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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
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-.
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
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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/
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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
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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,
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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
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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
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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 '
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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
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' 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
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F i G i J R E 3 . 1
3 . 50-PAGE
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OOCUNEHTN O . E ? 70452
I
7
F i g u r e 3 . 2
m . t
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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'
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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 .-
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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
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FIGURE 4.1
4&PAGE
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Y
z4
. I
XV
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.
F I G U R Ea . 2
4.4-A G E
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STA732
2) GENERAL ELECTRICT700-GI -700 TURBOSHAFT ENGINES
. . .
J- . WHEEL BASE(28'.IL9 ) - - -- '
- .USELAGE1ENGTH 150*.Z5'*)- - _ _
JH-60A BLACK HAWK GENERAL ARRANGEMENT
.. .
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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 .
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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
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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
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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
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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
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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& '
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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
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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
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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
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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 .
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1_= - - -
tKiiLI K O R S K YA I R C M
MAINROTORFLOW DIAGRAM
CONTROLSYSYEM
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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
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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
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SER 70452
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5.1-16Page
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O O C U M E N Tn o . 'SER 70452
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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-
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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
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VXBDOT
V YBDOT
VZBDOT
PDOT
QDOT
RDOT
VXE
VYB
VZB
P
QR
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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 .
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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
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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
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__.-
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
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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
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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
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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
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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
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' 1
O O C U M E N TY O . SZR 70452
5.1-49PAGE'
Y n m.G
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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
.._. -
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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
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.. . ._ . . ....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
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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
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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
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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
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~-- .. . . . . . ... . .. . .~... .
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
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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-
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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
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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'
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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
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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
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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 .
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5.2-6PAGPf
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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
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* a m . 0
_yI '1
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7
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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
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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
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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
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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
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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 )
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.:,-
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
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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
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- -
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)
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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 )
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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
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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
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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- * ---. _ _
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- -. . . . .... .- ,
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 '
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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 )
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.. . .- - -
.
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 )
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- -- . .
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
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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 )
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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
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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
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-
FUSELAGE {AWINGMOMENT COEFFICIENTDUETO SIDESLIP (Cont‘d)
t
. . i. . . - . - - - . ,.
. . -. . . . . . .
F I G U R E2 . 5 . 1 1 i b )
5.2-37-ace
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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 .
. -.. ..-
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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
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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
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I Vd w
5.3-5-A 6 E
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5.3-6PA G E-
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5.3-7PIGt.
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. ... . - .. - . . _. .
T
'---
5.3-8IA G E
Y 21 m. c
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5.3-9-A G E
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573
5.3-10PA G E-
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=
ZSt rOL
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5.3-13PAGE
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--- - . - - -
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 .
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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'
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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--
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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
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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
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,
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._
- -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
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-
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-
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-
c
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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
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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
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.~ . .
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
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- - -
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
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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
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- - - -
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 )
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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
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-- -----
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 )
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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
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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
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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 )
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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
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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
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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 )
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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 )
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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 )
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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 .
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II 1
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VERTICAL TAILDRAGCOEFFICIENTDUE TO SIDESLIP (Cont 'd )
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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
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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
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F I G U R E4.1.1
5 . 4 - 3m
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DOCUMENTn? . SER ?045?
5.4-5Page
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D O C U M E N Tn o . SER 70452
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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
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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
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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
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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-
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5.4-14PIGT'
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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'
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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
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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.
%=*
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( 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
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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
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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
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BLACKHAWKHELICOPTERMOTIONSENSORS
I
FIGURE5.1.2
5 . 5 - 6PAGE
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lmmpBKORSKYAIRCRAFT b
w 3
P *
Q
M
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FIGURE5 .1 .3 (a )
5 . 5 - 7-ACE
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4 5 d W S R
FROH ROLLRATE6YRO
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t 7 DLG- -.139X/DLC
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BLACK HAWK ROLLSAS CHANNELS
ANALOG
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s i i
F I G U R E5.1.4
5 .5 -10_
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F I G U R E5.1 . 5 ( a )5 .5 -11P1Gt'
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FIGURE 5.1.5(b)
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FIGURE5 .1 .6 (a )
I-zs
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D O C U M E N TN O . SER 70452
FIGURE 5 . 1 . 6 ( b )
5 . 5 - 1 5PAGE-
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- - -
OOCUMENTN O . SER 70452
y Mu
FIGURE5.1.6(c)
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I
FIGURE5.1.6(d)
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--
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
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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-
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- - -
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'
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D O C U M E N TN O . SER 7.3452
ENGINE/FUELCONTROL/DRI VE REPRESE NTATION
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Cri:G NAL FAGE ISOF POOR QUALITY
' I
SER70452
7,
1 yII .III
FIGURE6.1.2
5 . 5 . 5
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*SZKORSWAIRCFIAFT
N E 1 CONTROLELECTRICCONTROLUj4IT..-
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RIGINALPAQE E3OF FOOH QUALITY
D O C U M E N TN O . SER 70452
I
FIGURE6.1.4
5.6-7PA6f
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5.6-8-A G E
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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-
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5.6-14PAGP'
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. ... .. . . . Z X
0J
5.6-16m
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5.6-18-.PAGE‘
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5.6-19TZF
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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,
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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
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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.
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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.
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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
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y.yl _-_.
5.6-23TzF
less bladesGas generator heat s i n k f ac to r
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5.6-27-AGE
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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
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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
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. -
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
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--=--- .
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
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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
.. ..- .-
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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
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- - .. . .-_I.. - . ___..2
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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
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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
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-. _.. ............. ~ ................. _ _
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
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. .
19
2..
OF POOR QUALITY
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, .--- .---+--------,
L. L ...-- I..._..._ i
..- .."---, 1-a. . . . .-_-.-.---- , -.
BLACKHAWK- EMGINETIME VA RY I N GCOEFFICIENT
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- ~t. . . . . . . . . . . . . . . . . . . . . f .
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. . . . . . - ..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
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....... -. ...... - ................ 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
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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
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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
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:,. -
Document No. $ER 70452
BLACKHAWK- EIIGIIYETIME VA RY I N GC O E F F I C I E N T
FIGUREC.5.13
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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
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. . . . . .. . . . . ... . . . . . . . , . 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
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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
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. -- --
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
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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
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ORIGINALPAGE I3OF POOR QljALlTY
D O C U H P H TN O . SE3 70452
WiDING GEARTI RE AtlD STRUT REPRESEJITATI ON
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LANDINGMODULEAXES S Y S t n ; l
.. .. .
L. I
t
I
FIGURE 7.1.2
5.7-6Page
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7-8
d
PQ
u7PAGE
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I
Ti
SER 70452
5.7-8m
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5.7-7 0Page'
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. _ ~ . I " _.... _ ._._._.._........ .I.I . ,_ c - - - - - -
- . . . .
II I
1 ' : ' ' t . I ' i
5 .7 -1 1
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- ~ -- ' I
SER 70452
5 .7 -13Page
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ORIGINALPKtikOF POOR QUALIW
SER 70452
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ORIGINALPAGE fSOF POOR Q5ALITY SER 70452
I'.'CC*I
5.7-1 5Paqe
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SER 70452
......*I
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@
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. .I I I
5-7-20rage
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5.7-21
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D=
7F2VE-d
7
-
5.7-23PAGP-
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%7 *
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r. - -- - -
5.7-26PAGE'
- , , e.----
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D O C U M E N TN O . ' SER 70452
5 . 7 - 2 7--iPAGE
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.)
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,
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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-
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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.
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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
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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.
-- - -.
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.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
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- 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 .
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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.
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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.
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>' .
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.
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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.
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5.7-40PAGO'
m 2) av.
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Y 29 m. E
5.7-41-A G E
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5.7-42PAGE
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5.7-43--IPASE
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5.7-44-AuE
Y 29 m. c
.
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r
-t
Y 29 m. 5
5.7-45m
D O C U M E N TN O . SER 70452
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5.7-46-A G E
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1
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f
i
i;
. 5.7-48_..
1 - . -
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5.7-49
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vr. - 1_ ..... - . . . - .. ,. ...
-
5 . 7 - 5 0
SER 70452
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SER 70452
i 1
(*)-’
,..._.I..,,
5 . 7 - 5 1
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. . .- . . . - ~ -7 : - , . ,,. I . ,. - - . , . . I T 1 - , : - . I 1 . 1 I n - 7, . , . , . ,
5.7-52
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--ORIGINALPAGE F9OF POOR QUALIW SER 70452
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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-
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.
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
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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
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5 . 8 - 4PASE '-
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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
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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
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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
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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
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.._- - -
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
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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 $kw, ue t o apparent frequency shif tsi n the gust spectrum.
5.9.1
5 ePA G E
y\ 29 REV. C
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VA L I DFOH DISCRETEFUNCTIONSONLY
Figure 5.9.1.1
5.9-5AGE
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D O C U M E N Tn o . SER 70452
.e-
q$ W G v;wo
I CHotrV 2 x G : o t t
W
' .Figure 5.9.1.2
5.966PAGE-
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'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
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Y 29 R t l .G
D O C U M E N Tn o . SER-70452
nr. --
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. .
” -
D O C U M E N TN O . SER-70452
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5.9-11PA G E
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D O C U M E N TN O . SER-70452
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ic
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3 3 1 V d
P F s
r- -*
‘ O N LN3Hn304ZSi70L- 83
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c
. *i . =
3 W d-SI-6 S
L
d
7
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1 5.9-17-
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--
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
. _._
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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
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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)
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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
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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.
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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.)
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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
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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
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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.
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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 '
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-----,1
SER 70452
5.10-5v
PAGE
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5.10-6p1Ba'
r n m . 0
- ' - - - - *
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f i g = fk 7f
. .-# ..
5.10-7m
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------ ---
I
i
4
- .-
5,1098-AGE
u n v . 6
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,38Vd
6-0 'Ei
,-,'
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5.10-10PAGE-
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. . , -
5.10-11PAGE-
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O O C U M E N TN O .
I .
SER 70452
5.10-12--Page
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_ _ _- - .
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.
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, . . .. - .
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-
...
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'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
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---.-----
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
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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 .
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- 7 ' '
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---
/ / /7.
T i - - = -
5.10-20PAEE'
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-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
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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
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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
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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'
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SER 704%
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COCKPIT COMPONENTI DENTII CAT1ON
FIGURE 6 . 1 . 2 ( a )
.
...
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"
COCKPIT COMPONENT IDENTIFICATION,
FIGURE6 .1 .2(b)
6.6PIEf'
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z0H
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C(
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FIGURE 6.1.3(&)
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.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
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- ~~ -
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
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Y R t V. G
-.
-------
EIr _ -
FIGURE 6.1.6
6.12-hGE
LIJ
n
L
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D O C U M E N TN O . SER 70452
II
FIGURE6.1.6 (Cont'd.)
6.1 3m
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D\ENABLE SWITCH\
I
TRIMRELEASESWITCH-
CYCLIC STICK G R I P
. .. .
HOOKE SWITC
- -
H
r
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SERVO SH UT OFF
ENGINE SPEED
'SEARCHLIGHTCONTROL
@-e
*
COLLECTIVESTICK GRIP. .
. .. .
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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