f the mathematical model.

I n i t i a l l y i t wil l be applied i n an

Informat ion defining the cockpit environment

1.1-PA G E

Page 5: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 5/360

2.0 INTRODUCTIONThis report is Volume I of two volumes, which document themathematical model of the UH-60A BLACK HAWK helicopter. Thiswork was funded under Contract NAS2-10626 by th e U.S. ArmyResearch and Techno1 ogy Laboratories (AYRADCOM) Ames R esearchCenter.

The objective of this contract was to provide the Army andNASA wi th a we1 docume nted, operati-onal and veri fied engi neeri ngsimulation of the BLACK HAWK helicopter. This work, undertakenby Sikorsky, provides t he Army with a flying qualities analysismethodology for the BLACK HAWKhelicopter which could eventuallybe extend ed to a real time pilot-jn-loop simulation. Themathematical model provided under this co ntract I's a tetalsys tem , free flight repres entati on based on t he Si korskyGeneral He1 icopter (Gen Hel) F1ight Dynamics simulation. Itis defined at a uniform level of sophistication currentlyconsidered appropriate for hand1 ing qualities evaluations.This model is also considered to. give representative performancetrends, but should not bs used to define critical performancecharacteristics.introduction of additional or more sophisticated modules.

The modular format presented facilitates the

Volume I of this report documents the basic BLACK HAWK mathematicalmodel, and in addition, defines supportive routines developedby Sikors ky under this contract. These routines include alanding interface, power unit, ground effects and rotor gustpenetration models. Presented i n this volume is an Overviewof the Simulation Model, Section 3, followed by a Descriptionof the BLACK H A W helicopter i n Section 4. Section 5 containsthe documentation of the Simulation modules. Each of themodule definitions is segregated with its own Table of Contents.Section 6 contains information defining th e BLACK HAWK cockpitrelevant to piiot-in-the-loop simulation. * Asingle copyAppendix to Volume I, containing extensive program verificationdata generated from a similar model on the Sikorsky SimulationFacility, provides NASA and Sikorsky with the necessary informationfor validating the BLACK HAWK helicopter simulation on theAmes Simulation facility.

Volume 1 1 o f this report documents,the deriv ation o f theequations, the assumptions inherent in the model and providessupportive discussion to aid in the understanding of the

mathematical model.

2.1-A G E

Y I9 P t V r,

.. ..

Page 6: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 6/360

.. , . . ~. .. .. ... . . .~. .. - '

3.0

Y ?9 REV

OVERVIEWOF THE SIMULATIONMODEL

D O C U N E Y TY O . SER 70452

The mathematical model o f BLACKHAWKprovided under thiscontr act is based on the Sikorsky General Helicopter (Gen Hel)Flight Dynamics Simulation. This model is a general ized,modular ized analytical represe ntatio n .of a total he1 icoptersystem. It normally operates in the time domain and allowst.he simulation o f any steady or maneuvering flight conditionwhich can be experienced by a pilot.

The overall st ructure of the model is presented on figures 3.and 3.2 i n functional and block diagram format respectively.The solution i n terms of aircraft motion is obtained iterativelyby summing the component forces and moments acting at theaircraft's center o f gravity and subsequently obtaining thebody axes accelerations. Resulting velocities and displacements '

then condition the environment for the components on the nextpass through the program. The datum axe s system used are aset of right coordinate body axes with the origin at thefuselage center of gravity. The X axis points towards thenose of the aircraft and is para-1 e1 to the center 1 ine of theaircraft. A l l calculations a re related to this axis system.The final aircraft motion is transferred into earth axes forsimulator, V F Rdispla y and instrum entati on drives. The mathematicalmodule defining the equatioc., of motion a re presented inSection 5.10.

-

The basic model is a total for ce, non-linea r, large anglerepresentation in six rigid body degrees of freedom.addition, rotor rigid blade flappilng, lagging and hub rotationaldegree s of freedom are represented. The latter degree of

freedom is coupled to the engine and fuel control.the lag degree of freedom is resisted by a non-linear lagdamper model.

The total rotor forces and moments are developed frcm a combinationo f the aerodynam ic, mas: and inertia loads acting on eachsimulated blade. The rator aerodynamics are developed using ablade element approach. The angle o f attac k and dynamicpressure on individual blade segments are determined from thethree orthogonal velocity components. These arise as a resultof airframe motion, rotor speed, blade motion and downwashresulting from the generation of thrust. I n the latter case,which represents the air mass degree o f freedom, a uniformdownwash is derived from momentum considerations, passedthrough a first order lag, and then distributed first harmonicallyas a function of rotor wake skew angle and the aerodynamic h u bmoment. Finall y, blade geometr ic pitch i s summed with theinflow angle of attack to obtain the total angle of attac k atthe blade segment.aerodynamics i s represented as a function of Mach number.

In

Motion in

The full angle of attack range for blade

3.1-A G E

Page 7: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 7/360

Y. 29 9EV. G

Blade inertia, mass an d weight effects 'are fully accounted forand their resulting loads, dependent on blade and aircraftmotio n, are -ad ded to the aerodynamic loads for each blade.

This suirmation gives the shear loads on the blade root hingepins. Total rotor forces are obtain ed by summing all theblade hinge p i n shears with regard to azimuth. Rotor moment sresult from the offset of the hinge shears from the center o fthe shaft.from aerodynamic and inertia moments about the hinge pins.During one pass through the program all segment s and allsimulated blades are computed.considerations th e simulated number of blades a re not madeequal to the actual number, then they are redistributed i nazimuth accordingly. The mathematical module defining therotor is presented in Section 5.1.

The fuselage is defined by six component aerodynamic charactsr-istics which are loaded from wind tunnel data which have beenextend analytically to large angles.the fuselage is developed from the free stream plus interferenceeffects from the rotor. These interference effects are basedon rotor loading and rotor wake skew angle.effects are not accounted for. The mathematical module definingthe fuselage is presented in Section 5.2.

The aerodynamics o f the empennage are treated separately fromthe forward airframe.definition of non-linear tail characteristics that wouldotherwise be lost in the simplifications of multivariate totalaircraft maps.can be made without reloading basic airfram e maps. The anglesof attack at the empennage are developed from the free stream

velocity, p l u s rotor wash and airfram e wash. Dynami c pressur eeffects from the airframe are accounted for by factoring thefree stream velocity component. By nec ess iry the wash anddynamic pressure effects are averaged over the stabilizingsurfaces. The tail rotor is repres ented by the linearisedclosed form Bailey theory solution. Terms in tip speed ratiogreater than /k squared have been eliminated. The airflowencounted by the tail rotor is developed in the same manner asthe empennage. A n empirical blockage factor, due to theproximity of the vertical tail, is applied to tlie thrustoutput.tail rotor are presented in Sections 5.3 and 5.4 respectively.

Blade flapping and lagging motion is determined

If because of execution time

The angle o f attack at

Local velocity

Thi s separate f ormul ati on a1 1ows good

With this approach, changes to the empennage

The mathematical modules def ni ng the Empennage and

2,

3 . 2-A G E

Page 8: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 8/360

D O C U M E N Tn o . SER 70452

The flight control system for BLACKHAWK presented in thismodel covers the primary mechanical flight control sytem andthe Automatic F1ight Control System (AFCS). The latter incorporatesthe Stability Augmentation System ( S A S ) , the Pitch Bias Actuator( P E A ) , the Flight Path Stabilizntion (FPS) and the Stabi latormechanization. These automatic control functions collectivelyenhance the stability and control characteristics of the BLACKHAWK. The analytical dafini tion of the control system givenin Section 5.5 incorporates the Sensors, shaping networks, -1ogi c swi tchi ng , authori ty 1i tni ts and actuators.thes e compo nents have wi de band-wi dths whi ch are beyond thefrequ encies normally associ ated with piloted simulation. Theyhave been included for completeness and accuracy i n analyticalevaluations. The model provided repres ents the control systemin a complete manner except for the FPS.the attitude hold and turn features have been defined.

Some of

In this case only

The engine/fuel control model provide d with this simua ltion isa 1 inearized representation with coefficients which vary as 3function of engine operating condition. The model adequatelyprovides for closing the rotor shaft speed loop throughout thenormal operating envelope of the ;le1 icopter. However, maneuverswhich result in significant rotor speed excursions may resultin discrepancies in the simulation. This engine module shouldnot be used for engin e perfo rmanc e evalua,;on. The modula rformulation does however, faci i ta tes the i ntroductfon o f asophisticated model i f neces sary at a later time. The interfaceof the engine with th e rotor module, shown on Figure 3.3, isvia the rotor clutch. This is programmed to disengage therotor shaft from the engine i f rotor required torque drcpsbelow zero. Under these circu mstanc es, the engin e speedfeedback t o the fuel control will cause the engine to s eek anopera ting condition dicta ted by the control. The clutch willreengage when the roto r speed drops below po wer turbine speed.The engine fuel control equations are presented i n Section5.6.

The landing interface module, Section 5.7, allows for groundcontact. It is a gener alized represent ation consi sting of alanding gear force reaction model compl ete with all necessaryspace/body geometry calculations to track a fre e he1 icopterduring a landing onto level ground. The landing gear isrepresented by separa te non-1 inear t ire and strut dynamiccharacteristics. Tire in-ground-plane loads are developed asa non-linear function o f the tire deflection and normal load.These forces are adjusted depending on the friction criteriawhich determines tire skid properties at the ground plane.The strut i s simulated by an isentropic air spring and velocitysquared damper in parallel. The output loads from the threelanding gears are finally transferred to the cente r o f gravitywhere they are summed with other external forces and moments.

3 . 3IA G E '

Page 9: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 9/360

Section 5.8 defines a s implified ground effects model.the development of this module it was evident that anythingmore than a simple model based empirically on distance abovethe ground plane, was beyond the scop e'of this contract.model provided, adjusts the downwash at the rotor (and thereforerotor loads) as a function of height above the ground planeand forward speed ( in terms of rotor wake skew aogle):

The gust penetration routine documented in Section 5.9 providesfor a gust front passing across the rotor disc from any direction.Behind the front, gust velocities are varied with distancefrom the front. The variation can be prescribed by a choic eof several discrete velocity prof 1es or a ccjnti nuous turbulenc eform due to Dryden.centers of fuselage and tail components may be subjected tohorizontal and vertical gust velocities whose magnitude is afunction of the geometric distance from the traversing gust

frqnt. Thus penetration or velocity distributional effectsare almost fully accounted f or in the rotor simulation and areadequately dealt with in the fusel age/tai 1 model.

During

The

Each rotor blade element and the aerodynamic

3 . 4-A G E

Page 10: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 10/360

' 1

\'.

GENHELFLIGHTDYNAMICSSIMULATlON

' 8 ' RIGID BLADES- FLAPPING AND LAGGIN02OTOR SPEED. OEGREEOF FREEDOML A G DAMPER\BLADE:ELEMENT AERO.YAWED FLOWMOMENTUMINFLOW WITH NARMONIC DlSTRlEUltON

( C L fl60', M =0-1.0 )

HOTOR OUWNWASHON EMPENNAGEAND TAIL ROTOR

ON FUSELAGESTICKSMIXING

SERVOS OW EMPENNAGE

RIGID FUSELAGE

<-6 OEGREES OF FREEDOM -EMPENNAG&IX COMPONENT AERO a , 903

AEPODYNP.MiCS

DKQG

SIDE1:ORCE )

F i G i J R E 3 . 1

3 . 50-PAGE

Page 11: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 11/360

OOCUNEHTN O . E ? 70452

I

7

F i g u r e 3 . 2

m . t

Page 12: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 12/360

O O C U M E N Tn o . S E R70452

E N G I N EINTEGRATION INTOG E N H E 1

CLUTCH

MAIN

FUEL CONTROL 1 P ' II I FLOW ]' I f - ODY STATES %

\' I PILOT\\ I\ I -3- LONG.

RGLLYAW+ )qyn

VERTICAL LATERAL

F I G U R E3 . 3

3.7-AGE'

Page 13: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 13/360

D O C U M E N TN O . SER 70452

4. 0 Descr i pt i cn of t he BLACK HAWK Hel i copt er

The UH- GOA I ACK HAWK,shorn i n t he f i gur es 4.1 and 4 . 2 , i s aut i l i t y t r anspor t hel i copt er devel oped by Si korsky f or t he Ar myunder t he UTTAS progr am Thi s medi um si t ed he1 i copt er i s desi gnedt o carr y el even combat - equi pped t r oops and a cr ew of t hr ee. TheBasi c St r uct ur al Desi gnGross Wei ght i s 16, 825 l bs. wi t h a maxi mumAl t ernat e Gr css Wei ght of 20, 250 pounds. M- i ssi ons i ncl ude: Tr oopAss aul t , Aeromedi cal Evacuat i ov, Aeri al Recover y and Ext ended RangeM s si ons . The BLACKHAWKhas a maxi mum l evel f l i ght speed i n excessof 150 knot s and a di vi ng speed i n excess o f 170 knots.

The BLACK HAWKhas a s i ngl e mai n r otor and a cant ed t ai l r otor 2 sshown on t he general ar r angement dr awi ng, f i gur e 4. 3.phys i cal charac te r i s t i cs i s gi ven on Tabl e 4. 1. The mai n r ot orc ons i s t s o f f our f ul l y ar t i c ul at ed t i t ani um f i berg l as s bl ades whi c har e r etai ned by a f l ex i bl e el as tomer i c bear i ng i n a f orgedt i t a ni um s i ngl e pi ec e hub and r est r ai ned i n pl ane by a convent i onalhydraul i c l ag damper . The 11. 0 f eet di amet er f our bl aded tai l r o tori s a bear i ng- l ess cr oss- beamar r angement wi t h the shaft t i l t ed 20degr ee; upwar ds. Bot h r ot or s have an SC1095 aero fo i l s ect i on. Theai r cr af t i s power ed by t wo Gener al El ect r i c Company,T 700- GE- 700engi nes mount ed on t op of t he cabi n whi ch t oget her pr ovi de approxi mat el y2,800 h.p. at nor mal cont i nuous r at i ng. These engi nes have Ham l t onSt andar d hydr aul i c , and General El ect r i c Company el ect r oni c f uelcont r ol component s. The dri vesystem cons i s t s o f mai n, i 3t er medi a te ,and tai l gear boxes wi t h i nt erconnect i ng shaf t s .

The f l i ght cont r ol sys t emon t he BLACKHAWKi s a r edundant hydr o-el ectr i cal - mechani cal syst em I t i ncl udes t hr ee t wo st age mai nr o tor se rvos , a S tabi l i t y Augment at i on Sys tem( S A S ), a , F l i ght Pat hSt abi l i t y Sys t e m( FPS) , and a t r i pl e redundant hydr aul i c suppl y.hor i zont al t a i l r o t a t es f r om a pos i t i ve angl e o f about 40 i n hoverup

A s i i nary of t he mass proper t i es charac t er i s t i cs i s gi ven on Tabl e4 . 2 .Si ven on f i gur e 4. 4.

A mor e comprehensi ve descr i pt i on o f t he BLACK HAWK hel i copt er i sgi ven i n Ref er ences 4. 1. 1, 4. 1. 2, and 4, 1. 3.

A l i s t of

The

t o zer o wi t h i ncr easi ng f orwar d speed.

Recommended overal l 1ongi t udi nal cent er of gravi t y 1i m t s ar e

4.1PClbE.

... i i L .-

Page 14: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 14/360

4.1

4.1.1

4.1 .2

4.1 ..3

References

F l i g h t I n t e r n a t i o n a l , Week. Ending 25 February 1978, Art ic lebyMark Lambert.

U.S. .my UH-60A He1i cop te r Development Production Program. PrimeItem Development Speci f ica t ion (PIDS) DARCOM-CP-2222-SlOOODPart IOctober 1 5 , 1979.

Uti-60A Fami 1 i a r i z a t i o n Tr ai ni ngCourse Manual - S ikorsky Tra in ingDocument.

4.2-A G E

Y 2s UI. 0

Page 15: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 15/360

FIGURE 4.1

4&PAGE

zwcn0

Y

z4

. I

XV

m

Page 16: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 16/360

.

F I G U R Ea . 2

4.4-A G E

. .I.. -_

Page 17: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 17/360

STA732

2) GENERAL ELECTRICT700-GI -700 TURBOSHAFT ENGINES

. . .

J- . WHEEL BASE(28'.IL9 ) - - -- '

- .USELAGE1ENGTH 150*.Z5'*)- - _ _

JH-60A BLACK HAWK GENERAL ARRANGEMENT

.. .

Page 18: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 18/360

Page 19: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 19/360

OF POOR QUALITY

DOCIJMENTN O . SER 70452l n m

t t C ) l ” E s P

S1KORSKYAIRCRAFT

BLACKHAWK

TABLE4.1. LIST OF PHYSICAL CHARACTERISTICS

MAIN ROTOR VERTI CAL STAB IL ZER

DiameterB1 d e sChordA i r f o i l61ade’ AreaSol i d i t yT i p SweepTwistS h a f t Angle

TAIL ROTOR

DiameterBladesChordA irf o i 1Biade AreaS o l i d i t yTwis tCant Angle

53.6741 .75 f t .

SC 10952186.8 f t

.082620 Deg.

-18 Deg.3 Deg.

11 f t .

.81 f t .SC 10951 7 . 8 2 f t 2

.1875

20 Deg.

4

-18 Dw.

HORIZONTALSTAB1LATOR

SpanArea

1 4 . 3 8 f t .4 5 f t 2

Root Chord 3.67 f t .

Sweep (1C) 0 Deg.

Aspect Ratio 4.6A irf o i 1Inc i dence/Dihedral 0 Deg.

T i p Chord 2 .54 f t .

aNACA0014

4.7PIGP‘

Span ’ 8.167 f t .Area 32.3 f t 2Root Chord 6 f t .T i p Chord , 2.83 f t . .Sweep ( I C ) 41 Deg.

Aspect Rat i o 1.92A i r f o i l NACA 0021

a

GENERAL

’ Ove rall Length 64.83 f t .Fus elag e Length 50.06 f t .Wheel Tread 8.88 f t .‘rlhee.1 Base 28.93 f t .

Page 20: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 20/360

m --

I

473626

475389

IZZ

442646

441 954

BLACKHAWK

TABLE4.2. SUMMARYOF MASS PROPERTIES CHARACTERISTICS

500923

465774

514803

4821 41

CONDITION

Design Mission - Troops

Aeromedica-1 Mss o n

Aerial Recovery Mission

Extended Range Mission

Basi St ruc ura 1 Desi gn- Fwd.Basic St ru ctu ra l Design- Aft

Maximum A 1t e r n a t e GM-Fwd

Maximum A1t e r n a t e GW-Aft

465328

432719

479012

447627

~~

WEIGHT

16000.9

15479.3

20250.0

19193.7

16330.9

16330.9

20250.0

20250.0

CENTEROFGRAVITYPOSIl

STA

358. o

359.0

359.6

352.5

345.7

360.2

347.1

360.2

3N

WL

251 .O

251.1

234.7

2 6 . 1

248.3

249.5

244.4

245.1

-

MOMENTOF INERTIA

--x x

5550

4058

00200

74633

71 141

68263

79532

77898

--

(Data from SER-70288 Prepared Under ContractDAAJOl -77-C-0001P 6 A )

Ixz

18886

-

1951U

227 30

28076

341 44

1 5268

33850

18408

Page 21: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 21/360

D O C U M E N Tn o . SER 70452

5.1 M A I NROTORMODULE

CONTENTS

5.1.1 Module Description

FIGURES

5.1.1.15.1.1.25.1.1.35.1.1.4 Lag damp er kinematic geometry5.1.1.5

Body axes to shaft axes transformationShaft axes to rotating blade span axes transformationDefinition of Yawed angle of attack

Main Rotor Equation flow diagram

5.1.2 Module Equations

5.1.3 Modul e Input/Output Defin ition

5.1.4 Komencl atu re

5.1.5 Black Hawk Main Rotor Input Data

FIGURES

5.1.5.1 Blade twist input5.1.5.25.1.5.35.1.5.4 Lag damper force characteristics

Blade Section 2D aerodynamic lift characteristicsBlade Section 2D aerodynamic drag characteristics

TABLES

5.1.5.1 Blade Twist Inp ut .5.1.5.25.1.5.35.1.5.4 Lag Damper Force Characteristics

Blaae Section 2D Aerodynamic Lift CharacteristicsBlade Section 2D Aerodynamic Drag Characteristics

5.1.6 References

5.1-2

5.1-75.1-85.1-95.1-105.1 - 1

5.1-12

5.1-28

5.1-39

5.1-49

5.1-505.1-515.1-535.;-55

5.1-575.1-585.1-615.1-64

5.1-65

5.1-1PA G E-

Page 22: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 22/360

7 . .mw -

5.1 Main Rotor Module

5.1.1 Module Description

The main rotor rnodel is based on a blade element analysis i nwhich total rotor forces and moments are developed from acombination of aerodynarnic, mass and inertia loads acting oneach simulated blade. The blade segment set up option definedfor this Black Hawk model is that o f equal annuli area sweptby the segment.to be minimized and distributes the segments towards thehigher dynamic pressure areas.

The total forces acting on the blade are derived from thetotal acce1eI:ation and veloci ty comp one nts at th e blade togeth erwith control inputs. Accelerations develop from body m o t h nand blade motion. Velocity co mponen ts are made up of body

velocities, gust velocities, th e rotor's own downwash andblade motion.

This technique allows the number of segments

Before calculations at the blade segment can be executedseveral axes transf ormati ons must be implemented. Initiallybody axes angular and translational accelerations and ~elocitiesare transferred to the rotor hub and rotated through the shaftinclination angles i o and i into rotor shaft axes. Theseangles with positive rotatidn of i about the Y axis followedby i about the resulting X s axis b e shown in Figure 1 . 1 . 1 .

Th e dody velocities are non-dime nsional ized by ro tor tip speed(s ) to conform with usual he1 icopt er analys is practice.Motion acc ruing from the rotor shaft degree o f freedom isderived from the engine module.

The rotor airmass degree af freedom is primarily based on auniforni downwash distribution developed from rotor thrust byapp ication of momentum theory.i s passed through J. first order lag, is modified to accountfor the changing distribut ion with forward speed and aerodynamicpitching and rolling moment loading on the rotor.first case the resulting uniform downbash is distributed 1stharmonically around the azimuth as a cosine function dependingon the inclination of the rotor wake.including this first harmonic distribution, which results ina uniform downwash at hover and a weighted distributiontowards the aft of the rotor disc at high speed, is discussedin Refeyence 1.6.1. Since this effect is really dependent onthe resultant velocit vector a lateral velocity term is also

added. The desirabil ty of adding a harmon ic distr ibutio n ofdownwash depending on aerodynamic rotor moments has not beenestablished f o r Black Hawk but the necessary equations areincorporated for comp eteness.

This uniform downwash, which

I n the

The desirability of

5 . 1 - 2PA G E-

Page 23: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 23/360

D O C U M E ~ T1 0 , SER 70452

The remaining contribution to the velocities at the bjadesegment is that due to blade motion. Blade flapping andlagging veiocities and angles are obtained by application of aFourier prediction technique, rather than direct integrationof acceleration. This approa ch is derived in Reference 1.6.2.This method although simple has been shown to be stable andaccurate for the frequencies of concern i n he1 icopte r stabil ityand control evaluatfons.

The blade segment total velocity components are developed i nthree parts. Those i ndependent of segment position, thosedependent on segment position and interference effects made upof downwash and gust effects. The velocities at the bladesegments are obtained by transforming the fixed shaft vectorsifito the rotating hub axes system, then transferring to theblade hinge position, transforming into bla de span axes throughthe Euler a n g l e s b ( fl apping) and S (lagging) and finallytransferring to the segment position on the blade.transformations are i 1lustrated on figure 1.1.2. These totalvelocity components are subsequently used to calculate theresultant velncity, local Mach number, yawed angle of attackand flow yaw angle.of velocity i s ommitted in calculating the Mach Niimber whichis used i n the aerodynamic map look-up.which describes the use of simple sweep theory, indicates tha.tMach Number should be based on the unyawed component of flow.

The total local segment angle of attack on the blade is madeup of the blade local pitch angl e and the yawed ang;e ofattack at the segment. The former is made up of the controlimpressed pitch (collective 8 cyclic A B > , itch/flapcoup1 ing ( s ) , pi tch/lag couby%i ( dl), &ord $d bladetwist and a aynamic component of blade twist due to torsionalelastic deformation. This emperical dynamic component isprescribed harmonica1 ly based on blade loading.angle of attack i s complicated by the requirement to resolveblade pitch into the local stream direction as shown in Figure1.1.3.for the tangent of blade pitch.

These

It should be noted that the radial component

Reference 1.6.3,

The yawed

The resulting equation assumes the series approximation

5.1-3PA G E-

Page 24: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 24/360

b

The treatment of the blade segment aerodynamic force calculationis comple tely non-1 inear.

provided for the range -1806 o( 4 180. Bivariate maps as afunction of angle of attack and Mach Number are used in therange -30 1 30 allowing good definition of blade stall.The complete coverage of angle o f attack a1 ows good def n.1ti onof aerodynamic characteristics on t he retreating blade side ofthe disc. This is important at high advan ce ratios. Theblade segment 1 ift coefficient is determined by applyingsimple sweep theory to the unyawed blade aerodynamic data.This i s rigorously applied in 'the linear lift range where theentry to the unyawed lift coefficient is transformed by thecosine of the yaw angle (i.e. & = d C O S X ) and theent ry Mach Numb er is a fu nc ti on $FA $e uny lwed com po ne nt offlow.where sweep theory is not valid.

aviod discontinuities in blade lift data as the blade proceedsaround the azimuth. Discon tinhi ties can result i n an unstableflapping and lagging solution.theory to the determination of drag is not well established.For this model, drag is determined by entering the drag map

A de ve lo pm en t of swe ep th eo ry ca n be foun d in RefZk&@e 1.6.3.Sikorsky evaluations of this theory, as applied to rotors, aredocumented in Reference 1.6.4. 'I map entry logic is developedi n the equations.is applied to the tip segment.of blade lift and drag coefficients as a function of dand Mach Number are give n in Se ction 5.1.5.segmental loads are resolved from local wind axes into bladespan axes and summed along each blade to obtain root shears atthe hinge. These forces are subse quently transformed intoltotating shaft axes. It should be noted t h a t p and a reEuler angles and order of treatm ent must be observed. Theaerodynamic moments used in the flapping and lagging motionequations are calculated at this point in the flow. Also, itis convenient to develop the aerodynamic feedbacks for therotor downwash calculation at this time.

Lift and drag characteristics are

At higher angles of attack some liberties are takenThese steps are taker1 to

Th e app:ication of sweep

data with the actual yawed angle of attack. ( d = q

It should be noted that a tip loss factorUnivariate and bivariate maps

The aerodynH& '

-.1-4PA G E

i. &a*-/. 1 --. r 5 --. ' ----

Page 25: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 25/360

D O C U M E N T N O .SER 70452

The blade inplane or lagging motion is restrained by a dampersystem.and the kinematics of this system are corplicated bv geometry.

A general zed representation is uti i zed as presented onFigure 1.1.4 . Essentially the relative positions of the pick-ups of the damper on the hub and blade are tracked. Fromthese valu5s an axial velocity is determined. This velocityis used to enter the map data presented i n Section 5.1.5. Theoutput of this map, which is an axial force, is multiplied bythe instantaneous moment arm to obtain the damper moment aboutthe hinge. Although flapping restrai nt equations are iricludedthey will not be activated for Black Hawk.

In the case of Black Hawk the damper i s non-linear

The contributions to the lagging and flapping motion about t h ehinge are the aerodynamic moments, the hinge restraint momentsand the inertia moments. The aerodynami c and hinge restraintcomponents have been previously discussed.

have been explicitly introduced into the flapping and laggingequations of motion.takes place in an intermediate set of blade span axes becauseof the defin ition of the Euler angles. Also small terms havebeen eliminated from these equations. A software provision toinhibit the 1 aggi ng degree of freedom has been incorporated.

The inertia components

It sh ould be noted that. lagging motion

Before the final shear forces and hub moments can be developedit is necessary to calculate the inertia shear loading on thehinge pins, Again sinal 1 ter ms have bee n el imi nated. Subs eque ntto these calculations the three component total shears at thehinge are determined and the total rotor forces in fixed shaftaxes at the h u b cente r developed. The rotor hub momentsresult from a combination of the shear forces at the hingepins and moments from the blade hinge restraint.manipulation of the equations is introduced on these finalequations which allow the sfmulatad blades to be differentfrom the actual number. This artifice is intended for use inpiloted simulation where computer execution time is crftical.With the lagging degree o f freedom operating, the major portiono f rotor torqu e is developed through the lag damper. Therefore,if lagging degree of freedom is selucted out, an alternativeequation containing the aerodynamic moment must be introducedas specified.

An arithmetic

5.1-5PA G E-

Page 26: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 26/360

-. -

The oscillating natureo f the rotor forces and moments make i texpedient t o f i l ter the outputs undersome circumstances. Asimple f i r s t order f i l t e r is used. The f inalrotor forces andmments are obtainedby transforming the filtered shaft axesforces and moments i n t o body'axes w i t h the origin a t theceqter o f gravity.co qm en t outputs t o gjve the total external forces and moments.jt the center of gravi.ty.

I t ifor the option o f select ing t o run w i t h the engine module i nor o u t .governing is assummed and the shaft torque reactionon theair fra me i s assummed equalt o roto r required torque. If theengine module is activated then i tso u t p u t torque i s introducedi n t o the airframe.

These are eventually summedw i t h other

inecessary t o make provisiqn i n these final rotor o u t p u t s

If the engine i s selected o u t , perfec t rotor speed

Finally, the rotor wake skew angle i s determined. This i s th eangle that the center l ineof the rotor wake makes w i t h therotor shaft .the variation of rotor wash o n the fuselage, wing and ta i l .

The sequencing of the programf l o w i n the main rotor i s cr i t ic aland should f o l l o w the equation f l ow in Section 5.1.2.

I t i s the dependent parameter usedt o establish

A block diagramo f the Main Rotor Module i s given on f igure1.1.5.in Section 5.1.5.

A l l i n p u t da ta for the e lack Hawk MainRotor i s specif ied

5 .1 -5-PA G E

Page 27: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 27/360

,

Page 28: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 28/360

"'

SHAFT AXES TO ROfATING BLADESPAN AXES-TRANSFORMATIE

\

0M,

X s , Y s , T s Shaft Axes SystemX[, v( , Z Ro ta tin g Shaft Axes SystemXES, YES,2 1 3 Blade Span Axes System

UT, UR, Up Blade Element Ve lo c i t i es Along

XBs , YBS,ZBS R e s p e c t i v e l y

8 a;dBare Euler A n g l e s w i t h6 R o t a t i o n a b o u tZs then Rot a t io n About XBs .a

FIGURE 1.1.2

5.1-8PA G E '-

Page 29: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 29/360

Page 30: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 30/360

LAG DAMPER KINEMATIC GEOMETRY

I *

- - - - ' - I7- - . -/ t

Lag Damper A x e s

XLDMRAl igned w i t h the b l a d e s p a n

and ( Y ,Z)LDMR o t a t e d t h rough O L D M R

F I G U R E1.1.4

5.1.10T K .

Page 31: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 31/360

1_= - - -

tKiiLI K O R S K YA I R C M

MAINROTORFLOW DIAGRAM

CONTROLSYSYEM

Swashpla teM o t l o n

S R 701452

ROTORBLADEERO. HELICOPTER

ENGINE flO 7ION MOTIONOADI IG

Dormwash Freedom A / C C.G. I n e g r a t on

I I TI l l I

1

I

*&

I

Total RotorForces And

To RotorDownwash

Blade Acce l .About The

Ca I c u l a t ons

To Mot onModule

To l l a d e H o t f on1ntegra:lon

Page 32: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 32/360

CUFF

5 . i - 1 2PAGE.

Y29 L t l . G

Page 33: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 33/360

5 . 1 - 1 3PAGP'

Page 34: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 34/360

SER 70452

Page 35: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 35/360

d a y %

5 . 1 - 1 5

Page

Page 36: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 36/360

5.1-16Page

Page 37: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 37/360

Page 38: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 38/360

Page 39: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 39/360

O O C U M E N Tn o . 'SER 70452

5.1-19PIGt.

Page 40: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 40/360

-? -

F----U N W W

SIKORSWAIRCRAFT TBuilloLoo1m 0 DOCUMENTN O . SER 70452

5 .1 -20PIGE'

Page 41: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 41/360

O O C U M E N Tn o . SER 70452

5 . 1 - 2 1PIGE‘

Page 42: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 42/360

-.

5 . 1 - 2 2PAGt.

Page 43: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 43/360

. . .

Page 44: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 44/360

oocuyr.nrN O . SEI? 70452

L

5.1-24-A G E '

Y 29 41. 6

Page 45: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 45/360

OOCUMEEITn o . SER 70452

37.3

5.1-25P1Gt.

r n I . 6

Page 46: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 46/360

3.1-256

PA G E '

Page 47: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 47/360

Page 48: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 48/360

>',',--, . , \ \ \ - A 1t I

U N mSlKORSKYAiRCFtAFT D O C U M E N TN O . SER 70452

Mir

J

NS

5.1-28PA G E

m 2s ev. G

- - .. h ,---_.?*(- d -a A S * -

- L A - ___... _.___ - ,...-LI-----IY-------

5.1-28PA G E

m 2s ev. G

--_&.?*(- d -a A S * -

- L A - ___... _.___ - ,...-LI-----IY-------

Page 49: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 49/360

Page 50: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 50/360

. .

5.1-30PA G E

Page 51: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 51/360

/

Page 52: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 52/360

Page 53: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 53/360

0 O C ' ' M E N TY O . SER 70452'.

5.1-33-AGE

Page 54: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 54/360

5 . 1 - 3 4PAOt.

Page 55: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 55/360

Page 56: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 56/360

- - -- ---

Page 57: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 57/360

__1 ,

Page 58: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 58/360

O O C U M E N T N O . SER 70452

YZS I t . G

&pf€

I

rc:

.

*

5.1 -38__iP4 G f

1'

Page 59: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 59/360

5. 1. 4 NOTATI ON FORTHE MAI N ROTOR MODULE-

Y 29 REV. I

SYMBOL.USED1 PROG RAMEQUATI ONS MNEMONI C UNI TS DESCRI PTI ON

'

bd

FSCGLCG~ G BWLC GB

-0

-

OFSTMR

SPRLMRRHROMGTMR

KSGMR

-KMRBKl

-CHDTMRCHDRMR-

WEI GHTBMRWTBDMRWTBODFSCGWLCGFSCGBWLCGB

I NDEX' I NDEX

I NDEX

FT

FT

FTRADS/SEC

NDI.(DND

FTFT

FT

FT2

LE

LB

LB

I ndi cat i ng 1 . . .NBS bl ades si mul ated. I ndi cat i ng1.. . lSS segment s/ bl adesi mul atedI ndi cat i ng 1.. . NBS-1 )NSSbl adesegment s

Bl ade hi nge of f set f r om cent erof ro tat i onSpar l ength exposedRotor r adi usRot or nom nal i nput rotat i onalspeedNor mal i zed of f setNormal i zed spar l engt h.Di st ance f r om hi nge t o segmentm dpoi nt

Segment chor dBl ade t o p chordBl ade r oot chor dBl ade segment ar ea

Tot al hel i copt er wei ghtNumber o f r ot or bl adesWei ght of me bl adeWei ght o f hel i copt er l ess bl adesTot al hel i copt er c,g. pos i t i on

C. G. posi t i on l ess r otor bl adesI N S

I NS

I NS I5. 1- 39PLCE-

Page 60: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 60/360

D O C U H E N T3 0 . S E R 70452

.5 .1 .4 (C 0n t. d) NOTATIONFOR THEMAIN ROTOR MODULE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

FSMR

WLf4R

xb

yb

zbP

qr

'xb

'zbP

9r

VYb

x Hy H

zH

'b'b

pb9,

9Y

gz

"XG

'YG'ZG

FSMRWLMR

VXBDOT

V YBDOT

VZBDOT

PDOT

QDOT

RDOT

VXE

VYB

VZB

P

QR

-..-THETAB

PHIBPSIB---'XG"YG"ZG

I NS

INSFT/SEC2FT/SEC2

FT/SEC2RADSs C ~

RADS/s c2R A D S / S E C ~

FTjSEC

FT/SECFT/SECRADS/ SEC

RADS/ S C

RADS/SEC

FTFTFT

DEG

DEGD E G

FT/SEC2

FT/SEC2FT/S 2

FT/SECFT/SECFT/SEC

5.1-40PA G E-

F u s e l a g e s t a t i o n f o r t h e m a i n r o t o r

Wa t e r l i n e s t a t i o n fo r the main ro to r

Accel . along X-axisAccel . a lon g Y-axis

Accel . along Z-axisAngu la r acce l abou t X-axisAngular accel about Y-axis

Angu la r acce l abou t Z-axisVel . a long X-axisVel. a l o n g Y-axisVel . a long Z-axisA n g u l a r r a t e a b o u tA n g u l a r r a t e i b o u tA n g u l a r r a t e a b o u t

L o n g i t u d i n a l r o t o rL a t e r a l r o t o r armVe r t i c a l r o t o r armP i t c h a t t i u d e

R oll a t t i u d eHeading

G r a v i t y v e c t o r sI

X-axisY-axisZ-axis

arm

P o i n t gust v e l o c i t i e s . Foruse when g u s t p e n e t r a t i o n i sn o t r e q u i r e d .

Page 61: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 61/360

RADS/S EC

RADS/SECRADS/SEC

S h a f t a n g u l a r rates

RADS/S EC

FT/SEC2ff SEC'

O O C U V E N TN O . SER 70452

5. A .4 (C d n t ' d ) NOTATION <OR THE MAIN ROTOR MODULE

SYMBOLUSED INEQUATIONS .

PROGRAMMNEMONIC UNITS DESCRIPTION

MUXHMR

MUYHMRMUZHMR

f l H

/u H/M. Y H

N D

ND

ND

h u b v e l o c i t i e s - normal ized

MUXSMR ND

MUYSMR ND/Lc xs

/MY S

S h a f t v e l o c i t i e s - normal izedI

MUZSMR 1ID

PSMR

QSMR

RSMR

PS. MR

QSMR

RS. MR

XH

Y H"H

n

V X H .MRV Y H . M R

V Z H .MR

FTISEC' IHub a c c e l e r a t i o n sFTISEC'

VXS. R

VYS. MRVZS.MR

xsV Ys

RADS/SEC2 R o t o r s h a f t a c c e l e r a t i o nRADS/ SEC

RADS/SEC Ro tor s h a f t datumspeed

R o t o r s h a f t speed

5.1 -4.1pAoP

Page 62: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 62/360

5 .1 .4 (Con t 'd ) NOTATIONFOR THE MAIN ROTORM O D U L E

SYMBOLUSED IN PROGRAMEQUATIONS M N E M O N I C UNITS DESCRIPTION

-PR44

c;3'6

Q3'A~~~

A ~ i

A~~~

A ~ i

/TOT

KTX

K1T H A

" HA

LHA

/C~~

c~~~

C~~~

BB1F

L

OMR.MR

OMRMRPSIMRB R M RB R .M R

BR..MRLGMR

LG. MR

LG. .MRAOFMR

A1FMR

81FMRAOLMR

A1LMR

B1LMR

UTOTMR

K1XMR

K l Y M RTHAMR

MHAMR

LHAMR

RH0CTHAMR

CMHAMRCLHAMR

N D

N D

DEG

RADSRADS/ SEC

RADSISEC~

RADS/ C ~

RADSRADS/SEC .

DEG

DEG

DEG

DEG

D E G

DEGr iD

N D

N DLB

FT L B

FT LB

SLUGS/FT3

5.1-42PA G E '-

Rotor s h a f t a c c e l e r a t i o n r a t i o

Rotor s h a f t s p e e d r a t i oRotor azimuth p o s i t i o nFlapping angleFlapping r a t e

F1 app i ng ac ce le r a t ionLagging angleLagging ra teLagging acce lera t ionSteady f l app in g (con ing)Long. f i r s t harmonic f l a p p i n gLateral f i r s t harmonic f lappingSteady laggingLong. f i r s t harmonic l agg ing

La te ra l f i r s t harmonic laggingTotal velocity component a tthe rotorLongitudinal Glauert i n f l o w "actorLateral Glauert i n f l o w f a c t o rAerodynamic componentof thrust

Aerodynamic componentof pi t c h i ngmomentAerodynamic componentof r o l l i n gmment

Air d e ns i t yThrust coe ff i c i en tP i t c h i n g moment coe ff i c i en tRoll ing moment coefficient

Page 63: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 63/360

Page 64: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 64/360

__.-

5 . 1 . 4 ( C o n t ' d ) NOTATION FOR THE MAIN ROTOR M O D U L E

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

I 'ACHMR

cos y

* C U F F*1sB1s

A SP

$ 3

K 1

K 2T~~~~~~

F~~~M Rb S

F P O

FPC

FPs

a

-

UPAMRU P B M RUPMR

UTAMR

UTBMR

UTMRURPMR

URBMR

URMR

UYAWMR

MACHMRVSOUNDCSGMMR ,

A1S

87 S

DELSMRDEL3MRKAFlMR

KAF2MR

THETA@

T H ~ ~ A M R

FPDYMR

NBSMR

NSSMRFPOMR

FPCMR

FPSMR

l /MDS1 RADS1 RADS1/RADS1 RADS

1/RADS1 RADS1 RADS1 RADS1 RADS

FT/SEC

REG

DEG

D E GD E GDEG

DEGLB

LB

LB .

LB

5.1-44-A G E

B l a d e s e g m e n t t o t a l v e l o c i t yComponents i n b lade spanaxes .

Total f low component a t t h eblade segment

Blade segment Mach Number.Speed o f soundCosine o f segment flow skew a n g l eColle c t ive b l a d e p i t c hL a t er a l c y c l i c b l ad e p i t c hL o n gi t ud i na l c y c l i c b l a d ep i t c h

Swashpla te phase angleHinge a ngl e-P i tch /Fla p coupl ingHinge angle coe ff i c i en t s -Pi tch/Lag coupl ingGeomet r i c b l ade p i t ch ang leR e s u l t a n t force a t b la de r o o tNumber o f b l a d e s s i m u l a t e d

Number o f segments s i u1a t dHarmonic components oftheb l a d e r e s u l t a n t f o r c e

fA 29 REV. c

Page 65: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 65/360

5 . 1 . 4 ( C o n t ' d ) NOTATION FOR THE MAIN ROTORMODULE

S *lBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

5.1-45-A G E

MODESP

KFPO

K F P C

KFPS

T~~~M R

e I

NY

A ~ ~ iRA~~~~~

ACL3MR

A CL4MRTRANS

LY

'CYBTLMR

A C D b i R

FP

FT

F R

FPbFTb

FRb

F X AF YAFZA

-KFPOMR

KFPCMR

KFPSMR

THDYMR

AFYNMR

ACLlMRACL2MRACL3MRACL4MRAFTFMR

CLMR

C D M RBTLMR

OCDMR

FPMR

FTMRFRMR

FPBMR

FTBMRFRBMR

FXAMR

FYAMR

FZAMR

DEG

DEG

DEG

DEG

DEGDEGDEG

DEG---

LB

LB

LB

LB

LB

LB

LB

LB

LE

Equiva len t b l ade f i r s t t o r s iona l modeHarmonic weight ing coeffi c i entsf a r b la de t o r s i o n a l wind-up .

B la de s eg m en t t o r s i o n a l a e f l e c t i o n

Actua l b l ade segment geomet r i c p i t ch

Blade segment ang le o f a t t ackA ng le o f a t t a c k b re a k p o i n t s

f o r l i f t curve.

Trans fo rmed ang le o f a t t ack fo r mape n t $ . yB la de se gm en t l i f t c o e f f i c i e n tBlade segment d r a g c o e f f i c i e n tBlade t i p l i f t l o ss f a c t o rPrcf i 1e d r ag c o r r e c t i onSegment ae ro fo rces

B l a d e a e r o f o r c a s - b l a d e s p a n a x i s

I B la de a e r o f o r c e s - s h a f t r o t a t i n g a x i s

YI 29 REV.G

Page 66: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 66/360

5 . 1 . 4 ( C o n t ' d )

Y. 29 RSV. C

FXI

F Y I

FzIXT

FYTFZT

M~~~

M~~~

T~~

M~~

L~~A~~~~

LDNR

C~~~~OLDMR

S O

RLDMR

'GEOMR

NGTATION FOR THE MAIN ROTORM O D U L E

SYMBOLUSE@ IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

FXIMR

FYIMRFZIMRFXTMR

FYTMR

FZTMRMFABMR

MLABMR

THAMRMHAMR

LHAMR

ALDMR

BLCMR

CLDMR

DLDMR

RLDMRTHLDMR

LAGCMR

XLDMRYLDMR

Z L D M RLDMR

L D .MR

FLDi

MRMFFDMRMFLDMR

MLLDMR

MLFDMR

LB

LB

L BLB B la de t o t a l f o r c e s - s h a f t r o t a t i n g a x i s

LB

. LB

B la de i n e r t i a l f o r c e s - s h a f t r o t a t i n g ax1

Aero moments a b o u t h i n g e - b la d e s p a n a x i sFTT LBB ILB

IT LB

FT LB

INS

INSINS

INS

INSDEG

DEG

INSINSINSINS

INSISEi

LBFT L9

FT LB

FT LB

FT LB

5.1-46PA C E-

Aerodynamic component ofthrust forceAerodynanic componentof p i t c h i n g momentAerodynamic component o f r o l l in g moment

I n p u t c o n s t a n t s d e f i n i n gthegeomet ry o f t he l ag damperk inemat i c s

Component displa cem net of ld g damper

( r e l a t i v e p i c k u p p o i n t s )

Ax ia l d i sp l acemen t o f lag damper

Axial ra te of lag damper

Axial force output f rom lag damper.F lapp ing moment due t o f l a p damper

Flapping moment d u e t o lag damper

Lagging moment d ue t o l a g damperLagging moment duet o f l ap damper

Page 67: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 67/360

D O C U M E N Tx . SEH 70452

FT LS

F T LB

FT L B

5.1 .4 ( C o n t ’ d ) NOTATION FOR THE MAINRQTORMODULE

Delta moments a t hub due ’io

blade constraints.

-.SYYBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

LBLE

LB

FT i.5

FT LBFT Le

ALHBC

A’HBC

A N H B C

vyb

%

%HH

J H

TH

LH

QH

HHB

~~

THB

L~~

Q H B

T~~~~~

QE

Ib

MHS

Tota l force component outputsfrornthe rotor i n shaft axes a t the hub

Total moment component outputs

f r o mthe rotor i n shaft axes a tthe hub

DLHBMR

DMHBMR

DNHBMR

KBETAKBETA.

MBMR

IBMR

WTBDMR

HHMR

JHMR

THMR

LHMR

MHMRQHMR

HHBMR

31iBMR

THBMR

LHBMR

MHBMR

QHBMR.

TFILMR

QMEG

Y 29 a t v. G

FT LB

S C

r E

5.1-

F T. L B IRotor force a n d moment f i 1 e rtime constantEngine torque - supplied by enginemodule i f elected.

7-A C E

Page 68: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 68/360

5.1 .4 (C o n t ' d ) NOTATIONFOR THE MAIN ROTORM O D U L E

SYMBOLUSEDIN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

XMR

Y~~

h R

M~~

NMRYPMR

c T / C

c t / f l

cJ/O-

CM

c L / C

c Q S

HPMR

XMRYMR

ZMR- LMR

MMR

NMRCHIPMRHPMR

CTSGMRCHSGMRCJSGMRCMSGMRCLSGMRCQSGMR

LB

LB

LB

FT LB

FT LB

FT LBDEG

1.1P

Rotor forces and moments i n bodya xe s a t the fuse lage c.g.

Rotor wake skew a n g l eHorsepower required by rotor.

Rotor shaft axes force and momentc o e f f i c i e n t s ( o u t p ut o n l y ) .

5.1-4s-A G E

SA 29 REV. G

Page 69: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 69/360

' 1

O O C U M E N TY O . SZR 70452

5.1-49PAGE'

Y n m.G

Page 70: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 70/360

BLACKHAWKBLAGETWISTINPUT

M A P NAME: T W H A M PN R P TYPE: U VAI N P U T VA R I A B L E(SI : XSEGMRO U T P U T V F I R I F I B L L : T H S T M A

P R I M A RYMdP:0 . 0 0 w u * n1.00 Prm)umn0.05 m m

. . . . . . . . ..

t --*----.-

FIGURE1.5.1

5. - 5 0-A G E

.._. -

Page 71: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 71/360

K I D Q B 8 e D O C U M E N TN O . SER 70452

Y 29 RCV.0

BLACKHAWKMAIN ROT3R BLADE SECTIONLIFT C O E F F I C I E N T- AIRFOILSC 1095

B L R C K H B W K- NASR STUDY 26 -SE P-8 0 CLMRHP ( 1 / 2 )

PRiFFlRY MAP:

SECONDARY YAP

MRP NRME: CLMAMPNRP TYPE: B I VUVRINPUT VARIABLEIS1 : RFTFMR MACHMROUTPUT VRRIRB LE: CLMR

-32.00 - L i n i n 0.0032.00 p l l L l l L i n i r i 1.00

2.00 a 0.10

- 180 .00 L i n i v1 8 0 . 0 0 w m ~ i n i n

2.00 (DDm

-DII0.m

' 9.10

0 . aa a

' L M

* 0.m. mo.m

' a m' a ma 1.m-

-'-20O.00 -'160.00 -'I~O.OO - ' ~ o . o o -I~o.oo $LOO ~ b . 0 0 8b.00 tk0.00 t's0.00 ~ O O . O OAFTFUR

FIGURE 1.5.2(a;

5 I - 5 i-A G E

Page 72: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 72/360

.. . ._ . . ....1

BLACK HAWKM A I NROTOR BLADE ECTIONLIFT COEFFICIENT- AIRFOILS C 1095 (Con t ' d )

BLRCKHRYK- HRSR STUOY 26-SEP-BO C l n A N P 12/21

FIGURE 1.5.2(b)

5 . 1 - 5 2-A G E

Page 73: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 73/360

D O C U M E N TNO. SER 70452

BLACKHAWKM A I NROTOR BLADE SECTION DRAG COEFFICIENT- AIRFOIL SC 1095-S L R C K H AW K- NRSA STUOT 26-SEP-80

M A P HARE: c o n A n PR R P TTPE: B V U V RI N P U T V R R I R B L E91 : R F Y H H ROUTPUT V R R I R B L E : C u n R

P R I M A R T HRP:-32.00 m u m n

32.00 m u u m n2.00 m m

SECONORRY HAP;-180.00 - u m n

180.00 m u m2.00 m m

CDRRHP 11/21

0.00

0.101.00

8I I I 1i - -

I I I

FIGURE1.5 .3(a)

5 . 1 - 5 3-A G E

Page 74: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 74/360

BLACKHAWKMAINROTORBLADE'SECTIONDRAG COEFFICIENT- AIRFOIL SC 1095 (Con t 'd l

BLRCXHRIIA- NRSR STUDY 26-SEP-82 CDqRIlP 12/21

0

0 1II

a

I I- . i I I II I I

FIGURE1 . 5 . 3 (b)

5 . 1 - 5 4-A G E

ao

Page 75: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 75/360

Page 76: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 76/360

BLACK HAWK MAIN ROTOR BLADELAGDAMPER FORCE CHARACTERISTICS {Cont'c',)

BLACKHRWK- HRSA STUOT 26-SEP-BO LOHRHP 12/21

0

FIGURE1,5.4(b)

5.1 -56-A G E

Page 77: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 77/360

~-- .. . . . . . ... . .. . .~... .

TABLE 1.5.1

BLACK HAWKMAIN ROTORPRESETBLADETWIST

TWMRMP::UVR93XS E M R WTWS T M ##T W M R L O

EXP 0.d,l.0,0.05TWMRLO: E x P 0.a.

E X P - 8 . 9 5 ,E X P , -5.3.

-1a.9E X P -9.65,

Y n Rtv. 5

;MAP ARCUMENT:LOOK UP ROUTINEi INPUT VARIABLE;OUTPUT VARIABLE;MAP NAMEiLOWER LIMITVUPPER LIMITBDEL TA

# . a , 0.0, a . a ,- 1 . 8 , -2.75, -3.55,

-7.1, -7.9,6.15,-10.3, -10.75, -12.3,

5 . 1 - 5 7-AGE'

-0.13-4.4-0.8-13.1

Page 78: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 78/360

a. - . )

,-c -- . .E Q C U M E ? I TN O . SE ? 70452

TABLE 1.5.2

BLACK HAWKM A I NROTOR BLADESECTION LIFT COEFFICIENT- AIRFOIL SC1095

A C L l M R : 11.0ACLZMR: 172.0ACL3MR: - 5 . 0A C L 4 M R : -172.B

; ** R OTOR C O E F. O F L I F T M APCLMRMP: BI VU VRI IO ;MAP ARGUMENT:LOOK UP ROU TINE

A F T FM R # # (1 7 ) : I N P U T VA R I A B L E# I ,M A CH M R# # (A 1 7) : I N P U T VA R I A B L E#2CLMRO#(A1 7 : O U T P U T VA R I A B L ECLMRLO :PR MARY ( B A S I C ) MAP NAME

E X P -32.0,32.8,2.0, 33:LOW. L I M . , UP. L I M . , D E LTA , I I T E M SEXP O . O , l . f l e , . T ;LOW. L I M . , U P. L I M : , D E LTA

E X P -180.0,180.0,2.0 :LRW. L I M . , U P. L I M . , D E LTAC L M R H I ; S EC ON D ARY ( H I C H A N G L E ) M A P N AM E

CLMRLO: EXPEXPEXPEXPEXPEXPEXP

E X PEXPEXPEXPEXPEXPE X P

EXPi X PEXPEXPEXPEXPEXP

E X PEXPEXPE X PEXP

EXPE X P

i PRI MAR Y MAP: AFTF MR FROM-32: M A C H N O . r. 0-0.9675, - 1 . 0 , -0.996,-%.984, -121.980, -0.976,.-0.724, -0.37, -0.19,-0.19, 0.03, 0.243,

0.89, 1.10, 1.25,0.9828. 0.9856, 0.9884.

.997 1 . 0 , 0.9675

: MACH N 0 . 1 . 1-0.9675, - 1 . 0 . -0.996,-0.984, -0.988, -0.976,

-0.19. .0.53. 0.243.-0.724, 70.37, -0.19,

0.89, 1 . 1 0 , 1.25,0.9828. 0.9856. 0.9884.

,997 1 . 0 , . . 0.9675.

: MACH N0.=.2-0.9675, - 1 - 0 , -0.996,-0.984 -0.980, -0.976,-5.724, -0.37 1 -0.19,-0.19, 0.03, 1.243,

0 . 8 9 , 1 . 1 0 . 1.25,0.9828, 0.9856, 0.9884,0.997, 1.0, 0.9675

: MACH N O . r . 3-0.9675, - 1 *0. -6.996,-0.984, -0.980, -5.976,-0.72 4, -0.37, -0.19,-0.19. 0 . 0 3 . 0.243,

0.89, 1 . 1 0 . 1.25,

0 . 9 8 2 8 , 0.9856, 0.9884,0.997, 1 . a , 0.9675

TO 32.DELTA-2,MACHMR F R O M0 T O 1.

-0.992, -0.988-0.972, - 1 .B7-0.39, -0.45

0.46, 0.671. 10, 0.980.9912, 0.9948

-8.992. - iT. 988-0.972, - I - 0 7-0.39, -a. 45

0.46, 0.671 1 0 , 0.980.9912. 8.9940

-0.992. -0.988-0.972, -1.07-0.39, -0.45

0.46, 0.671.10, 0.980.9912, 0.9940

-0.992. -0.988-0.972, -1.07-6.39, -0.45

0.46, 0.671. 10, 0.980.9912, 0.994

5.1-58PAGE-

Page 79: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 79/360

Page 80: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 80/360

Page 81: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 81/360

Page 82: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 82/360

Page 83: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 83/360

C D M R H I : E X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PE X PEX PE X P

E X PE X PE X ?E X PE X PE S PE X P

_ _ - -.. . , . . ..._..

TABLE 1.5.3 ( C o n t ' d

; H I G H ANGLE M A P : AFYWMR FROM-180 TO 180, OELTA*2.367, ,733 v0 ,

1.03,. 8 4 ,.64,.E7875 I

1.1225.1.36625,1.61,1.8575,2.0525,2.08625,1.98.1.. 7 8 1 25 , 1.335 I

.9725,

.63,

.267,

. 012 ,.0075,.017,.345,.63,. Y 725,

1 .335,1.70125,1 .98,2.08625,2.9525,1.8575,1.61,

1.36625,1.1225,.87875,.64,.84,

1.03,.0

.995,

. 8 ,

.6875,,9275,

1.17125,1.415,1.66,1.905,2 - 0 7 8 75 ,2.08,1.52875,1.6275,1.2615,

.9,.562,.195,. 0 0 8 ,. 0 m ,.026,. 4 ,.6975,

' 1 . 0 4 5 ,1.4075,1.775,2.005,2.0925,2.02625,1.01,1.56125,

1.3175,I .07375,. 8 3 ,. 68, . 8 8 ,

1.065.

.96,' 76 ,.735,.97625,

1.22,I . 46375,1.71,1.9525,2.105,2.055,1.8775,1.55375,1.19,

,8325,.488 ,.12,,80795. 5 0 8 5* 145,,455,,765.

1.1175,1.48,1.82625,2.03,2,09875,2.0,1.76,1 .5125,

1 ,26875.1 a825 t

* 7825,. 72, - 9 2 ,

1.1.

1.1,. 9 2 ,. 72,.7825 ,

1.025.1,26875,1.5125,1 .76 ,2.0,2 098752.03,1 8 2 6 2 5 9

1.48,1.1175,

.765,

.417,

. 0 4 5 ,

.0075,

. 0 0 9 ,

.23,, 507 ,.8325,

1 .19,1.55375,1.8775,2.555,2.105,1.9525,1 .71,1.46375,

1.22,.99625,.735 ,.76 ,.96,.733

1.073751.31751.561251.812 .if26282.09252.0051.9751.08751.045

,697534

e 0 18 ,0075,811.293.56. 9

1.26251.62751.92875

2.082 .if78751.9051.661.415

1.17125.9275,6875. 8 ,995

.367

5.1-63-AGE

Page 84: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 84/360

aacumEurN O . S E A 70452

TABLE1.5.4

B L A C K HAWK M I N RO TO R B L AD ELAG DAMPER-FORCE CHARACTERISTICS

-

L D M X M P : : U V S U V S # # { M A P A R G U M EN T : L O O K U P R O U T I N ELD.M R I WA 1 6 1F L D . f I R + # ( A 1 6 ) { O U T P U T VA R I A B L ELDMRLO . L O W RANGE M A P N A M E

L U M R H I : H I C H R A NG E M A P N AM E

i N P U T V A R I A B L E

E X P 0 . : a , 2 . 0 , 0 . 1 ; L O WE R L I M I T , U P P E R L I M I T , D E L ' T A

E X P 2 . 8 , 7 . 0 , 1 . 0 I L ~O WE R L I M I T q U P P E R L I M I T g D E L T A

. ; LOW A N 6 L E M A P ; L D , M R0 TO 2 . 0 , D E L T A .1L D M R L O : E X P 0.0, 10B.0, 230.0, 3 8 0 . 0 , 600.0

EXP 9 0 0 . 0 , 1 3 0 0 , 0 , 1650.0, 2080.0, 2 4 0 0 . 0E X P 2 9 6 0 . 0 , 3 2 3 0 . 0 , 3360.0, 3 4 5 0 . 0 , 3 5 2 5 e 0E X P 3565.0; 3 5 9 0 . 3 , 3 6 1 1 . 0 , 3 6 3 0 . 0 , 2 6 5 0 . 0

. E X P 3 6 6 8 . 0

: H I G H A N G L E M A P: L D . M R2 . 0 TO 7.0 , D E L f A = 1 . 0LDMRHI: E n P 3660 .8 , 3 7 u . 0 , 3 8 8 s . ~ , 1 8 7 5 . 0 , 3 9 4 0 . 0

E X P 4000.0

5.1-64PIIOE'

\

Page 85: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 85/360

Page 86: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 86/360

-

5.2 FUSEL4GE MODULE

5.2-1CONTENTS

5.2.1 Modu le Description 5.2-2

FIGURES

5.2.1.1 Fusela ge Equati on Flow Diagra m

5.2.2 Module Equations

5.2.3

5.2.4 Nomenclature

Module Input/Output Def nifian

5.2-4.

5.2-1 1

5.2-12

5.2-155.2.5 Black Hawk Fusela ge Input Data

TABLES

5.2.5.15.2.5.25.2.5.3

Inplane Component of Rotor Wash on the FuselageDownwash Component of Rotor Wash on the FuselageFuselage Drag Coefficient Due to Angle o f AttackIncremental Fuselage Drag Coefficient Due to Sidesl ipFuselage Side Force Coefficient Due to SideslipFuselage Lift Coefficient Due to Angle of AttackIncremental Fuselage Lift Coefficient Due to Sidesl ipFuselage Rolling Moment Coefficient Due to SideslipFusel age Pitchi lg Moment Coef i ci ent D ue t o Angle of At tackIncremental Fuselage Pitching Moment Due to SideslipFuselage Yawing Moment Coefficient Due to Sideslip

5.2-165.2-165.2-175.2-175.2.5.4

5.2.5.55.2.5.6

5.2-175.2-18

5.2.5.75.2.5.8

5.2-185.2-185.2-195.2. 195.2-79

5.2.5.95.2.5.10

5.2.5.11FIGURES

5.2.5.1 Inplan e Compon ent of Rotor Wash on the Fusela ge5.2.5.2 Downwash Component c f Rotor Wash on the Fuselage5.2.5.3 Fusela ge Drag Coef fici ent Due to Angle of Attack5.2.5.4 Increm ental Fusela ge Drag Coeffi cient Due to Sidesl ip5.2.5.5 Fuselage Side Force Coefficient Due to Sideslip5.2.5.6 Fusela ge Lift Coeffi cient Due to Angle of Attack5.2.5.7 Incrementa Fuselage Lift Coefficient Due to Sidesl ip5.2.5.8 Fusela ge Rolling Moment Coeffi cient Due to Sidesl ip5.2.5.9 Fuselage Pitching Moment Coefficient Due to Angle of Attack5.2.5.10 Increm ental Fuselag e Pitchi ng Moment Due to Sidesl ip5.2.5.11 Fuselage Yawing Moment Coefficient Due to Sidesl ip

5.2-205.2-215.2-225.2-245.2-265.2-285.2-305.2-315.2-335.2-355.2-36

5.2.5 References

5.2-1-PAr,E

--.-

Page 87: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 87/360

--

5.2 Fusel age Modul e

5.2.1 Modu e Descrp

t on

D O C U M E N Tn o . SER-70452

The effects of rotor wash 7 the airframe have been treated ingross terms. No atte mpt ha:, been made to determine the localflow under the rotor disc and apply it to an element analysisof the fuselage. The implication of the method used is thatany variations in local velocity effects have been ignored.It is considered that th e technique used provides the essentialeffects o f more interference velocity with increased rotorload, and varies as the rotor wake deflects rearward withincreased forward speed.

The angles of attack and sideslip are derived from the bodyaxes components of velocity.f ight path velocity , gust components and rotor downwash.

definition o f the angles are those used in the wind tunnel.That is, angle o f attack is the geometric angle subtended bythe model relative to tunnel axis at zero yaw angle. It doesnot change with yaw ang7e. Angle of sideslip, equal to minusyaw, is defined as yaw table angle in the horizontal plane ofthe tunnel, irrespective of angle of attack.noted that these angles are not Euler angles.

The fuselage aerodynamic characteristics are specific to theBlack Hawk helicopter. They are not genera lized in any wayand are derived directly from wind p n n e l tgsts. The aero-dynami c coeffi cients in terms of ft and ft , for forces andmoments respectively, are presented as functions of angle o fattack and sideslip i n Section 5.2.5.and moments are subsequently transfwmed into body axes at thefuselage center of gravity.tunnel tests up to post stall crinditions must be extended to-90° to cover the low speed Plight regimes. Near hover, themost important forces (tail off) are the vertical drag andside force. These can be estimated fairly accurately.Because of the definiticos of angle of attack and sideslip thetransformation equation gives invalid body axes forces andmoments when these angles approach 9

These comprise the components ofThe

It should be

These wind axes forces

The data obtained from wind

5 . 2 - 2-PA G E

Page 88: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 88/360

--

To avoi d problems during pilot-in-the-loop simulation, filtersare presented which fade out the transformation and introducefixed body axes parameters, estimated specifically for hoverarid l o w speed flight. For open loop anlaysis the longitudinaldegrees-of-freedom are representative. It should be notedhowever, that inaccuracie s will be encounted in pure sideflight (i.e., roto r sid e wa sh on the fuselage does not exist).A block diagram indicating the fuselage module f l o w i s presentedon figure 2.1.1.

.

5 . 2 - 3PA G E

tl 29 W .

Page 89: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 89/360

Page 90: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 90/360

Page 91: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 91/360

-

--- -

5.2-6PAGPf

. .-.-._. ._I

Page 92: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 92/360

...71 ’_

LI

Page 93: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 93/360

Page 94: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 94/360

"

i:

Page 95: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 95/360

Page 96: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 96/360

Page 97: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 97/360

5 . 2 . 4 Notat.;sn f o r t h e Fuse l aqe M o d u k

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UN ITS DESC RIPTION

SA 29 REV. C

'XWF

'YWF

'ZWF

V~~~~v~IW

v~~~~

EKXWF

EKYWF

EKZWF

DW0

RT

S T

'WF

WF

lw WFI

o( WWF

/ WF

P W F

9 F /

----

VXWF

VYWF

VZW F

V X I t l F

V YIWF

VZIWF

EKXW F

EKYWF

EKYWF

DWSHMR

OMGTMR

RMR

QWF

ALFWF

AFABWF

ALFWWF

B ETAW F

P S WF

PSABW F

SNAFWFCSAFWF

SNBTW F

CSB f wF

FT/SEC

FT/SEC

FT/SEC

FT/ SEC

FT/SEC

FT/SEC

---

-RADS/ SECFT

DEG

DEG

DEG

DEGDEG

DEG

To t a l v e l o c i t y com ponents a t t h e

f u s e l a g e c e n t e r o f g r a v i t y ,

Roto r wash i n t e r f e r e nc e on t he

fu se l age.

R o t o r wash i n t e r f e r e n c e f ac to r s

Main ro tor un i form downwash .

Rotor speed

R o t o r r a d i u s

Dynam.ic p r e s s u r e a t t h e body

Body a x i s ang l e o f a t t a c k

ABS (ALFWF)

I J ing angle of a t tack

S i d e s l i p a n g l e

W/T model yaw angle ;=-BETAWF)

ABS (PSIWF)

S I N ALFWF)COS (ALFWF)

s N BETAWF

COS(BETAWF

5.2-12-PA G E

Page 98: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 98/360

Page 99: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 99/360

Page 100: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 100/360

* a m . 0

_yI '1

-

5 . 2 - 1 5PAGP'

Page 101: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 101/360

Page 102: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 102/360

7

----

BLACK HAVK (TAIL OFF IRS O F F )

TABLE 2 . 5 . 3

FUSELAGE DRAG CO EF FI CI EN T DUE TO ANGLE OFATTACKDQFMP::UVRUVR#O ;MAP ARGU MENT :LOO K UP ROU TIN E

EXP

EXP

DPFLO:

DQFHI :

ALFWF*# ;INPU T VARIABLEDOFI# ;OUT PUT VARIABLEDQFLO :LOW ANGLE MAP NAME

DOFHI ;HIGH ANGL E MAP NAME *

-?0.0,90.0,10.0 ;LO WER LIM T,UPPER LIMIT,DELTA-HIGH A NGL E

EXP 45 .BE 3 3 7 . 5 8 , 3 1 . 6 8 , 2 7 . 4 8 , 2 5 . 0 6EXP 2 3 . 5 8 , 2 3 . 5 8 , 2 5 . 0 8 , 2 7 . 5 8 , 3 1 . 2 8EXP 3 6 . 5 8 , 4 3 8 8 , 5 1 . 0 8

EXP 150.0, 145.0, 133.0, 114.0- 8 8 . 0EXP 6 1 . 0 , 4 5 . 0 8 , 3 1 . 6 8 , 2 5 . 0 6 , 2 3 . 5 8EXP 2 7 . 5 8 , 3 6 .5 8 , 5 1 88, 6 6 . 0 , 84.0E XP 1 1 0 . 0 , 132.0, 1 4 5 . 0 , 150.0

- 2 0 . 0 , 3 0 . 0 , 5 . 0 ;LOWER LIMIT,UPPER LIMITpDELTA-LOW ANG LE

; LOW ANGLE MAP: ALFWF- 3 8 T O 30 , DELTA15

; HIGH ANGLE MAP: ALFUF - 9 0 TO 9 0 , DELTA-10

TABLE 2.5.4

INCREMENTAL FUSELAGE DRAG COEFFICIENT DUE TOSIDESLIPDOQFMP::UVRUVR##- :MAP ARGUMENT:LOOK UP ROUTINE

PSABWFe4 ; INPUT VARIABLEDOOF#* :OUTP UT VARIA BLED D Q F L O ;LOW ANGL E MAP NAME

DDQFHI :HIGH ANGLE MAP NAMEEXP 0 . 8 . 3 0 . 0 . 5 . 0 ;LOWE R LIMIT,UPPER LIMIT,DELTA-LOW AN GLE

EXP 3 8 . 0 , 9 8 . 0 , 1 0 . 0 ;LOVER LIHlf,UPPER LIMfT,DELTA-HIGH A NG LE

; LOW ANGLE MAP: PSI(ABS1 8 TO 3 0 , DELTA-5OOQFLO: EXP 0.0, 1 . a , 4 . 3 , 9 . 0 , 1 6 . 3

; HIGH ANGLE MAP: PSI(ABS) 3 0 TO 9 8 , DELTA-10O D Q F H I : EXP 3 8 . 5 , 7 6 . 5 , 1 1 3 . 5 , 1 4 1 . 5 , 1 6 4 . 5

EXP 2 8 . 0 , 3 8 . 5I

EXP 1 6 9 . 5 , 170.5

TABLE2.5.5

FUSELAGE SIDE FORCE COEFFICIENT DUETO S I D E S L I P

YQFf4P::UVSUVSW :MAP ARGUM EPT:L OOK UP ROUTS NEP S IWFO# ;INP UT VARIABLEvas ## ;OUTPUT VARIABLEVQFLO ;LOW ANGL E MAP NAME

VPFHX :HIGH ANG LE MAP NAMEEXP D a , 3 0 . 0 . 5 . 0 :LOWER LIMIf,UPPER LIMIT,DELTA-LOW AN GLE

EXP 30.0,90,0,10.0 ;LOW ER LIMI7,UPPER LIMIT,CELTA-HGIH AN GLE

; LOW ANGL E MAP: PSIWF B T O 39, DELTA-5 Y(PSI)*-Y(-PSI)YQFLO: EXP 0.0,

E X P 65.8,11 .0 ,7 2 . 0

23.0, 35.8, 5 8 . 8

t HIGH ANGL E MAP: PSIWF 3 0 TO 90, CPLTA-10 Y(PSX)*-Y(-PSI)YQFHI: EXP 7 2 . 0 , 92.0, 103.0, 10Al.d, 8 4 . 0

E X P 64.0, 3 7 -16

5 . 2 - 1 7TG?

Page 103: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 103/360

BLACK HAWK(TA1L OFF IRS OFF)

TABLE 2 .5 .6

U SE LA GE L I F T C C E F F I C I E N T DUETO ANGLE O F ATTACK

LQFMP::UVRUVR##AL WF

;MAP AR6UMENT:LOOK UP ROUTIN E:INPUT VARIABLE

L Q F W ;OUTPUT VARIABLELPFCO (LOW ANGLE MAP NAME

LQFHI ; H I G H ANGL5 MAP NAMEEXP - 3 0 . 0 , 3 4 . 8 , 5 . 0 :LOWER.LIMIT,UPPER LIMIT,DELTA-LOW A NG LE

EXP -90.6.90.8.10.0 (LOWE R LIMXT,UPP ER LIMIT,DELTA-HIGH ANGL E

; LOW 4NGLE MAP: ALFWF - 3 8 ' T O 3 0 , DELTA-5LQFLO : EXP -78.R, - 5 2 . 0 , -3§.R, -25.0, - 1 3 . 0

EXP -5.0, 1.g. 10.0, 2 0 . 0 , 2 5 . 0EXP 3 8 . 0 , 34.0, 37.0

; HZGH A N G L E MAP: ALFWF -90 TO 9 0 , DELTAmIBLQFHI: EXP -24.0. -54 B , -72.0, -61 0 , - 8 6 . 0

EXP -63.0, -70.0, -35.0, -13 .0 , 1.0

EXP 2a.0, 30.0, 37 a , 43-01 48.0EXP 5 0 . 0 , 4 8 . 0 , 39.0, 22 d

TABLE 2 . 5 . 7

-N CR EM EN TA L F U SE LA GE L I E C O E F F I C I E N T D UETO S I D E S L I P

0LQFMP::UVRW . :MAPARCUMENT:LOOVU P R O U T I N E .PS WFUe INPUT VARIABLEDLaF#* iOUTPLiT VA RI AB LEDLQFLO LOU ANGLE MAP NAME

EX? -30.8,30.0,5.8 (LOWE R LIYIT,UPPER LIMIT,DELPA-LOW ANGLE

PLQFLO: EXP 38.0, 28.0, 12.0, 7.0, 3 . 0; LOU ANG LE MAP: PSIWF -30 TO 38, DELTAaS

EXP 2.0, 0.0, 2.0, 5 . 0 , 10.0EXP 1 5 - 8 9

22.8, 3 0 :0

TABLE 2.5.8

FUSELAGE ROLLINGMOMENTCOEFFI$,LENT DUETO S I D E S L I P

RQFMP::UVSUVSI# :MAP ARCUMEN1 :LOOK UP RO UT XN EP S I W F W 4 INPUT VARIABLER Q F W O U TP U T VA R IA B LERQFLO :LOW ANG LE MAP NAME

ROFHI :HIGH ANG LE MAP NAMEEXP 0 . 0 , 3 0 . 0 , 5 . 0 ;LOWER LIMIT,UPPER LIMIT,DELTA-LOW AN GLE

EXP 30.0,98.0,10.0 ;LOVE R LIMIT,UPPER LIMIT,DELTA-HGIH ANGL E

: LOW ANGLE MAF: PSIWF 0 TO 3 8 , DE LT A= S R(PS1 )m-R(-PSI )RQFLO: EXP 0.0, 0.0.. 0.0, - 3 0 . 0 , - 7 5 .x

EXP -1 20.0 - 1 10.0; HI GH ANG LE MAP: PSI WF 3 0 TO 9 0 , DELTAmlR R(PS1 )--R(-PSI

RQFHX: EXP -110.0, -106.0, -103.0, -101.0, -10P.BEXP -100.0, -100.0

5.2-15PAGE-

Page 104: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 104/360

BLAC K HAWK'(TA1L OFF XRS OFF )

TA B L E 2 . 5 . 9

FUSELAGE PITCHING MOMENT COEFFJCIENT DUETO ANGLE OF ATTACK

MQFMP::UVRUYRI* ;MAP ARGUMEN1:LOOKUP ROUTINEAL FWF## ;INP UT VARIABLEM Q F M ; O U TP U T VAR IA BL EMQFLO :LOW ANGLE MAP NA ME

MQFH :HIGH ANGLE MAP NAMEE X P -38.0,38.9.5.0 ;LOW ER LIMIT,UPPER LIMI1,DELTA-LOW ANGL E .E X P -90.0,90.0,10.0 +LO WER LXMIT,UPPER LIMIT,DELTA-HGIH ANGL E

MQFLO: E X P -740.0. -755.5 -630.0. -520.1. -380.0; LOW ANGLE.M A P : A L F W F- 3 0 TO 3 0 , DELTA-5

E X P -230.0, -90.0, 10.0; 100.0; 290.5E X P 450.0, 600.0, 750.0

; HIGH ANGLE MAP: ALFUF -90 TO 9 0 , DELTA-I0MPFHI: E X P -200 .8 , -470.5, -645.0, -730.0, - 7 6 0 . 8

E X P r765.0, - 7 4 5 . 0 , -630.5, . -385.0, ' -90.0E X P 100.0, 4 5 0 750.0, 810 .0 , 825.0

. E X P 7 a ~ . ~ , 650.0, 470.0, 200. 0

TABLE 2.5.10

INCREMENTAL FUSELAGE PIT CH IN G MOMENT DUE TO SI D E S LI P

; BLACK HAWK FUSEL AGE DEL PITCHM O MVS PSIWF(A8S)DMQFMP::UVRII) ;MAP ARCUM ENT:L OOK UP ROUTINE

PSABWF## :INPU T VARIA BLEDMaFII :OUTPUT VARIABLEDMQFL O :LOW RANGE MAP NAME

E X P 0,3,38.0,5.8 ;LOWE R LIMIT,UPPER LIMIT.DELTA-LOW ANGL E MAP

8 LOW ANGLE MAP: PSItABS) 0 TO 30, DELTA-S0MQFLU:EXP 0 .3 , 15.0, 20.0, 50.0, 90.0

E X P 130.0, 1 8 0 . 0

TABLE 2.5.11

FUSELAGE YAWING MOMENT COE FFIC IENT DUE TO S ID E SL IPNQFMP::UVRUVR#I) :MAP ARGU MENT :LO OKU P ROUTINF

P S IWF#Cr :IN PUT VAR IAB LENQFtW ;OUTPUT VARIABLENQFLO ;LOW ANGLE MAP NAME

NaFHI :HIGH ANGLE M A P NAMEE X P -30.8,30.0,5.0 :LOWER IIMIT ,UPP ER LIMIT,DE LTA-LOW ANGLE

E X P -90.0,90.0,10.0 :LOWER L X M I T, U P P E R LXMIT,DELTA-HIGH ANGLE

NQFLO: E X P b 1 4 0 . 8 , - 1 9 0 . 0 , - 2 4 0 . 0 , -220.0, -180 .0E X P -100.B, B.E, 100.0, 180.0, 228.8

t LOU ANGLE MAP: PSIWF -30 TO 30, DELTA-5

E X P 240.0, 190.0, 1 4 0 . 0

t HIGH ANGLE MAP: PSIWF -9B TO 9 0 , OELTA*l0NQFHI: E X P 4 4 0 . 0 , 392.0, 332.0, 259.0, 160.0

E X ? 40.0, -140.5, -2 0 .0, -180.0, 0.0E X P 1 9 0 . 0 , 240.0, 140.0, 59 .g, - 3 0 . 0E X P -125.0, -228.0, -320.0, -420.0

5 . 2 - 1 9PAGE

.. *.&-

Page 105: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 105/360

Page 106: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 106/360

I

SER 70452

DOWNWASHFROMTHE MAINR@TORONTO THE FUSELAGE

M A P NRHE: EZYFMPtlRP TYPE: e i vINPUT VRRIRBLE S1 : CHIPMA C R l F M RO U 7 P U T VRRIRBLE: E K Z W

P R I l l A R YMAP:0.00 - L t m -6.00

100.00 r r a m n 6.0010.00 a r m 6.0J

FIGURE2.5.2

5 . 2 - 2 1

Page-

Page 107: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 107/360

FUSELAGE DRAG CO EF FI CI EN T DUETO ANGLEOF ATTACK

aLSCKHAHK - N R S A STUOY 23-SEP-80 O O F Y P 11/21

MAP NRME: o a wHAP T Y P E : UVRUVRI N P U T V F I A I R B L E[SI : flLFHFO U T P U T V R R I A B L E : OOF

P R I M R RYWRP:-30.00 m ~ i n t n

30. 00 ium L i n i n5 . 0 0 mlu

-90.00 LLodlcintri90. 00 omu~ i n i n10.00 a m

S E C O N U R RYWW;

t

I I I

" -, -

e-+ioo.oo -b .oo -ba.oo -ko.oo' io.ilo a:oo z b . 0 0 ' 1rb.00 eb.io sb.oo loo,RLFWF

FIGURE2 . 5 . 3 ( a )

Page 108: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 108/360

.:,-

SEX-704 2

FUSELAGEDRAGCOEFFICIENTDUETO ANGLEOF ATTACK( c o n t ' d )

BLACKHRUK- Nrl$R STUQY 23-SEP-80 OO FMP 12/21

FIGURE2 . 5 . 3 ( b )

5 . 2 - 2 3

Page

.-

Page 109: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 109/360

INCREMENTAL FUSELAGEDKAGC O E F F I C I E N TDUE TO S I D E S L I P

NRP NRNE: O U O F M PN A P T Y P E : U V R U V RI NPJT VFlRI ABLEIS) : P S R e W FO U T f l J T VA R I A B L E : O O O F

PA I PA R T WRP:0.00 0 . I R L I Z I W

30.00 4 1 c ~ i a t n5.00 -?=

30.00 amnunin90.00 p e c ~ ~ i m n10.00 POR

S E C J N O P RYR R P :

FIGUKE2 . 5 . 4 ( a )

5 .2-24

Page

Page 110: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 110/360

- -

p------SER 70452

INCREMENTAL FUSELAGEDRAGCOEFFICIENTD U ETO SICESLIP (Cont'd)

BLRCKHAnr - N A S A S T U D Y 23-JEP-80 OOQFR P 12/21

8

?IGURE2.5.4(b)

5 . 2 - 2 5--Page

Page 111: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 111/360

SER 70452

FUSELAGE SIDEFORCE CO EF FI CI EN T DljETO S I D E S L I P

B L g C K H RW K- N R S A STUOY 2 3 - S E P - 8 0 I C F Y P ' [ 1 / 2 1

MRP NAME: TQFRPNRP TYPE:INPUT VRR IAEL E[SI : PS IhFOUTPUT VARIi lELE: YPF

PRIRRRY HRP:

u v s u v s

-3O.CO m u m30.CO m u m i n

5 .CO E I U

SECONOARY M A P :

0

-9O.CO M u m9 O . C O m u m10. c3 a m

I . I ' I, . _ .

. .

FIGURE2 , 5 . 5 ( a )

5.2-26Page

Page 112: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 112/360

FUSELAGE SIDEFORCE COEFFICIENT DUETO SIDESLIP (cont' )

BLACMHflHM- NRSR S T U O Y 23-SEP-60 YOFHP :2/21

L - . I 1

I /I I

FIGURE2 . 5 . 5 ( b )

5 . 2 - 2 7-Page

Page 113: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 113/360

FUSELAGE LIFT COEFFICIENT CUETO ANGLE OFATTACK

BLQCKHRHW- N R S R STUCY 22-SEP-80 LOFMP :1 /21

MAP NAHE: LOFMPH R P TYPE: U V R U V RI N P U T V R R I R B L EIS1 : ALFWFOUTPUT VARIREL E: LOF

PRIRARY NAP:-30.00 PIALIRITI

30. 0 a r m untn5 .03 m n

- 9 0 . 0 0 m u n n90.00 m u n 1 n10.00 WAm

SECONOARY NAP:

%1oo.oo -bo.oa .ko.oo - io .oo -2c.00 O:QO 2b.m ub.oo sb.00 8o.00 ibo.ooALFWF

F I G U R E2 . 5 . 6 ( a )

5.2-28Page

-

Page 114: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 114/360

S E R 70452

FUSELAGELIFT COEFFICIENT DUETO ANGLEOF ATTACK( C o n t ' d )

ELACXHAHU- NRSR STUDY XJ-SEP-BO LOFHP 12/21

t

I

l ----s -- I

FIGURE2 . 5 . 6 ( b )

5.2-29Page

A- * ---. _ _

Page 115: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 115/360

- -. . . . .... .- ,

ORIGINAL.PAGE 18OF POOR QUALITY

SER 70452

INCREMENTAL FUSELAGELIFT COEFFICIENT DUETC SIDESLIP

M R P NFIRE; OLOFMPRFlP TTPE: U V RINPUT VFlRIR8LEIS1 : . P S I Y FO U T P U TVRRIRBLE: OLPF

P R I M R A YNAP:-30.00 M u m

30.00 w m u n n5 . 0 0 =n

X

1 - -

FIGURE2.5.7 '

5.2-30Page

Page 116: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 116/360

FUSELAGEROLLING MOMENTCOEFFICIENTDUE TO SIDESLIP

0

HAP TTPE: UVSUYSINPUT V R R I A B L E[SI : P S I U FOUTPUT V R R I R S L E : RPF

PRIRRRY M A P :-30.00 M u m

30.00 m u u n5.00 QLn4

-90 . 00 M i n i n

90.00 P r r m L I m n10.00 -m

SECONOART k A P :

I . . . .\r , , . , i I - -l I 1 h . I I , i ---

I . .

T I ' I ,-----t-.---\, .. . . I- I

.

FIGURE2 . 5 . 8 i a )

5.2-31Page

Page 117: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 117/360

.. . .- - -

.

FUSELAGE ROLLING MOMENT CO EFF ICI EN T DUE TO SI D ES L IP( C o n t ' d )

ROFW 12/21

0

9

I 1I

. . I

, .I

I

I I I 1 . 1 1I

I . .

FIGURE2 . 5 . 8 ( b )

5 .2 -32Page

Page 118: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 118/360

- -- . .

FUSELAGEPITCHINGMOMENTCOEFFICIENTDUETO ANGLEOF ATTACK

00

H R P N R t l E z R Q F WIMP TTPE: U V R U Y RINPUT Y R R I A B L ~ I S I R L F M FUUTPGT VA R I R B C E : N O F

P A I I l A R Y8 R P :-20.00 O I R L : ~ ~

50. 30 m I .1l l

5.30 m m

S E C O N O R RT RP:I - 9 0 . 30 L i n i n

P O . S 0 emmuaniO.30 mrm

FIGURE2.5.9(a)

5 .2 -33 .--?age

Page 119: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 119/360

FUSELAGE PITCHING MOMENT COEFFICIEiiTDUETO ANGLEOF ATTACK (Cont'd)

ELRCXHAHK-NRSR

STUDY ? ~ - s E P - ~ o HOFHP 12/21

I I - . I , I/ I

I I ' / I I

I

I1r r - -+

I_..-

.

--.

n I

FIGURE 2 . 5 . 9 ( b )

Page 120: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 120/360

I L - . - -SE ? 70452

INCREMENTAL FUSELAGE PITCHING MOMENTD U ETO SIDESLIP

MFlP NAME: OMOFMPNAP TYPE: UVRI N P U T V E I A IR B L E t S ): PSR8WFOUTPUT VARIABLE: OMOF

PRIMRRY RRP:0 . 0 0 m u a n

5 . 0 0 .0 . 0 n n m ~ m t i

0

9- 1 I 1 . 1 I I

L --- I

FIGURE2.5.10

5.2-35Page

Page 121: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 121/360

FUSELAGEYAW I N GMOMENT COEFFICIENTDUETO SIDESLIP

a L R C K H f l d t l - N R S R S T U O Y 2 3 - S E P - 3 0 NCFtiP 11/21

FIGURE2 . 5 . 1 1 ( a )

. *---__ l _____ ._L- -

5 . 2 - 3 5-Pa9e

_ - .

Page 122: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 122/360

-

FUSELAGE {AWINGMOMENT COEFFICIENTDUETO SIDESLIP (Cont‘d)

t

. . i. . . - . - - - . ,.

. . -. . . . . . .

F I G U R E2 . 5 . 1 1 i b )

5.2-37-ace

Page 123: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 123/360

5.3 EMPENNAGE MODULE

CONTENTS

5.3.1 Module Descriptlon

FIGURES

5.3.1 .l Empennage Ar I :, System

5.3.1.2 Empennage Eq uation Flow Dlagram

5.3.2 Module Equations

5.3.3 Module Input/O utputDefinition

5.3.4 Nomenclature

5.3.5 BLACKHAWKEmpennage InputData

TABLES

5.3.5.15.3.5.25.3.5.35.3.5.45.3.5.55.3.5.65.3.5 .?

5.3.5.95.3.5.10

5.3.5.8

Maln Rotor 1nplane.Washa t the Horlzontal Tal lMain Rotor Downwash .a t the Horirontal Tai lDynamlc.Pressure Loss a t . he Horfzontal . Ta i lFuselage Downwasha t . he Horlzoatal Tai 1Horfmontal Tall L. fe Co eff icle nt Due t o Angle o f AttackHorltontal Tail P r t g Coefflclent Due t o Angle o f AttackDynamic Pressure Loss a t the Vartlcal Tai lFuselage Sldewasha t the Verttcal TallVertical 'hll Lift Coefficient Due t o Sldesl tpVertical Tail Drag Coefficient Due t o Sidesl ip

FIGURES

5.3.5.15.3.5.25.3.5.35.3.5.45.3.5.55.3.5.65.3.5.75.3.5.85.3.5.95.3.5.10

Maln Rotor fnplane Wash a t the Horizontal TallMain Rotor Downwasha t the Horizontal TallDynamic PressureL o s s a t the Horizontal TallFuselage Downwash a t the Horizontal Tal lHorizontal Tail Lift Coefficient Due t o Angle of AttackHorizontal Ta i l Drag Coefficient Due t o Angle of AttackDynamlc Pressure Loss a t the Vertlcal TailFuselage Sidewasha t the Vertlcal Tal lVertical Ta i l Lif t Coefflclent Due t o S i d e s l i pYettical Tall 9rag Coefficient Due t o Sldesl lp

5.3-1

5.3-2

5.3-3

5 e 3 4

5. -5

5.3-1 3

5.3-1 4

5.3-19

5.3-205. -205.3-215.3-215.3-215..3-225.3-225.3-225.3-23 '

5.3-23

5.3-245.3-255. -265. -275.3-295.3-315.3-335.3-345.3-365.3-38

5.3.6 References

L .

. -.. ..-

Page 124: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 124/360

5.3 Empennage Module

D O C U M E Y TY O . SER 70452

5.3.1 Modu e Des cr p t on

This module calculates the aerodyanmic forces on the horizontaland vertical tail surfaces resulting from the local zirflow.The velocities are derived at, and the aerodynamic forcesa s s u m e d to act at, the panel center of pressure. Aerodynamicforces are developed i n the local fl ow wind axes system andsubsequently transferred to the body axes system at the fuselageCG as defined on Figure 3.1.1. The overall module eq u a t i mflow i s shown in.tblock diagr am form on Figure 3.1.2.

The tail can experience aerodynamic interference effects frommany sources. Compo nents of flow from t5.e main roto r andfuselag e are define at present in this module. However, theequations are formulated to allow easy insertion of othercomponents. Three components of rotor wash are developed asa function o f rotor wake skew angle and blade longitudinalflapping. Tai 1 dynamic pressure blockage and downwesh fromthe forebody are developed as a function of angle of attackand sides1 ip.the velocity delayed to account for the time taken by theairflow to reach the tail.

Small downwash/sidewash angles are assumed and

The total velocity components for the tail are made up ofcontributions from the basic body axes translational andangular velocities, gust effects, rotor wash, fuselage downwasnand sidewash. Dynamic pressure 1oss i s i ntroduced by iactirri ngthe components o f the free stream flow. The actual total

dynamic pressure at the tail is calculated from the resultantvelocity vector.of dynamic pressure at low speeds where downwash fro:, therotor predominates the flow at the tai . The 1ift and dragforces at the tail are obtained from isolated tail data andare a function of tail total angle of attack.the vertical tail, angle of attack has the same connotation assideslip.resolved into body axes at the tail. (Moments from the tailabout its own axis are not accounted for. )component forces at the empennage are trancfe rred to the CGtogether with the corresponding moments.

This allows a more representative definition

I n the case of

The lift and drag forces in local wind axes are

finally, the

5.3-2-PA G E

Page 125: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 125/360

Q R l G l N A LP \GE ISOF PDGfi QUALITY

UMcTtDSJKORSKYAIRCRAFT - 9

xk3 - CG

--

Flgure 3.1.1

Y n u v . 6

Page 126: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 126/360

Page 127: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 127/360

I Vd w

5.3-5-A 6 E

Page 128: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 128/360

5.3-6PA G E-

Page 129: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 129/360

5.3-7PIGt.

Page 130: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 130/360

. ... . - .. - . . _. .

T

'---

5.3-8IA G E

Y 21 m. c

Page 131: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 131/360

5.3-9-A G E

Page 132: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 132/360

573

5.3-10PA G E-

Page 133: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 133/360

=

ZSt rOL

Page 134: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 134/360

Page 135: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 135/360

5.3-13PAGE

Page 136: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 136/360

--- - . - - -

5.3.4 NOTATION FOR THEEMPENNAGEMODULE

SYMBOLUSED IN PROGR MEQUATI ONS MNEMONIC U NIts DESCRIPTION

FSH1

FSCGb

F H t1WLH1

WLCGb

W~~1B L H1

ELCGb

8~~E~~~1E K ~ ~

EKZH1% PMR

a i FMR

OWSHMR

. n T

RT

V~~~~1v~MRH1~ M R H

Q H ~ ~ W F

a WF

@WF

P w F

i 4 29 R I V. G

FSHl

FSCG8

KHwLHl

GILCGB

KH+1

B ~ ~ i

BLCGB

KH+2

E K X H lE K Y H l

EKZHlCH1PMR

AALFMR

DNSHMROMGTMR

RMRVXMRH1VYMRH1VXMRHlQHlQWF

ALFWF

PSIWF

B ETAWF

INS

I NSFTINS

INSFT

INS

INSFTNO

ND

NODEG

DEG

N O

MDS/SECFT

FT/SEC

Fr/SECFr/SEC

N D

DEG

DEG

9EG

5.3-14PAGE-

F u s e l a g e s t a t j o n for h o r i z o n t a l

t a i l C . P.

F u s e l a g e s t a t i o n for CG

Wa t e r l i n e s t a t i o n f o r h o r i zo n t a l

t a i l C.P.

Wa te rl in e s t a t i o n f o r CG

B u t t 1ine s t a t i o n for Hor izon ta lt a i l C.P.

But t l i ne s t a t ion for CG

Rotor wash f a c t o r s

Rotor Wake Skew angleRotor 1oFgi t u d $a 1 f 1app i ngRotor u n iform dhnwash

rim rotor speed

Rotor r a d i u sRotor interference v,l oc it y a t the

C

H o r i z o n t a i l . t a i l .

i

Hor izonta lt a i 1 flynami

c pressurer a t i oFuse lage ang le i f a t t a c k . .

Fuselage headingFuselage s i des1i p .

Page 137: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 137/360

5 . 3 . 4 (Continued) NOTATION FOR THE EMPENNAGEWODllLE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION -----K~~1E?SH1

'Xb

'XIH 1'YIH 1

P

9r

'XH1"YH1

'ZH 1

v~~FH1

V~~~1

XGH1

v~GHiVZGH1

p9

KQHl

EPSHl, V X B

VZWFHl

VXIHl

VYIH1

VZIHlP

qr

VXHl

VYH1

VZHl

.VXGHl

V YGHlVZGH1

RH0

QH1

ALFHl

ALFHH1

BETH 1

H 1

@ H t i l

dH1

ND

DEG Downwasha n g l eFT/SEC Fuselage X axis v e l o c i t yTT/SEC

FT/SEC H o r i z on t a l t a i l t o t a l i n t e r f e r e n c e

FT/SEC ve 1o ci t yFT/SEC

Fuse/Tai1 downwash ve lo ci t y

RADS/SEC Body ax es a n g u la r r a t e s .RADS/S C

RADS/S C

FT/SEC

FT/SEC t a i l .TT/SEC

Tot al v e l o c i t y a t t h e h o r i z o n t a l

FT/SEC 1 Gust v e l o c i t y a t ;he h o r i z o n t a l

t a i 1 .

FT/SEC

SLUG/FT3

LB/m2

DEG

DEGDEG Sides: ip ang le

A ir densi t y .Dynamic pressure a t t h eh o r i z o n t a l t a i 1

Body ax i s a n g l e o f a t t a c kTo t a l t a i l a n g l e o f a t t a c k

5.3-15PAGt'

Page 138: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 138/360

5.3.4 (Cont inued) NOTATION FOR THE EMPENNAGEMODULE

FT/SEC

FT/SEC

Ff /SEC

SYMBOLCSED IN PROGRAM .EqUATIONS MNEMONIC UNITS

Rotor in ter ference veloci t ies

DESCRIPTION

FT/SEC

V~~~~1

"ZMRV1'YMRV1

t a i 1 .

s~~~VYWF\I1

FTISEC

F'i"/SECf l / S E C

vxv1vYv1vzv1

vYGV1'XGV1

'ZGV I

Gust veloci ty a t the ver t i ca lt a i l .

FT/SECFT/SEC

vxIv1vY111 1

%IV 1Qv1

Inteference veloci tya t thev e r t i c a l t a i 1.

VXMRV1VYMRVIVZMRV1

SIGV 1

VYWFV1

VXVlVYv1

VZVl

VXGWl

VYGVl

VZGVl

VXIVlVYIVlVZIVlQVl

AFVFlBETV1dE' VVl

SNAFYlCSdFV1

SNBTVlCSBTVl

DEG : Fuselage sidewash angleFT/SEC Fuselage sidewash velocity

DES Angle o f at tackDEG Sides i p

DEG Total s i de sl i p angle

-. SIN(ALFV1)- COS(ALFVl )

- SIN(SEl'Vl )

- COS(BETVl )

5.3. 16PAGE--

Page 139: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 139/360

5 . 3 . 4 ( Cont i nued) NOTATIONFOH THE EMPENNAGE MODULE

SYMBOLUSED I N PROGRAMEQUATIONS MNEWONI C U N I T S D E S C R I P T I O N

--w

-

C~~ 1H1

yIi 1zH1LHI

'H 1

MH1NH1

FSVI

FVT1WLV1

BLV1

BVT1'KXV 1EKYV1

EK Z V1

SNAFHLCSAFHlSNBTHl

SCPTHl

CLH1

CDHl

XH1YH1ZH1

LH1MH1NH1

FSVT1

KV

WLVT1B LV T l

KV+2

EKXV1EKYV1EKZV1

----

N O

-N D

1BLBLBFT LB

FT LBFT LB

I NS

FTINSI NS

FT.---

5.3-1 7-PA G E

S I N ALFHl)COS( ALFH1)SI N ( BETH1)COS ( BETH1)

Coef of l i f tCoef of dr ag.

Hor i zont al t ai l f or ces andmoment s

Fusel age St at i on f or t he ver t i calt ai l C. P.

Wat er l i ne St at i on fo r t he ver t i c alt ai ? C. P.

But t l i ne St at i on f or t he ver t i c alt a i l C. P.

Rotor wash f actor s

Page 140: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 140/360

5.3 .4 (Con t inued) NOTATION FOR THE EMPENNAGE MOW1.E

SYMBOLUSED I N PROGRAM

UNITS DESCRIPTIONQUATIONS MNEM0NI C

QV QWF

c LV lK Q V l

' D V l

xv1

yv1

LV 1"'V 1NV1

7" V1

QV1Q J F

4 KWV1

CLVlC D V l

i

xv1Yv1zv1

LVlMV1NV1

- Dynamic p r e s s u r e r a t i o , r a t i o

- SQRT ( dy na mic p r e s s u r e r a t i o )

Coef of l i f tD

ND Coef of d rag

LE Ve r t ic a l t a ' l forces and momentsLE

L6

FT LB

Ff LEFT LB

5.3-18PA G E-

Tota.1 Empennage forces and moments

LB

LBLB

Page 141: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 141/360

,

Page 142: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 142/360

._

- -D O C U M E N TN O . SER 70452

BLACK H AW K

TABLE3&5.5

MAIN ROTOR INPLANE WASH AT THE HORIZONTAL TAIL

EXH1MP::BIVlllr ;MAP ARGUMENT:LOOKU P ROUTINEE X P CHIPMR##,AA lFMR## :INPUT VARIABLE el, I N P U T VARIABLE #2

E X P 0.0,100.8,10.0,13 ;LO U LIM,UP PER LIM,DE .TA,+ENTRYS(OCT)-CHIPMRE X P -6,0,6.0,6.0 ;LOW LIM,UPPER LIM,DELTA-AAIFMR

EKXH ## ;OUT PUT VARIABLEEXHlLO ;LOW ANGLE MAP N A M E

: LOW ANGLEM A P CHIPMR B TO 189 ( D E L m 1 0 ) AAlFMR -6.0.6: .AAIFMR--6

-E X H I L 0 : E X P 0 . 0 , - 0 . 2 , 0.05, 0.3, 0.54

E X P 0 . a . 1 - 8 4 1.3, 1.55, 0.88 . 0

: AAlFMRmZE X P -0.4 - 0 . 6 , -0.2 0.12, 0.36E X P 8 - 6 9 8.83, 1 - 0 6 . 1-39 0 . 6 6

a .0

: AAIFMR-6E X P -8.56, -0.8, -1.74, -8.32, 0.04E X P a.32, 0.6, 0.86, r.12, 0 . 5 4

0 . 0

TABLE 3 . 5 . 2

MAIN ROTORDOWNWASHAT THE HORIZONTAL TAIL

E Z H I M P : : B I V # ~ :MAP ARGUMENT:LOOKU P ROUTINEE X P CHIPMR+e+AAlFMR#* ; INPUT VARIABLE 9 1 , INPUT VARIABLE #2

EKZHl#+ ;OUTPUT VA R I A B L EEtH LO :LOW A N G L EM A P N A M E

E X P 8 . 0 , 1 0 0 ~ 0 ~ 1 0 . 0 , 1 3 LOW LIM,UPPER L I M , D E LTA , + E N T R Y S ( O C t ) - C H I P M RE X P -6.0.6.8.6.0 ;LOW LIM,UPPER LIM,OELTA-MIFMR

: LOU ANGLE MAP CHIPMR0 TU 180 ( D E L - l B I AAlFMR - 6 0 6I A A I F M R = - B

-0.13, 0.8, 1.8, 1.82, 1.861 .88 , 1.91, 1.04, I . 6 9 , 1.421.14

EZH1LO:EXPE X P

t A A l F M R = $0 . 4 , 0.94, 1.84, 1.91, 1.98X P

E X P 2.84, 2 . 8 8 , 2.14, 1.89, 1.621.35

: AAlFMRm6E X ? 0 . 7 s ; f .36,E X P 2 . 1 4 . 2.21 ,

1 . 5 6

1 . 9 1 ,2 . 2 0 ,

1.98,2 . 1 6 ,

2 . 0 61 . 9 6

5.3-20-A G E

Page 143: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 143/360

-

7 LACK HAWK

TABLE 3 . 5 . 3---DYNAMI C PRESSURE LOSS AT THE HORI ZONTAL TAI LQH1MP::UVRi)w

A L F U F WOH QWFIIQHlLO ;LOW A N G L EM A P - N A M E

EXP -38.0,30.0,5.0 $LOWERLlMXT, UPPER LIMIT, DELTA

: LOU ANGLE MAP ALFHHI -3 0 TO 3 0 DELTA-51 . a , 1 .a , 8 - 9 5 0.76, 0.76HlLO: EXP

EXPEXP 0.91, 1 .a , i . B

0 . 7 6 , 0.75, 0.76 0.76, 0 . 8 2

TABLE3 . 5 . 4

FUSELAGE DOWNWASH AT THE HORI ZONTALTAI L

EPH1MP ::UVRU VRw ;MAP ARGUMENP:LOOK UP ROUTINEALFVF#r ;INPU T VARIABLEEPSHl## ;OU TPU T VARIABLEEPHlLO ;LOW ANGLE MAP NAME

EPHIHI ;HIGH ANGLE MAP NAMEEXP -30.0,36.0.5.0 ;LO WER LI MIT ,UP PER LIM1T.DELTA-LOW AN GL E

EXP -90.0,90.0,10-8 {LOWE R LIMITsUPPEX LIMITSDEL TA-HIGH ANGL E

I LOU ANGLE MAP ALFHHl -30 TO 30 DELTA-5

1.4, 1.1, 8.8, 0.55E X P 0.5, a . 4 5 , 0.4, 0.38, 0.33E X F 8.19, -8.12 -0.4

EPHILO: E X P 1 . a ,

; H I G H ANGLE MAP ALFHHl -3.9 TO 9 0 DELTA-101 . d. 0 , 8 . 2 5 , 8.7, 1.2,

1.9, 1.8. 1.1. 0.55 * 3.4s0.38, a . 19, -8.4 -8.7, -R. 75

EXP -0.65, -8:45, -8.15, 0.0

EPHlHZ: EXPEXPE X P

TABLE3. 5. 5

HORI ZONTAL TAI L LI FT COEFFI CI ENT DUE TO ANGLE OF ATTACK

,A SP EC T RATIO*4.6 ,8014 AIRFCIL;MAP ARGUMENT:LOOK UP ROUTINE{INPUT VARIABLE;OUTP UT VARIABLE

CL HlMP

; L O WA N G L EM A P - N A M E%LOWE R LIMIT,UPPER LIMIT,DELTW-LOW ANGLE;HIGH ANGLE MAP NAME

EXP

EXP ;LOVER LIMXT,UPPER LIMIT,DELTA-HIGH ANGLE

; LOW ANGLE MAP ALFHHl0 TO 30,DELTA*5 CL(ALF)--CL(-ALF)

8.0, 8.356, 0.71, 1 .a39 0 . 9 5LHlLO: E X PEXP 8.735, 0 . 7 4 5

I HIGH ANGLE MAP ALFHHl 3 9 TO 9 0 , D E LTA m l 0 CL(ALF)m-CL(-ALF)a. 558LHIHI: EXP 0 . 7 4 5 , 8.847, 0 . 8 4 7 , 8 . 7 4 5 ,

E X ' P 0 . 2 9 4 , 8 . 8

5.3-21PA6t-

Y 1) MY. c

-

c

Page 144: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 144/360

BLACK HAWK

TABLE 3.5.5

HORIZONTAL T A i L DRAG C OE FF IC IE NT DUE TO ANGLE O F ATTACKC D H I M P ::UVR'U'VR#(~ . ' . ' ' $M AP , RGUM€NT':LOOK UP ROUTINE:

AFAHHl#+ ;fNPUT VARIAB LEC D H I M ; O UT P U T VAR IA BL ECPHILO ;LOW ANGLE MAP NAME

CDHIHI $HIG H ANGLE MAP NAMEEXP 0.0,30.0,5.0 iLOWER LIMIT*UP PER LIMIT*DEL TA .

EXP 38.8,90.0,10.0 ;LOWER LIMIT,UPPER LIMI1,DELTA

; LOW ANGLE MAP ALFHHI0 TO 30,DELTA*5 CD(ALF)-CD(-ALF)CPHLLO: EXP 0.ar , 0.022, 0 . 0 4 , 0 . 1 9 , - 0 . 3 E

EXP 8.37, 0.43

: HIGH ANGLE MAP ALFHHl 30 TO 90,DELTA-lIb CD(ALF )=CD(-ALF)C D H I H I : EXP 0.43, 8.531. ' 8.702, 0 . 8 8 8 t 1 - 8 5

EXP 1.161, 1.2

TABLE 3.5.7

DYNAMIC PRESSURE LOSSA T a E V E RT I C A L TA I L

OVlMP:: U V R W I M P RCIIMENT:LOOK UP ROU'l?-NE-P A WC## ; INPUT VARIABLE~ P ~ C I W F + ~ ;OUTPUT VARIABLEQP3LO ;LOU AHGLE MAP NAME

EXP 0.0,30.0,5.0,7 SL OW E R LsIMIT, UPP ER LIMIT. DELTA, NO O F ENTRYS(PSABWF1

; LOW AN GL E MAP PSI(ABS.1 8 TO 3 0 DELTA-5

EXP 8.62, 0.64, 8 - 6 6 . 8.72, 8 .?9EXP 8.88, 1.08

TABLE 3.5.8

FUSELAGE SIDEWASHAT T H E V E RT I C A L TA I L

SGV IMP : VSUVS#C ;HAP ARGUMENT:LCOK.UP ROUTINEPSIUFU# INPUT VARIABLESIGPS## ;OUTP UT VARI ABLESGP3LQ ;LO U ANGLE MAP NAME

SGPOHI \HI GH ANGLE MAP NAMEEXP 8 . 0 , 3 8 . 0 , 5 , 0 ILOWER LIMIT, UPPER LIMIT, DELIA-LOW ANGLE

E X P 8.0,98.0,30.0 ;LOWER LIMIT, UPPER LIMIT, DELTA-HIGH ANGL E

; LOW ANGLE MAP PSIWF8 TO 30 DELTA-5EXP 8,B, -8.4, -0.6, 0.8, 1.4EXP 8.6, 6.2

; HlCH ANGLE MAP PSIWF B TO 9 0 DELTA-38EXP 6.8, 0.2, 0 . 8 , 8 . 8

Page 145: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 145/360

TABLE 3 .5 .9

V E RT I C A L TA I L L I F T C O E F F I C I E N T D U ETO S I D E S L I P

3 5-32.3 FT**2 ,ASPECT RATIO -1.92 ,0021 MOD AIRFOILCLV1MP::UVRUVRCe ;MA P ARGUMEN T:LOOK UP ROUT INE

3ET V V #e ; INPUT VARIABLECLVI#* ;OUT PUT VARIABLECLVIL 0 ;LOW ANGLE MAP NAME

CLVIHI ;HIGH ANG LE MAP NAMEEXP -30.0,30.0,5.0 ;LO WER LIMI T,UP PER LSMIT,D ELTA-L OW ANG LE

EXP -90.8,90.0,10.0 ;LOW ER LIMI TSUP PER LIMfT3DELTA -HIGH ANGL E

; LOU ANGLE MAP BETVVl -3 0 TO 30,DELTA-5CLV1LS:EXP -1.08, -1.30, -0.93, - 0 . 7 3 , -8.5

.EXP -0.28, - 0 . 0 6 , 0 . 1 6 , 0.38, 0.61EXP 0.82. 8 . 8 9 , 0. 9

: HIGH ANGLE MAP BETVVl -90 TO 98,DELTA-10CLY1HI:EXP - 0 . 0 , -0.12, - 0 . 2 8 , -0.46, -8.66

EXP - 0 . 8 8 , -1.08, -0.93, -8.5, -0.06EXP 0.38, 1.82, 0. 9 , 0.8, 0.63EXP 8.48, 8.32, 0.17, 0 . 0

TABLE 3 .5 .10

VERTICAL TAIL DRAG COEFFICIENT DUETO S I D E S L I P

CCVlMP: VRUVR## ;HAP ARGUMENT:LOOK U P ROUTINEBETVV1e# ; INPUT VARIABLEC O U l # * ;OUTPUT VARIABLEC D V lLO ;LOW ANGLE MAP NAME

COVIHI tHIGH ANGL E MAP NAMEE X P -30.0.30.0,5.0 ;LO WER LIMIT ,UPP ER LIMIT,D ELTA-L OW AN GL E

E X P -90.0+90.0,18-0 SL OWE R LIMIT.UPPER LIMIf'OELTA-HIGH ANG LE

: LOU ANGLE MAP BETVVl - 38 TO 30,PELTA-8CDVlLO: E X P 0.36, 8.265, 0 . If4 0.118 0.066

E X P 0 833 0.018, 0 . 0 2 1 , 0 . 0 4 4 , 0 .092E X P 0.162, 0.248, 0.355

; HIGH ANGLE MAP BETVVl - 9 8 TO 90,DELlA-5CDVlHi: E X P 1.1, 1 . 0 2 5 , 0.965, 0 . 8 7 5 , 0.745

EXP 0.575, 0.36, 0.174, 8 . 8 6 6 0.01 eE X P 0.044, 0 . 1 6 2 , 0.355, 0.58, 0.78EXP 8.875. 0.965, 1.02, 1.08

Page 146: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 146/360

.~ . .

MAIN ROTOR INPILANEWASH AT THE HORIZONTAL T A I L

flAP NFIME: E X H l H PM A P TTPE: E I VINPUT V R R I q B L EIS1 : C H I P M R A A l F M ROUTPUT VRRIRELE: EKXH1

PR In m MAP:0.00 n m -6.00

100.00 a m - 6.0010.00 .LD 6.00

FIGURE3.5.1

Page 147: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 147/360

- - -

MAIN ROTORGOWNWASHAT THE HORIZONTALTAIL

HAP NAME:MAP TYPE:I N P U T VA R[ABLEOUTPUT Y R R I R B L

P R I R R I I YMRPr

EZHI R Pe I v

Si : CHIPHR A F l l C U R: ' EKZ Hl

0.00 .I - -6.00100.00 P m u n n 6.00

O, 00 m~rm 6.00

R, , I I . -7

7

. i I . I

I

I I

I

I '

'

I

I,, .

I . ' . .

g

FIGURE3 . 5 . 2

5.3-25-Page

Page 148: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 148/360

F"DYNAMICPRESSURELOSS AT THE H O R I Z O N TA L TA I L

G H l f l PbVR

M A P NRME:M A P T Y P E :I N P U T V R R I R E L E(SI : R L F W FOUTPUT VRAIRBLE: w i w

P R I t t A A t H R P :-30.00 LIP-

30.00.00 a m

- 8

_-

FIGURE3 . 5 . 3

Page 149: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 149/360

- - - -

FUSELAGE DOWNWASH AT THE HORIZONT AL T A I L

MRP NRME: EPH M Pn w T Y P E : U V R U V Ri N P U T V R R I A B L E(SI : R L F W FO U T P U Tv m I R e L E : EPSH1

EPHI tP 11/21

PRIMRAY HRP:-30.00 u u m

30.00 n u m5.00 QTn

-9fr.00 - u n n90.00 m u i n10.00 Et.

SECONORRTn w :

1 - i I I

3h

FIGURE 3 . 5 . 4 ( a )

Page 150: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 150/360

OF POOR QUALITYSl AlRc~T k - d

% d". Docunent No. SER 70452.

FUSELAGEDOWNWASHAT THE HORIZONTAL TAIL (Cont d )

8LRCKHRYK.. NASRSTUOY 23-SEP-60 EPHIHP 12/21

\ . . I

g L . i I , . , ' I . I " I I I

I IrI

-1 .I

I I I I I

I

. . I . I. 1, . II .

--------;: --..-_LU

Page 151: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 151/360

-- -----

SY RCRAET 1 OHlGlPIAL P, -,:.L Lli

&-. OF POOF? QYALfTv Document No. SER 70452

HORIZONTALT A I L LIFT COEFFICIENTD U ETO A N G t E O F ATTACK

S L A C ; ~ ~ F I H KN A S f i S T U O T 24-SEP-40

M R P N A M E :M R P T Y P E :LNPUTV F ~ R I R ~ L Erj : A L F H H IO U T P U T V R AI R8.LE;

P R I M A R T M A P :-?O. 00

30.005.00

-90.0090.0010.00

S E C O N O R ATM A P :

CLH1MPu v s u v s

CLH1

S

.. . ._-...I

-. ....... .....-. . . . . . . . . . . . . . . .................... .- -.. . ...... - ..---.. A_. . ,-- ---.- . _ .

,.._ ._ ._.___. . . . _ . . . ^.

. -.-- - ...... .... ,.. . . . . . . . . . - . -_ . .. ..I_.....,-_._c_ . . - -. --.--...

I ........... ____....... . ............. .. - . . . . . . . . . . ---.. -- -....-- I

..... _ - ..____._ ._ - _--. . _...-. .._.- ,. .-... I_.._CI,. ..... .- - . . . . . . . . ..--.-. --.. ...... -.-. --. .... ............ ...-.- -...-. ....... ........._.....- I. - - - - ..........

............. _.-.. _ , . . . . . . . . . . . . . . . . . -_ . . . . . .

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

.__. . . . . . . . . . . . . . . . -.- . . . . . . . . . ,

I ._. _..- .-. ..... _.- . * ..... - . . . . .-... . . . . . . . . . . . ..- . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . ......_.......

40.00 80.00 80.00 lbU.00f l L F H H l

FIGURE3 . 5 . 5 ( a )

Page 152: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 152/360

HORIZONTALTAIL LIFTC O E F F I C I E N TD U ETO ANGLE OF ATTACK (Cont 'd)

8LRCKHFlHX- N A S R STUOY 29-SEP-80

.............. .-. . . . . . . . . . . . . . . .I-

... . . . . _ .- . ... . . . . . . . . . . . . * . .

FIGURE

.-.-

3 . 5 . 5 ( b )5.3-30

I

Page

Page 153: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 153/360

HORIZONTAL T A IL DRAG COEF FICIENTDUE TO ANGLEOF ATTACK

BLRCnMaHn -

a

M R P N A M E ;M A P TYPE:

NPUT V R R I R B L EIS1 : R F R H H lO U T ?U T V R R I A S L E :

P R I M A R YIIFIP:0.00

30.00s o 00

S E C O N O R RTtiFIP:36.0090.0010.00

C O Hr PIPU VA U VA

C D H1

C O H l M P 11/21

R FA H H I

Page 154: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 154/360

unent No. SER 70

ca

Y).

5.

a .

0-

H O R I Z O N TA L TA I LDRAG C9EFFiCIENTDUE TOANGLE OFATTACK (Con t ' d )

I i I II1 -,

1 -~.

1 . , I ' II # i . I I ' I I , II j I i , I I

I I ' II . I i I

II I . I 1 . . . 1 i

/ IJ

. I I ' j i . 1 . 1 I- - I 1 ' . I / [ i . i

I I

1I I . . ..

I - 1' I

1, . -

I . <

ElLRCKHFlWK- NASR S T U O Y 23-SEP-84 COHlllP 12/21

a

FIGURE3 . 5 . 6 ( b )

Page 155: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 155/360

I >@r?lC~~<: 'sL ~ . ,OF POGR <&'i'ntlTy

Dc;.*ment No. SER 70452I K Q R S K YA J R C M /eonma&-

D Y N A M I CPRESSURELOSS AT THE VERTICALTAIL

M A P H R f l E :M R P TYPE:I N P U T Vi R I R 8 L E(S : PSilEWFO U T P U TV R R I R B L E :

PRIMFlRT NRP:0.00

? C . 305.30

Q V 1flPU V R

Q Vl Q U F

.-.-.--.---..--___I____- ....-.--

_-.

_ c _ , - _ c _ - - ,LL-- .. I . --9 ____I ._

. I_. ___O

a - c

p -.---- .- -_I--. -.._I_-- --- .- --- I_0

- . - --- _._? .- -I- --- --.. -. C --. --.-.--....-...... -..... -__ - ____ .------ c

I_I_ _. - . . _ , ._-

.-- .--..I. - _._--. - . + . -... . ._---_ .. _.__ __ ___-. __._._,3

6--.--*. -c .. . .. . I---. ......... ----..

..I. . . . . . . . . - . ,.. ..... ._..- .....

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

_I._................ -. .-- __. .

____-

-- .-- .. . ---.-.. -- ... ._-. l_lC.. ....... - .-..........

. . . .p - -._

..

.-- ........ -- - --. I . ........ *. ... ._ . * ..........-.--- - - ... --. .. -.-. . . . . . . ..-. . +. . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . -.I . . . - - ~ - - . . I . . . ---.-.-. ...... _ . - .

- - - . . . . . . . . . . . . . . . . . . . . . . . . .- . - * . . _ ___.--I *- -.

. . . . . . . . . . . . . . . . . . . . . . ......... .. . ... . . . . . . . . . . . . . . . . - ,

2-. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .e 4 . . . . . . ..... ....... . .. . . . . . . . . . . - - -,

- - - -.....g,

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

=titjo u:oo L o o 12.30 Ih.00 ZY.SO 21.00 32.00 ' 36.00 4 0 .

FIGURE3 . 5 . 7

Page 156: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 156/360

FUSELAGESfDEWASHAT T HE V E RT I C A L TA I L

B L i l C K H A U K-

8

?IA SR S 'IUO Y 25-SEF -90 S G V l P P I 11 2 1

S G VtnPU V R U V R

S I C V l

tlRP E :H R P T T P L ' sI N P U T V R S I R E L ES1 : P S I W FOUTPUT V t lR I RELE:

P R I R A R Ti49P:-30.00

30.005 . 0 0

P I A LImn

wq m uun

S E C O N O R RYPAP:-90.00

90.0030.00

FIGURE3 .5 .8 (a )

5.3-34T Z F

Page 157: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 157/360

FUSELAGE SIDEWASH AT THE VERTICAL TA IL ( C o n t ' d )

ELRCKHAHK- MfiSfl S T U O Y 2s-SEP-40 SGVlHP r2/21

FIGURE 3 . 5 . 8 ( b )

Page 158: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 158/360

VERTICAL TAIL LIFT COEFFICIENT DUETO SIDESLIP

ELSCKHRNK - NRSFI S T U O I 2 5 - S E P - 8 0

MRP NRPIE:MRP T Y P E :I N P U T VA R I R B L E[SI : B E T V VJ U T P U T Y R R I R B L E :

P R I t l F I RYY R P :-30.00

30.005.00

S E C O N O A AY M A P :-90.00

90.0010.00

c ~ vn pU Y R U V R

C LV1

DIA u n nm an

m m

Document No. SER 70452

C LV M P 1 /21

FIGURE3 .5 .9 (a )

Page 159: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 159/360

VERTICALTAIL LIFT COEFFICIENTDUETO SIDESLIP (Cont 'd)

BLRCXHRHif- N l S R STU[IT 23-SEP-80

-,100 1b.00 24.~0 32.00 uh.00+- e&?YO.OO -i2.00 - w o o - i r. ao b.a

FIGURE3 . 5 . 9 ( b )

Page 160: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 160/360

I-.o .

j . . ' i II

II 1

. . I I I I II I

I I I II I I I I I

I I

I I I . . I I--+I I I I .

I.

-.

VERTICAL TAILDRAGCOEFFICIENT DUETO SIDESLIP

MFlP NAME: C O V1N PR4AP TYPE: UVRUVRI N P U T V R R I A E L E(51 : B E T V V lO U T P U TVFIRIAELE: C O Y

P R I l l A R YM A P :- 3 0 . 0 0 m u m

30.00 m u m5.00 r p m

-90.00 M u a n90.00 m u o nlO.00 mln

S E C O N O A RY YA P :

t i l V H P 11/21

4 i I- -c,,,7 I I . . I I 1

I 1I ' I ' - I i

I I

I I

i .

I -- II I -

II 1

I - I - : I iI 1 . III I

I 1 'H . . I I

FIGURE3.5 .'I O(a )

5 .3-38Page

L . .

Page 161: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 161/360

_ -

-

N0

VERTICAL TAILDRAGCOEFFICIENTDUE TO SIDESLIP (Cont 'd )

\ I ?. I\ I I 1 i 1

\

i I

II A --

b I I , I

i.

I # .

- -

BLRCKHRWU

-NRSA STUDY 25-SEP-BO

0

3

-4 0 . 0 0 .it.oo -Tu.oo -':d.CO 4.00 ee$c& a h 0 T u 0 i b . ~ 3h.00 ub.00

FIGLIRE3 .5 .10 (b )

". _._.. . -

Page 162: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 162/360

5 . 4 T A I L ROTOR MODULE

CONTENTS

5 . 4 . 1 Module Description

FIGURES

5 . 4 . 1 . 1 Equation Flow Diagram

5 . 4 . 2 Module Equaticms

5 . 4 . 3 Module InputAutput Definition

5 . 3 . 4 Nomencl ature

5 . 4 . 5

5 . 4 . 6 References

Black Hawk Tail Rotor I n p u t Data

5.4-1PA G E-

_ . ..... - -

D O C U M E N Txc , SER-TZr4'32

5.4-1

5 .4 -2

5 .4 -3

5 .4 -4

5 .4-9

5.4-10

5.4-14

5.4-15

Page 163: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 163/360

5.4 Tail Rotor Module

5.4.1 Modfile Descri ption

D O C U M E N Tdo. SER 70452

This module calculates the forces and moments at the center ofgravity which are genera ted by a canted tail rotor. Thisrotor is represented basically by a simplified, closed form,Bailey Solution as developed in Reference 4.6.1. All terms i ntip speed ratio C f i greater than squared have been eliminated.I n orde:- t o obtain the actual tail rotor coll ect ive pitchvalue, (8 ) , the Bailey equatiorls have been modified toaccount fik 6 (pitch-flap couplfng). This reduces the btadepitch which is impressed by the control system.

The airflow impinging or the tail rotsr i s developed from thefree stream, rotcr wash and fllselage sidewa sh, togethe r withbody angular rate effects. Th e total compone nts of velocityare resolved t h o u g h th e cant angle into the tail' rotor shaftaxe s system.

The Baile;y theory equation is normally presented as thethrust coefficient in terms of the It' coefficients. Itshould be noted that the equations have been manipulated toobtain an expressioti for downwash. This was found to benecessary to obtaitl an unconditionally stable solution.important that program flow follows the equation flow f or astabl e tail rotor solution (Figure 4.1.1).

A blockage factor K i s applied to the final thrust outputto account for the Jk& mity of the vertical tai l.correction is empirical and based on flight test data of otherhe1 i opters.

This simplified tail rotor model only calculates thrust. Noaccount of H force is included in the final tail rotor forceoutputs.and moments in body axes, at the center of gravity.

It is

This

The tail rotor thrust is finally resolved into forceI

Page 164: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 164/360

-------

cc 'I,

F I G U R E4.1.1

5 . 4 - 3m

Page 165: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 165/360

.

. J W d-t-b'S

I

Page 166: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 166/360

DOCUMENTn? . SER ?045?

5.4-5Page

Page 167: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 167/360

Page 168: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 168/360

2 -2Y

5 . 4 - 7-A6t '

Page 169: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 169/360

- r - T-- TIC

Y-- -

DOCUMENTN O . %R 70452

Page 170: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 170/360

D O C U M E N Tn o . SER 70452

fi.58f AGEI

I

YUST

I

5.4-9

m

Page 171: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 171/360

--..- ...__.-

-----. I . . "'{

fii- y f '. L

SlKOFaSKVAIRCRAFT o o c u n c n iNO. S E R 70452

5.4.4 NOTATION FOR THE TAIL ROTORMODULE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNTS DESCRIPTION

F~~~

F~CGB

F~~

LTR

LCGB

\TRBLTRB~~~~B~~

%PMR

a l FMR

%HMRS T

RT

E~~~~

E~~~~

€KZTR

XMRTR

v~MRTR

%MRTR

@WF

P f-QTRQWF

K~~~IGTR

FSTR

FSCGB

KTR

WLTR

WLCGB

KTR+lBLTR

BLCGB

KTR+E

CHIPMR

AA1FMR

DWSHMR

OMGTMR

RMR

EKXTR

EKYTREKZTR

VXMRTR

VYMRTR

VZMRTR

A 1FAWF

PSIWFQTRQWF

KQTR

SIGTR

INSINSFr

INSINS

FrI N S '

INSFrDEGDEG

N DRADS/ SEC

FrND

N DND

Fr/SECFI'/SEC

FT/SEC

D E GD E G-

-DEG

F us el ag e s t a t i o n f o r t a i l r o t o rF u s e l a g e s t a t i o n fcr CG

Tai l ro to r long i tud ina l a rmWa te rl in e s t a t i o n f o r t a i l r o t o rWa t e r l i n e s t a t i o n f o r C GTa i l r o t o r v e r t i c a l armB u t tl i ne s t a t i o n f o r t a i l r o t o rButtline s t a t i o n f o r the CG

Ta i l r o t o r l a t e r a l armRstor Wake Skew Ang -Longitudinal main r o t o r f l a p p i n gUniform downwash a tthe main ro torTrimned r o t c r speedMain r o t o r r a d i u sMain rot or wash fa ct or s

Main rotor wash a t the t a i l r o t o r

Fuselage angl e of a t t ac kFuselage yaw a t t i udeDynamic Pressure r a t i o a t thet a i l r o t o r

Fuselage sidewash a t the t a i l r o t o r

----

5.4-10-M E

Page 172: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 172/360

5.4 .4 (C on t 'd ) NOTATION FORTHE TAIL ROTORMODULE

SYMBOLtiSED IN PROGRAMEQUATIONS MNEMONIC UNITS

~-

DESCRIPTION

'xb

'zb'YWFTR

vYb

V~~~~v~ITRV~~~~

V~~~~

v~GTR

V~~~~P

qr

V~~~~"YTRB

%TRB

V~~~

V~~~V~~~

PTR~ T R

RTRA X T R

/CcYTR .

/CCZTR

/CcTR

V X BVY6

VZB

VYWFTR

VXITRVYITRVZITRVXGTRVYGTRVZGTRP

9rVXTRB

YYTRBViTRB

VXTRVYTRVZTRGAMTROMEGTRRTRMUXTRMUYTRMUZTRMUTR

FT/SEC Body .xes vel oc i t i e sFTISECFT/SECFT/SEC Fuse lage sidewash ve lo ci tyFT/SEC Total in te rf er en ce vel o c i t i es a tFT/SEC the t a i l r o t o rFTISECFT/SEC Body axes gu st v el o ci t i esFT/SECFT/SECRADS/SEC Body ax es an gu la r r a t e sPADS/ S C

RADS/SECFT/SEC

FT/SECFT/SECFT/SECFT/SECFT/SEC

DEG Ta i l r o t o r c a n t a n g l eRADS/SEC Ta.il r o t o r trim speed

Fr Ta i l r o t o r r a d i u sN DN D r o t o r t i p s pe ed .N DND

Tota l ve loc i t i e s a i t the t a i l r o t o r

in body axes.

To t a l v e l o c i t i e s a t the t a i l r o t o ri n s h a f t a x e s .

1

Shaf t axes ve loc i t i e s no rmali t e d by

5.4-11-A G E

Page 173: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 173/360

SIKORSKYNRCRAF" O O C U I E N TN O . SER 70452

5.4 .4 (C o n t ' d j NOTATIONFOR THE TAIL ROTOR MODULE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

t,5.1t3.2

B

G

t3. 3

A~~

b~~

C r R

%RT~~

ao/T~~

$3

B i ~ ~ ~ ~0~~D~~~~~

~ T RSMR

K~~~~~

'WSTTR

'BVTTR

YRX~~Y~~Z~~

BTLTR

ATRBTR

CHRDTR

"TTR

DELTTR

DEL3TRB1ASTR

-DWSHTRTWSTTRLAMBTROMGMRKBLKTRVBVTTRCDTR

RH0

XTRYTR

ZTR

-

1 RADS-

FT

DEG

LB-DEG

DEG

DEG.. -D E W%R

-RADS/SEC-

FT2

SLUGS;FT3

LBLB

LB

5.4-12-A C E

1Bai ley Coeff i c i en t s

Blade t i p l o s s f a c t o rConstant .

Blade sec t ion l i f t curve Slope (2D)Actual number of b lad r; onthe

t a i l r o t o rBlade Chord f o r the Ta i l r o t o rTa i l rotor comnanded blade pitchTai l Rotor Thrus tRate o f change of coning w i t h

t h r u s tFlapping hinge offset ang leBlade p i t c h c o r r e c t i o n t o l i n e a r twistActual Blade pi tchUniform downwash a t the t a i l r o t o r discLinear blade twis tf a 1 bar inflowActual ro tor speedTa i l rotor blockage from v e r t i c a l t a i lAirspeed breakpo in t fo r blockage f ac to rTa i l r o to r d ragA ir d e n s i t y

Tail r o t o r f o r c e s a t the CG i nbody axes

Page 174: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 174/360

L~~ LTR FT LB

MTR FT LB'

Tail rator moments at the CG i nbody axes

OOCUHIENTNO. SER 70452

5.4.4 (Cont'd) NOTATION FOR THE TAI L ROTOR MODU LE

5 . 4 - 1 3PA G E-

Page 175: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 175/360

5.4-14PIGT'

Page 176: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 176/360

D O C U M E N Tn o . SER 70452

5.4.6 References

1. Simplified Theoretical Method of Determining the Characteristicsof a Lifting Rotor i n forward Flight, Bailey, NACAReport 716

5 . 4 - 1 5PAGE'

Page 177: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 177/360

O O C U M E Y TN O . SER 70452

5.5 FLIGHT CONTROLSYSTEMMODULE

CONTENTS

5.5.1 F l i g h t C o n t r o l Sy stem M od ul e D e s c r i p t i o n

FIGURES

5.5-1

5.5-2

5.5.1.15.5.1.2 BLACKHAWKg e l i c o p t e r M o t i o n S e n s o r s5.5.1.3 ( a ) BLACKHAWK P i t c hSAS Channels5.5.1.3 ( b ) BLACK HAWKR o l l SAS Channels5.5.1.3 ( c ) BLACKHAWK Yaw SASChannels5.5,1.4 BLACKHAWKP i t c h B i a s A c t u a t or5,5.1.5 ( a ) BLACK HAWKP i t c h FPS Channel5.5.1.5 ( b ) BLACKHAWKRoll FPS Channei5.5.1.5 ( c ) BLACKHAWKYaw FPS Channel

Overview o f the Co nt ro l System Simulati(on 5.5-55.5-65.5-75.5-85.5-95.5-105.5-115.5-125.5-13

5.5.1.6 ( a ) BLACKHAWKC o l l e c t i v e C o n t r o l5.5.1.6 ( b ) BLACK HAWKL a t e r a l C y c l i c C o n t r o l5.5.1.6 ( c ) BLACKHAWKL o n s i t u d i n a l C y c l i c C o n t r o l5.5.1.6 ( d ) BLACKHAWKTa i l R o t o r C o l l e c t i v e C o n t r o l5.5.1.7 BLACKHAWKS t a b i 1a t o r C o n t r o l System5.5.2 Module Inpu t /Outp u t D e f i n i t io n5.5.3 BLACKHAWKCo ntr ol System Genera l I n pu t Data

5.5-1PAGE-

5.5-145,5-155.5-165.5-175.5-185.5-195.5-20

Page 178: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 178/360

5 . 5 FLIGHTCONTROLSYSTEM MODULE

5.5.1 F1i g h t Control Simulatiiln Module DescriptionT h e simulation o f the f l i g h t control system is presented e nt ire lyi nterms o f block diagrams indicating the transfer function betweensignals . The Background information presented i n Section 3 . 5 o fVolume I1 complements this descriptiono f the cantrol systemsimulation. An cverview of the control system simulation nomenclature,f o r the various elements, i s presented on Figure 5.1 . l , The blockdiagrams, subsequently pr%sented, are alignedw i t h the flow o f t h i sf igure .o f some cont ro l system componentsi s hide. This lead s t o timeconstants o f some o f the transfer functions being small. For completenessthese components have been retainedi n the model, thus xaking i t necessaryt o p r o v i d e a t e s t for cycle tfme i n the corresponding algorithmst o ensureu ni ty g a i n ' i f cycle time i s l a rg e r e l a t i v e t o the function's t imecozstant .

I t will be noted i n studying this sect ion, t h a t the bandwidth

( a ) Sensors - The transfer functionsfor the sensors are presented5iTTjCr-e 5.1.2.

( b ) S t a b i l i t y Augmentation System(SAS) - The simulation definitiansfor. pi tch , roll. and yaw SAS channels are shown on Figures 5.1.3( a ) , ( b ) , and (c ) respec tively. Each f igure incorporates therepresentat ior, o f t he d ig i t a l and analog SAS channels. Ingeneral , the hel icoptermotion sensed by the gyroscopes ispassed through signal conditioning f i l t e r s before being shapedby the SAS networks, The signa l i s then processed t h r o u g h awashout, i f required, a n d the 2:l gain change switch . The

switch definition i s - ON/ON, b o t h channels working a t ga in1.0, ON/OFF, d i g i t a l channel only workinga t gain 2.0, OFF/ON,analog channel only workinga t g a i n 2 .0 .i s r e s t r ic t e d i n amplitude by a 5 % a u t h o r i t y l imi t . I n thecase o f the d i g i t a l channel, the signal i s passed through Bzero order hold t o account f o r update delays. A switch i n theyaw channel inhibits the lagged rate terma t speeds above60 knots and introduces lagged lateral accelerat ionf o r a i d i nt u r n coordination.

F i n a l l y , the signal

The following logic appliesfor a l l cofitrol system channels:In the IC Mode: 1. Outputs o f all synchronizers are zero.

2 . Outputs o f a l l i n t eg ra t e r s are zero 3rhave defined ini t ial values.

n the Compute Mode: The logic i s defined on the block diagrams.

( c ) Pitch Bias Actuator ( P B A ) - The PEA representat ion i s presentedon f igure 5.1.4.I t should be noted t h a t the p i tch ra te s ignal i sp icked o f f

The i n p u t signals are derived as indicated.

%=*

Page 179: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 179/360

Page 180: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 180/360

( f ) S t a b i l a t o r - The representation o f the ana log networkc o n t r o i l i n g t he s t ab i l a to r is presented o n f igure 5. 1.7..T h e network provides for the feedback o f veloci ty,co l l ec t ive s t i ck , l a t e ra l acce le ra t ionand pi tch ra tescheduled as a function o f forward speed. T he o u t p u tfrom the network is passed through the dynamicso f thel i m i t e d ra te ta i l servo. For the simulation provisioni s made for ar alt er na ti vei n p u t (STBSET) for use i nanalysis.

5.5-4- .m

PLGE

Page 181: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 181/360

DOCUMENTN O . SER 70452

OVERVIEWOFTHE CONTROL SYSTEM SIMULATION

Ih ? LOOP "SERYQ

XAILSBl SI L XBIL XBILS

THOIL XCIL XCILSTHRIL XPIL XPILS

k 9 R t V t

I.(

XBBAS

~-

GllTERLOOP

SERVO

OUTERLOO?

XAOLSXBOLSXCOLS -XPOLS

A 1SBL W LB 1S0L XBBLTHO0L XC0LTHRL POL

BlSSW THOSUM*AlSSUMI I THRUSH

XBSUM B1SSUM B l S M I XXCSUM THOSUM THOMIXXPSUM THRSLlM THMIX

XAXBxcXP A1S + 1

81s + 1THETAO + 1THETTR+ 1

XA+1XB+1::c+1Y D I I

t r i m n l n g a t i t o p i l o tA 1 S + 20 1 c * 9

I n r I a l a 7 L

THETAO+ 2T H m R + 2- . . . -

canned InputsFAl o t - I n - l o o p

XP+2

FIGURE 5.1.1

5.5-5-A G E

+ 1SB1STHETAOTHETYK

Page 182: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 182/360

BLACKHAWKHELICOPTERMOTIONSENSORS

I

FIGURE5.1.2

5 . 5 - 6PAGE

Page 183: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 183/360

lmmpBKORSKYAIRCRAFT b

w 3

P *

Q

M

P

FIGURE5 .1 .3 (a )

5 . 5 - 7-ACE

Page 184: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 184/360

4 5 d W S R

FROH ROLLRATE6YRO

+ 4

-L l H l T

t 7 DLG- -.139X/DLC

ROMROLL

VERTICALGYRO_1_31 I

I D I G I TA L

T u .H

wU-v

BLACK HAWK ROLLSAS CHANNELS

ANALOG

00

cz;L4

2

Page 185: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 185/360

. - . _

Sl3NNWH3 SVS MVA IMVHI3Wl8

cuIn-a-0h

LLwV I 9oww

0r

X

wI:3

0

--,E LL3 0

, N I09> A

e

i v i9 Ia

Page 186: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 186/360

s i i

F I G U R E5.1.4

5 .5 -10_

PAGE'

Page 187: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 187/360

?I I

F I G U R E5.1 . 5 ( a )5 .5 -11P1Gt'

Page 188: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 188/360

r - - - --

II (I

Q ob

FIGURE 5.1.5(b)

5.5-12PACE'

Page 189: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 189/360

Page 190: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 190/360

FIGURE5 .1 .6 (a )

I-zs

Page 191: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 191/360

D O C U M E N TN O . SER 70452

FIGURE 5 . 1 . 6 ( b )

5 . 5 - 1 5PAGE-

L

UCI

xu4-Im

..I.. -./.-. ..

Page 192: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 192/360

- - -

OOCUMENTN O . SER 70452

y Mu

FIGURE5.1.6(c)

5 .5 - 16PAGt-

Page 193: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 193/360

I

FIGURE5.1.6(d)

c c * 7

A

0

I

z

a

Page 194: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 194/360

9E'$Y

'*

-4(mI

III

'?

V

FIGURE5 1 . 7

5 , 5 - 18 -A G E

Y 29 UV. 6

Page 195: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 195/360

--

UNWED43- 0

SIKORSUYAIRCRAFT

Y z l m . c

ORIGINALPAGC :SOF POOR QlJALlTY

35.5-1 9

PACE'

Page 196: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 196/360

. 3 W d

02-E"S

9 " u s

-

Page 197: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 197/360

--

5.6 ENGINE/FUELCONTROLMODULE

5 .6 -1ONI'ENTS

5.6.1 Module Description 5.6-2

FIGURES

5.6 .1 .1 Eng ine /Fue l Con t ro I l Dr iv e Rep resen ta t ion5.6.1.2 Engine/Fuel Con trol Flow Diagram5.6.1.3 Elec t r i c Fuel Control U n i t f l o w Diagram5.6 .1 .4 Rotor Degree of Freedom - C l u t c h R e p r e s e n t a t f o n

5.6.2 Module Equ ations

5.6-45.6-55.6-65.6-7

5.6-8

5.6.3 Module I n p u t / O u t p u tDefini t ion 5.6-195.6 .4 NomentTa t re 5.6-20

5.6-24.6.5 BLACKHAWKEngine/Fuel Control Inp ut Data

TABLES

5.6 .5 .1 Steady S t a t e Engine Performance5.6 .5 .25.6 .5 .35 .6 .5 .4 S teady S t a t e Fuel F l o w Required5 .6 .5 .5 S teady S t a t e Di scha rgePressure5.6 .5 .6 Engine Tfme Va r y i n g C o e f f i c i e n t s

Col 1ect i v e / S t a t i c Droop Compensation R igg i ngLoad Demand SpindleCam Outpu t

5.6-255-6-255.6-265.6-265.6.275.6.27

FIGURES

5 . 6 . 5 . 75.6.5.25.6.5.35.6.5.45.6.5.55.6.5.65.6 .5 .75.6.5.85.6 .5 .95.6 .5 .105.6.5.11

5.6.5.125.6.5.1.3

S teady S ta t e Eng ine Pe r fo rmanceCol l ec t i v e /S ta t i c Droop Compensat ion RiggingL o a d Demand S p i n d l e CamO u t p u tS t e a d y S t a t e Fuel F l o w RequiredS t e a d y S t a t e Discharge PressurcP a r t i a l P g / P a r t i a l WFv s . Gas Generator SpeedP a r t i a l P 3 / P a r t i a l NGGv s . Gas Genera to r SpeedDelta WF/Delta P 3 v s . Gas Genera tor SpeedPar t i a l QG; /Pa r t i a l W Fv s . Gas Generator SpeedP a r t i a l Q G G / P a r t i a l NGG i s . Gas Genera to r SpeedP a r t i a l Q p T / P a r t i a l )$IF vs. Gas Generator Speed

P a r t i a l Q p T / P a r t i a l N F r v s . Gas Generator SpeedP a r t i a l Q p T / P a r t i a l NGGv s . Gas Generator Speed

5.6-295.6.305.6.315.6.325.6.335.6.345.6.355.6.365.6.375.6.385 - 6 - 3 95.6.405 .'6.41

5.6.42.6 .6 References

Page 198: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 198/360

D O C U M E N TN C . SER 70452

5.6 ENGINE/FUELCONTROLMODULE

5.6.1 Module DescriptionThis engine/fuel cont ro l model i s basic ally a l inearized represen-t a t i o n w i t h coefficients which vary as a function o f engine operat ingcon ditio n. This model adequately providesfor closing the rotor s h a f tspeed loop throughout the normal operating envelopeo f the helicopteq,However, maneuvers which resulti n s i g n i f i c a n t r o t o r speed excursion4may r e s u l t i n discrepancies i n the simulation. All the usual res t r ic -t ions and assumptions o f l inear s imulat ion are applicableand should .be observed. In an analysis mode deviatfonsfrom trim a re no t l a rge ,b u t f o r pi lo t-i n- th e- lo op op era tio n some meansof continuouslysynchro.nizing the steady state engine torque must be developed.Thisengine module shouldn o t be used for engine performance evaluation.

The elements o f th e model a re shownon the simplified block diagramo f Figure 6.1.1.fuel c o n t r o l , gas turbine, power turbine,a n d rotor shaft speeddegree-of-freedom interfacew i t h the Gen. He1 . rotor. This modelwhich derives total S.H.P. a t the rotor sha f t by appropr ia te lyfac tor ing the o u t p u t from one engine i s appl icable f o r evaluat ionsi n the governed range.disconnect of t he ro to r d rive a tzero torque required by the rotor.This al lows autoro tat ion sand recover ies t o be executed.

They comprise the control interfacew i t h Gen. Hel.,

A transmission clutch i s represented allowing

I n i t i a l i z a t i o n o f the engine/fuel cont ro l module i s accomplished byus ing the steady state engine performance requiredt o trim thehe1 ic op te r simula tion i n f r e e f l g 5 t .

A basic background t o the complete T . 7 Q O engine/fuel cont ro l systemi s g iven i n references 6.6.1 2nd 6.6.2. detailed block diagramo fthe simulation is qiven i n Figure 6.1.2.

The basic engine cont ro l system operation i s through the in terac t iono f the Electr ical (ECU, Figure 6.1. 3) , and Hydromechanical(HMU)control units . In general , the HMUprovides for gas generator speedcontrol a n d r a p i d response to power demand. The ECU trims the HMUt o sat isfy the requirementso f the load so as t o maintain rotor speed.The Load Demand Spindle (L3S) i s a function o f co l l ec t ive p i t chs e t t i n g and pruvides compensationt o reduce rotor t r a n s i e n t droop.Any s t eady s t a t e e r ro r s r e su l t ingfrom i ncons i st en t co l l ec t ivepos i t ioning are trimned by the ECU. In the s imula t ion , th is i st r i imed by the difference between actualgas generator speed (fromsteady performanced a t a and t h a t r e su l t ing from the c o l l e c t i v e s e t t i n g ) .Thesr :harac ter i s t ics are implemented i n the simulation.

5.6-2PA G E-

Page 199: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 199/360

- - -

D O C U ~ E N TO. SER 70452

I n general, isochronous governingo f the rotor speed ismaintained

by developing an error r e l a t i v e t o the reference speedandcomnanding more or less power t o s t a b i l i z e a t the required speed.Basically, t h i s process involves the speederror demanding achange i n gas generator speed (NGG)electr ical network, Figure6.1.3. T h i s sign al i s summedw i t hthe LDS i n p u t i n the HMU, ana compared w i t h the actual gas generatorspeed. The subsequen t e r r o r , commands changesi n fuel f lowleading t o a higher o r lower gas turbine speedand changes i nthe gas f low.a t the dr iveshaf t from the power turbine.o u t p u t from one engine (Qp t ) i s der ived from three sources.direct changes ' i n fuel f l o w, from changes i n gas generator speeaand as a r e s u l t o f changes i n power turbine speed.a re summed t o o b t a i n a t o t a l change i n engine torque from trim and

subsequently factoredby the number o f operating engines andengine/rotor gearingr a t i o , t o o b t a i n engine torque o u t p u t t othe ro tor shaf t .

v ia the shaping of the ECU

This i n t u r n provides increasedor decreased power

FromIn the simulation, torque

These increments

The interface w i t h the main program is presented on Figures 6.1 . land 6.1.2. The rotor can be visualized i n simple terms as adamper respondingt o changes i n ro to r speed. However, the si gn if ic an te f f e c t of the r o t o r r e l a t e s t o the changes i n torque loadingas a r e s u l t o f control inputs and changing statcs. Rotor sha f tacce le ra t ions r e su l t from torque differences i n o u t p u t from thepower turbine and torque required by the rot or. The simulation i si n i t i a l i z e d a t trim such t h a t t h e r o t o r i s a t the i n p u t speed and

the rotor from the engine a t a zero rotor torque level. When GenHe1 i s be ing executed i n combination w i t h the engine, t o t a l enginetorque must replace rotor torque asa reaction i n the airframe equations.

AQ-0. A clutch is modelled, Figure 6.1.4 , which will disengage

5.6-3PllOt'

Page 200: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 200/360

D O C U M E N TN O . SER 7.3452

ENGINE/FUELCONTROL/DRI VE REPRESE NTATION

Page 201: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 201/360

Cri:G NAL FAGE ISOF POOR QUALITY

' I

SER70452

7,

1 yII .III

FIGURE6.1.2

5 . 5 . 5

Page 202: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 202/360

*SZKORSWAIRCFIAFT

N E 1 CONTROLELECTRICCONTROLUj4IT..-

I I

c I

11 : -

5.6-6--I X

Y ?9 q C Y i

. -

e

.

Page 203: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 203/360

RIGINALPAQE E3OF FOOH QUALITY

D O C U M E N TN O . SER 70452

I

FIGURE6.1.4

5.6-7PA6f

Page 204: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 204/360

5.6-8-A G E

Page 205: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 205/360

S1Kc3YYSW ORIGINAL?AX i3AIRCRAFT P OF POOR Q i l k L l l Y D O C U H E N TN O , SER 70452

QRQTRy>

5.6-9PA6E-

u n M.6

Page 206: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 206/360

. 3 D V d-0 -9'5

Page 207: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 207/360

Page 208: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 208/360

Page 209: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 209/360

.39Vd-E 1-9's

Page 210: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 210/360

- . . ....T

5.6-14PAGP'

Page 211: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 211/360

- p_

Page 212: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 212/360

. ... .. . . . Z X

0J

5.6-16m

Page 213: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 213/360

.39Wd

L 1-9‘ 5

Page 214: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 214/360

5.6-18-.PAGE‘

Page 215: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 215/360

5.6-19TZF

Page 216: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 216/360

5.6.4

u

YMBOLUSED IN PROGRAM

EQUATIONS MNEMONI C UNITS DESCRIPTION

I*

QR Q T R I M

Q T R I M

KQ

QMRI\'GG

N ~ ~ ) ~ ~ ~ ~NE

N~~~~~OSCAM

xC

( L ~ ~ ~ ) ~ ~ ~ ~(TOTFUL) mw

( N ~ ~ ) ~ ~ ~

N P T l00LDSEINPTD

N P T

QTRIM

FLQREQ

QRQTRM

QTRIM

KTRQ

QHMRGGWM

GGSS

NETOT.

NGGLDS

LDS

XCPC

LDSTRM

SUM2

NPTREF

NPT100

NPTDP

NPT .

QTRIM

FLQREQ

1 b FT

l b FT

-

l b FrRPM

% RPM-% RPM

DEG% COLL

% \RPM

L B / H R

RPM

RPM

X RPM

% SPM

J b FT

I t FT

5.6-20PAGB'

Tota l torque required a t trim.Fi lte re d torque required by themain ro tor.Factor t o account f o r t a i l rotor

torque p l u s lossesActual rotor torque required.Gas generator speedGas generator speed a t triln.Number o f engines.Load demand spindle ou tpu t .Load demand spindle rotation,Col 1ec t i ve s t i ck posi t ion.

Synchronized LDS o u t p u t a t trim.Total fuel f low.

Power turbine referencespeed, RPM. (Set by Sync w i t hrotor speed a t trim).

100%power turbine speedLDS incremental i n p u t from trim.Power turbine speed error.Actual power turbine speed.F i J tered Rotor Torque .

Fi l te red Rotor Torqueused

i nthe clutch model,

Page 217: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 217/360

OF POOR QUALITY

NOTATION FOR THE E N G I N F U E LCONTROL M O D U I

SYMBOLUSED I N PROGR MEQUATIONS r MNEMONIC UNITS DESCRIPTION-I 061

4

v~~v~~

"G

Q I N T

vS

vss%M

V~~

B

DMDM

INS

EcuGEEC u ~ ~ ~

ID61

V H G

VLG

VGVG

QINTBBBBB

vsvs .vssVDM

VDMDMAMA

VTM

INS

GGRPMR

X RPM-

RPM-SECSSECS---;"oRPM

5.6-21PLCP'

SA 21 Rn. 0

Elec t ron4c Control Uni t

Shaping Network Vari ab1es

Inc remen ta l ECU o u t p u t

Power t u r b i n e t o rotor gear ing .To t a l ECUo u t p u t

ECU g a i n c o n s t a n t sECU time c o n s t a n t s

ECU time c o n s t a n t sECU dead b a n d d e f i n i t i o nECU l o g i c v a r i a b l e sECU g a i n c o n s t a n t s

Demanded change i n G . G .r e f e r e n c e speed.

Page 218: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 218/360

5.6,4 ( C o n t ' d . )NOTATION FOR THE ENGINE/FUEL CONTROL MODULE

SYMBOLU S E 3 IN PROGRAMEQUATIONS MNEMONIC UNITS RESCRIPT1ON

LDSEI

A N G G ET~~~

ANf .A w f l

A p3

TP3

A QGG

A N G G

A 'EffTMV

KCF

A QPT

GG

A Q E

QE

4 sdi soA N P t

3.1,

GGRPME

TNGG

FUEL

ACT WF

P3 D

TP3I NCWf

TMVGGQD.GGRPMD

P f Q

P T E-

Q HE+OSHAF.

O S H A R

QMSFONPTD

% RPM

. % RPM

SEC.

LR/HR

LB/HR

.

SEC.

LB/HR

SEC.

LE/FTRPM

-SLUGS iT2

LB FT

LB FT

LB TT

R A E /SEC2

RADS/S C

RADS/ EC

5.6-22PAGE'

Increment i n LDS o u t p u t

from trim.G.G. speed error.SPD servo time cons tan t

Incrementa7 fuel f low demanded

Actual metered incrementi n fuel f low.Change i n compressor dischargepressure.Lag i n fuel feedback loop.Compensated demandi n fuel f low

Fuel metering valve time constantGas generator accelerat ing torqueIncremental change in gas

generator speed.Conversion factor.I n e r t i a o f G.G. ro to r.P.T. incremental torqueo u t p u t

per engine.P.T.. incremental torque o u t p u t

( a t rotor speed)P.T. total torque o u t p u t

Rotor shaft accelerat ionActual shaft speed.I n i t i a l s h a f t speed.

Incremental P.7 ' . Speed From Ref.

Page 219: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 219/360

SUKORSKYAIRCRAFT ORtGINALPAGE '' O O C U ~ E N Tno. SER 70452' OF POOR QUALITY

NOTATIONFOR THE ENGINE/FUELCONTROL MODULE

~~~

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS

%' R

a R

OMMRO RADS/SEC Trim rotor speed.OMRAT. RAOS/SEC2 Rotor hub accelera t ionOMGRR RADS/ SEC Rotor hub speed.

- Rotor speed relat ive t o trim.RATJTOTE SLUGS Fr2 Inertia upstream o f c l u t c h;REST SLUGSFr2 Inerta downstreamo f clutch

J ~ ~ ~ ~

REST

KHS KHS

Y 29 RCV. 6

.d

y.yl _-_.

5.6-23TzF

less bladesGas generator heat s i n k f ac to r

Page 220: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 220/360

. 3 W d-PZ-9 s

Page 221: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 221/360

" IS A L n m.5

Page 222: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 222/360

80/OO

6 57075808590?5/oo

5 6-26m

Page 223: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 223/360

5.6-27-AGE

Page 224: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 224/360

_c

5 6-28PAGE'

Page 225: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 225/360

BLACKHAWKSTEADYS ?ATE E N G I N EPEFF0R:lANCE

ORlGINALFAp;;<TfJawrwmu-43L. OF POOR QUALITY Document No. SER 70452

URP NRME:R R P T Y P E :

M R PA1U VA .

I N P U T V R R I R B L EIS1 : Q R Q T ' f N l t N G i N E 'OUTPUT VA R I R B L E : GCSS

QRQfRt"/ENGINEx 0

FIGURE6.5.1

5 6-297 q F

Page 226: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 226/360

Document No. SER 70452

BLACK HANK CO LLECTLVE S T A TI C DROOPCO;?P€XATORRIGGIfiG

0

4

x, ¶ %

F I G U R E6.5 .2

5.6-30-Page

Page 227: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 227/360

. -

f

BLACKHAWK- LOAD DE ?AND S P I N D L EC4P.1 OUTPUT

M A P NRME: M R P C 2M A P TYPE: U V RI N P U T VRRIAELEIS1 : LOSOUTPUT YFIRIRELE: NGGLPI

P R I M A ATMAP:0.00 M u n n

LOO.00 ummunin20.00 6 1 1

Q

I*

-

6b.m 7 b . a rb.m & .a Ibdm dbP.00 1b.m 2b.m 3b.m

F I G U R E6.5.3

Page 228: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 228/360

--=--- .

BLACK HAWK-ENGINE STEADYSTPITEFUEL FLOWR E Q U I R E D

M R P FIRME:MRP T T P E :

M R P R SU VA...

?NPUT V n f l I R E L E ~ S I G C S SOUTPUT V R R I R B L - : sun2

FIGURE5.5.4

5.6-32Page

Page 229: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 229/360

BLACK HAWK- ENGINE

0n

DISCHAl iGEPRESSUREFOR STEADY CONDITIONS

MAP NARE: MRPfl2MAP TYPE: U V RI N P U T VA R I A E L EIS1 : CCRPWOUTPUT VARIABLE: KFUN*2

CRIRRRY NRP:7 0 . 0 0 m u a n

100.00 m c t l t n5.00 m i l )

F I G U R E6.5.5

.. ..- .-

Page 230: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 230/360

Document No. SER 70452

BLACK HAWK- ENGINETIME VARYING COEFFICIENT

U R P NRRE: U W R 4U R P TYPE: U V RINPUT Y R R I R e L ES1 : GGRPHOUTPUT VRRIRRLE: KFUN+rl

P R I R R R YNAP:70.00 -um

100.00 m u m5.00 w m

e- -_ ~ --_.

e I

8e

8

-.-_ __-- . --~ ..-... -- .I_-.C.._.. .--- ---.--..---- -.-- .-.f--.-- . ---- ._.- . C - . . .

I...__.r . _-- .i

L ._--_-. -.--_.--. .-- -

........... L . . . . . . . r . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . .- .-- ....-_ -..-. .---.-...-----.- C-.I..-..-*I.-C..-..----C- ....

. I_. .I.-.* .... . a

i . .0

_ c . I ...I

_.-..._ :. c. ..-- -..---- . .C .

- - .. . .-_I.. - . ___..2

0

.... . _-.. .... -- .... ..-.- . -.-.I

e -t I

I I '

. . L

-I I a

84 ' .m III.m 1b.m okm A m e b a 0 0 7 1 1 m r l o ~ ob

-

C&k? J.

FIGURE6.5.6

Page 231: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 231/360

Document No. SEi? 70452

BLACKHAWK- E N G I N E T I M E VA RY I N G C O E F F I C I E N T

* Y P N R U E :*RP TTPF.

N'rlP87l l V R

. ..-: . . . . . . . . . . . . . . . . . . . -.... .- . . . . . .... . 3 -

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

. ...... .. . . . -__. --e ~..._I.,... . . . . . . . . . . . . . .._..--. . . _ - _ . . . . . .._- _..- ............

-- L.-..

. . . . . . . . . . . . . . . . . ...... I . . . -- .... .-.._L . ..-. .

FIGURE6 . 5 . 7

Page 232: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 232/360

-. _.. ............. ~ ................. _ _

F

AP3

BLACK HARK- ENGINETIWE VARYINGCOEFFICIEMT

U R P mne:M R PTYPE:i N P U T ' J R A I R R L EIS1 :OUTPUT VRAIRELE:

P R I M RY M A P :

MAP83UVR

K f U N + 3GGRPM

70.00 m u m00.30 ammuan

5.00 a m

SER 70452

I

4.0 1 b . a 2 b . a .a 4ii.a .a 7 b . a 8b.m sb.a rbtIdb ? b

FIGURE 6.5.3

Page 233: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 233/360

. .

19

2..

OF POOR QUALITY

. . I

, .--- .---+--------,

L. L ...-- I..._..._ i

..- .."---, 1-a. . . . .-_-.-.---- , -.

BLACKHAWK- EMGINETIME VA RY I N GCOEFFICIENT

0

n-0-

8 - .

- - .. . . . . . . , . . . . . . . . . . . . . . --.- . . . . . . . . . . .__*. ....... -... ....... -._.. t- * '

. . . . . . . .-p..* ...- . --i ........ ..-- ..... --.- . ..-. . ..-_ ........ -̂ ~ _.-.. . ......._..._--.. __...

.... . . . . . . . . -... . . . . . . . . . . . . - . . . _ . . - . _ . . . _ - - i . . . . - . . . .-

- ~t. . . . . . . . . . . . . . . . . . . . . f .

.

. . . . . . - ..e.. ... ..- . . _ . A ..-- ....-- . -... . * . - . . . . . . . . . . . . . . . _._ .. ._. _.. " r _..-._-. .- .. . . . . ............ ........ ...-. ...... - ...... *... . . : . . ._- . ...._.....-..__.._.._... +... ...

MAP NRME: MRP85MAP TYPE: U V RI N P U T V R R - R B L E1s) : G t A P f lOUTPUT V d I f l B L E : K F U N * 5

PA I f l R R TMflP:70.00 ~ u m n- 100.00 a m m u a m

~ Q G G+ NGG% 5.00 a m

lF

... . ti. ................ . . . . . . . . . . . . . . . .......... . . . . . . . - . : . ..- . . . . . - _ . . . . . . . . -..

6b.w 7 b . m a 0 . 0 ~ 9b.m I

FIGURE6.5.9

5 .6 -37Page

Page 234: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 234/360

....... -. ...... - ................ z; Z 7 . V - ...

Document No. SER 70452

BLACKHAWK- ENGINETIME \ P,l?Y IF.(: 3 E F F I C I E N T

MRP N R R E : H R P f l SHRP T Y P E : U V RI N P U T V R R I R B L ES1 : GGRPMOUTPUT V R R I R R L E : KFUN*S

P f lI R R RY MRP:7 0 . 0 0 m u m

100.00 m u m5 . 0 0 m m

FIGURE6.5 .10

Page 235: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 235/360

Document No. SER 70452

SLACKHANK- ENGINETIME VA RY I N GCOEFFICIENT .I

P R I M A R YM R P :

FIGURE6.5.11

w

Page 236: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 236/360

BLP.CKHAWK- ENGINETIME VARYING COEFFICIENT

MRP w n E :HRP TYPE:INPUT V R R I R E L ES1 :OUTPUT VRRIRBLE:

P R l H R RY 8RP:

H A P E l OUVR

r ( F U N * 1 0GCRPM

FIGURE 6 . 5 . 1 2

Page 237: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 237/360

:,. -

Document No. $ER 70452

BLACKHAWK- EIIGIIYETIME VA RY I N GC O E F F I C I E N T

FIGUREC.5.13

Page 238: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 238/360

1.

2.

T700 Fuel and Control System, J. J. Curran,AHS National Forum Paper, May 1973

General Electric, T700 Operations Manual

5.6-42-A G E

w 29 REV. t

Page 239: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 239/360

. . . . . .. . . . . ... . . . . . . . , . r T ~ ~ ~ ~ ~

-5.7 LANDINGINTERFACE MODULE

CONTENTS

5.7.1 Module Des cripti or

FIGURES

5.7.1.13. 7. 1. 2 Landing ModuleAxes System5.7 .1 .3 Landing Gear Geometry5.7 .1 .4 Landing In te r f ac e Equat ion Flow

Landing Gear - Tire and S t r u t R e p r e s e n t a t i o n

5.7 .2 Landing In te r f ac e Module Equat ions

5.7.3

5.7 .4 Nomencla ture

Landing In te r face Inpu t /Outpu t Da ta Def in i t ion

5 . 7 . 5 BLACKHAWKLanding Module Input Data

TABLES

5.7.5.1 Cube Root S o l u t i o n for I n p l a n e S t i f f n e s s E q u a t i o n s5.7 .5 .2 Main Tire L a t e r a l S t i f f n e s s5 .7 .5 .3 Main Tire Vert ica l Load Deflection Data5.7 .5 .4 Main Ti re Ve r t i c a l S t i f f n e s s5 . 7 . 5 . 5 Tai l Tire Vertical Load Deflection Data5.7.5.6 Tai 1 T i r e Ve r t i c a l Stiffness

FIGURES

5.7.5.15.7.5.2 M a i n Ti r e L a t e r a l Stiffness5.7 .5 .3 Main Ti r e Ve r t i c a l Load Deflection Data5.7.5.4 Main Tire Vertical S t i f f n e s s5.7.5.5 Ta i l Tire Vert ica l Load Deflection Data5 . 7 . 5 . 6 Ta i l Ti re Ve r t i c a l Stiffness

C u b e R o o t S o l u t i o n f o r I n p l a n e S t i f f n e s s E q u a t i o n s

5.7-1

PACE.-

5.7-1

5.7-2

5.7-55.7-6

5.7-85.7-7

5.7-9

5.7-27

5.7-28

5.7-40

5 .741’5.7-425.7-435.7-445.7-46

5.7-47

5.7-485.7-195.7-515.7-525.7-535.7-54

u n m.0

Page 240: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 240/360

--

DOCUMENTn o . SER 70452

5.7 LANDING INTER FACE MODUL E

5.7.1 Modul e Descr iptio n

This generalized representation consists of a landing gearforce reaction model complet e with a1 1 necessary spacehodygeometry calculations to track a free helicopter landing ontoa level ground plane.separate non-linear tire and strut dynamic characteristics asshown i n Figure 7.1.1. Tire in-ground-plane loads are developedas a non-linear function of the tire deflection and normalload. These forces are adjusted depending on the frictioncriteria which determines tire skid characteristics at thedeck surface. Finally, strut loads are summed with otherexternal forces and moments at the helicopter CG.

The landing gear is represented by

Axes S stems.e d u l e s shown i n Figure 7.1.2. All landing gearforces and moments are formulated in axes parallel to theprimary body axes system passing through the CG. The spaceaxes system of which the ground plane is set at WLFD is usedto determine the landing gear proximity to the ground.friction forces are cnecked i n the sp ace axes system.

Two axes systems are used in this landing

Inplane

Landinq gear qeometry.of the landing gear, Figure 7.1.3;strut moves along th e line parallel to the helicopter Z axis.No account is taken of drag linkage constraints which causethe axle to move in an arc in the X-Z plane. This geometrytogethe r with the Gen He1 calculated position of the helicopterC.G. posi tion in space,is used to establish t he location ofthe tire, axle reference and gear reference points for eachgear in space axes.determine the proximity of tire contact and subsequent tireand strut deflections.

In the equations defining the geometryIt i s assumed that the

These coordinates are used later to

Determination of tire contact.conta ct, for an a rbitr ary 'orientati on of the he1 icopt er re1 ieson establishing the length o f a normal line from the groundplane to the axle reference position. When the distance alongthe gear line becomes less than the tire radius, contact hasoccurred.tire deflection.point on the width of the tire. In the model the contactpoint i s assumed to be at the center of the tire tread, irrespectiveof the distortion resulting from radial or axial loading.

The determination of tire

Subsequently, th i s difference i s defined as radi a1I n practice tire contact can occur at any

5 , 7 - 2PA G E

5

-. - . - - A

Page 241: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 241/360

. -- --

Determination of tire inplane deflections and loads. In orderto establish the degree o f inplane deflection and correspondingloading on the tire; it is necessary to tra ck the intersection-of the landing gear line relative to the ground plane.two equations of the gear line, (each projected into a twodimensional plane) are sol ved for the i tersecti on coordi nateswith the ground plane. When contact for an individual tire i sestablished, the point of intersectian is retained and onsubsequent iterations through the program, tire deflection isdetermined by comparing the new and old gear line intersections.The coordinates of the initial contact are retained until thetire leaves the ground or. s mo'dified by the ti re slip ping .The latter aspect is discussed later.of t h e ' d e fl e c t io n s i n t o h e l i c o p t e r b o d y a x e s , t h e t h r e ecomponwts of deflection at each'tire are used to enter the"tire characteristics data file," to obtain the three componentsof tire force.

Essentially

Following the transformation

Determinat ion of ti re co ntact conditions.determination of tire forces from the he1 icopter/qround plane

Following the

re?at ive motion, a test of the ability of the inpfane frictionforces to resist the applied forces, without slipping, must beestablished. The tire forces obtained in helicopter axes mustbe transferred to the ground plane for the friction'check.Classical fyiction considerations provide for a coefficient ofstatic friction and a coefficient for sliding friction.the former case (when brakes are set), the maximum amo unt ofinplane load which can be resisted without slipping, is proportionalto the coefficie nt of friction and the normal loading. Whenthis level is exceeded, motion will result. Then the forceresisting the motion will depend on a reduced (sliding) coeff icien tof friction and the normal force. In practice, there is a

smooth transistio n between the two conditions. However, themodel assumes a discrete change. A further assumption i s thatthe test for frictional loads in the model assumes that X andY inplane components can be tested separately. I n practice,the resultant force determines slip conditions. This latterassumption was made t o simplify the model and facilitate theintroduction of brakes. When th e brakes are activated, it isassumed that the wheels are locked.low coefficient of friction is introduced into the tire Xdirection. The wheel degree of freedom i s not currentlyrepresented and therefore spin up (say on landing) inertialoads are not calculated. If slip is not occurring, calculat edtire f orces are passed unchanged.the inplane forces are set to the value for sliding friction.

In

For brakes off, a very

If slippage i s occurring,

5 . 7 - 3-A G E

Page 242: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 242/360

O C C U M N T no. SER 70452

Reinitialization of the original tire contact point as aresylt of siippaqe. Under conditions of no-slip the tireinti ane def ection is develooed from consecutive calculationsof' t'ie gear line inte rsec tion w ith the grou nd plane. During

' slip conditions, the contact point for the tire moves and theinitialization of the gear-line intersection must be revisedto reflect the tire movement and establish a new value for thecontact point to be used on the next pass through the program.

..-

Acceleration of %he landinq gear strut.the loads transferred to th e airframe by the strut will be .

Under steady conditions,-

equal to t he ti re reaction s.the acceleration of the unsprung mass can modify the loading.Under light loading condition (where a significant portion ofhelic opte r weigh t is reacted by the rcitor), the stru t operat esin a preload range.load is less than the strut preload setting, tire loads aretransferred to the airfr ame with zero strut deflection. Oncethe preload setting is exceeded, the strut (unsprung mars) isaccelerated depending on its own dynamic characteristics, thetire applied loads and the unsprung mass. Note that logicprecludes the equation flow reverting back to the preload modeuntil the natural transient provides a zero strut deflectioncondition.damping and an isothermal air spring. A software switch isprovided wh ich a1 lows bypassing the str ut calculation.. Finally,the strut loads are transferred to the helicopter CG forsummation with other external forces.

However*, .under transient conditions ,

Under these conditions, where ti re reaction

The strut is assumed to have velocity squared

5 . 7 - 4-A G E

.

Page 243: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 243/360

ORIGINALPAGE I3OF POOR QljALlTY

D O C U H P H TN O . SE3 70452

WiDING GEARTI RE AtlD STRUT REPRESEJITATI ON

Page 244: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 244/360

LANDINGMODULEAXES S Y S t n ; l

.. .. .

L. I

t

I

FIGURE 7.1.2

5.7-6Page

Page 245: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 245/360

7-8

d

PQ

u7PAGE

.-

i

Page 246: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 246/360

I

Ti

SER 70452

5.7-8m

Page 247: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 247/360

Page 248: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 248/360

5.7-7 0Page'

Page 249: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 249/360

. _ ~ . I " _.... _ ._._._.._........ .I.I . ,_ c - - - - - -

- . . . .

II I

1 ' : ' ' t . I ' i

5 .7 -1 1

Page 250: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 250/360

--

Page 251: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 251/360

- ~ -- ' I

SER 70452

5 .7 -13Page

Page 252: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 252/360

ORIGINALPKtikOF POOR QUALIW

SER 70452

Page 253: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 253/360

ORIGINALPAGE fSOF POOR Q5ALITY SER 70452

I'.'CC*I

5.7-1 5Paqe

Page 254: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 254/360

SER 70452

......*I

Page 255: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 255/360

Page 256: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 256/360

@

Page 257: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 257/360

Page 258: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 258/360

. .I I I

5-7-20rage

Page 259: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 259/360

-

5.7-21

Page 260: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 260/360

Page 261: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 261/360

D=

7F2VE-d

7

-

5.7-23PAGP-

_ I . “ I -

Page 262: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 262/360

%7 *

Page 263: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 263/360

Page 264: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 264/360

r. - -- - -

5.7-26PAGE'

- , , e.----

Page 265: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 265/360

D O C U M E N TN O . ' SER 70452

5 . 7 - 2 7--iPAGE

.-

Page 266: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 266/360

.)

5 : 7 . 4 NOTATION FOR G E N .HEL. LANDINGSIMULATION

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTI ON

'SH

'SH

'

'SHO

'SHO

'SHO

SH FT

SH+1 FT

SH+2 FT

SHO FT

SHOtl FT

SHW2 FT

v N v N FTISEC

v E vE FTI S EC

FTISECvz "2 -

FSCGB

WLCGlj

FSNGA

FSMGA

BLMGA

He1i copter center o f gravity

position in space axes.

In i t i a l pos i t ion o f he1 ic op ter

in space axes.

He1 copter space axes veloci t ies.

Helicopter c.g. l e s s r o t o r.

INS 'NS. ISCGS

WLCGB

FSNGA. INS. Fuse. s tat . o f nose g.ear strut.

FSMGA INS. Fuse. stat. o f main gear strut.

BLMGA INS. B u t t . s t a t . of main gear strut

.-.._.-.__---. *ad. a. -*; .76 ?.. .._. . .. I,

Page 267: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 267/360

oocunEtuN O . SER 70452SSKORSW ORlGINALPACE E8AIRCRAFT OF POOA Q U A L l T Y

NOTATIONFOR G E N .HEL. LANDINGSIMULATION-

SYCIBOLUSED iNEQUATIONS '

PROGRAMMNEMONIC U Ni ' iS DESCRIPTION

WLNGAO

WLMGAO

X~~~

X~~~

Y~~~

RMGA

LMGA

Z~~~

z~~~Z~~~~

R~~R~~

PHBS]

X~~~~

Y~~~~

Z~~~~

X~~~~~

RMTSOZRMSO

WLNGAO INS

WLRMGA INS

NGA FT

RMGA, LMGA: FT

NGA+l FT

RMGA+l FT

LMGA+l FT

NGA+2 FT

RMGA+2 FrLMGA+2 FT

RTNF INS

RTMF INS

Defined i n theMotion Module

NTSO FT

NTSW1 FT

NTSCk.2 FT

RMTS0 FT

RMTSO+l FTRMTS0+2 FT

WL. posit ion of free extensiono f the axle.

Pgsi tio n o f freely extendedaxles i n body axes.

Nominal nose t i r e ra diu s.Nominal main t i r e r ad ius .

Helicopter body t o space axestrans format i on matri x .

Nose tire reference positionin space axes under freeextension.

Right t i re reference posi t ion

in space axes under freeextensi on .

5.7-29PA G E-

Page 268: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 268/360

Page 269: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 269/360

FT

FrFT

R i g h t gear reference josi t i oni n space axes

D O C U M E N TN O . SER 70452

NOTATION FOR GEN.HEL. LANDINGSIMULATION

- -

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRI PTION

RMGSR

RMGSR+l

RMGSR t 2

~ M G WYMGRSRZ~~~ R

'MGLSR

'MGLSRZ~~~~~

LMGSR

LMGSR+lLMGSR+Z

Fr Left gear reference position

FT i n space axesFT c

WLFD WLFD FT Height o f ground plane .

d~~~ .

d~~~

d~~~

D N N ADNRA

DNLA

FT [ Normal distance from the ground

FTplane t o axle reference point fornose, r i g h t and l e f t gear.

CSANGCSBNG

CSGNG

I Direction cosines o f gearline.

DLTNG

DLTRG

D LT t G

FT Nose t i re r a d i a l def lec t ion .Fr Righ t t i r e r a d i a l def lec t ion .FT L e f t t i r e r a d i a l def lec t ion .

( a ) ~ ~ , .G, LG

( b ) ~ ~ ,G, LG( c ) ~ ~ ,G, LG

( d ) ~ ~ ,G, LG

Coefficients o f gear l ineequation projections i n 2 D

for the nose, r i g h t and l e f t1and1ng gear.

5.7-31PA G E

Page 270: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 270/360

D O L U H E N TN O , SER 70452

FT

FT

FT

NOTATIONFOR G E N .H E L .L A N D I N GSIMULATION

Ini t ial deck contact posi t ionsbefore distort ion o f t i r e s .

SYMBOLUSED IN PROGRAMEQUATIONS M N E M O N I C UNITS DESCRIPTION

( ID)NGO

( yIDINGO( Z ~ ~ ) ~ ~ ~

(x~D ) R G O( y D)RGO

(z ~ ~ )GO( x ~ o )GO( y ~ ~ )GO

( z ~ ~ ) ~ ~ ~

( INT NG

( yI N T ) N G

( IN T )N G

( INTIRG( z ~ ~ ~ )G

( I I ~ TG( INT)L G( INT LG

( I NT) RG

Y 29 R f V. G

I DNG

I DNG+1I DNG+2

I DRG

I DRG+l

I D R G t 2I D L G

I DLG+lI DLG+2

I NTNG

INTNG+l

I NTNG+2

I NTRMG

I NTRMG+lI NTRMG+2

I NTLMG

I NTLMG+lI NTLMG+2

DELNG

DELNG+lDELNG+2

DELRNG

DELRNG+l

DELRNG+2

FTFT

Fr

FT

FT

FT

FTFT

FrFT

FrFTFT

FT

FT

FTFT

FT

FT

Intersection of gear l ine w i t h

deck plane in space axes forthe nose gear.Intersection o f gear l ine withdeck plane in spaceaxe< f o rthe r i g h t gear.Intersection o f gear line withdeck plane in space axestorfor l e f t g e a r.

Tire deflections in the deckplane for the nose gear.

Tire deflect ions i n t he deckplane for the r ight gear.

5.7-32-AGE

'.

i

Page 271: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 271/360

NOTATIONFOR GEN. HEL. LANDING SIMU LATIO N

SYMBOLUSED I N PROGRAMEQUAT IONS MNEMONIC UN ITS DES CRIPT ION

[AHSB]

KTXN ,R,L(KTx)N. R. L.

KTYN, , 1KYZN, ,L

(KTY)N,R, L

(KTz)N, R, L

FrFT

FT

FT

FT

FTFT

FTFTFT

FTFT

lb/FT

' Ib/FT

1b/FT

LB

LB

LB

5.7-33-kGE

Tire def lec t ions i n the deckplane f o r t he l e f t gea r.

Ti re def lec t ions i n hel icopterbody axes for nose gear.

Tire deflect ion5 i n hel icopterbody axes for r i g h t gear.

T i e defl ec t ion i n he1 i copterbody axes for l e f t gea r.

Helicopter space t o body axest ransfo rmat ion ma r i x .

Tire 3 component s t i f f n e s scoeff i c i en t s - Note t h a t thesecan be replaced by l oad ing maps.

Tire forces i n helicopterbody axes f o r the nose gear.

-- - -.

Page 272: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 272/360

.NOTATIONFOR G E N .HEL. LANDING SIMULATION

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS

~~

DESCRIPTION

( x ) ~ ~ ~T HRFTHR+1

( z ) ~ ~ ~T HR+2

( x ) ~ ~ ~ ~THL

( y ) ~ ~ ~T HL+1

FTHL+2

( y FTHR

( Z )FTHL

DMDMDNDN

df4

d N

PMRPMR

RAT PRMpM

pRM

N~~

N~~

p N

RN

NTN

NTM

PNPN

RAT PRN

FTDN

FTDN+:FTDN+2

FTDR

FTDR+lFTDR+2

FTDL

FTDL+I

FTDLQ

LB Tire forces i n hel icopterLB

LBbody axes f o r the r i g h t gear.

LB Tire forces i n he1i.copterLB

LB

body axes for t he l e f t gea r.

INCHES Main gear t i re d iameterINCHES Nose gear t i r e diameter

l b / i n 2 Majn gear t i r e pressurel b / i n 2 Main gear rated t i r e pressure

- No. o f tai l gear wheels

- No. o f main gear wheels .

lb / in 2 Nose gear t i r e pressurei n / i n Nose gea r r a ted t i r e p ressure

LB

LB

LB

L9

LBLB

LB

LB

LB

Tim forces i n the space axes b u t

a l i g n e d a l o n g hel icopter X axisf a r the nose gear.T i r e forces i n the space axes b u t

a l i g n e d along hel icopter X axisfor the r i g h t gear.

I Tire forces i n the space axes b u t

aligned a l o n g he l i cop te r X axisI f o r t h e l e f t gear.

Y. 29 Rf3. G

Page 273: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 273/360

- I .

NOTATIONFOR GEN. HEL. LANDING SIM ULAT ION

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONI C UNITS D E S C R I P T I O N

Y 29 111. t

KMUXX

KMUXBK

KMUXOK M U

TTBMM

FTDW

FTDLM

K S L I P

F T D N W l

FTDRM+l

FTDLM+l

DELSPN

DELSPR

DELSPL

DELSPN+l

DELS P R+1DELS PL+1

LB

LB

LB

LB

LB

LB

tT

F7FT

FTFTFT

5.7-35-AGE

Factor f o r brakesValue o f K/,J brakes o n .\/a;ue of Krg brakes o f f .Longitudinal tire coef. o f f r i c t i on.

Max. f r ic t ion . load t h a t canbe sus ta ined i n the X direc t ion . ,

Factor f o r s l i d i n g f r i c t i o n .

Max. f r i c t i o n l oad t h a t can besus ta ined in the Y d i rec t ion .

Amountof t i r e deflect ionsus ta ined dur ing s l ipcond i t i o n sin the X d i rec t ion .

Amountof t i r e d e f l e c t i o nsus ta ined dur ing s l ipco i id i t ionsin the Y d i rec t ion .

Page 274: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 274/360

DOCUNENTNO. SER 7 0 4 5 2

NOTATIONFOR GEN.HEL. LANDINGS I M U L AT I O N

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

( X ) ~ ~ ~ ~

(Y FTAR

FTAN

FTAN+l

FTAN+2

FTAN+3

FTAN+4

FTAN+S

FTAR

fTAR+1

FTAR+2

FTA.Ri3

FTAR-i.4

FTAR+S

3 A LFTAL+1FTAL+2

FTAL+3

FTAL+4

FTAL+5

DELSSN

DELSSN+l

DELSSN+2

L B

L B

L B

ET

FT

FT

LB

L B

L B

FT

FTFT

LBL B

L B

FT

FrFf

FT

FT

FT

5.7-36PA G E

Tire forces and moments a t theax1e . e ference pos i t ion,, nosegear.

Ti re forces and moments a t theax1e reference posit i on , right

gear.

Tire forces and moments a t theaxle reference pos i t ion , le f tgear.

mount of s l ippage of gea rin te r sec t ion p o i n t i s spaceaxes, nose gear.

Page 275: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 275/360

O O C U H E N TY O . SER 70452

NOTATIONFOR GEN.HEL. LANDING SIMULAT ION

SYMBOLUSEDIri PROGRAMEQUATIONS MfaEMONI C UNITS DESCRIPTION -

"NG

M~~

DELSSR

DELSSR+l

DELSSR+2

DELSSL

DELSSL+l

DELSSL+2

DL. .NG

D t . .RG

DL. .LG

DL.NG

DL. RG

DL. LG

DLNG

DLRG

DL LG

FPREN

FPREM

FSTRN

FSTRR

FSTRL

MASNG

MASMG

FT

FTFv

FTFT

FT

F T IT

FTFrFTFT

RFTFT

LB

LB

LB

LB

LB

SLUGS

SLUGS

5.7-37-AGE

\Amountof sl ippage o f gearin tersec t ion p o i n t is spa'ceaxes, right gear.

Amountof s i ppage of gearin tersec t ion p o i n t i 3 spaceaxes , le f t gear.

Wheel ax12 motion a long s t r u t1ine

Nose gear strut preload.Main gear strut preload.

S t r u t force t ransferred t oairframe f o r the nose, r i g h t

and l e f t gea r.

Unsprung mass of nose gear.Unsprung mass o f main gear.

Page 276: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 276/360

>' .

O O C U H E N TN O . SER 70452

NOTATIONFOR G E N .HEL. L A N D I N GSiMULATION

SYM W L .USED J PROGRAMEQUATI ONS MNEMONI C UNITS ' DESCRIPTION

-'NGc~~

RTRT TLFRTT

C RGHCLGHCRGL

CLGL

KOLEOM

KOLEON

(x ,FGRN( FGRN

( z ) ~ ~ ~ ~( L, FGRN

( M FGRN

( FGRN

( x ) ~ ~ ~ ~

( y ) ~ ~ ~ ~

( FGRR

( L )FGRR

( M )FGRR

( N ) ~ ~ ~ ~

SA 29 VV. 0

-

C N GCMG

RTRT TLFRTT

CRGHCLGH

CRGL

CLGL

KOLEOM

KSP+7KSP+lO

KOLEONKSP+6

FGRN

FGRN+lFGRN+2

FGRN+3

FGRN+4

FGRN+S

FGRR

FGRR+lFGRR+2

FGRR+3

FGRR+4

FGRR+S

LB/(FT/SEC) ' Velocity squared dampingf o rL B / ( F T / S E C ) * Inose and main gear s t ru t s

*

Velocity break points onFT/SECT/SEC Is t r u t damping

LB/ (FT/SEC)' Corresponding damping ccjcf.L R / (FT/SEC)2 of velocity squared dampingLB/(FT/SEC) ' for the main gear.L B / ( F T / S E C ) *

LB-FT

FT

FTLB- FTFT

LB

LB

LB

FT

FT

Fr

LB

LB

LB

FT

nn

Isothermal a i r spring coe f. maingear.

free extension of main gear.

Isothermal ai r spring coef. nose gearFree extension of nose gear.

Gear forces and moment a tthe gear reference posit ions-nose gear.

Gear forces and moment a tthe gear reference posit ions-r ight gear.

Page 277: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 277/360

DOCUMENTY O . SER 70452

NOTATION FOR GEN. HEL. LANDING SIMUL ATION

SYMBOLUSED IN PROGRAM+EQUATIONS MNEMONI C UNITS D E S C R I P T I O N

( FGRL

( y ) ~ ~ ~ ~

. ( z ) ~ ~ ~ ~

( L )FGRL

FGRL

( N ) GRL

x~~LG

Z~~LLG

M~~

LG

FGRL

FG RL+1

FGRL+2

FGRL+3

FGRL+4

FGRL+S

XLG

YL G

ZLG

LLG

MLG

NLG

LB

LB

LB

FT

FT

FT

LB

LB

LB

Fr

FT

FT

i

Gear forces and moment a tthe gear reference posit ions-left gear.

Total gear loads a t thehelicopter CG i n body axes.

Page 278: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 278/360

5.7-40PAGO'

m 2) av.

Page 279: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 279/360

Y 29 m. E

5.7-41-A G E

Page 280: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 280/360

-

5.7-42PAGE

Page 281: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 281/360

7

---=---

5.7-43--IPASE

Page 282: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 282/360

5.7-44-AuE

Y 29 m. c

.

Page 283: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 283/360

r

-t

Y 29 m. 5

5.7-45m

D O C U M E N TN O . SER 70452

Page 284: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 284/360

- -

5.7-46-A G E

Page 285: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 285/360

1

Page 286: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 286/360

f

i

i;

. 5.7-48_..

1 - . -

Page 287: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 287/360

5.7-49

Page 288: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 288/360

vr. - 1_ ..... - . . . - .. ,. ...

-

5 . 7 - 5 0

SER 70452

Page 289: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 289/360

SER 70452

i 1

(*)-’

,..._.I..,,

5 . 7 - 5 1

Page 290: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 290/360

. . .- . . . - ~ -7 : - , . ,,. I . ,. - - . , . . I T 1 - , : - . I 1 . 1 I n - 7, . , . , . ,

5.7-52

Page 291: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 291/360

- - -

Page 292: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 292/360

--ORIGINALPAGE F9OF POOR QUALIW SER 70452

Page 293: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 293/360

5.8

5.8.1

5.8.2

5.8.3

5.8.4

5.8. S

5.8-6

G R O U N DEFFECTMODULECONTENTS

Module Description

Ground Effect Module Equations

Module I n p u t / O u t p u t Defini t ion

Nomenclature

BLACKHAWKGround Effect I n p u t Data

References

5.8-1

5.8-2

5.8-3

5.8-4

5.8-5

5.8-6 .

i.8-7

Y a El. Q

5.8-1PACE-

Page 294: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 294/360

.

5.8.1 Modul e Desc ript ion

This module simulates the effect of ground proximity on ahelicopter by modifying the main rotor downwash equation,

The modification factor was derived from Black Hawk hover-power flight test results (ReTerence 5.8.6-1).

k

The modification factor is reduced as flight speed i s increasedat constant height by a wake angle correction

It -i s l ikely that recent and on-going research on this subject(Re fer enc e 5.8.6-2) will lead eventually t o an empirical modeldescribing +,he local rotor inflow velocity due to the hyper-bolically shaped ground vortex and its image that has beenshown i s exist at low speeds. Unfortunat ely, sufficie nt datafo r corr.c:;ation of such a model has n o t yet been published.

. .

i

uP A G E

Page 295: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 295/360

The par t i s square bracke ts [ ] i s the ground proximity e f f e c t(usually switched t o 1 when 2>5 x R), t h e r e s t o f the equationi s as quoted i n the main rotor downwash section.

- .5-3C A G E

Page 296: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 296/360

-

---

5 . 8 - 4PASE '-

Page 297: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 297/360

Page 298: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 298/360

r

5 . 8 . 5 . I n p u t Data

No separate i n p u t data i s requ ired. The parameters .115 and2/3 in equation 5.8.2-1, were empirically derived from data i nReference 5.8.6 -1 which i s pert inen t to Bla.ck Hawk a i r c r a f t .

5.3-6PA G E-

Y 29 R t V. t

Page 299: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 299/360

5.8.6 References

1 .

2.

LTC Alan R. Todd t o Mr. R. Merritt , Sikorsky AircraftLetter "Free hover performance"22 October 1976

Sheridan & Wjesman "Aerodynamicso f He1 icopter F1i g h tNear the Ground" AHS Paper 77.33-04 May, 1977

5.8-7-A G E

CJ 29 ?CY 3I

Page 300: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 300/360

I

5.9

5,9.1

GUST MODULE

CONTENTS

Module Description

FIGURES

5.9.1.1 Gust F r o n t Geometry5.9.1.2 Gust S e l e c t i o n F u n c t i o n5.9.1.3 . Gust Penetration Geometry

5.9.2 Gust Module Equa t ions

5.9.3 Module Inpu t /Outpu t Def in i t i on

5.9.4 Nomencla tu re

5.9.5 Gust I n p u t Data

5.9.6 Refe rences

5.9-1-PA G E

5.9-1

5.9-2

5.9-55.9-65.9-7

5.9-8

5.9-17

5.9-18

5.9-23

5 9-24

Page 301: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 301/360

5.9

5.9.1

a *

D O C U M E N TN O . SER-70452

Gust Module

Description

This module proauces locala r v e l o c i t i e s a t a l l rotor-blzdesegment positions and a t the fuselage and empennage aerodynamiccenters, caused by various types o f gusts. The i n p u t gusts maybe discrete or continuous.

The o u t p u t veloci t ies are ca lcula tedi n the local axis-systemi n which they are toabe used. T h u s the fuselage and t a i l termsare i n body axes while those a t the blade segments arei n bladeflapped and lagged axes.

The d is cr et e g usts a re Characterized by..havinga f r o n t 1ine designatingthe beginning of a dis turbance , t ravel l ingt h rough the atmospherea t veloci ty V on a compass bearing pj~ Figure 5.9.1.1). Behindth i s f r o n t l i#e, the change i n a i r ve loc i ty can assume a s t ep orrounded ranp o r pulse shape, characterizedby a magnitude llHGAMpand r ise-t ime G (Figure 5.9.1.2). Since the a i r c r a f ti s defined t o bdDf?ying i n i t i a l l y a t V on compass bearing @the g u s t f r o n t can sweep across the aiQ?aft (or be penetrated bBo't h e a i r c r a f t ) from any direction and a t any speed, by m a n i p u l a t i n gthe relat ive speedsand compass bearings.

The continuous gusts are representedby the Dryden Model. Thegu st i s assumed t o be aligned w i t h the aircraft heading sucht h a t

o n l y longitudinal a n d ver t ica l vectors are defined. This i sanecessary res t r ic t ion , w h i c h avoids frequency shifts that wouldinvalidate the gust spectrum model. A t a i r c r a f t trim speedsgreater t h a n 50 f t / s e c , a s ta t iona ry gus t f i e ld i s t raversed bythe a i r c r a f t ; a t trim speeds less t h a n 50 f t / s ec , the gus t f i e ldt r ave r ses the a i r c ra f ta t 50 ft/sec. While the l a t t e r p rocessi s not a very appealing artifice mathematically,i t i s necessaryi n order t o a v o i d unreal is t ic t ime lags i n the gus t def in i t ionequations and f l y i n g t h e a i r c r a f t i n a constant up or down-draughta t hover.

A penetrat ion distanceG ( f t . ) i s defined which repre sentst hedistance t h a t t he a i r c ra f t r e fe rence hub centroid has penetratedi n t o the gust.

t o the edge of the rotor d i s k i n the upwind direc t ion .A rearward approaching gus t i sn o t possible w i t h o u t fu r the rmanipulation of the model. The propagation rateof the gus t f ie ldacross the rotor i s definedby V which then allows the penetra-t i o n o f any blade-segment, t o be'khculated (GPRjk,see fig ur e 5.9.1.3).

I n i t i a l l y t he g u s t f r o n t i s assumed t o be close

5.9-2-A G E

Page 302: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 302/360

.._- - -

D O C U M E N TY O . SER-70452

5.9.1 Description (Cont-inued)

For the d iscre te gus ts GpR.k 1 s introduced expl'

o f gust values, determined a t f ixed t ime (dist i : snt erv als ,(TABINK) are avail able . Thesed a t a are obtainea by passingindependent, Gaussian, u n i t R.M'.S.no-;se signals, produced bypassing uniformly distributed white noiset h r a u g h the inverseGaussian d i s t r i b u t i o n function (Reference5.9.6-Z), t h r o u g h theDryden fi l t e r s . The assumption i s made th a t pe rtu rba tio nsi nspeed and heading are small enough such that the time cmstantsi n the gus t functions can be considered constant,and t h a t d a t a

can be loaded i n t o the tables a t f ixed d i sp lacewnt in t e rva l s .These assumptions are consistentw i t h the frequency/kirspeeacon t ra in t s o f the Dryden Model application.

The g u s t veloci t ies genera ted by e i t h e r d i s c r e t e or continuousfunct ions , a re i n an axi.s se t def ined by the ho,-izontal gustfro nt. Three transformation matrice s ar e requiredt o o r i e n ti n t o the blade axes and one for tne body axes. These veloci t iesare added to the other local velocit iesa t the var ious s ta t ions .

' l v i n to the?d

. d ir ec tl y . However, fo r the continue us gust c. . fi a t ab leprof i le equat icns and the dust increment can b

The vertical gust component contributest o the t o t a l i n f l o w o fthe main rotor. Becsuse a basica l ly uniform i n f low i s assuinedin the Gen He1 rotor simulation, t h p change i n i n f l o w can besinul ated by a d d i n g a representative ve1oc.rt y over tne whole

di sc , The div isio n o f the blade i n t o segments i n Ger, He1 i ssuch 8s t o give equal areas of swep'c a n n u l i . , making i t possiblet o t ake a simple mean as the represdnta t ive veloci tyof theadditional i n f low. Following the transformationo f the t -d i rec t ioncomponent from space t o (through body ) shaft axes, the meanincremental velocity (VGAVMR)can be aaded t o the downwashequation t o compensate the total inf low.

The gust velocitya t the fuselage i s assumed t o be the samevalue experienced a t the rotor hub. The empennage velocities arebased on the hub veloci ty w i t h a n approximate time delayt oaccount f o r the penetrat ion O F the specific component.

This model o f gust pene.tra,tionmay be cr i t ic ized on the groundst h a t the p o i n t fuselage a. ir laad used i s not cons istantw i t hthe detai led penetrat iono f the rotor blades. Fixed wing simulationsc o m n ly overcome the distr ibution problemby introducing correla t e dnon-inert ial rotat ional ra te s duet o Gust (Reference 5.9.6-1).

5.9-3-PA G E

Page 303: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 303/360

D O C U M E N TNO. SER-70452

Descrip t i o n (Continued)I t i s f e l t t ha t t he sepa ra tion o fthe t a i l used here, accounts for asu f f i c i e n t ly l a rge port iono f the non-rotor component gust d i s t r i -b u t i o n e f f e c t s and tha t fur ther te rms (for which the re a re l i t t l ei f any data) are unnecessary. In the same vein i t i s s u f f i c i e n t l yaccurate (and convenient i n the implementation) t o assume theaerodynantic centero f the fuselage t o be a t the c.g.

Discre te la tera l gusts may be handled by or ienta t ion of .However, the continuous g u s t case i s invalidated by usinfa &value other than zero f o r $kw, ue t o apparent frequency shif tsi n the gust spectrum.

5.9.1

5 ePA G E

y\ 29 REV. C

Page 304: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 304/360

VA L I DFOH DISCRETEFUNCTIONSONLY

Figure 5.9.1.1

5.9-5AGE

Page 305: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 305/360

D O C U M E N Tn o . SER 70452

.e-

q$ W G v;wo

I CHotrV 2 x G : o t t

W

' .Figure 5.9.1.2

5.966PAGE-

Page 306: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 306/360

'OR1G:NAL PPKX 1."

D O C U M E N TY O . SER 70452IKORSW OF POOR QUALiTYAIRCRAFT

B L

5 . 9 - 7PACt'

F i g u r e 5.9.1.3

Page 307: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 307/360

Page 308: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 308/360

Y 29 R t l .G

D O C U M E N Tn o . SER-70452

nr. --

5.9-9PA G E

Page 309: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 309/360

. .

” -

D O C U M E N TN O . SER-70452

5.9-10PA G E

Page 310: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 310/360

5.9-11PA G E

Page 311: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 311/360

D O C U M E N TN O . SER-70452

SA 29 QEV. G

Page 312: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 312/360

ic

Page 313: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 313/360

3 3 1 V d

P F s

r- -*

‘ O N LN3Hn304ZSi70L- 83

Page 314: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 314/360

c

. *i . =

3 W d-SI-6 S

L

d

7

Page 315: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 315/360

Page 316: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 316/360

1 5.9-17-

PA G E

54 29 n t v . G

Page 317: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 317/360

--

5.9.4 N o t a t i o n f o r Gust Module

SYMBOLUSED IN PROGRAMEQUATTOK- NEMONI C UNITS DESCRIPTION

\

'b .

'b

'bo

' W

9,

VKT

VHW

VFLD

AD

TIME

AFT

FSMR

FSTR

R~~INPPNT

MAXPNT

GO

GP

ICUPD

PSIDOT

PSIB

PSIBO

PSIRW

PSIWD

VKT

VHW

VFLD

TABINK

TIME

DELFT

FSMR

FSTR

RMR

INPPNT

MAXPNT

GOO

TABRUN

ICUPD

RAD/SEC

DEG

DEG

DEG

D E G

KNOTS

FT/SEC

FT/SEC

FT

SEC

FT

INS

INS

FT

-*

FT

FT

FT

S a 8PA G E

. Rate of Change of A / C Headintj

A / C Heading

I n i t i a l H e a d i n g

Relative Wind Headiris

Wind Heading

Airspeed

Wind Speed

Gust Propaga t ion Ra te

Gust Table Space

I n t e g r a t i o n Time I n t e r v a l

Tab le In i t i a l Dead Space

Fuse, S t a t i o n f o r T.R. Hub

Fuse. S t a t i o n f o r T.R. Hub

Radius of Main Rotor

Table Loading i n I.C. Mode

Maximurr. Ta b l e P o i n t s

(= 'RMR

Tab le Run Dis tan ce

S t a r t of D a ta i n T a b l e

. _._

Page 318: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 318/360

5.9.4 F lo ta t ion f o r Gust Module (Cont inued)

~~

SYMBOLUSED I N PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

TABLEH

TABLEV

G '

5

y 2

GPR'

TABMAX

GMAX

VHWG

VVWG

VHGAMPVVGAMP

TABLEH -TABLEH -GGGPRM FT

KSGMR ND

KMRBKl NO

P S I M R DEG

LGMR RADS

GPRSP FT

TABMAX

GGGMAX

VHWG

VVGIG

VHGAMPVVGAMP

GHQISGVDI S

auav

L"

5.9-19--P S C E

-FT

FT/SEC

FT/SEC

FT/SEC)FT/SEC)

FT )F T )

I)

Y 29 REV. G

.-

Table o f H o r i z o n t a l Ve l o c i t

Ta b le o f Ve r t i c a l Ve l o c it i e c

Hub Cen t ro id Pene t r a t ionD i s t a n c e

Normali e d O ff s e t '

O i s t ance f rom Hinge toSegment Midpoint

R o t o r A z i m u t h P o s i t i o n

Lagging Angle

Pe ne t ra t io n of Any BladeSegment

Max Number o f T able L oc at io

Max Dis tanc e in th e Tables

H o r i z o n t a l G u st Ve l o c i t y

Ve r t i c a l G us t Ve l o c i t y

Disc re t e Gus t P ro f i l e Amp-1i ude Func t ions

D i s c r e t e Gust P r o f i l e D i s -t ance Func t ions

D r y d e n F i l t e r I n p u t s

Page 319: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 319/360

1

- :

5.9.4

ORIGINALPAGE 18OF POOR QUALlTV'

N o t a t i o n f o r Gust Module (Continued)

- _ _~ - ~

SYMBOLlJSE5 IN PROGMMEQUATIONS MNEMONIC UNITS OESCRIPTION

L"

+bLAC

FSCGB

FSMR

GPAC'

e b1

'

if3

T1

T2

T 3

0

VHWGR

VVWGR

UPGMRD

UTGMRO

GAUSSH

GAUSSV

LPRAC

FSCGB

FSMR

GPACP

THETAB

PHIE

TlMAXT

T2MAXT

T3MAXT

--FT

INS

INS

FT

DEG

0 G

DEG

DEG

---

VHGIGR FT/sEC

VVWGR FT/SEC

UPGMR FT/SEC

UTGMR FT/SEC

5.9-20PA G E-

) Hor izon ta l and Ver t i ca l) Gaussian Ratidom Number

iRotor ' t o C GOffse t

Fuselage S t a t i o n f o r . C.G.

F u s e l a g e S t a t i o n s f o r MainRotor

Gust P e n e t r a t i o n o f C.G.

Airframe P i tcii Atti tude

Airframe Roll A t t i t u d e

Long. R o t o r S h a f t I n c i d e n c e

La t . Ro to r Sha f t Inc idence .

S p a c e 4 o d y Tr a n s f . M a t r i x

B o d p S h a f t Tr an sf . Ya t r i x

S h a f t G l a d e Tr c n s f . M a t r ix

H o r i z o n t a l Gust Vel. fromTab1e

Ve r t i c a l Gust Vel. from

Ta b l eThree Component Gust Veloci t i

) a t the Blade Segment)

Page 320: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 320/360

Of7lGINP.LTREE 2OF POOR QUALITY

5.9.4.

N o t a t i o n f o r Gust Module'

SYMBOL

UNITS DESCRIPTIONUSED I N PROGRAM

_z EQUATI ONS MNEMCNIC

VRGMR

UP iMR

UTGMR

URGMR

X r

U'tS

DWo

VGAVMR

VZSGUS

nT

bMR

NSS

VHWGAC

VVWGAC

VXGWF

VYGWF

VZGWF

URGMR

-

--

LAMBMR

MUZSMR

DWSHMR

VGAVMR

OMGTMR

8MR

ssVHWGAC

VVWGAC

VXGWF

VYGtlF

VZGWF

FT/SEC

N0

ND

NO

NO

ND

NO

NO

FT/SEC

RADSISEC

--

5.9-21PA G E

1)Three Component In ter fer-)ence; Components a t t h e)Rotor. Summed t o Memora)UPIMRI, UTIMRI, URMRI.11

Total Normal Rotor Inf low

Ve r t i c a l S h a f t Ve l o c i t y,Normali ed

Un ifo rm Component o f Down-Wash

Ave ra ge G us t Ve l o c i t y a t theR ,tor Di k

Vertical Shaft Component,Av. Gust Ve lo ci ty

Rotor Speed

Number of Rotor B1ades

Number of Segm ents/Bla de

Ve l o c i t y

FT/SEC ) H o r i z o n t a l a n d Ve r i t c a l Com-

FT/SEC ) the Fuse C.G.) ponents of G ust Ve l o c i t y a t

FT/SEC ) Components of Gust Velocity) i n Body Axes a t t h e C.G.

FT/SEC )

R / S E C )

Y 29 REV. G

Page 321: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 321/360

F

5.9.4 N b t a t i o n f o r Gust Module (Continued)

USED IN PROGRAMEQUATIONS MNEMONI C ..UNITS DESCRIPTION

V x b VXB FT/SEC

HTVTTR

HTVTTR

F T / S E C

Body Axes L o n g i t u d i n a lVel oci t y

Components o f G u s t Ve l o c i t ya t the H o r i z o n t a l Ta i l ,Ver t i ca l Ta i l and Ta i l Ro to r.

5.9-22P h C E

Y 29 9 1 V. S

Page 322: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 322/360

5.9.5 Data

D O C U M E N Tn o SER 70452

The only data of concern here are the continous gust powerspectrum parameters.Gen He1 or i s arbitrary (e.g. VHGAMpand G~~~~ describing adiscrete gust).

The following values are take n from Re ference 5.9.6-1:

All other data is defined elsewhere in

A1ti tude(h)S1750 ft ( h ) )1750 f t

A 1ti tude

1750 . , 145 h"3

1750 h

(For lateral gusts, bv 6 nd L, = Lu.)

5.9- 23PA G E-

Page 323: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 323/360

5.9.6 References

5.9-24-A G E

J O C U M E Y TY O . SER 70452

1. ' 'Background Information and User Guide f o r MIL-F-8785B(ASG) , I

"Military Specification - Flying Qualities of PilotedAirplanes", AFFDL-TR-69-72, C. R. C h a l k , et. al.,August 1969.

2. "Modeling Turbulence for F1 g h t Simulation at NASA-Ames" ,CSCR No. 4 Benton L. Parris, January, 1975. I

i

Page 324: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 324/360

5.10

5.10.1

HELICOPTER MOTIONMODULE

CONTENTS

Module Descr ip t ion

FIGURES

5.10.1.1 Body Axes System

5.10.2 Module Equations

5.10.3 Module Input /Output Def in i t ior t

5.10.4 Nomenclature

5.10.5 Black Hawk Input Data

5.10.6 References

5.10-1m

D O C U M E N TN O . SER 70452

5.10-1

5.10-2

I

5.10-3

5.10-4

5.10-13

5.10-14

5.10-19'

5.10-21

Page 325: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 325/360

5.10 He1 icopter Motion Module

5.10.1 Module Description--

I‘ ’

O O C U M E Y TY O . SER 70452

The force: ~ n i r oments derived from the various simulatedcomponents of the aircraft are summed to develop the totalexternal forces and moments at the airframe center o f gravityin body axes, Figure 10.1.1. Introduced at this point, forconvenience, are the gyroscopic moments resulting from rotatingcomponents.items of rotating mass aligned with the three body axes.total external forces and moments are introduced into thegeneral equations of motion from whiTh the 6 components ofacceleration are solved. It will be seen by comparing

with those on page 116 o f Reference 10.6.1, that certainsmall terms have been eliminated. It should be noted thatthese are the equations o f the aircraft less rotor blades,

(which have their own degrees o f freedom) and the appropriatemass is used. In order to obtain stable solutions under alloperational ccnditions it i s recommended t hat some velocityprediction t echniq ue be used in the determination o f the bodyaxes velocities,as presented . It should also be noted thatsince the p and r equation are coupled, they should be solvedsimultaneously as written.are given, followed by the body to space velocity axes transfor-mation. Large angles are assumed.

These equations are set up to cover any number ofThe

The Euler angular rate equations

The three component equations of motion, for any specifiedpoint on the helicopter are presented in general fo rm basicallyfor output. However, lateral acceleration is fed back to thecontrol system. It i s recommend that at least two entries to

these equations be provided to cover subsequent analyst require-ments. The remaining equations in this section are providedfor analyst output.

5.10-2-PA G E

Page 326: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 326/360

BODY AXES SYSTEM1

i

Xb, Y f b Body Axes System. Origin a t the. Center of Grav i ty. X A x i s P a r a l l e l

t o A i r c r a f t Center Line.

FIGURE10.1.1

5.10-3-PA C E '

Page 327: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 327/360

Page 328: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 328/360

-----,1

SER 70452

5.10-5v

PAGE

Page 329: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 329/360

5.10-6p1Ba'

r n m . 0

- ' - - - - *

Page 330: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 330/360

f i g = fk 7f

. .-# ..

5.10-7m

Page 331: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 331/360

------ ---

I

i

4

- .-

5,1098-AGE

u n v . 6

.

Page 332: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 332/360

,38Vd

6-0 'Ei

,-,'

Page 333: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 333/360

5.10-10PAGE-

Page 334: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 334/360

. . , -

5.10-11PAGE-

Page 335: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 335/360

O O C U M E N TN O .

I .

SER 70452

5.10-12--Page

Page 336: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 336/360

Page 337: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 337/360

_ _ _- - .

SUMXB LB

SUMYB LB

SUMZB LB

SUMLB FT LB

SUMMB FT LB

SUMNB FT LB

5.10.4 NOTATIONFOR THE HELICOPTERMOTICNMODULE

Total external force actinga t

the fuselzge c.g. along the X Yand Z axes respectivelyTotal external moments acting aboutthe X , Y and Z axes respectively

SYMBOL .USED IN PROGRAMEQUATIONS MNEMONIC UNITS DESCRIPTION

SUMXBI

S U W B iSUMZB

SUMLB

S MMB

S MNB

( " ' )MR(*. )TRL. . MF

( ....( - - - L G

)ADD

H X G YH Y G Y

HZGY

XGYJ YGY

ZGY

XGY

'Y GY

LGY

MGYNGY

' GY

Tai 1 rotor componentsFusel age componentsEmpennage componentsLand1ng Gear componentsAdditional Arbitrary Inputs

HXGYHYGY

HZGY3XGYJYGYJZGYWXGY

WYGY

WZGYLGY

MGY

NGY

SLUG FT2

SLUG FT2

SLUG FT2

RADS SC

RADS/SEC

RADS/SEC

FT LB

FT LB

FT LB

Gyroscopic effects, angularMomentum

Ratat ion inert ia a b o u t the X , Yand2 axes respectively.

Rotational speed o f components.

Gyroscopic ef fe ct s. Totalmoments i n body axes.

Page 338: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 338/360

, . . .. - .

5.10.4 NOTATIONFOR THE HELICOPTER MOTION MODULE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONIC UN IT S DES CRI PTI ON

'Xb'

r

F T / S E C 1Half pass predicted body axes

'Yb'

'Zb '

W

I XIY

IZ

xz

'bd

s GB

W~~~~

B~~~~

Xb

Y b

Zb

P

9r

'xb

'zbv Y

WEIGHT

I XIY

IZI xz

WTBOD

FSCGB

WLCGB

BLCGB

VXBDOTVYBDOT

VZBDOT

PDOT

QDOT

RDOT

VXB

YXBYZB

FT/SEC velocities.

FT/ S C

LB Aircraft gross weight

SLUGS FTL Inertia about body X-axis1

SLUGSF f L Inertia about body Y-axis

SLUGSFT Inertia about body Z-axis

SLUGSFT C r o s s coupling inertia

22

LB Weight o f the body

INSINS

INS

Fuselage station of the body c.g.

Materline station of the body c.g.

Buttline station o f the body c.g.

F T / S E C 2 Accel. along X-axisFT/SEC* Accel. along Y-axis

F T / S E C 2 Accel. along Z-axis

RADS/SEC2 Angular accel . about X-axis

RADS/SEC2 Angular accel. about Y-axis

RADS/SEC2 Angular accel. about Z-axis

F T / S E C Vel. along Y-axis

F T / S E C Vel. along Y-axisFT/SEC Vel. along Z-axis

5.10-15PA G E-

...

Page 339: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 339/360

'i5 . 1 0 . 4 NOTATION FOR THE HELICOPTER MOTIONMODULE

SYMBOLUSED IN PROGRAMEQUATIONS MNEMONI C UNITS DESCRIPTION

P

9r

?b

?b

pb

[ AHBS']

v Nv E"2

P

QR

THEDOT

PHIDOT

PSIDOT

THETABPHIB

PSIB

POEG

QDEG

RDEG .

SNTHEBCSTHEBSNPHIB

CSPHIESNPSIBCSPSIB-

VNVE

V t

RADS/S C

RADS/SECRADS/SEC

D E WS C

DEG/SEC

DEG/SEC

DEG

DEG

DEG

DEG/SECDEG/SEC

DEG/SEC

-------

FT/SECFT SECFT/SEC

Angula r r a t e abou t X-ax i sAngu la r r a t e abou t Y-ax i sA n gu la r r a t e a b o u t Z - a x is

Pi tch r a t e

Roll rate

Head ing ra t e

P i t c hRoll

Yaw

Angula r r a t e abou t X-ax i sAngu la r r a t e abou t Y-ax i s

Angular r a t e abou t Z-ax i s

SIN(THETAB1COS (THETAESIN(PHIB)

COS{PHIB)

SIN(PS1B)

Body to space axes t r ans fo rmat ionmatrix.

Velocity t o tbe no r thVe l o c i t y t o the e a s t

Vel oci t y down

COS( PSIB)

5.70-16--A G E

Page 340: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 340/360

---.-----

T-

5.10.4 NOTATIONFOR THE HELICOPTER MOTION MODULE

SYMBOLUSED I N PROGRAMEQUATIONS MNEMONIC UNITS D E S C R I P T I O N

NORTH

E A S T

A LT

C

X T

KT

a":qF

FSPS

wLPS

BLPS

1PS

h P S

b P S

NORTH

EAST

ALT

vcGAMTRU

NX

NY

NZ

VKT

ALFRE

BETFRE

QFRE

FSPSiwLPS

BLPSi

AXPSl

AYPSl

AZPS

Fr P o s i t i o n northFT Pos i t i on e a s tFT A1t i ude

FT/MIN

DEG True c l imb ang le

C1 imb ve loci t y

G ' s Body Axes l o a d f ac to r sG ' s

G ' s

KNOTS Ve l o c i t y i n X-2 p l a n e

Free stream a i r f low v a r i a b l e sEG

DEG

LE/ IT2

INS

INSINS

FT

FT Vert ica l armFT L a t e r a l arm

Fuselage s t a t i o n of p o i n t o f

Wate r l ine s t a t i o n o f p o i n t o f

B u t t l i n e s t a t i o n o f p o i n t of

Longit u d ina 1 arm

F T / S E C ~

R/SEC*

FT/SEC*

P o i n t +I accel . a long X-axis

Point #I acce l . a long Y-axisP o i n t #I acce l . a long Z-ax i s

5.10-1 7-PA G E

% 29 411. t

tit eresti nt erest

n t e r e s t

Page 341: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 341/360

SIKORSWAIRCRAFT

5 .10 .4 NOTATIONFOR THE HELICOPTERMOTIONMODULE

SYMBOLUSED INEQUATIONS

PROGMMMNEMONIC UNITS DESCRIPTION

xps .V

5 P S

%pS

.CNG[IL

LATBL

VXPSlVYPS 1

U P S 1

LNGBLl

LATBL1

FT/SEC P o i n t #I v e l # a l o n g

FT/SEC P o i n t #I v e l . a longFT/SEC P o i n t #I v e l . a l o n g

DEG

DEG

5.10-18-A G f

L o n g i t u d i n a l b a l l.L a t e r a l ball.

X-axis.Y-axis.Z-axis .

Page 342: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 342/360

- 7 ' '

u - 1 9PA6t

m a m.6

Page 343: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 343/360

---

/ / /7.

T i - - = -

5.10-20PAEE'

Page 344: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 344/360

-SJKBRSKYAlRClRAFT &Vu- 3

5.10.6 References

Dynamics o f F l i g h t , Etkin, B . , John Wiley & Sons Znc.,1959.

1.

.

5.10-21-hGb

SA 29 REV. G

Page 345: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 345/360

6.0 DEFINITIONOF THE BLACKHAWKCOCKPIT

CONTENTS'

6.1 Overall Coc kpi t Arr ang eme nt

6.2 Pilot's Primary Con tro ls

6.3 Control Range Cha ra cte rls ti cs

6.4 Control Force Feel Ch ara cte ri sti cs

6.5 References

FIGURES

6.1.16.1.2(a)

6.1.2Cb)

6.1.3(a)

6.1.3(b)

6.1.3(c)

6.1.4

6.1.5

6.1.6

6.2.1

6.2.2

6.3.1

6.4.1

UH-6A BLACKHAWKCockpit

Cockpit Component Identification

Cockpit Component Iden tffic ation (Cont 'd. )Cockpit Geometric Deflni t ion

Cockpit Geometric DeftnitSon (Cont 'd)

Cockpit Geometric Deffnition (Cont d)

Upper Console Panel Assembly

Lower Console Panel Assembly

Instrument Panel Assembl y

Cyclic Stick Grip

Collective Stick Grip

BLACK HANK Angular Control Motions and Displacements

BLACKHAWKCcntrol Forces and Gradients

6.1

6.2

6.2

6.2'

6.2

6,3

6.4

6.5

6.6

6.7

6.8

6.9

6.1 06.11

6.1 2

6.14

6.1 5

6.:6

6.17

Page 346: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 346/360

6.0

6.1

I

I

-6.2

6.3

6 . 4

DEFINITIONOF THE BLACKHANKCOCKPIT

Overall Cockpit Arrangement

The overal? layout o f the cockpit environment i s shown on thephotograph, Figure 1.1. This gene ral view i s suppo rtedbyi d e n t i f i c a t i o n o f cockpit componentson Figures 1.2a and 7 . 2 b .The cockpi t geometr ic def in i t ion , re la t ingt o t h e p i l o t ' s s e a t ,controls and instrumentation, I s presented on Figures 1.3d,1.3b and 1 . 3 ~ s 3-view general arrangement drawings.defining the upper and lower consoles are showno n Figures 1 .4and 1 . 5 respect ively.functions on the upper console and the Stabi latorlAuto F l i g h tControl Panel on the lower console.arrangement i s shownan .Figure 1.6.

P i l o t ' s Primary Controls

A diagram o f t h e p i l o t ' s c y c l i c s t i c kg r i p i s presented on Figure2 .7 . T h e g r i p i nco rpora t e s t he fo l lowing f tn t ionsof s igni f icance:

Diagrams

The most s ign i f i can t i t ems a rethe switching

The flight instrument panel

Stick triin - provides fo r l a t e r a l arid longitudinal s t icktrim a t 1/2"/sec.

T r i m re lease - while depressed the forc e system i s deac tivatedleaving a l i m p s t i c k .

A diagram o f the p i l o t ' s c o l l e c t i v e s t i c kg r i p i s presented onFigure 2.2. A f r i c t i on dev ice on the pi lot 's lever can be turnedt o adjus t the amount of f r i c t i o n and prevent t he c o l l e c t i v e s t i c kfrom creepiilg.

Control Range Characteristics

The control not ion , b o t h i n t e n s o f control displacement i n incheso f travel and angular sweep ar e presented on Figure3.1. AIsoprovided are the corresponding angular outputsa t the rotor head.

Control Force Feel Character4 s t i cs

The control forces, gradientsand breakouts f o r the primary cont ro lsare give,? on Figure 4.1.measurements a t th e50% control posi t ion.

More detailed informat ion concerning al l aspectso f the cockpit maybe sbtainad f r o m References 6.5.1 t h r o u g h 6.5.4.

The values presented were derivedfrom

Page 347: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 347/360

6.5 REFERENCES

1. Black Hawk P i l o t Manual TM55-1520-237-10

2.

3. Black Hawk Fa ul t I s o l a t i o n Manual TM55-lXJ-237-MTF

4. Black Hawk S i m u l a t i o n F l i g h s Tra in ing Sys tem Device 2038.NAKRAEQIPCEN 76-C -0086-4001 VolumeI ADDENDUM1 .

'.Black Hawk MOS 35K Avionics Mechanics Manual

6.3PAGP'

Page 348: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 348/360

SER 704%

Page 349: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 349/360

COCKPIT COMPONENTI DENTII CAT1ON

FIGURE 6 . 1 . 2 ( a )

.

...

Page 350: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 350/360

"

COCKPIT COMPONENT IDENTIFICATION,

FIGURE6 .1 .2(b)

6.6PIEf'

Page 351: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 351/360

z0H

IC(

C(

zLLwnu

I

m

a

sCI

ca.YV0u

C(

I

\ \ ' I / / -A\ w

FIGURE 6.1.3(&)

6.7PACf'

Page 352: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 352/360

Page 353: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 353/360

.C O C K P I T G E O M E T R I C D E F I N I T I O N

RE EXTIWISHER

~.~PILOT'S CHiriPLOT'S ': IN HlNWW

INSTRUMENTPANEL

F I G U R E6.1.3(c)

6.9-ASE

Page 354: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 354/360

- ~~ -

0 0 0 0 0 0 0 .o 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

~ ~ ~ O O O O O Q Q O

H I'corn '0

01)

6PTm Y Tmn

UPPER CONSOLEPmEL ASSEFBLY

FIGURE 6.1.4

U

6.1.0lqjz

Page 355: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 355/360

sl

0c;Pm

Ur05m;o00

0m r

m

Ed

I

Page 356: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 356/360

Y R t V. G

-.

-------

EIr _ -

FIGURE 6.1.6

6.12-hGE

LIJ

n

L

Page 357: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 357/360

D O C U M E N TN O . SER 70452

II

FIGURE6.1.6 (Cont'd.)

6.1 3m

Page 358: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 358/360

D\ENABLE SWITCH\

I

TRIMRELEASESWITCH-

CYCLIC STICK G R I P

. .. .

HOOKE SWITC

- -

H

r

Page 359: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 359/360

SERVO SH UT OFF

ENGINE SPEED

'SEARCHLIGHTCONTROL

@-e

*

COLLECTIVESTICK GRIP. .

. .. .

Page 360: UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

8/10/2019 UH-60A Blackhawk Eng. Simulation Program, Vol. 1, Math Model

http://slidepdf.com/reader/full/uh-60a-blackhawk-eng-simulation-program-vol-1-math-model 360/360

BLACKHAWKANGULARCONTROLMOTIONSA N DDISPLACEMENTS

High Col lec t iveLow Col 3ec t ive*** Mid C o l l e c t i v e* H* W t h C v e r t r a v e l**** .Considers Control Reduct ion

***

d u e t o r edundan t quadran t

CONTROL-P OSITIO N

COLLECT1VELowHighA

LONGITUDINALCYCLIc

Forward *Pinned**Aft ***A

LATERALCYCLIC

Left *Pinned **RightA

PEDAL-Left***Pinned ***Right ***A ***

nj I P, )

L__

-010.010.0

-

. 5.03.895.0

10.0

-5.0

5.010.0

.96

-2.69

02.695.38

-

FIGURE6.3.1

6.1 6

-22.546.5524.05

..

13.9510.8413.9527.9

-11 .63

2.2411.6323.26

-10.33

0IO. 3320.66

OUTPUT@REFERENCE ROTOR

(DEG)

AboveAbove

Neut ra lC y c l i cForwardA f tAft

Ve r t i c a l

LeftLeftRigh t

Ve r t i c a l

LeftOnRight

-

-

-

-

H o r i z o n t a l 1 QcUFF' 9.9i 25.9

16.0

BIS

16.5-11.0-12.3

28.8

AI

-8.0-1.54

8.016.0

****QTRCUFF

29.915.00. I

29.8


Recommended