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NAVIRADE-VCEN 1205-3

TABLE OF CONTENTS

Section Pg

INTRODJUCTION . . . . . . . . . . . . . . . . . . . . . 1

II ASPECTS (OVETUING Tlh CHOICE OF THE OPTIMUM ANALOGOOMPUTER . . . .. . .. . . .. 0 0 0 0 a. .. 6.. . . . 2

A. AIRCWAlT LATA COhVSION FOR USE IN THE COMUTER 2

B. SIMPLICITY OF SIJLATION EQUATIONS ........ 3

C. COM PTER FEXIBIL17Y .. S.......... . .. 4

E. CHOICEOCARERFC..... ............. • 5

. AMPLIFICATION S . . . . .. . . . . . . . . . 9

2. INTEGROATION . . . . . . . . . . . . . . . . . 10

3. MU'LTIPLICATION .......... • . • • . • 10

4. TRIGONOI• TRIC RESOLUTION........... 10

5. FUNCTION GNRMATION ..... . . . . . 10

III MECHANIZATION OF EQUATIO::S OF NOTION . . ... . .. 12

A. GENERAL EZN.AN..ZATION........ o 12

B. HELICOPTER MECHANIZATION............ 26

1. SINGLE ROTOR HELICOPTER ........... 26

2. TANDEM ROTOR HELICOPTER . . . . . . . . . . . 54

C. V/STOL MCHANIZATION .... . ...... . . . . 61

1. SIMILARITY OF V/STOL EQUATIONS . . . . . . . . 63

2. TILT-WING MECHANIZATION ... ........ 65

IV SUMMARY

A. AIRCRAFT DATA CONVERSION FOR ISE IN THE COMPUTFTI . 97

B. SIMPLICITY OF SIMULATION EVUATIONS . . . . . . . . 97

C. COMPUTER FLEXIBILITY ............... 97

NAVTRADEVCEN 1?05-3

TffEOF CCNTFVTS

Section

D. C0OPUTATI I O OAL3EE.. ... . ......... 898

E. C110179R.A H OF CARRIE . . . . . . . . . . . . . . . . * 9fiF . CHOT'j"E OF SYSTEM . . . . . . . . .98

v 3IBLIOGRAHY .. . . . .. . . . . 99

VI •JOG,- fLATlJRE AND EUATI 0'Lr .... .......... .

A. HELICOPTER . . . . . . . . . . . . . 100

I. NOMENCLATURE . . . . . . . . . . . . .. . 100

2. HELICOPTER SIýIJLATION EQUATIONS ...... . 108

B. V/STOL AIRCRAFT (TILT-WING) ........... 131

1. NOMENCLATURE USED IN XC-142A EWUATIONS . , , 131

2. TILT WINO AIRCRAFT SIMULATION E'IATIC( . . . 133

0

NAVTAI A:,CL:: 12O5-3

LIZT )F TAMLES

Comparison of Fied I-ling and Helicopter ?Pacimum

Angular Rates and Accelerations . . . . . . . .. . 6

2. Block T-rmino>[v . . . . . . .I 4

3. Sy,,%ols Used it, ".echanization ......... . 15

)•, •'ler Lnizlc Tabn,,lnt.'- ...... .. • 9

5. Wind Resolution Tabulation ......... . . . 23

6. Aerodrnaic Variables Single Rotor Helicopter .... 30

7. Tal Rotor Aerodynamics . * .......... 31

8. Fuselage Aerodynamics ............. * • 34

9. Local Vertical Velocity. . . ........... 3•

10. Tangential Velocity . . . 37

OII. Blade Angle of Attack ..............0. 40

12. Blade Element Flapping Moment and Lift . . . . . . . w

13. Bl&de Element Drag and Main Rotor Torque . . . . . . 44

14. Flap Angle Coefficients and Main Rotor Lift . . , . ,

15. Rotor Hub Noments .... ...... ... . . .# 47

16. Rotor Forces and Angular Velocity . . . ..... .

17. Force Summations . . . . . . . . . . . .. 50

18. Single Rotor Tabulation . . , .... .... . 53

19. Single Rotor Summnary ................ 54

20. Single Rotor - Tande lotor Comparivon .. ... . '.5

21. Additional Components Tandem Rotor Helicopter .... 61

22. Tandem Rotor Summary ....... .... .... 62

23. Tilt-',Jing Aerodonamics Tabulatien Plock (),) ... . 9L

2L. -' tibulation .... ....... .............. . 5

S25. Tit vin[, ':u u'ry ..................... . . . . 96

iii

:.AVTRAI VCEI2' 12-3lISd 01F• ILLU)ST[•TIOINS

Figure Page

1. General Dlock Diagram............... 13

2. Center of Gravity (c.[.) Ti-ss, and Inertia . . . . . 17

3. Velocity Integration PC 1.echanization . . . . . . 18

4. Block (10) AC Mechanization ............ 20

5. Euler Angle AC. Neaanisation. . .......... . 21

6. :iiler Angles XC fcALat~on. .......... 22

7. Velocity Summation and Wind Resolution . . . . . . 2L

8. Velocity Summation and W1ind Resolution DCMechanization . . . . . . . ... .# .* • o 25

9. Siraiified Block Diagram Single Rotor Helicopter . . 27

10. Aerodynamic Variables .. *... . . . . . . .. .@ .@ 28

Ii. Tail Rotor Aerodynamics . . .* *. .a * , .a. 32

12. Fuselage Aerodynamics AC MOechanizaticn . • . • . . . 33

13. Simplificd Block Diagram , ..... .. . .* 35

14. Local Vertical Velocity . ..... . . . . . . . . . 36

15. Tangential Velocity . . . . . . . . . . . .... . . 38

36. Blade Anrle of Attack . . ....... . . . . . . 39

17. Blade Elcment Flapping Moment, and Lift . . . . . . 41

18. Blade Elemint Drag . . . . . . . . . • . . . • . . . 42

19. Blade Element Drag and Main Rotor Torque .. . . . . 43

20. Flap Angle Coefficients . .e.t.. • .* @ • e * * 45

21. Blade Flap Angle AC Mechanization ... . . . L 46

22. Rotor Hub Moments . . . . .. . . •. • . . . . h8

23. Rotor Forcee and Angular Velocity . . . . . . . . . . 49

24. Force Sunmations . . . . . . • . ...... . • • 51

25. Noment Summation and Angular Rates . . . . . . . . 52

iv

NAVTAL¼EVCEN 1205-3

LIST OF ILLUSTRATIONS

26. Swash Plate Angles and S.A.S ........ . . . . 58

27. Aft Rotor Terms, Tandem Rotor Helicopter ACMe!cchanization ... . . . . . .. a . . .0 # 0 * a 59

?V. Tsndem liotor Angulnr Velocities AC iechantzntion . .

29. Simplified glock Diagram . . . . . . . .. .. 66

30. Aerodynamic Variables AC Mechanization ....... 67

'11. Prope...r Ae-dynAmC,'q Velocities AC Mechanization 69

31b. Propeller Aerodynamics Velocities AC Mechanization 70

32. Propeller Aerodynamics Advance Ratio AC Fk6chanization 71

33. Propeller Aerodynamics Coefficients ........... . 72

31t. Propeller Aerodynamics Coefficients AC I*chanlzation 73

35. Propeller AcrodyrnPiics Tn ,nrn O AC Mechanization . 7b

36. Propeller Aerodynamics , MnP Nn and Yn AC

I4echsnizntion ....................... 75

37. Propcllcr A•erochrnrIcs Y amd N Components . . • 76

3P', Propeller ;Xcrodynnmics Forces A'! ilechaniztion . . 77

39. Proreller Aerodynm!c 1fomrnt - (61 ) AC Mechnntztion 78

hO. Propeller Aerodynamics. Moment - (t0 )p G0

Yech,-nization..................... 79

)Jt. Propeller Aervvn,-mics !',*ient - (AN )P AC

Lech.anization . ...................

Wirr Aerodyn.'mucs a , V. ... .............. S1

)t3. Wine Aerodyvn-nicn Coefficients AC Lcchanization . . 2

4n4. - Aerodn.nmics Coefficients AC M'chnnizAtion . . 83

145. Wing Aerodynsmic., For!-e.s -nd ctIaents A'Mechanization ............... .................. P4

Il. Vertical Stabilizer Aerodynnmmcs F-)rce and 'lomentsA'; NchC niz tion . . . . . . . . . . . . . . . P5

V

NJ'vTR•,",,12,E: ! 2J-3

LIST OF nI" A'rR AT I(I'S

Fig~ure e

L7. horiortAl Stabilizer 86

Lp. Tail Rotor Aerodynamics Force and Moments(Sheet 1) AC Mechanization . . . . . . . . . . .

L9. Fuselage Aerodynamics Forces and Moments ACMechanization ........ .................... . 89

50. Force 7 Moment EAC Mechanization ............. . 91

51. Integrntior - Veloclte- (U, V, W) AC Mechanization 92

Lrte~r-ticn - ýn!-ular Velocities (r, I], r) PC1-echanization.................... 93

vi

NAVvRAMVC': 12O0-3

rwItUCTION

The economical production of hellcepte4r vimAlators is a coorlex prob-Jon in which experience is not an widespread as in the fLxad-vir4 field. rhosimulation of small perturbation reaction as practiced by helicsrter *anu-faoturers s be sufficient for their purposes, but it is impossible toertend this approach to the unrestricted cam without gross modifications.As a matter of history, them ard~fications r-,pesred to be of such magnA-tude that prior to the design of the first full flight regim helicoptertrainer (Dpvioe 2F5, R-37A Helicopter) 'par, Inc. sought a nore ana-] 1 tioal #chem for the expressions of helicopter flight. The lnvewtigationtook full advantage of earlier wori performed at 4ACA and various otherinstitution* and agencies. As a result of this effort te PKodified SladsElent Approach was developed and was further expanded and improved duringthe development of the R9S-2 WT, pEvioe 2?64. Further extensions andsimplifioations of the technique werv then applied to the HiB-i OFT.Device 2••T5. The equations utilised by the Modified Mlade Element Approachare developed in reference 1.

A varieV of sources have, in thq past established criteria for theselection of computer components and seytems for aircraft siml•lation.Their diagnosis has been thorough and well-establishod. Mark B. Connellyin Computers for Aircraft Sliulation, port 7591-R-2, developed underOQR Contracts W5 ori-078 95 and N61339-J4, produced a remarkable presenta-tion of anal.og computer omponent analysis. No attempt will be NM* hereto repeat or improve on tha. analysis. References will be made to Mr.Connely's report and in places injections of practical consAderationsand variations imposed by the chosen method of heieupter simlationwill be made which influence choices of cocpuver components. After areview of co3quter comonents, the chosen comonents will be employedin the simulation task.

1

NAW'RATEVCEN 2205-3

SECTION II

ASPECTS GOVERNING THE CHOICE OF THE OPTIMUM ANALOG COMPU'IO

This volume wili present recomandations derived from the study ofthe iaxiOAtion equations as set forth in Volume I and II. The *ecos-mendationiT are intended as a guide to the selection of an optimaum analogmechanisatior. for the single rotor helicopter, tandem rotor helicopter,,and tilt .4ing slimulat ion equations. No attempt will be made, here topresen~t an analrsis of analog computer characteristics. Sufficient studyreports exist that, adequately present the details of analog computertecbLmiquas,, and reference will be made to these reports in support ofcertain technique selections in the optimisation of the aschanisations.

In the selection of a comp~uter type to be used for aircraft simala-tion purposes thcre am~ several factors that must be considered to arriveat an optimam selection. The optimum comupter must have, first of afl, ameana of communication in order to accept inp~ut data which describes thesimulation problem and defines the Aircraft operatic~nal characteristics.Secondly,, the uimulation equations which describe the problem parmetersmiast be able to be simplified to the extent required by the problemaaurac7 and still be expressed in the uuohtne language. A third *on-sideration is the need for computer flexibility in order to accept theanticipated aircraft manufacturers design changes. The computAtionalsequenc6, dictated ty the optimim use of oomponents and the ty'pe ofcoqmuter,, is a fourth point of consideration. The fifth and most im-portant factor is the choice of carrier to be ised in the computer.

A.* AIR~CRAFT TITA CONVERSION FOR USE IN MI' COMPUTK

Considering the first point mentioned above, it has been the writer'sexperience that the aircraft data supplied ty the adrcraft mawifacturersis, of necessity, empirical In nature. For instance, the coefficient, oflift versuzs angle of attack curves for rotor airfoils are plots of windtunnel empirical data. Since this data is predominan~tly empirical andpresented in tbe form of smooth curves as flunctions of' one or two varia-bles,, the introduction and storage of these functions is particularlysuited to analog function generation techniques.

These techniques, as the reader veil knows ame manifested inseveral different formu such as tapped or sh"4e potentiometers or someform of electronic f'unction generators, such as diodo ftuuction genera-tors.* These techniques usually produci straight line approxiustaions ofthe desired function. The accuracy of the approximation is determinedby the ntumber of break points selected during the dosigui.

The person selecting th. met-hod of fanction genieration to use inthe computer shouli take into consideration~ Uie required simulationaccuracy and flexibility of the chosen mwthod as %ell as cost considers-tions. 11e prostent state-of -the.-art, Creference i4) provides the servopotenti ometer as the west economical means of generating slowly vary-ing

2

RiVTRA3VCEN 1205-3

functions, like the aerodynandc functions required in OF/VMT' s. Theelectronic methods provide a mre accurate and flexible method but at ahigher coat.

The optium choice of function generation recomended for the V/8TLsimulation then is the servo potentLometer, since this In the most econom-ical method and provides sufficient accuracy for the desired simulation.Once the choice has been made to use potentiometers the data conversionaspects do not bear ar7 further on the choice of the computer sincepotentiometers are equally usefUl in either an AC or DC carrier computer.

B. SIMPLICITY OF SIMULATION EMATIONS

The mechanization of unabridged equations of notion for an OFT willproduce a needless superfluity of equipment that is completely out ofproportion to the amount required to provide adequate training. Conse-quently it is highly desirable to simplity the equations of simulationto the extent that an optima balance exists between the informationsupplied by the equations and the information required for training pur-poses. For instance, in Volume I (reference 1) equations 5-25a, b, abd cgive the complete expressions for velocities in the X body axes as

X% a /-- g sin e + Vor - Woq) dt

vo a g4 coo e sin 0 + wop - Uor) tMi

zWO gT 1 cos e cos 0* ÷ Uoq - VGp) dt

In order to simplify the expressions and provide a less complex

mechaniation it was noted that U0 is usually the predominantly large

vslociiy. Consequently the contributions of the VG a&M W cross-

coupling terse s be omitted giving the final expressions

U0 a A!- g sin 0) dti

TV-) A i+ g coso sin 0 - Uor) dt

wo = A-* g cos 0 cos 4 + U~q.) dt-i

as given by 5416 of Volume 1.

RAVTmVCIN 1205-3

Although this simplification does alter the validity of the expres-ionsi the errols aused in the final velocities are negligible and not

deteotable by the student and consequently the sawe training value inobtained with loes hardoare than if the simplification had not been made.In this moaner, the balance between input and output informtion isachieved.

The extent of simulation required by the trainer specifications isthe limiting factor that controls the extent of simplification of thesimulation equations. In general, the hardware reduction bears a directproportion to the amount of simplification of the simulation equations.Consequently, the simplification of the equations does not influence thechoice of the computer but only reduces the complexity of the finalmachanisation.

C. 0KPUM FLUI BILITT

The flexibility of a computer is the ease with which the computercan be reprogrammed to perform a different computation. In the designof OF/VT' s the procuring agency usually desires the development of thetrainer to be performed concurrently with the development of the aircraftbeing simulated. This necessitates a close liaison with the aircraftmunufacturer in order to keep abreast of design changes required duringthe aircraft development. Consequently, the design of the OF/WT mustInclude a consideration of the flexibility of the selected computer inorder that airframe design changes mmy be quickly and efficiently in-corporated into the OF/Vff design.

Fortunately the changes made by the si rframea a•facturers areusually slight modifications to the numerical functions describing theaesrornazics, such as the coefficients of lift and drag. In an analogcomputer these functions are formed by tapped or shaped potentiometerson the various servo shafts. A change in these constants would resultin OF/WST modification to the associated potentiometers and amplifiergain adjustments. If as in section II.A the choice is made to usepotentiometers as function generators, no flexibility advantage isrealised in either an AC or EC carrier computer. Consequently, theflexility consideration does not affect the choice of analog computerfor the OF/lST.

D. COMPUTATIONAL SEQUENCE

The computational sequence formed by the interconnection of thecomputational elements directly affects the optimum use of componentsno matter what tVpe of computer is selected for the OF/WT. This isobviously true if one considers the result of forming a computationalsequence without regard to optima component use. For exzaple, theexpression for the HSS-2 landi gear pitching moments is given inVolui I as

mi - 4.38(Faf + F ±) 3.99 *I 5.36 LW

0

NhLV'TRA!ErVCrN, 1205-3

This could be mechanized by first forming (F~ *W F I) as the output of

a sumtdng amplifier and then scaling Ls.38 (F~ eW+FL at the input of a

second muidng amplifier which sums 4~.38 (FRW * j with -i)8.99 F .W

5.36 X,,, Obviousl.y the optiimum sequence that should be used here is to

scale I4.38 P R and iL.38 ?LW sepa~rately into a single wuminng amplifier

with -18.99 *T 5~.36 X.~ and thus eliminate one uuzwiing amplifier.

Whila this is an extremely obvious example it does illustrate the valueof sequence considerations for component optimization,

Computational sequence also affects the extent of simulation achieve,-ble with a given computer. Since a finite response time is inherent ineach individual comptutational element, the accumulative response time ofa complete computational loop must be matched to the response times of theaosteiu being uimimlated if a realistic simulation is to be achieved. Forexampleg the CH4~6-A tandem-rotor helicopter response is such that a 1.58inch step input of longitudinal forward stick deflea tion will produce asmeimimat pitch acceleration of 24s degrees per second ,and the time toreach this mxiuma acceleration is 0.33 seconds after initiation of thestick deflection. If the simulator is to present a realistic simulationof this computational loop the pitch rate servo,, ql1, must exhibit atleast the response Indicated above,, if a similar stop inrput to the longi-tudinal stick is applied to the siu1lator. This will certainly occur ifthe coqmptational sequence is arranged to minimize the computationalelements and the response time& of the q, integrator shaft is scaled toproduce the required loop response.

Thus, it Is evident the computtional sequence is an extremely im-portant aspect as far &as obtaining a mininmi component quantity for anoptimla response match. However, it hap very littl-3 bearing on anoptimium choice of computer type, as an AC or DC carrier.

E. CHOICE OF CA.RRIEJR

The choice of the carrier to be used for a particular simulationcomputer design is by far the most Important aspect to be consideredin the selection of an optimaiu computer. There are three possiblesolutions that Wa be decided upon. They are, namely, an AC carrier,a DC carrier or a hybrid AC-DC combination. Oune additional decisionmest be made in the event an AC carrier is to be used,, and that is thefrequancy of the AC carrier.

let us first consider the AC carrier computer and decide whichfrequency is best suited for application in V/STOL aircraft simulation.The most stringent requirement of the computer Is the response charac-terietics dictated by the angular rates and accelerations of the air-craft to be similated. Table I is a comparison of mx~imi rates andaccelerations of fixed wing and helicopter type aircraft. The fixedwing aircraft values are taken from the KlIT-Whirlvind and the Goodyear-Cyclone program (pages 174i-175~, reference 41). The helicopter angulAr

5

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C-SOZTWARTMO

NAv'rRh.UCEN 1205-3

rates and accelerations are those used in the P188-2 flight trainer andthose furnished to Melpa bry 'Vertol Division of Boeing Aircraft for theCHis6-.A flight trainer. It is easily seen that there is a great differ-ence in the mszim- response capabilities of the fixed wing aircraftand the helicopters chosen. Likewise there is a variation in the oompu-tational sped requirement of flight simulator comp~uters for helicopterand fixed wing aircraft.

Assuxiing that the response of a 60 cycle system is marginal infixed wing applications, it can be seen in Tab1o 1 that a 60 cyclesystem is better than uimply marginal for helicopter simlation sincenone of the helicopter angular rates and accelerations in Table 1 areas large &as the fixed wing rates and accelerations. Note that #

4,r and :P are not too different from helicopter to fixed wing, however

there is a marked difference in p and 0. The required comput~ationalspeed is based on the highest single rate and acceleration,, i.e. rollrate and roll acceleration for the fixed wIng aircraft.

Chapter IT,, page 25 of reference 4s gives an analysis of servo systemisand concludes that 400O cycle servos should result in a servo responsethat is three to four time better than is possible with a ooqparable 60cycle system. This is quite true,, an. )ne usey wonder why bother with 60cycle systems if 400O cycle systems o~fer such improvement in response aswell as accuracy and size. Both large and mall coqputera hae" =cccess-fuVly utilized 400O cycle systems. For eza spl, operational airbornecomp~uters are predomi-santly 4~00 cycle systems, also large operationalshipboard fire control systemts operate from a 4s00 cycle carrier. If mochsystems are developed, then why should flight trainer mewufacturers behesitant to discard a 60 cycle carrier systemi? Unlike the manufacturerof operational tactical systems the flight trainer smanfacturer does notdevelop f~ ight trainers with weight and size reductions as a primes designgoal. Neither does the prototype serve simply as a production model.What argument then can induce a simulator mwf acturer to discard anoperational 60 cycle system to develop 400O cycle systems with littlehope of operational improvemint? Before discussing this developmentconsider another point before the problem is considered from a broadviewpoint. Suppose the case arises where the carrier sysutsm explaWeintrodmoes reduced fidelity into the system at maxi~ma aOcciertions,, butoperates at a sufficiently high response to follow satisfactori" thehighest accelerations or rates that one would normally expect-.which nobe quite different from the maximumi. Compared to other aspects of thetrainer how important is maximum fidelity in this extreme operatingregion? These regions are most often reached just before a crs,"situation oocurs. Very little,, if azu, actual training Is acoccqlishedat the extreme operation region of the aircraft. Regardless of the im.-portance of highl~y accurate simulation in these area., the decision.concerning the choice of carrier frequency are based on a balance ofperforumince and cost.

P~rorssing from the earlier assumption that the response, of eithera 60 or 00Q cycle system is sufficient for helicopter simalation, but

7

NLVTRAMVCEN 12o5-3

that a 400 cycle carrier offers a greater response margin of safety,consider some other factors that affect the choice of carrier frequency.Factors influencing carrier frequency choice are listed on pages 26 and27 of reference 4. The statements contained in reference 4 are verytrue but the injection of some practical considerations may lead to amore selective choice of carrier frequency. The seven factors whichfollow are similar to those listed in reference 4.

i, 60 cycle power is widely available; 400 cycle power must begenerated at the OFT in kilowatt quantities and in some ca3es, withundistorted waveshape and carefully controlled phase.

2. A 400 cps carrier produces a smaller and lighter weight computer.

This, of course, is the primary reasoning behind the adoption of a 400cps carrier for airborne and shipboard equipment, but is seldom highlyinfluential in flight trainer design unless space for some special reasonis at a premium.

3. The problem of phase shift (due to stray capacitance and in-ductance) and pickup is more Mkely to occur in a 400 cps system thanin a 60 cps system. As reference'4 points out, pickup may be elininat-ed by proper engineering precautions such as the maintenance of lowdriving irpedance levels, shielding, and careful placement of wiring.This sounds easy to accoplish, but the consideration of the practicalaspects of the accomlishment a be enlightening. We must rememberthat OFT prototype development periods are commonly 16 to 18 mon'he, andthe present trend is toward fixed-price contracts. shielding, for ex-ample, should be avoided whenever possible for a number of reasons.First, shielded wires produce as mwa maintenance troubles (which leadto an increase of computer cost with no increase in design) as anw othersingle factor, particularly in the course of prototype debugging, wherewiring is constantly being flexed. The ferrules at the end of eachshielded wire cut through the insulation shorting the conductor to theshield and consequently to ground. Each time this occurs, the traineris turned off and check-out halts. Components are also lost, particularlypotentiometers where the wiper becomes grounded due to a fault in theshielded cable. Shielded cable is also costly, bulky, stiff and general-ly very difficult to work with particularly in large quantities. Anotherpoint to consider here is the difficulty of simultaneously reducing straycapacitance and using shielded cable. Available shielded cable has acapacitance of approximately lOoMf per foot. Extremely long cable runeare sometimes necessary especially in two trailer trainers. If thesecable runs are shielded then gjuffer amuplifiers must be used to reducethe source impedance sufficiently to minimise phase shift. High im-pedance wire-wound potentiometers also produce conditions (high sourceimpedance and high inductance) which leads to further phase shift.

4. The fact that most aircraft instruients utilize a 400 cyclecarrier is of no consequence since a 400 cycle synchro transmitter maybe driven by a servo operating on arn desirable carrier. With thepresent trend of reducing GF'!, instrumnts are generally built to anycarrier specified by the contractor.

8

NAVTRAIEVCEN 1205-3

5. Amplifier design for a 400 cps system will be simpler in thatthe lower sideband component of any reasonable signal does not approachzero frequency as it may in the case of a 60 cps system. Particularly inthe case of transistorized amplifiers, a 400 cycle center frequency iseasier and cheaper to obtain than a 60 cycle midfrequency.

6. Tachometers to .03% linearity as discussed in reference 4 arevery expensive and greatly exceed the requirements of present-day train-ing devices. Tachometer linearities in the order of 1% with zero speedvoltages as low as 9 millivolts are much more comnon. These ay be =ore

cheaply obtained either as 400 or 60 cps units.

7. The seventh factor discussed in reference 4 states the advantagesof using magnetic amplifiers to reduce the power and maintenance require-ments. The following reductions were realized in a study by GoodyearAircraft Compaq7: number of tubes--54.5%, power consumition-56.25%,size--46%. Since the advantage may be realized only while employing a400 cycle carrier, it is implied that this is an advantage that should becredited to a 400 cps carrier. A good deal of these advantages aredependent upon the size and characteristics of the tube type amplifiers.There is also the unanswered question as to whether or not a conversionto transistor circuitry would not have produced equivalent or largerreductions of maintenance and power consumption.

It is recommended then from the above that if an AC computer isselected for the V/STOL mechanization a 60 cycle system should be chosen.While it is true that a 400 cycle system would provide a definite advan-tage in response ane accuracy, it is felt that these advantages are over-shadowed by the reducee response requirements of the V/STOL aircraftfrequencies. Also the de-emrhasis of computer size restrictions insimulators and the maintenance and phase shift problems introduced by400 cycle carrier further enhance the 60 cycle carrier choice.

Having selected the frequency of the carrier in the event that anAC computer is chosen the choice must now be made between an AC carrier,a DC carrier, or an AC-DC hybrid computer. First, let us me a cocas'-son between AC and =C computers on the basis of the various computationaltechniques. Reference 4 gives an excellent discussion of the relativemerits of AC and DC techniques. A summary of each of the discussionsis presented here in support of the choice between AC and DC computersfor the V/SIOL mechanization.

1. AMPLIFICATION. Amplifiers occur in very large quantities inOF/WST analog computers due to the fact that they are used in ao mazndifferent applications, such as isolation, summation, servo motor drive,inversion, etc. Consequently, the AC amplifier is afforded a large ad-vantage over the DC aMplifier in quantity required for a given mechani-zation, since the AC amplifier can produce both polarity outputs byvirtue of its center-tapped output transformer. The MC computer requirestwo separate amplifiers whenever both signal polarities are required.Also DC amplifiers have an inherent drift problem and require a specialconsideration in the design to insure that adequate regulation is

9

NAVTRAZVCEN 1205-3

prvdad by the power cupplies. This is not required during the designof the AC co~mpter. Mea also to the dri.ft problem,, DC az~lifiers areusuallY mor oomplmx, since stabilisation circuits are required. Theo00y adMantae of the DO amp~lifier over the AC amplifier is its abilityto for& various transfeor functions by the use of paesive nstwork, Conse-quently, the advantage definitely lies with the AC computer as far asamplif ication is concerned.

2. INTERLTION. VC electronic integration techniques have several.decided adva.tages over AC servo integration methods. The EC tech-nique can integrate much higher frequency signals, have a much higherdynamic range,, have a smother output,, cost less and require less spaceand power. One featuroe, however, prevents them from being suited toMF/W9T application. That is their inability to perform long term openloop integration@ as is required in the Integration of the Ruiler anglederivatives for instance. This application requires an angular outputof unlimited ranzge which can only be obtained with servo integrators..While a MC servo integrator can be used a DC tachometer is required toprovide a response better than an AG servo integrator. Unfortunateoly,this increases starting and runninag friction. As far an integrationtechniques are concerned then AC servo integrator. are slightly moredesirable for the V/MOL machanisation.

3. ?UTLTPIMC&TION. No advantage Ilies with either AC or DC arstems iniperformi~ng inat4plicaton operations,, since nothing can compete sconomi-cally or from, the standpoint of versatility with the servo potentiometer*

4,* naw ~TRC USOILYTION. The use of AC resolvers for ooordinateresolution as opposed to sine-cosine potentiometers provide@ greateracowray,p greater resolution,, longer life,, and less friction. If thepoorer conformance of aime-cosine potentiometers to the tri-gonometrictuiction. can be tolerated then trigonometric resolution can be acca.-pUmbed In an AC qrstem sor economically using potentiopeters ratherthan resolvers. This can be seen by considering that both the re-solver and the potentiometers reqtire two iziput and two output ampli-fiears. Sven though it's true that the running of components takesplace internally in the resolver,, the potentiometer outputs can besm-iad in the succeeding input amplifiers. The AC techniques defi-nitely have the advantage here.

5. FWCTON aDMATI0I. Economically aind versatility-wise thi smervopotentionster has the advantage here. Consequentljy, AC or VC systemare equally optimam since potentiometers can be used in either system.

On the basis of the merits of the computing techniques describedabove it appears that the AC carrier coomputer would have the advan-tage over the DC carrier compter in the maohani sation of the V/STOLaircraft. In all of the areas discussed, except function generationand multiplication,, the AC methods would appear to be the more optimum,in the mechbanization of sons of the supersonic fixed wing aircraft,where the signal frequencies that would be encountered were expected

10

NAVTR&eVCEN 1205-3

to be much higher th&n one or two cycles, some of the tqbrid methods ofDC integration followed by an AC position shaft or DC electronic functiongeneration might be more applicable. In general, it has been the experi-ence of the writer that if the requirements of the simulation problemare such that either an AC or DC carrier computer is adequate to performthe simulation, then the only thing that is achieved by combining AC andDC techniques is additional equipment. This additional equipment isrequired to make up the AC-DC interface.

It is therefore recommended, on the basis of axamination of themerits of the various techniques, that the optimum mechanization forthe V/STOL aircraft would be a 60 cycle AC computer. Section III willexamine the mechanizations in detail from the standpoint of optimusequence and optimum cost and complexity.

11

NAVTRAEVCEN 1205-3

SVCTION III

1LCHANIZATION OF EQUATIONS OF MOTION

A. GENERAL MECHANIZATION

This section deals with the mechanization of the equations of Notionfor helicopter and V/STOL aircraft. The mechanizations of these aircraftwill reflect the use of 60 cps AC, 400 cps AC, DC and possible AC-DC hybridcarrier frequencies, however the flow charts in this section are developedfor an AC mechanization with explanation of additions or deletions tothese flow charts that are necessary to form flow charts for DC and AC-DOmechanizations. To aid in this extensive task a general flow chart inde-pendent of aircraft type and applicable to either helicopter or V/ST5Laircraft is developed. In Figure 1 areas of mechanization are the blockscontaining a bracketed number i.e. (1). The second task is then to developthe blocks in Figure 1 that are dependent upon the particular aircraft type.This leads to the helicopter and V/STOL mechanizations. Tabulations of thevarious components necessary to mechanize the various blocks in Figure 1 willbe made as a function of AC or DC mechanization so that conclusions regardingoptimm mechanization can be made in Section IV.

Before developing the blocks in Figure 1 that have identical repre-sentation for any aircraft in this section, a few ground rules will beestablished. Inputs to a block are described by arrow heads intersectingthe blocks and outputs are defined as lines intersecting a block. Table 2contains definitions of numbered blocks in Figure 1 and Table 3 establishesthe meaning of the symbols in the mechanization flow charts. In the actualmechanization all inputs for a particular flow chart are assumed to bepreviously generated. Each block in Figure 1 will be considered in thefollowing paragraphs.

Block (1) - Pilot Control. The signal inputs that will be shownfor the various aircraft will be due to control stick movements. Theparticular signal inputs will be observed as inputs to Block (4) for eachaircraft described. Inputs to Block (2) are not considered.

Block (2) - !nins Simlation. The signal inputs to Block (4) fromthe &Wine I~lation representiWe required performance output parameters.Siualation of engines is not described in this report; only the specificoutput terms necessary for the simulation of the particular aircraft.

Block 03) Aero Variables. The aerodenamic (Aero) variables aregenerated by signals that complete the major loop in the cogmter repre-senting the aircraft equations of notion. Block (8) for the V/STOL air-craft and Block (12h) for the helicopters feedback the velocities U, V andW to Block (3). Block (10) or Block (12) feed back the pressure altitude(hp) to Block (3).

Block (41) ero Terms. In this block the aerocdnanic equations areformied that wl resiat M n the generation of the aerodynamic forces (I

Ta amd Za) and moments (Las, % and %). The mechanization representi

12

NAVTRADEVCai 120C-3

I k* fj -

44,

07

L 3C

TI- _ _ _ _ _ _ _ _ _ _ _

r-- r-

IM

'-4

4-1'

'-4 *s5.

b~4

4)G

Figure 1. General Riock Diagram

133

NAVTRAMVCRR 1205-3

XOCK HMA•CO0PTM V/570L AIRCRAT

(1) Pilot Control Pilot Control

(2) En•.n Simulation Rgine Simulation

(3) Aerojmamic Variables Aervcrnasdc Variables

WAsroc~raaic Terms Aero~rnamai Termu

(5) Force Summations Force Sumations

(6) Conter of Gravity (e.g.) Center of ravity (e.g.)Naas, Inertia Wass, Interia

(7) Moment Summtions Moment ftmtione

(8) Linear Velocities Linear Velocities

(9) AnqguLl" Rates Angular Rate@

(10) Form Earth Axis Resolve Linear VelocitiesVelocities to Inertial Velocities

(11) Formation of Formation ofMiler Angles Baler Angles

(12) -zmtion of Wind andAircraft Inertial Velocities

(12h) Summtion of Windand Body Aris, True orOround Velocities

(13) Wind Inputs fromInstructor

(11h) Resolution of WindInputs to Body Axes

110) Instructor Inpt In)structor rnput

Table 2. Mock Tormnoloo

usQ

NAVTWRADEVCEN 105-3

A > A+B.C7 ý ý SwUMv'.ng Amlilfier

C -

G(t)Gt)+H(t) +(t)H(t) C, Amplifier and Position Servo

J(t)

((t) t)(t)H(t) +J(t) ]dtH(t) G Amplifier and Integrating Servo

+A.A+A •,/ •+AS

f •Potentioeter+A /+Ae/

-AA cose + B sine

1 ResolverA sine + cos e 0

+AA c os 0Sine-Cosine Potentioneter(Various signs of cos e and sin o

A sin ) can result depending on initial-A wiper orientation)

Ground

iiFunction

Table 3. Symbols Used in Mechanization

15

NAVTRAU•VCEN 1205-3

the Aero terms will be shown for each particular aircraft further on inthis section.

Block (5) Force. The force sunmitions are basically the sawe for allaircraft. Each force conponent (Xa, Ta and Za) has an associated mumming

amplifier. The inputs from Block (4) are the important portion of themschanisation.

Mock (6) Mass. C.G. Mass (M) and center of gravity (c.g.) loca-tion are obtained as servo shaft positions. This mchanization involvessimple summation. In Figure 2 notice that the feedback potentiometer isconnected for division operation for mass mchanisation. The shaft posi-tion is then an inverse function (1). This is done to avoid the scaling

computations required for potentiometer divisions since M is used as adivisor in its associated equations. Shift in c.g. in Figure 2 is alongthe x."boc axis and is denoted by dx. Usually c.g. shifts along thex-boct are the only shifts considered, however if a c.g. shift in the yor z bo"y axis is important for a particular aircraft, it will be mention-ed at that time.

lock W7 Moment. The msnt surnations are basically the same for

all aft. mmnt component (L.,, a Na) has an associatedsumodig amplifier. The inputs from Block (4) are the important portionof the mchanisation.

Block (8) Velocities. In block (8) the interest is in developingthe linear velocities (U, V and W). These are computed by 8umming therespective force (X, T or Z) divided by the mas of the aircraft withthe appropriate gravity and angular rate affects and then integrating.Figure 3 shows the three integrations to get V1, 9U mid V0 withassociated inputs. Servo shaft positions are not required to meahanisethese velocities but since Figure 3 is for an AC mohanisation, servoshafts are required for the integrators. The intepations could havebeen done W Just as well and nore economically. Choice of AC or Wshould not be made at the subgeeten level-but for large computationareas. This will be done in the sumnry.

Block 9) AnI11a Rates. Having computed the moments in Mock (7),the calculation of the respective angular rate (p, q%, or r) is accom-plished by the integration of the respective momnt 2hich has beendivided by the proper inertia term. Integrations can be peeformad byAC servo, DC servo or DC resistive capacitance circuits. Blocks (4)and (7) are the important determinants as to whether to use AC or 11in mechanisation. Consequently, the development of Aero Terms as wellas the suzmay mohanisition considerations of Section M will have adecisive influence on the wa in uhich the integration is performed.

26

NAV-1RADEVCEN 1205-3

MBas i C

Mf

I2 'Xý T, e

~dBas ic

KK -41 ditnefrmcg

n~ai 1 1'S 1 2fulms

2 Xxi 0.ST2 ST2 £wd Retf

Basi base on

M i Nasic 'f norSn * number ofre

I + K Mf + n 1 + n2 1 2 sto nres ofandKas *id du~ tass 2 ofe fmeaTpss

d NM-dxBsc+Adaf orw1 +Ard and2 aft repetwel KSaft STubsto:s

n I or Type num or 2f

Figuire 2. C;enter of (irAvity (c.g.)Mass, and Inertia

17

"AVTRlADEZVC.':,% 120C-3

.,4

000

OP)0

0I

0.9

00

0 04

0 3E

bo

f, Le-4

++

Figtwe 3. Velocity Integ~rationP~Mechanization,

NLVTRLZVCEN 1205-3

Mock (10) Resolve to Inertial, Bod axis velocities (U, V, W) forV/STOL aircraft are resolved to the inertial frame through the Rulerangles (9, @, t) then added to instructor inputs to give the earthboundrates. For the helicopter, ground velocities (U., VG, wG) are resolved

in Block (10) to form earthbound rates. Figure 4 shows an optimummchaniation for this resolution. Resolvers have been chosen to performthe coordinate resolution to the inertial framu since it is necessary toprovide the accuracy to insure reliable integration for position. Theintegrators in Figure 4 miet have the capability of long integrationtimes, since these outputs are generally used for plotting boards andaltimeters.

Block (1) Ruler !%lea. The computation of Wuler Angles is aoombination of cooriate resolution and integration. Figure 5 is anAC meohanizsation using resolvers and AC servos for integration. Figure 6is a DC mechaniiation using DC aplifiers, sine-cosine potentiometers andMC electronic integrators followed tr DO position servos.

AC DC

Coqponent No. Wt. No. Wt.

Amplifier 7 7 12 24

servo 3 21 3 21

S-C Pote 2 4 1

Resolvers 1 -/_

ColeztY 13 29 19 16

Table 4. Baler Angle Tabulation

The weight factor, (Vt.) of coaonents, in Table 4 are those usedby Connelly in references 3 and 4s. e weighting of components will beused for later evaluation of mechanizsations. The weight factors are asfollows: an AC amplifier is one (1), a DC aplifier is two (2), AC andrC servos are seven (7), a potentiometer is one-fourth (i/4), a resolveris one-half (1/2) and function generation is unspecified as to weight,but is specified by number (no.). AzW function generation is assumedto be done by potentiometers which would be equal in number in an AC orIC system*

mLock (12) V/STOL Velocity. At this point inertial velocitiesU1 , Vi and rate of climb (R/C) are mixed with instructor wind inputs

(ka and tw) to yield the earthbound rates (i, o, R/c). This is a sitple

process and consequently requires two summing amplifiers.

19

NAVTRADEVCEN 1205-3

I.n

100

S-,I

to _ _CCD

0.9

<aA3 004

ip I . .

Fig[ure Mock (10) AC Mechan~ization20

02

NAVTRADEVCEN 1205-3

*C1

0X

00 4

one

r4

0+U

0

cic

144

Figure 5. Rulaer Angle AC Mhehanization

21

NAVTRADEVC&I 1205-3

CDq

+ *

++

CF44

C,~

I-

CD.

to

tou.6 ir ~ DCeatuto

err,

&V'TAR VCZN 1205-3

Klock (12h) Helicopter Velocity. In the helicopter simulation thevelcit oupus (~j ~, WO) from Block (8) ame summd with the wind

velocities (U,$ Wv, Y) from the instructor in order to give bo"y axes

velocities in the air mass (U, V, W). This operation is a simple suingprocess and consequently requires three summing amplifiers. This summingis done in Figure 7 by amplifiers (7-2), (7-3), and (7-4). However, ifM• computation is used, a servo is indicated for W and both signs arenecessary for U and V so that two more amplifiers are needed for generat-ing (+V, -V and +U, -U).

Bloc (13) Wind. These are simply signal inputs from the instruc-tor so that no equipment is specified.

Klock (l) Wind Re solution. oIn aock (13h) instructor inputs repre-sentin wind direction (t.)anM velocity (IC) are transformed to componentsU%, Vw and WV for the helicopter simlation. In the AC mchanisation of

Figure 7,V. is the input to amplifier (7-1). E the use of a sine-cosine(S-C) potentiomter and resolvers, the velocities U,,, Vw and W ar6 ob-

SVtaimnd. Figure 8 is the DC representation of Figure 7.

AC DC

Component No. Wt. N. Wt.

Awml.fn- 6 6 34 28

1 7 1 7

S-C Pots 1 1A 6 1-1/2

&esolvers 3 1-1/2 ____

"2W1X L - I1 -3& 16-1/

Table 5. Wind Resolution Tabulation

Table 5 is a comparison of the AC and C mechanisations of equationsshmm in Figures 7 and 8.

Klock M) instructorls Inputs. These inputs are signals controlledby poM Iemoters at the Instructor's console. There is no associatedeqipment for this operation. This is the last block to be considered inFigue 1. The next task is to consider inchanisation of specific aircraftof which the single rotor helicopter will be the first.

23

FROM

INSTRUCTORSTATION

vw wI V(

ww

-VW -vw COS(tvW-1

~ IN(,+18O0 /w C t S( 40-'w + 1800)

~ ~S~~y~V ~10)/- SIN( w- WW + 1800)

/ UG

U a UG-UW

W.a WG .-WW

NAVTRADEVCEN 1205-3

+ Ij

-U

/ 7-3

- REF

wvwa V [SN OSIN *COS ('9# - , 4 +1800) + COS 0SIN (w .w1800)] t*w a w [SIN 0 COS*COS ( ,e-ww' + 1800) + SIN *SIN ('-#-- + 1800)]

Figure 7 Velocity Summotion and Wind Resolution AC Mechanization 24

NAVTRADEVCD1 1205-3

00

00

0, 0

0

U00

C'CO

Pi~gwre 8.Velocity Suummation andWind Resoluti')n T)C. MechAnizttinn

NAVTRADEVCEN 1205-3

Wind blows from *W heading (true) atw ')ft./sec.

Uw (a ) wl OS 0 cos, - 1*( 1800)

vW a-)XVI'I in 0 sin -0 cos(! - *1800)

- con S sin(! - Tw # 180,)}

Ww (.-)) sin 0 coo -0 ,oO(, r. 180*)

*sin t sin(Y - T * 180 O}

U a U0 +N

w a IWO +

Figurv 8. (Cont'd.) Velocity Sumfhticonand Wind Resolution rc Mechanisatioe nC

25a

NAVTRALMVCZN 1205-3

B. JfLICOPTER MECHLNIZATION

Mechanisations for two helicopters are considered--the single rotorhelicopter represented by the HSS-2 and Me tandem rotor helicopter repre-sented by the CH-46A. The major portion of the mechanization discussedis for the single rotor equations of motion. In Volume I of this report(NLVTRAUMEN 1205-1) it was shown that the tandem rotor could be siamla,-ed by considering one rotor as a function of the other rotor-that is tosq that a single rotor simlation i, sufficient for the tandem rotorsimulation.

1. SINGLE ROTOR !ELICOPTE. Figure 9 is a block diagram for the HS&-2,Device 2F64,, single rotor helicopter which is similar to Figure 1. Againeach block in the flow diagram will be considered separately. On eachmechanisation dr AMng are the applicable equations from Section VI.Mechanisation drawings are for AC carrier except in a few cases where itwas necessary to include DC machanisations for the sake of clarity. Thesedrawings y be used for 60 or 400 cycle AC as well as DC with slightmodification. Each block in Figure 9 will now be considered and themaechanizations discussed with regard to optimisation. Definitions ofhelicopter symbols are outlined in Section VI.A.l.

Uuo W ilot Control.. lock (1) of Figure 9 produose the out-puts (Ao .$,Be)as a result of control movement. Definitions of

these term are contained in Section TI.

Block C) Block (2) of Fiure_ 9 has as outputsTthe toqes Q, )ortet• engines in the H%-•. These are

considered as available signals since no engin, simulation is consideredhere.

Mock ( Aro V a . Te AC mecanization of Bock (3) of7,ems 9is hon in Pi~vO I Equations 41, 6.2, 6 6 and 6. 82 areseahanised to produce the outputs a, p, q,/, VT am i n * The

mechanisation of Wimen is included in Figure 10 since it is direc•l

related to the generation of the aerodymaic variables. A literslstep-by-step discussion of Figure 10 will now be given. This will notbe done for W of the remaining drawline since the methods of meohmi-sationB in Figure 10 are repeated throughout the report, and such acontinuous literal discussion when the equations are on each drasw1iand each line in the drawing is labeled would be laborlos, redundantand difficult to read.

In Figure 10 Wi in formed by dividing main rotor lift over airmea

density (- a) by the total velocity of the helicopter (VT). This

signal (_K1MtVT) is fed into a servo amplifier whereby WVmea is

generated by a servo shaft. Wi is used as position ieedbaok and themean

rate feedback is Wi

26

A'~S iU OFp

(4)S• FUSELAGE

"AEROOYNAMICS

q MF

UVy LuF

#

SAOSAISOI$ (4) FXF

MAIN ROTOR FyrS( EL 0 ER AERO -

-- P VTWim DYNAMICSENGINE (2) rw1b

SIMULATION (ER OTR P qa MI

LU 2

6 VAERO.W OTI

DYNAMIC TAIL ROTORV VARIABLES AERODYNAMICSw (3) T __

imVT V •

A ______ ql

OF OF LF

(4) so LMRFXR FORCE Xa

FUSELAGE -yR SUMMATION YoAEROWYNiWICS IW"- (5) z

MF __YTR 0

NF I -" - e

i (4) FXR

R I MAIN ROTOR FyRAERO-

DYNAMICS LRH IF MF X0 YO Zo d. da

p q1 j 0M FR.*

J MOMENT",or 'v __SUMMATION

S, LR4 M•

(41 LTR LMTAIL ROTOR -0 TR m

AERODYNAMICS a

YTR

P q| r 0 VT p qI

UG VELOCITY (121U Vc SUM*.ATION

xa GROUND UG V UMTO

"••Yo VELOCITIES VG Uw Vw w"

Uw Vw W,

WIND RESOLU

d CENTER OF GRAVITY

ANDMASS(b) "v

INSTRUCTOR IN

Lp ANGULAR p EULERlollM RATES qlI ;ANGLES

a(911)

NAVTRADEVCEN 1205-3

UG VELOCITY (12h)VG SUMMATION UvG V

WG Uw vw Ww

lUw Vw mWIND RESOLUTION

j~(I 3 h)

1"""1 1(11G

VG N

EARTHBOUND EI~ ', IWG RATES R c

INSTRUCTOR INPUTS (10)(14)

! eP

____________________hp --

P EULER-- l ANGLES 0

(11) ,

Figure 9. Simplified Block Diogrom Single Rotor Helicopter27

-LMR /

-LMR '~*

w.>

U-f

hpp

AREF fP

3. 11 a - 40 *ARC TAN W- f (i" Wu

5.2 P - ARC TANrI 'U 2 , [ W. f ( W m o mg ) f ( W ) j 2 -5-61 VT. 1U2 V [W.4(WUim) I (Wf

LUR

.) Wo 2p" FT " ( .-. . W . V

-REF

>w -I (W,,") f (W) -V

COS

7 VT

Figure 10. Aero

NAVTRADEVCEN 1205-3

I.II e.40 'ARC TAN WI (Wi ig.). 1)I

5.21 p -ARC TAN,\U21()]

5.12

5.1j 2p0l fyj2 -U2 LMR-Il

> V COS p- SIN p (LU Cos( .- 40) *W- CWi,,.)f w) SIN (0-40)]

:OS~~~{W. 40 (W)Jwi M w) I IM-0

7 V

22

N*TUMCK, 12o5-3

VT is formed next in Figure 10. A function of vertical velocity,

-f(W), is developed first. This is then multiplied by a function ofW to give -f(W)f(W ). The functions are generated by shaped

lumean imeanpotentiometers, f 1 and f2* Next, -f(W)f( a)_ is added to vertical

imeanvelocity, W, in a su ng amplifier to form the output [W - f(W)f(W )]

which is then fed into the stator winding of a resolver on the a servoshaft. The other stator winding of the resolver in driven by the heli-copter forward velocity, U, through a resolver drive amplifier. The out-put of'onerotor forms the function [W - f(W)f(W )] cos a - U sin a

which is fed to motor amplifier of the a servo shaft. Now, sinoe outputof the resolver is the driving source of the servo shaft, the servoshaft will continue to drive the resolver until the resolver output ismro. When this occus, then

(w - f(v)f(W. )] oo a -U sin a 0

[W - f•w)f~wion)]and sin..._ , tan a -=1 -. f(~ V o

COB a U

If the resolver is meroed such that (a - 4 - 0 when a - 40 then equation5.1 will have been mhanized, [W - f(W)f(iMM )] coo (a - 40) -

U sin (a - 40) will be identically equal to sero and the servo shaft willform the function a. Sin the shaft of the resolver is now positionedantontically to a and the resolver is seroed so that its shaft posi-tions to Ca - 40) the remmining rotor winding form the functionU cos (a - 40) + [W - f(V)f(C'J 1an)] sin (a - 40) which is eai3.y seen

to identically equalV +'U W _V f f(W)f (W -n if one considers U

and the W function as legs of a right triangle and the bypotenuse asthe sum of the projections of the logeoa shown in the dketch below.

I W29W- P(W) (W;

II

29

I&VTA cIXN 1205-3

In a manner similar to the above the helicopter sideward velocity, 4 1V. and U2 + (W - fW)f(Wi ))2 are used to drive a resolver on the

manservo shaft. The relatiion V cos - sin [U cos (a - 40) + ýW - f(W)f

(W i) 3 sin (a - 4 0 )1 is used to drive the servo shaft so that themean I

shaft positions to the angle equal to P aM equation 6.2 is mechanised.The remaining rotor output is conveniently found to be the helicoptertotal velocity, VTO since it forms the square root of the sun of the

squares of the resolver inputs in the same manner as the a resolver.The output, VT, is fed to a motor amplifier to drive the VT servo shaft.

The last mechanization in Figure 10 im that of cdnamic pressure (q).Initially, functions of pressure altitude (h p) &re fed into an amplifier

as air density (P) to form a/7 serveo. A,/' servo shaft potentiometerwiper output is fed into a buffer amplifier whose output drives apotentiometer located on a VT servo shaft. The wiper output of this

potentiometer is OVT which is fed into a buffer amplifier whose output

is 1/2 P VT and drives a potentiometer located on a VT servo ahaft.

The wiper output of this potentiometer is 1/2/9 VT which is equal to q.

In turn, q is fed into an anplifier which drives the q position se"ro.

DC mechanization of Figure 10 involves sine-cosine potentiomettersand additional amplifiers for buffer and sign inversion purposes toreplace resolvers. If resolvers are used with DC, modulators and de-modulators would be necessary. This component complexity is due tothe interfacing of AC and DC equipment. Table 6 is a comparison of ACand DC components.

ACDC

Component No. Wt. No. Wt.

AMIlifier 12 12 18 )6

Servo 6 42 6 42

S-C Pots 4 1

Resolvers 2 1 1 1 1

Convlexil '6_1_1_1_1 60li

Table 6. Aerodynanic Variables Single Rotor Helicopter

30

N&V¶RA1EWCEN 1.205-

I For each resolver in the AC mechanization two sine-cosino potentiometsrmand three additional amplifiers are neceseary .,,r a i mc•hanizatior.

Block (4) Aero Terms. The AC mechanization of Flock •2, Figure t

is divided into three parts--Tail Rotor Aerot-Aady ics, %sclage Aer',-dynamics and Main Rotor Aerodynarics.

a. Tail Rotor Aero~jiaurR cs,, In Figure 1 is aetown the AC secbaizza-

tion of the tail rotor eqation (667 through 6.17 and 6.26). 11ecomponent tabulattor) is in Table 7. A literal discuemion would besimilar to that of ,Block (3) Ae-o Variables, Figure l'.

AC__A

Component No. Wt. No. Wt.

Amplifier 19 19 25, 50

Servo 7 49 7 49 _.

Pets 8 2 6

S-C Pots.. . 41

Resolvers 2 IFunction (UT A

Geeration 1 I -0

complexj t t 7 71 102

Table 7. Tail Rotor Aerodynamics

The function generators (f) are composed of potentionetera either inAC or M mechanization. It is concetvable that more buffer and signinversion amplifiers ms7 be necessary to ,,chieve function generationfor the DC mechanization.

b. Fuseae Aerob s. The mechanization of ffuselage aero-eynamics issimply a mincing operation of function generator outputs.Figure 12 is the recommended AC mechanization. Me DC mechanizationwould be dependent on the relationship of the con•onents vitU theremainder of the mechanization, however tC mechanization should bethe sams as that shown in Figure 12. Table 8 is a list of componentsshowing the similarity .YPtween a PC nechanizattnn and the V'mechanization ')f Figure I,.

31

U SIN GTR(U Kqq1)COSe TR 0

O~pTR FP

f(V~~f~~p) aTT-Kr p

UPT

-G OTR

ASE -

REF-

REF

--- 9Ad-- F KIp f(UPTR) F Kuf(pT) (A

F F

RE-RE

-RFF

#RZ. . EF _ K''(*TR) ,ATRADEVCEM 1205-3

REF--•J

AI

PTR "F(e)

QTR •-(COTR P "RT 2(0 R2 TRRT) 6.1

CQTR ' 0.0084 f (CTTR)

CTTR -0.0480 f (#TR .0.0211 1( TR) I (A) B3 2

UPTR - (V-36.06r 2.74 0 /36.5

A - 0.1945 f (G) + 0.1790 1 (ITR)

"TR" TAN-' [(W - 36.06q 1)Y/U]

KUP1 f(U- ( U SIN "TR -(W 36.06ql) COS *

1 TR TAN- (V.36.06 r +2.74 / /U 2(W" 36.06q) 2JO * U2 . (W .36.06 qI) 2 SIN P TR -(V -36.06r * 2.74 )COS P TR

VTR • L/2 + (V-36.06r 2.74p)2 ,(W!t36.06 ql) 2

1- 0.0564 VTRf (CTTR)

TR " 10.03 a C-4.8

KTR PCTTR Q 7 Y - CTTRPR273.025

> KjTRa CTTR //

S Y TR

F;gore 11. Toil Rotor Aerody.nomcs AC Mechanozatoew

32

NAVTRADEVCEN 1205-3

UN

a-4

+ C-N0- 0

e CNCN _j

C K

'A A

b44

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ti, 1%

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5' 33

NAVTRAWiVCEN 1205-3

AC DCI

CoMronent No. Wt. No. Wt.

&Wl ifier _H5 5 1 5

Pots -

Complexity 6 1 - J 6 l/4

Table 8. Fuselage Aerodynamics

c, Main Rotor Aerodynamics. The main rotor aerodynamics mechani-zation of Whe blae element equations involves more computing equipmentthan that required to generate all other functions in the mechanizationof the equations of motion. For this reason the main rotor aerodynamicmechanization is divided into several smaller mechanizations to facili-tate discussion and insertion in the report.

Figure 13 is a simplified block diagram showing the interconnec-tion and function flow between these subsections.

(1) Block (W) Local Vertical Velocity. Consider first themechanization of The local vertical velocity, Up . in

Mock (1) of Figure 14. Eighteen U functions of both

polarities must be developed from external inputs U, V, W,Wi ,11, p and ql and internally generated feedback inputs

mean

&IS' bs and P*. This involves the basic operations ofpotentiometer multiplying and amplifier summing. Sincethese are such simple operations the optimization decisionis entire]l decided on the economics and complexit aspects.The DC mechanization differs from the AC only in the numberof amplifiers requied for the positive and negative functions.The DC mechanization required 36 amplifiers instead of 18.From the standpoint of econow the AC mechanization with lessamplifiers seems optimum. The complexity of the equipment is

certainly in proportion to the number of components. ConsultTable 9 for tabulation of components.

AC DC

Component No. Wt. No. Wt.

Awlif ir 18 18 36 26

Potn -7 -/ 7 /

Coiplexity 21 3/4 39 3/A.

Table 9. Local Vertical Velocity

34

P ci oibi5 0

q IU LOCAL

VERTICAL UVELOCITY P r.

w (1) I

p4-I

0 € BL.

I9 ANT

A L'1

TANGENTIAL UTVELOCITY -

(2)

...U• tA

N A

UTp BLADE (b) R'TIy ELEMENT

DRAG ANDMAIN ROTOR

"I N TORQUE

ROTOR H- MOMEN1

-u U 2COr

._a ls (9 )

BLADE DRAGAINLE OF _ _T2C__ATTACK '14-Y (5) -_y

BLADEFLAP

/ ELEMENT I1-41 FLAP ANGLEI b ... (8)"- "FLAPPING I--1COEFFICIENTS --os:)"- / MOMENT !AIND MAIN •L"

AND LIFT M IROTOR LIFT

F-gure 13 SIMPLIF

SI BLADE (b) QMRu LOCAL "' ELEMENT

VERlICAL Up W DRAG ANDV VELOCITY W-y " MAIN ROTORW(1 1~ TORQUE

,. .o. - i i.-

ROTOR HUE'MOMENTS

(9) BLADE DRAG

h __ANGLE OF UT2C

ATTACK "WY (5)

BLADEFLAP

ANGLE I ~-(8) BLADE L Lp

ELEMENT p

TANGENTIAL TFLAPPINGV VLC TY UT MOMENT

AND LIFT M(2) U4)

SIMPLIFIf

NAViRADEVCEN 1205-3

-40 QM• R

OER__ QEL ROTOR

QTR FORCESAND

1 ANGULAR

-D, VELOCITI ES

L 0 FXR

/1 FFYR

ROTOR HUB -

- *MOMENTS2CI

_UT CD Wy

"Is (9) LRHbis M R H _

BLADEFLAP

-"- bi bi$ (8)FLAP ANGLEL ---

COEFFICIENTS -aO

JpM/ ROTOR LIFT

PQ I

Figure 13 SIMPLIFIED BLOCK r)IAGRAM ROTOR AERODYNAMICS

35f

T P,

/ go ,

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I *~ I I

_ TT

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HAVTAADEVCEN 1205.3

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NAVTRAMEVCEN 12o5-3

(2) Block (2) Tangential Velocity.- The tangential rotor velocity,shown in Figure 15 is a sum of functions of U, V andfl toobtain the 18 blade element tangential velocities, U .

Since succeeding functions are formed by taking functions ofUT ýy, the outputs of this mechanisation must be shaft posi-

tions. Optimization of this mechanization involves theselection of function generation methods to form the functionsof UT _y. The present analog state-of-the-art does not furnish

arw more simple and straightforward method than paddedpotentiometers. Hence, since servo shafts are required forthe potentiometers, the mechanization is equally optimum byeither AC or DC methods. Table 10 is the summary of componentcomplexity derived from Figure 15.

AC DCCooionent No. Wt. No. Wt.

Amlifier 18 18 18 3

SE18 126 18 126

Complexity 162

Table 10. Tangential Velocity

(3) Block (3) Blade Anile of Attack. The eighteen blade elementangles of attack, a-, are also required as shaft posi-tions to form functions of angle of attack for later use.Also each a*_, is a function of U P . Then the mechanisa-

UT

tion in Figure 16 follows logically since UT _y exists as

a shaft position and it is a simple procedure to dividetwo functions using potentiometers. Considering the ACmechanization shown in Figure 16 for optimising purposesit can be seen that the only area that would differ sig-nificantly from a MC mechanisation would be the require-ment of positive and negative functions of 8. Hence theDC mechanisation would require three more amplifiers thanthe AC mechanisation. Table 11 reflects component complexitVof Figure 16.

37

LAMES-

NAVTRADEVCEN 1205.3

- -7

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,38 - ,-

0 ,o C,

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NAYTRADEYCEN 1205.3

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Figue 1. TngeniolVelcit AC echniztio38i

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AC DC

Component No. Wt. No. Wt.Amlif ier 21 21 24 h8

Servo 18 126 18 126

Pots 21, 5 1/4 21 5 1/4

Complexity 152 1/14 179 1/4

Table 11. Blade Angle of Attack

(4) Block (4) Blade Element Flapping Moment and Lift. The bladeelement flapping moment (Ný) and the blade element lift (L*)

are formed from the sums of functions of and U asan T

can be seen in Figure 17. Here again both positive and nega-tive output functions are required which results in the onlydifference between the AC and DC mechanizations. In thiscase 12 additional amplifiers are required in the DC mechaniza-tion to give both signs of MP and L *. Table 12 reflects

component complexity of Figure 17.

AC DC

Component No. Wt. No. Wt.

Amplifier 12 12 24 24F~unction (f)

Generation 36 36 -

Compexi ty 12 24

Table 12. Blaie Element Flapping Moment and Lift

(5) Block (5) Bla.ie Element Drag,. Figure 18 is the mechaniza-tion of the blade element dxag computation, This mechaniza-tion in itself can be equal ly optimum in either AC or DCmethods. This is evident since the entire mechanization issimply a combination of potentlometer function generators onservo shaPt s.

(6) Block (6) Blade Element Drag and Main Rotor Torque. Thecomputation of blade alement drag and main rotor torque isthe same type of summation of potentiometer function genera-tions as in Figure 19. Here again the only difference

41

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Figure 19 Slade EIwm~nv Drag and Main Rotor Torqu~e AC Mech~anizatone

43

NLVTRAZVCEN 1205-3

between AC and D, optimum mechanizations is the number ofamplifiers required in the DC, mechanization to provide bothpositive and negative functions. There are 9 aulifiersused in developing blade element drag and main rotor torquein Figure 19. Plus and minus functions are available fromeach of these 9 amplifiers for the AC mechanization. Inorder to do the mechanization with DC components, 9 additionalamplifiers are necessary for sign purposes. Table 13 reflectsthe component complexity of Figure 19.

AC DC

Conyonent No. Wt. No. Wt.

Amplifier 10 10 19 38Function (f)Generation 36 - 36 -

Com~lexit 10 38

Table 13. Blade Element Drag and Main Rotor Torque

(7) Block (7) Flag Angle Coefficient and Main Rotor Lift. Figure20 is the mechanization for flap angle coefficients and mainrotor lift. The critical area in the optimization considera-tion is the requirement of positive and negative a o. DC

methods in this mechanization require I additional amplifier.Table I4 reflects component complexity of Figure 20.

AC DC

Component No. Wt. No. Wt.

Anlifier 8 8 9 18

Servo 2 14 2 14

Pots 6 1 1/2 6 11/2Function (f)Generation 2 - 2 -

Cow lexity 23 1/2 . 33 1/2

Table 14. Flap Angle Coefficients and Main Rotor Lift

(8) Block (8) Blade Flap !Agle. The blade flap angle computationis the difference betweer flap angle coefficients to form the

outputs in the form of servo shaft positions. It is seen

in Figure 21 that this mechanization would be equivalent ineither an AC or a DC mechanization.

/<1'

UU

H �I ®

a. a.

K

0-I--

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NAVTRADEVCEN 12

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S/A

k-

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CD.

*0 -j -j -

Figure 20. Flop Angle Coefficients and Main

CEN 120Q

a,- l e--

+I

a

9-

i ______Main__

NAVTRADEVCEN 1205-3

-VfJ

+ I I.

I

Sal

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201 ,_.

LZZ

"" -1

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Figure 20. Flop Angle Costficient$ ond Main Rotor Lift AC Mechanization

45

NAVTRADEVCLEN 2O-

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K4VTRAWVMC 1205-3

(9) Block (9) Rotor Hub Moments. As seen in Figure 22, the rotorhub moments are functions of the sums of functions of blad*element lift (L*), rotor angular- velocity P), flapping angle

coefficiAents (s a1 bls) and air density (/P). The mechanization

is a simple straightforward suzmuation of functions and does

not req:ire a positive and negative output. Consequently,thiso method would also be equally optimum in either a DC oran AC yastem. Table 15 reflects component complexity ofFigure 22.

AC _ DC

Component No. Wt. NO. wt.

Amplifier 4 J 4 aPots 6 1 3/2 6 1l'

Table 15. Rotor Hub Moments

(10) Block (10) Rotor Forces and Angular Velocity. Figure 23 isthe mechanization for the rotor forces, mhere is no areain the mechanization that will cause the AC to 4 !ffer fromthe DC mech!nization. The integration of the torque summationto obtain rotor angular velocity could be accomplished by anelectronic DC integrator, but rotor angular velocity 0) isrequired as a servo shaft position for multiplicatiun (W).The mechanization as htown in Figure 23 can be done uit thesame amount of equipment in either a DC or AC system. Table16 reflects the component complexity of Figure 23.

AC DC

Component No. Wt. No. Wt.

_Amplifier 3 3 3 6

Servo 1 7 1 7

Pots 10 21/2 10 21

convlexity ____j12 12 - 15 1/12

Table 16. Rotor Forces and Angular Velocity

This co mletes the rotor aerobnamics. The discussion will continuewith Block (5) of Figure 23.

47

p

41240

0 'R P,

* LO _ _ _ _ _ _ _ _ _ _ _ _

;Lo --- 41

;L120

NAVTRADEVCEN

AIN-

/

/

. /

I I

r .u

Figure 2)2. Rotor Hub Moments

DEVCEN

------ -----

------ ------

loments

NAVTRADEVCEN 1205-3

I-.H

/--/

/

/---P •M RH/

MRH - Lq, COS . ]Mere 9 g2 a1,

m8y 8. g2b15

MBYB 0 12 cis

Figure 22. Rotor Hub Moments AC Mechonization

48

,' I .. . . . . . . . / •

P6Oj • 'r '

'•Lo

T'

II7L1120

L2

_40

P24OL240

L_ 3000A ' - /

1 I 20_ _ _ _ __ _ _ _ _ __ _ _ _ _

+1 D01

-- Do

OER -

OMR

_____ _____ _ ___ O J

D12--- - -- - - __ _

1

1

D18

OER

GEL _ _

OTR

NAVTRADEVCEN 1205-3

-- 1IPFXR

. ,.lob

lp FyR

-IYR

Nb /

REFER TO EQUJATIONS

FXR 1 (.0173 Ly1,. COS V.- Dy SIN V)

FR- I?

FXRU b (-.0173 p Ly SIN '- Dy COS If)

FYR a If(0 3~L~IYyO

SMR + TR + QER, + OEL + QRB -1 700

10, 275

Figure 23. Rotor Forces oitd Anglor Aelccity AC Mechanizotion

49

NLVT•A•VCZN 1205-3

Block W Force1. The AC mechanization of Block (5), Figureis shown in Figure 24. Equations 621, '6.24 and 6.27 &r mehanized togive the force outputs (Za, Ya' Za)u Table 17 reflects the componentcomp1exity of Figure 24,

AC Dini -

--

Comonent No. Wt. No. Wte&MLtfier 12 12 16 16

Servo WO16

S-C Pots 1 4 1

Table 17* Force Sumtions

Four extra amplifiers are necessary for DC mechanization so that bothsigns of a function are available f c operation of the sine-cosinepotentiometers in Figure 24.

Block (6) Mass, c.g. Block (6) of Figure 9 in moehanied as inSection III.A.

Block (7) Moments and Block (9) r Rate.. The AC 1mohani-zation of ocks (7) and (9) s 9 IS mhorn gure 25. Rqua-tions 6.30, 6.34 and 6.39 are mechanised to give outputs (La, Map Na)

and then each moment is integrated after dividing by the appropriateinertia term to give the angular rates (p,q 1 , r). The 1C machanisa-

tion is essentially the same as the AC mnbanizatio".

Mlocks (8) throuj (14). These blocks of Figure 9 have been dis-cussedTi•ction III.A. The correspondence betmen Figure 9 andFigure I is as follows:

Block (8), Figure 9 mechanized by Figure 3.

Block (10), Figure 9 mechanized W Figure 4.

Blork (11), Figure 9 mechanised by Figure 5.

Block (12h), Figure 9 mechanized by Figav 7.

Block (13h), Figure 9 mechanised by Figure 7.

Block (14), Figure 9 instructor inputs as noted In Section III.A.

This conrletes tUe mechanization of the single rotor helioopter.

50

~ LF 1 -L F C O S .

LF L- K &LF SIN

-LF + DF COSp

+ D F D D C O S 0

D0 F COS 0

DF

-DF + DF SIN 0

-DF

.-DF SIN p I-

-.DF S1 p

YF -- DF SIN p

-DSI.OS FWZLG -- FR .,FLW-FTW A Zo ---

-DF COS uSIN P XF aLF SIN a DF COS a SINp

0.025 ZLG -.KB (PBR P BL)

PBR iKK--

~BL - KB (PBR P BL) RW

HtWH -

YTR-

YWM

A v

FYR-11ý

ZF -- LF COS a -DF S IN *C-OSp

-COFULt F F SIN. - D CO *SN

0.02 ZLG -KW TWB zBL

N. w

wwT

RF R

NAVTRADEVCEN 205-3

FXR . Xa

AXaX

KG XLG K [0.025 ZLG. KB (PBR + PBL) KG X0 -XF+XLG+FXR AX+XWH

XF a LF SIN v.DFCOSGCOSP

RW XLG- K [ .025 ZLG -o2.53 (BR +BL) KG]

HLW - a YF + YTR + FYR + A Ya + YWHHTW YF U-DF SIN p

Zan ZF *ZLG +LMR +Z +ZWH

ZF -. LF COS -.DF SIN a COS III

ZLG T (FRW + FLW + FTW)

YO

Figure 24. Force Summations AC Mechanization

51

/ Kq~~TR Lft4*Ky1FyROK~yTR*tF#K qj

FYR.--- -- - .-

ye da yo daLLG

-FLw -

kXt MM *XMd5 +MV -Kooi

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ye -yd

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m Ye ____

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UG --- MG 3IRW9

Me9 -o y0 di M * NN

5 43 NL G K 164> 1P

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M, P

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MAVYRADEYCEM IMS)

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6w - KurfKG

5 31 Lp - IUS y 53 LW*~Lw FRW) S536 MR -- 15FXft 073LMR

:G fNLG KK PDR- PS 6r,

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52

NAVTRA EVCEN 1205-3

tag= Single.Rotor Helicopter. Figure 1, the general block diagramof the equation solution of the single rotor helicopter, has been develop-ed block by block. Table 18 is a tabulation of the various components(amplifier, servo, potentiometer, sine-cosine potentiometer, and resolver)for the single rotor helicopter. It should be noted that items specifiedas functions generated in the mechanization have not been included inTable 18 since they are assumed to be potentiometer derived and the samefor both AC and DC mechanizations. In order to compare AC and DC systemsthe weight factors used by Mark F. Connelly in reference 4 are applied tothe totals which result in Table 18. The weights resulting from eachcomponent are tabulated in Table 19. The sumiazry in Table 19 gives thecomplexity of the single rotor helicopter for AC and DC systems. TheAC system has a complexity of 751-3/A versus 1106-1/2 for the DC system.This is a marked difference. The difference is primarily due to usinga weight factor of two (2) for the DC amplifier and one (1) for the ACamplifier.

. . .Amifiers Servo Pots S-C ots Resolver

AC DC AC DC AC DC AC DC AC Dc

Block (1) .

Bil.•. (21

Block (3) 12 18 6 6 5 5 4 2

Block (4) 118 167 52 52 73 73 4 2

BloIC1 (5) -164

Block (6) 3 3 3 3 2 2

Block (7)(9) 20 20 3 3 12 12

Block (8) 4 5 3 3 7 7 2 2

Block (10) 9 _. . 1. 5 3 3 ,.,.6,,, 2

Block (11) 7 12 3 3 2 4 1

Block (12) 3 5 1 1 1 1 _

Block (13) 6 14 1 1 1 1 6 3

Block (

TOTAL 194 275 75 75 10hJ 104 9 22 10

Table 18. Single Rotor Tabulation

53

NAVTRADEVCEr 1205-3

AC DC

No. Wt. No. Wt.

Amplifier 194 194 275 550

Servo 75 525 75 525

Pot 104 26 104 26

S-C Pots 9 1 3/4 22 5 1/2

Resolver 10 5 .....

Complexity 751 3/4 1106 1/2

Table 19. Single Rotor Summary

Suppose that both AC and DC riplifiers both have weight one (1),then the DC complexity is 831-1/2 %iich is closer tut still largerthan the AC complexity. Thib difference (751-3/4 and 831-1/2) isprimarily due to the increased umber of DC amplifiers necessary tosolve the mechanization proble:-. Consequently, unless DC amplifier,can b• redesigned to be competitive in complexity with AC amplifiersor the choice for a DC system is based on reasons other than com-ponent complexity, the AC system is favored. Al

2. TANDE4 ROTOR HELICOPTER. The mechanization of a tandem rotorhelicopter simulation equations can be accomplished by againconsidering Figure 9 which is the block diagram of the single rotorhelicopter. The difference in mechanization between single andtandem rotor helicopters is contained in Block (4) Figure 9--the aero-dynamiic terms. The aerodynic terms for the single rotor helicopterwere considered in three parts--tail rotor aerodynamics, fuselageaerodynamic and main rotor aerodynarics. For the mechanization of thetandem rotor the aerodynamic terms are in two parts--fuselage aero-dynamics and rotor aerodynamics. In reference I it was shown that therotor equations of motion of the tandem rotor helicopter could be de-veloped by using a set of equations sim-ilar to the single rotor heli-copter. The essence of this development in reference I is thatequations describing the main rotor if the single rotor helicopter areused to describe the forward rotor of the tandem rotor helicopter. Rearrotor effects in the tandem rotor helicopter are mechanized by ratiosof the swash plate angles of front and rear rotor. Only the frontrotor is simulated. Since this is an overlap tandem rotor helicopter(CH-46A), effects rf rotor interference are also mechanized.

In Section VI, equations 6.91 through 6.169 for a tandem rotorhelicopter--the CH-46A are presented. These equations are directlyanalogous to equations 6-1 through 6-90 of the single rotor helicopter.Table 20 is a comparison of single and tandem rctor equations andassociated figures used in the single rotor mechanization. Table 20

54

NAVTRLtCVCEIN 1205-3

Mechanized Coparable MechanizedSingle Rotor by Tandem Rotor byEquation Nos. rip" u() Equation Nos. Figure(a)

Block (l) N.A N/i ,A N/A

Block (2) N/A ,/I NIA

Block (3) 6.1 6.2, 6.6 10 6.91, 6.92, 6.95 106.81 6.161 ,

BLock (4)

Tail Rotor 6.7 to 6.17, 11 None N/A6.26

Fusela 6.4, 6.5, 6.33, 12 6.94, 6.93 6.108 126.36, 6.41 6.112, 6.1.16

Aft Rotor None N/A 6.107, 6.111, 615s, 26,6.126, 6.129, 6.132, 276.134p 6.143, 6.145

Rotor (Main) Rotor (Front) Rotor

BI Block (1) 6.45 14 6.119 14

Block (2) 6.4 15 6.118 15

Block (3) 6.46, 6.47, 6.48 16 6.120, 6.121, 6.122 16

Block (4) 6.499, 6.52 17 6.123, 6.127 17

Block (5) 6.58 18 6.136 18

Block (6) 6.50, 6.51, 6.54 19 6.124, 6.125, 6.130 19

Block (7) 6.53, 6.61, 6.62 20 6.128, 6.139, 6.140 206.63 6.11l

Block (8) 6.59 21 6.137 21

Mock (9) 6.64, 6.65 22 6.142, 6.144 22

Block (10) 6.55, 6.56, 6.83 23 6.131 6.133, 23(6.16) 28

Block (5) 6.21, 6. 2 2 , 6.23 24 6.99, 6.100, 6.97 2 424, 6.25, 6.27 6.101, 6.102

6.28, 6.29- 6.103, 6.104. 6.96

Table 20. Single Rotor - Tandem Rotor Comparison

55

NAVTRDFVMN 1205-3

Heohardied Comparable MechanizedSingle Rotor by Tandem Rotor byEquation Nos. Fiu (s) Equation Nos. Figure(s)

Block (6) 6.90 2 6.169 2

Block (7) 6.30, 6.31, 6.32 6.105, 6.106, 6.48and (9) 6.34, 6.36, 6.37 25 6.109, 6.110 25

6.39, 6.40, 6. 2 6.273, 6.1176.43, 6.79, 6.80 6.158, 6.159, 6..60

__ __ _ __ _ 6 .81 . .. . ..... ...... _ _....

EiLock (8) 6.67, 6.68, 6.69 3 6.146, 6.1477, 6.148 3

Block (10) 6.70, 6.71, 6.72 4 6.1149, 6.150, 6.151 46.84. 6.85, 6.86 6.161, 6. A6. 6.1.65

Mlook (11) 6.87, 6.88, 6.89 5 6.166, 6.167, 6.168 5

Block 12h 6.73, 6.74, 6.75 7 6.152, 6.153, 6.154 7and 13h 6.76, 6.77. 6.78 6.155, 6.156. 6.,57_ •

Block (14) N/A N/A NIA N/A

Table 20. Single Rotor Tandem Rotor Comparison (Cont'd.)

56

NAVTRAUMCEN 1205-.3

thus enables the identification of figures used in the single rotormechanization with tandem rotor equations and a consequent count ofelectronic components. Note that the particular Inputs to some of theamplifiers msy increase or decrease in the tandem rotor helicopter ascompared to the single rotor but the components associated with thefigures listed in Table 20 will be the sern.

In order to describe the aft rotor, a few additional equations arenecessary. The additional equations needed are 6,107, 6.111, 6.115,6.126, 6.1299 6.132, 6.134v 6.14A3 and 6.145. Bfore mechanising theseeqations, the aft rotor wash plate angles will be mechanizod.

The wash plate angles and SAS mechanization considered for thetandem helicopter simulation is an addition to the rotor aero enaxicsof the single rotor device. In this mechanization the wash plateangles are developed in order that aft rotor terms are vritt~n asfunctions of forward rotor terms. Figure 26 is the mechanization ofthese functions. The DC mechanization would require three additionalamplifiers ty virtue of the requirement of three functions of bothpolarities. Servo integrators are used to obtain the delta mashplate functions. A DC mechanization using electronic integrators wouldrequire follower position servos.

Figure 27 shows the AC mechanization of the aft rotor equations.There are 12 amplifiers and 4 potentiometers used In the AC moehensa-tion plus funoticns not specified as to equipmnt. The C meohaniationwould require 15 aniplfiers and 4 potentiometwes plus the ftictions.The additional amplifiers in the DC mechanisations are due to polariiyof functions.

One further area is of interest in the tandem rotor simulation-,angular velocity The mechanization of the dual rotor angular velociycomputation is shown in Figure 28. In comparison to the single r6torangular velocity mechanization, Figure 23, it is seen thatiA is COmputedessential2 the sas wvy as in Figure 23 but there are now to rotortorque terms. One is the torque contributed by the forward rotor. heother term is the torque contributed by the aft rotor.

Table 21 id a swunary of the components nsceesary to meohanise thetandem rotor helicopter in addition to those necessary for the singlerotor heliccpter less tail rotor as reflected In Figures 26, 27 and 28.The numbers under function generation in Table 21 would actually bemechanized ty potentiometers. It is assumod that ihere functions (f)are used in the mechanization drawings, the meohanization oam beaccompliWhed by the same amount of equipmant-AC or DC.

57

K / Trim

4.ql SF

qE-- f

Re(

SOLL

*RP

/+ /

-u - U

M G

A1FR

,AAI5 + +A

m G -

AO5FR K + K aeCs + K

AOIAR K + KsCo.K,

,Sl-..BsAR A SB1 Al IFRU a *~ f

Al BAR. -. WLe+ K

I I8 SAR BISFR K

OISAR - -K + K hq,.)

A LAlso Al BAR -Al FR

815l AR A B1 I s SSAR -K

AAI aAOAR- O FR

Figure 26.

iA A/ I e c l oc*

> CMAA 0 _ m G

Al sFR

L I 4AlSFR

~A5AR

eCo + K

wCo +K SR -- 81AR AB 15sS.L.KF G -- - - --- ,I

+ al15ARULO .K oF

Al SFR '11 I

hOFR

ire 26. S

NAVTRADEVCEN 1205-3

"$Ic +AOSFR* A AOSF

-SA -AsF

AAlR *9F ML.sP G B1 . . fq

A-sF

AiSARU - nLe +K IRP*

BIFRu K

B15AR - K + KfRqx)LA1 5 8 Al ,AR -Al5FR

£815. B ISAR K

£ A1 3 a AOSAR A If R

Figure 26. Swosh Plate Angles 8 S.A.S. for Tandem Rotor Helicopter

58

NAVTRADEVCEN 1205-3

J\

~~I4~~ '-4 - - -

MAR 4 - 276 , 6 e ~

r-4 ~ NA 1-- 7,a -7.65 FYAR

F -[7K65F 168)XAR x AR

N -16.8LF).'AR yF

AA

A 0

as

Fipuare 27. Aft Wotor Termvs, Tandem~ Rotor HelicopterAC Mechanization.

NAVT'RADKVCD 1205-3

41

'ARcY 1 R*A

ITOT ' ARt

figure 28. Tandem Rotor Angular VelocitiesAC P cchan ization

60

&VTRArmCmN 1205-3

Co!Ronent No. Wt. No. Wt.

ALMlifier 25 25 1 62

fervo _5 _35 5

Pots 16 4 16 ., _

Function (V•

__naraton - 9 _ _9S-i

Complexity "_ 101

Table 21. Additional Components Tandem Rotor Helicopter

This completes the mechanization of the tandem rotor helicopter.

STandem Rotor Helicoter. The tandem rotor mechanization hasbeen deeioped in term of the single rotor mechanization (Section III.B.).The arguments presented in the single rotor sumar (Section III.B.) areequally valid for the tandem rotor helicopter. Table 22 is a suniary oftandem rotor component complexity. This table is constructed by takingthe component totals of the single rotor helicopter (Table 19) and thensubtracting out components due to the mechanization of the ta!.l rotor

40 in the single rotor helicopter (Table 7) and then adding the additionalcomponents due to tandem rotor mechanization (Table 21). The AC systemfor the tandem rotor helicopter has a complexity of 744-3/4 versus

i0o5-i/2 for the DC system. This is practically the same as the com-plexity for the single rotor helicopter AC system--751-3A, DC qseteb-1106-1/2. Consequently, using the same rationale as in Section III.B.,the AC system is favored for the tandem rotor helicopter.

C. V/STOL MECHANIZATION

Mechanization for the tilt wing aircraft, the XC-142A, of Ling-Tenco-Vought, Hiller, Wan is considered in this portion of the report.In reference 2 the equations of motion for the tilt-wing were develop-ed and the necessary equations for mechanization of the tilt-wing arereproduced in Section VI. It should be noted that equations of motionwere developed for four other V/ST0L configurations in reference 2:the tilt-duct represented by the DMAK VZ-4A, the tilt-propeller repre-sented by the Curtiss Wright X-19, the fan-in-wing represented by theGeneral Electric/iqan XV-5A and the rotating thrust represented by theHawker Aircraft P.1127. Mechanization of the tilt-<uct and tilt-propeller equations of motion would be similar to the tilt-wing mechani-zation. Mechanization of the fan-in-wing and rotating thrust equationsof motion would be similar to mechanizations of ordinary jet aircrafttaking into account variations in the thrust components. E accointingfor these thrust variations in the equations of motion, existing mechani-zations for jet aircraft such as those presented in reference 3 are validfor the fan-in-wing and rotating thrust. The mechanization for the tilt-

61

NAVTYLADZVOD 1205-3

%^ r-

0~%0

o 0o

r-4

z- _9-_ _ _

- - -- =4~0

o- go-

Tal 22 TadmRtrSmI

62-

NAVTRAEVCEI 1 o05-3

wing may not be optimum since the mechanitation reflects the equations ofmotion wqich could change as data from tio manufactarer become availableabout the par ticular aircraft. Mechanization of the tilt-wing presentedhei-e is bassed upon the best information available at the time of thisri-port.

References are made to the appropriate tilt-wing equations in,oction VI in some of the mechanizations drawings where the equationsare lengthy. On other drawings the equations are written explicitly.

i. SIMIARITY OF V/STOL EQUATIONS. Before developing the tilt-wingmechanization in detail consider the similarity of the tilt-duct andtilt-prop oquations to the tilt-wing equations and the liluness of thefan-in-wir.: and rotn!ing thrust e, ations to existing equations ofmotion for je' aircraft. In these comparisons which follow only theX-force equations will be compared, the Y-force and Z-force equationscontain like similarities.

First consider the tilt-wing, tilt-duct and tilt-prop. X-forceequations from Reference 2.

X-Force Equation: Tilt-Wing (XC-142A)

m(U + Woq - Vr) + mg sin e (3-1)4

"(Cx)w Sf(CT S) +7 (Tn Cos w- oo,8An sinw9 n-l

- CO (i- a C sin (it - 6t)] s.) - Sq CD0[D t osit %) L ct t-qD

X-Force Equation: Tilt-Duct (VZ-kA)

m(U + Wq, - Vr) + mg sin e (3-2)

2S(C X)w S + q.Sv(CX)R1 . + K, 2 (CT 00o iD - CN sin iY * Tr

-(C Cos (i - - C sin (it - t)] Sq(-%-)- Sq CD[Dt oe(t t) L t q

X-Force Equationt Tilt-Prop (X-19)

4

63

NAYTRLMYCIN 1205-3

Comaring equations (3-2) 2and (-3) to (3-1) the only differenoes ae the 40ter 1v (x)C +ý2 L (8T CooiD -CN sin iD) +Tr in ( 3 -2) andt~'c~ TJulN '~a i aNa

(Cx)WaSqm in (3-3). %o,(Cx)R and Tr are due to the reaction controls

in the tilt duct aircraft. The termI K (CT Din Y0 isC

thrust wJprission for the duct fans in aoefficient for*,

To f•u-ther illustrate the uiuilarities of the force equations (3-1,3-2, and 3-3) suppose that the incident angles (ivs ip and ij0) are sero.Then there results:

u(T + Wq - Vr) + a sin e (3-ia)

. (C2 %, * ÷ . Tn~ - [CD oo0(itu8t-) C- sin(it-%a)]jS( 2 .) - Sq CDn-i

,(i + Wq. - Vr) + mg sin O (3-2a)

2..(Cx~ q~rv(CxRC +"2 C T a

[ CD coon -i ab + C i (i t t)] Sq(~. Sq CD

m6U + Wq1 -Vi). +~ n ine0 (3-3a)

14(CX~v %f Tn +(Cz)wa Squa -Sq CD

n-I 0

Zquations (3-ia), (3-2a) and 0 -3a) re ver7 similar. Fbehanisation ofthe tilt-wing equation (3-1) vill therefore demonstrate the simulationtechnique. The Y and Z force equation. for the tilt-wing, tilt-duct andtilt-prop have the san degree of likeno•s as the I-force equations.

Newt, let us compar the fan-in-ving and rotating thrust I-force

equations from Reference 2 to slmalation equations used for jet aircraft.

fan-ln-Wing: X-Force Equation

,(j + wq. -Vr) a qStCz(a, Ma) + C1 (fi) * C .* 8?] (3-)

+ Tj Cog o. * + T, f sin W , - vg sin o

64

NLV1TRHAVCEN 1205-3

Rotating Thrust: X-Force Equation

m0 + Wq1 - Vr) - qS[C( + C'+ C *XF . 8F + Cx(i)) (3.5)

+ T cos (9 + Y - mg sin e

Ordinary Simulation: X-F'.-=e Equation

m0 + Wq1 - Vr) - qS[C 'a, Ma) Cx() F) (3.6)X% 5F

+ T cos a T - mg sin 0

The only difference among equations (3 .4), (3.5) and (3.6) is inthe thrust terms. Using equation (3.6) as a guide consider (3,4) and(3.5). Equation (3.5) has as a thrust term T cos (a + aT). 0 is

the rotation of thrust producers. If the aircraft is in normal flight(e - O) and T cos (08 + aT) T cos aT which is the same as equation

(3.6).

The thrust term in equation (3.4) is Tj oosa T + TF sin OL. If

the fan-in-wing is in normal flight *L - 0 and consequently equation

* , (3.4) is the same as equation (3.6). The only added term is TF sin eL

in equation (3.4) and is of smll consequence, though necessary, fromthe mechanisaion viewpoint.

Similar arguments can be applied for the T-force, Z-force andmoment equations.

2. TILT-WING MECHANIZATION. Figure 29 is a block diagram for thetilt-winog aircraft similar to Figure 1. Each mechanization drawingrefers to the appropriate equations in Section VI. As per the heli-copter mechanization, each block in Figure 29 will be considered. Acoiionent count will be done in the sumuary indicating differences inAC and DC mechanization.

Block (1) Pilot Control. Block (1) of Figure 29 contains outputsdue to control of the pilot.

Block. (2) Engine Similation. Block (2) of Figure 29 is notsicmfated.

Block (3) Aero Variables. The AC mechanization of Block (3),Figure 29 is shown in Figure 30 in order to give outputs aFNOF, qPand VB. This mechanization is similar to that shown in Figure 10 for

the single rotor helicopter.

U V WWN (&Z ) wing

iw AERO

n(A) AL0 wing

K AMES PILOT CONTROL 8R n ~w (AN-)-;n

NT) (AM)F.(ANp

iFUSELAGER (AL)ROpAn(mapo

NAVTRADEVCEN 1205-3

Xa VELOCITIES U U UAVELOCIT

X0 y (8) V RESOLUTIO 1 (12)

-u TO INERTIA U 1 C

SO N ... AX E SR

iV

SGRAVITY AND (13)MASS

Lo(6) ddi L Iw 11w

,w wiP EULER I>

"--•• MOMENT - q, ANGLES w•_ v* *

SUMMATION Mo Lo ANGULAR P - r (1 -(7) Ma VELOCITIES q I INSTRUCTOF

No (9) INPUTSSN o ( 1 4 )

Figure 29. Simplified Block Diogrom V STOL (Tilt-Wng) Aircroft

66

NT VF I (ax0)prop87 tw MAING (AZ 0 pw

717.~o) .w

ENGINE0 O SMA~iIN A)Ro 4

WINO(2) AERO (AL 0)V

ST UIO rYNAMCC

(12) (3) &a~m UMAIN Y

SIMULAIONFUSEABLAGE EROj

NAVTRADEVCEN 1205-3

SVELOITE UVELOCITY

S (O) URESOLUTI U1 SUMMATION

z W U TOV 1-cK UI(12 R Ca AXES RC

i p, ql, r V (10) . twhp

I t W R C

CENTER OF SW IN DGRAVITY ANDJ WIND

MASS (13)

(w w

P EULER '

q, ANGLES 0 ww vw

La ANGULAR p r 011) '_

VELOCITIES q, INSTRUCTOR(9) INPUTS

Na r (14)

Figue 29 Smplif,ed Block Diagrom V STOL (Tilt-Wing) A.,crorf

66

NAVTRADEfVCZN I20c;-l

tn i

.- 4kNj

oI+

J&-.

0 tp

0

19AIN

0,

0

+44 r-4 46

Fij-ure 30. Aerodyniam'ic VariablesC~ Jacharitsatior,

NAITRADEVC N 1205-3

Aock () Aererms. The AC mechanization of Block (h), Fiture 79is divided into the Folow-ing six partst

1. M-4in Preller Aerodynamics. Figures 31 through 11l mechanize the'iquatiors nving do wo wi ropeller aerodynamics. Figure 31 develC4isvelocities associated with each proreller. Figure 32 develops the advanceratio associAted with each propeller. Figures 33 and 3 h show coefficients'ised in propeller aerodynamics developed as functions of advance ratioand propeller blade ritch. Fiure 35 is the mechanization of each pro-peller thrust (Tn) and torque (Q). Figure 36 is the mechanization of the

normal component of thrust (N n) and propeller moments (Tn and Mt). Figure

37 resolves Mn and Tn into arpropriate components due to wing tilt (1,) andorientation of Nn by the angle P no Figure 38 is the mechanization of theforce components ((4Xa)p, (AY)p, (AZa) p)due to propeller effects. Finally,

Figure3 39, 0O and 4l are the mechanization of the respective moment com-ponents ((ALa)p, (6Ma)p, (ANa)p) due to propeller effects. Equations

6.175 through 6.197 represent propeller aerodynamic effects.

2. Wing Aer amics. Figures 42 through 05 mechanize the equationsrepresenting wing aerodynamics. Figure h2 shows '.C mechanization ofwing velocity components, wing angle of attack (aw), wing sideslip (Pw)and total velocity of the wing (V ). Figures 43 and 44 show formation of

waerodynamics coefficients. Finally, Figure 45 is resulting wing force andmoment contributions. Equations 6.198 through 6.221 represent wing aero-dynamic effects.

3. Vertical Stabilizer Aerody ics. Figure 16 shows the AC mechani-zation of equaetons Z.2Z to 6.227 for-To force and moment contributionsdue to the vertical stabilizer.

4. Horizontal Stabilizer Aerodynamics. Figure I7 shows the AC mechani-zation of equations 6.2W to 0.233 for the force and moment contributionsdue to the horizontal stabilizer.

5. Tail Rotor Ae2odaamics. Figure Lt shows the AC mechanization ofequations 6.234 to 6.2b6 for the force and moment contributions due tothe tail rotor.

6. Fuselae Aerodynmics. Figure 49 shows the AC mechanization ofequations 6.2h7 to 6.251 for the force and moment contributions due tothe effects of lie fuselage.

Blocks ( ) through (1h). These blocks of Figure 29 are similar to

the saxe numbered blocks for the single and tandem rotor helicopter.

9lock (5), ?ipure 29 mechanized by Figure 50.

Block (6W Figure 29 mechanized as In Section III.A.

68

C'.6*4 0C0

r/ w I) CI

0 000

a0 0 * -

a 0r 0% -

rV4

r-4 .r44

0 0 0

0 r U IDCO-

C. 4 r- r4

L

7

p. U$4F.4 r4 M~4:

t~ 'too

.,4 0

F*ur 11a Prpl erdnmc 1Vlcte

AQ ecaizto

.9 - - 09

NAVTRADEVCEN 1205-3

4

! 4h

U 3at a oa.

70 0 U

or .go sS

bý4

AC Mechanzatio

70U

WAVTRAP1~hVCEIN l?fl-3

4r - - -

CU U U C11

INNNX

N

Al

z a

r. r

31 3 Ing

p.4l N n

Ftu"32 roelerAroynmisAdane aioACMeonia0o

I41N 11

NAVRi')FlPVOW 1205-.3

4-o c cf G

r% 0

C4 N1 C3

r4 jo

NN

CC

J'L~

00

0) L

P4plire 33. Propeler Avrodynei'ics C6.ffticints

72

NAV'IIADZYCIN 1205-3

9-4 9

9-, 02 -q

9 In

*o A

Fiur 3.Prpelr erdyaic CefiietAC Mehaiato

K~ K7K

NAVTRADEVrDI 1205.3

------- 2 (PM)T 2

CT3 3

D~n2L C

h

Of~

andA ac 2 calatm

T T"

NAVTRADEVCZN 1205-3

0 N2 (Representative Prop Smed)

NJN

Cx m

C ot

"3 142

M3

iim

Vcaz 36 Pri. I*-)naic Ptn NjanNC Micanuto

YIW

Y2-

;V2 a-,

______ iw '

NAVTRADEVCEN 1205-3

iv-

MnSW0 SN TO

____ n n TO

&No

Figure 37. Propeller Aerodynamics Y and M Components AC Mechanization76

NAVIlIAEVCt; 12095-1~

Too

ToAM To (a~r in)

-NA 10bc;, 4 atior

i24E To

"NAVTRADLFVCS1 120,5-3

0U

o- -l

0n ~

0 0

I _ 9-4

F~igr 19 Prpele Aeoyamc MmetA

kC Mcaiton

78

NAVThADgVCV 1205-3

0 C

U CL

'I+

W4S%.- Ox

S r'CLU

Bor

(S

00

bdS InI, .6

00 v 0

-: 3ff 4 -;2 CV

Figure L, 06 Propeller AerodyrmamicsMoment - (&MOO) PAC Mechar~isatimr

79

NAVTRADEVCZN 1205-3

9cAV

a .

a p2 a) p3 ]x2

"i P ~ln )CoS/ns tw "

Figure Li. Propeller AerodynamicsHoMent (AN) AC Mechanization

80

M&VTR&M==V 1205.3

4*4

4n -

N+

+ -

# C-

P 19I

1-4

&C Hsabaniaation

ATh&"PM U205.3

C'DOO VN4

gy0(I

c D a 2 .f(N x)2

2 cD 3 p

%c Pef (N) c e C!.0* CL,, -6 +CL43 - %

CA 10 (,I) IWC1A 4 7 44 Mww, v

C p *

rV~ sl, 4

C "If(%#W

CD ;f(h (

Ac mmut.

52 q

NAVTh.ADNVCSN 1205-3

aMae

C3 u

A~ L

l~igw Win Aerdlynmcs Coff cietAG lbhnsto

M3b

IAVMPDKVCD 1205-3

9 9COP OPC

ca co

chn U) U)33

go 3X V

le is10 01 00 -

a -

3iw Win A odm i's frs adNwAC' __histo

U) U)

NAJTRAE7C 1205-3

f__OF) bSq (.Z!) f (q)

+6R

- -- "-IC bSq(jt) -f(q)

111-ý P)IF(AN )ysT

aVT n qVCe~~ S Ci( P-C) .. b~"q

c~ *c, ~ .8R.27.- fc.* r

811 3 'a)p

V f8R

•/

i/ //• _S REF i-

iw + aw _ /

A

/g(C L ) - g( , C L -) (Mw i g M % ) =

L a f (MTS

p

/ //

- • at

+ it

f w / C D o t -f (M N , aw 4, /

Sp /

l----- .IP 0, - a"t)

5.228- t F + t-

CL °f(MN, at)

- f (MN a t CL

/ ,CL

CDL A I' CDo t f A(N, at) *

f (MN, a at) T

SCDt CL

- qlVB

+W

-W-

N A

-CLt COS (it at)

1/CDt SIN (t at)/

/I

-CLt SIN (it a,)

j t

,/

/ I

CI S Cmq = f (MN, hp)

/ 4

//

////

Sc2S Cmqjf (MN, h p

//

/ a

""s cr B m4

Figure 47

F OR(

CLt

it -,

q 1 V00

/ 4 a-n 4t M/

-W

NAVTRADEVCEN 1205 13

Sq

/ I/"

/I

J'I

/I/ I

/

a~ HS

/is

HS (A c HS,

////

//

c 2Sp( (C,,, -BCm W)4 qj q) n1

Figure 47 HORIZONTAL STABILIZER AERODYNAMICS

FORCES AND MOMENT AC MECHANIZATION

86

FAWRAVOCJ 1205-3

I z ,

! 4

>°oI

rod4

rA

Figur•e ,. Tpil Roor Aerodynamies Fo~rce and Mn~ment 3 (Sh oot 1)

AC Mechanization

87

NAVTRADIVCDE 1205-3

(* )oR m 90 *(OF -

WTt-V3 con -0 4 rRq'

4TR- (') (.;)

*)C T T

(hza)TR a TT

CTR aI.CL(BT)2

4%T VB si *OT

*60 vT

(6Na)Tm *M(%T TTR T

CPTR

Equ&ations for Tail Rotor Aerodynamics Force and MomentsAC )bohanizatin,.

Figure L4. Tail Rotor Aeoironamice Fores and Momenta (Shooet 2)AC Mbahanization

88

NAV1¶IADWICEN 1205-3

Sc Da f (ymW0

-q

-(Axa)s ar

RJ7 PF 7

+qC! -J~~

0

(A11)ar T

-~SbC *f(py Y)Py

+q (AN)a

-qOxaFa - qs"0(aNF 5).bCzýF p,

(AT -t)F - 0iý P

(AMa)F - q$ O(Cmo * C

Figure L9. ?uselag. AerodtriamicsPorcas anid Hoinnt AC lbehaintation

89

tVTRAWVCN 12o"5-3

mock (7) Figru• 29 mechanised by Figu.e 50. 40

lock (8), Ficaro 29 mebmniased b rFgure 51.

EUack (9), Fjig 29 maabanimed by Figure 52 .

mock (10, Figure 29 mechanised by Figure 4.

Block (11) Pigure 29 medianised by Figure t.

MvIck (12), Figure 29 necbaniued as in Section lIlIA.

Block (13), Figure 29 meokanied as in Section III.A.

Mlock (12), Figure 29-instructor iqmts as in Section lII.A.

This 001pleto the mehaamiation of the tilt-wing aircraft.

aft. The mehanization of the tilt-wingaircra ftw ci shed ealuating the block diagram of the aircraft(Figure 29) block tr block just a for the single and tanden-rotor hell-copters in accord with Figre 1. As for the helicopters, an evaluationof oomponent oomlexity is dons In order to choose beteen an AC or Xossten of mechanization. Table 21 is an accounting of the tilt-wing aero-Onam:ics, MLock (4i) of Figure 29. In Table 23 the various frigures thathave alr*•a been considered are interpreted according to component(amplifier, servo, potentiometer, sin--osuine potentiometer and resolver)count for AC and DC machanJsations. The results of Table 23 are in-oorporated'Anto Table 24 which is the total tabulation of tilt-wingCoWpoitnta just as was done for the single rotor helicopter in Table 18.The tilt-wing wamy' is showm in Table 25 which corresponds to Tables19 and 22 for the helioopter..

The complexity of the tilt-wing AC system is 566-1A versus915-IA for the DC systen. As in the AC and DC system ccaparisone forthe helicoptors, this difference in oomplexity is marked. Again thedifference in complexity is primarily due to the greater number ofamplifiers needed for the DC mechanisation (the need of slgr inversionsfor mae functions) and the weight associated vith the D' amplifierbeing greater than of the AC amplifier* Consequentj,, unless DCamplifiers can be redesignGd to give both signs of a function and areoqmpetitive in eomplexity, or the ohoici for a DC myrtem is based onother factors than components, the AC syi-tem is favored.

90

KAVTR.ADEVcIE ??0-3

A•a L

;X

(ez )

Ta F(LZ q'h s

(AZ aT

(Az I

(A L)

(AL)

apv

,mm

AU Me•• iAaioU Nt(Lr; 'I

Irifure S a Force IMorment X

MrrAzcvrN 1205-341

,-W

X&

-REF

"" V

Ta

Figre51,Itea in"

g~ ~ ~ C o c o s c o oe

Z K

. Aur 51 Intoegraton

Velocities (U, V, W) AC Mechanization

92

!AVTRA~rJ"E: 120t-3

a

- li

fmr r2 In. *I1

7))

NAVTRADkNCZN 1205-3

Servo Pot Resolver

A AC', r -N_,. DC A -, DC AC DC AC DC

V L 1 19 1 1 4 4

? 24-j2

3L 14 4 3.6 16

35 e- 16 16, • •.- n~m.•l .= J • - _

_7 22 38 16 16

36 1 23 36 12 12

39 5 2 2

e 2 1 4 4

42 12 Ii 3 3 2 2 6 3a -..- - - - -.. . .. Il I -

43 5 10- -I ll - -... - - l - [ -I

6 7•-' L] 13

44 3 3 13 13

071 1 9 9 2 2

14 1

Table 23. TI"-'Anr Aerodynamice Tab.iation

Block ,

94

NAVTRADEVCEI 1205-3

A ir Ser Pot S-C Pot Resolve-

AC DC AC DC AC DC AC DC AC DC--- = =

Block (2)

Block (2) ---Block(•

""• ý 1 11 13 5 5 3 3 4 -

Block (4)kýýf 31 147 198 23 23 55 155 39 39 5Block (5)

Blook (6) ,3 3 3 3 2 2Block (7)

"#;.ok -(8)- - -

Block (9)_ _ _- 9 3 3 _ 3 1

M1ook (10) 9 15 3 3 6 1

7lock (11) 7 12 3 3 2 4 1

-lock (12) 2 2

Mook (13)

Block (14&)

Total 195 263 43 43 174 174 46 53 9

Table 24. Tilt-Wing Tabulation

95

NAV•tADEVCV4 1205-3

AC DC

No. Wt. 1o. Wt.

Awlifter 395 195 263 526

Srvo •3 30L 43 301

!o t73-V 17 4

s-C Pot 46 2.-IAg 58 22-2 1

Teaolwlr 9 •

CO,,•#ss 555-.V4 893-./6

Table 25. Tilt Wing 8mam

96

AiTRAIZVCEN 1205-3

9CTION rV

SULRY

This report presents a set of guidelines for the selection of theoptimum analog mechanisation of the V/3TOL simulations set forth inreports NAVTRAMMVCEN 1205-1 and 1205-2. The ridelines were developedas a series of recommendations by consieeration and discuazion ofcertain aspects governing the selection of an optimum computer. Theseaspects are summarized below and the resultant recomendations brieflystated.

A. AIRCRAFT DkTA CONVERSION FOR USE IN THE COMPUTR

Raw aircraft data supplied by the aircraft munufacturer is gener-ally empirical in nature and supplied in the form of smooth curves.Ihe most economical and least complex method of storing and preentingthis information to the computer is through the use of tapped or shapedpotentiometers driven by servo shafts. Since potentiometers my beused with equal facility in either AC or DC computers, the conversionof data does not Af1uene-. hs choice of computer type one wa or theother.

B. STMPLICITY OF SIMULATION EQUATIONS

To obtain an optimum simulation of a given set of simulationequations it is necessary to simplify the given equations by remnvalof mathemetically insignificant and pbyslcally insignificant terms ofthe equations. This is done to the extent allowed by the requiredextent of simulation. The equations mechanized in this report werealreacd in the simplified state when taken from Volume I and II.Since the simplification of the equations is a first step in thesimulation process, the optimization obtained by the sixplificationswould be the same in either an AC or DC computer. Hence, as withdata conversion, equation simplification does not influence the choiceof computer.

C. COKMMPTR FLEXl flhITT

The need for flexibilit in the computer used for aircraftsimulation is aprarent when one considers the usual requirementthat the simulator be developed concurrently with the developmentof the aircraft to be simulated. Tho aircraft manufactiere areforced to work with & great deal of epiirical data a34 ronsequentlyrequired to redirect design efforts Jn order to obtain the exactaeroyVnamc characteristics selected as a design goal. This resultsin a considerable amount of engineering changes, Since these ohangeeare manifested as changes to the aerodynamic functions stored intapped potentiometers it is a simple matter to retap the potentiometersin either an AC or a Er. computer since both use potentiometers. Conse-quently, as in paragraph A. above, thid aspect does not influence thecomputer choice.

97

RiVTRAWMCZN 1205-3

D. WOU~!TATI0K&L SEQUENCE

The comp~utational sequence used during the mechanization of a set ofsimulation equations is an extremly linportant optimization technique. Ithas a direct effsect on the accuracy, flexibility and complexity of thecomputer. However, as in As B, and C above, it has no direct beairing onthe choice of a comput~er type as AC or DC. Owce the choice has been madeto use AC or DC carrier comp~utations the computational sequence can beutilised to arrive at an opt~imum mechanization.

E. CHOICE OF CARRIER

The choice of carrier to be used in the ainui~ation computer is themoset important aspect to be considered when making the selection ofcomputer type. The simu lation problem muist be wmiwned to determine thethe computer response requirement# dictated by the expected signal fre-quencies. In Section II this was done for the V/S&t simulation firstto determine which AC carrier should be used. It was decided that ifan AC carrier were to be used it should be 60 cycles. This decision vasmade since the advantages of accuracy and response of a 400 cycle systemare overshadowed by the reduced response requirement# of the V/MMVuimlation,, the relative ease in meeting computer usie restrictions inflight simulators, and the maintenance and phase shift problemis intro-duced by 4~00 qrcle carriers. Having narrowed the choice to either aDC or AC system the advantages and disadvantages afforded by the variouscomputational techniques were then discussed.

It was decided that out of the five basic oomputational techniques ofamp~lifications integrationp altip.ioation,, trigonomuetric resolution "ifunction generation the AC techniques afforded the best applicabilitr tothe V/STOL simu~lation problem I n all areas except function generationand multiplication. In these two areas the techniques mere found to beequally weighted. Consequently., as far as applicability of techniquesis concerned, the choice of computer type is recommended as a 60 crycle ACcarrier computer.

F. CHOICE 0F SSTDI~

The results of the above discussions in conjunction with thecoumponent summaries of Section III indicate clearl~y the optimazcomputer to be used on the V/5"IL simulation mechanization is the 60cycle AC ooW~tor. Not onl~y can the mechanization be done with losscomponents but the cost and comput~er sise are also reduced.

98

NIJI•'•TA•.VN 1205-3

SECTION V

BI1JIOGM•PRJ

2. Volume II, V•TIL Nalsi, WTRALVCEN 1205-2

3. Conne11l', Mark E2., Simulationl of A~ircrabft., Re'port 7591-R~-1,15 February 1958

4. Connell•7, Mark Y'., C!Muters for Airoraft Simu!ttion,Report 7591-R-2, 15 Neember 199.

5. Northrop Aircaft, Inc., W'EW of 1he &Ltr m i, BuAerReport AE-61-11, september 19>2

6. Vertol, Technical Aircraft Data for the DoseLn and Fabrication&t Q2.•, ged-l M e&Ir irat.i.ona.• t .r -Volum 3 of 3 volums, Reor. t 30. 1o--U.

99

WNTRAM. 1205-3

SECTION V1

MOHENCIATM AND EZ'ATIONS

Tho toll;5w4V4 list of qmbols to used throughout this report.Th% 1'i.L9t WA0 q ',18 Are &riIW In alpambetioal order with lower caselstti'al" IJws*td fi.rstg then apital li•,ers followed i preek letters andXviwbolg at stsol~mon. or~in,

q R ý TON U1(ITS POSITIVE MM~

JMA2 004 ow1~g nls r~aftan UP

1xJagituII&l& flap sngle radianH Rearward

Late", flp angle radians Right

SLoMit~diriA oter of pmvitv feet Forward *fzeferenrxwe vnt

LaUUr center of grwvi t position feet Right otreference i oint

Nomrla Center of pyj position feet Below referce

point

g (Tevi• .- ?vanaa- 32.2 ft/8" 2

P"nssre ultitwd. feet Uamds

Rate of climb ft/sec upward

q Imsospredi•l. druido pren.-e lb/ftm2

qT uselavg Omamlo Proww lb/ft 2

q* PitchI rate red/so Nos up

q*-d S element *undo p rav lb/ft2

r Turning rate rad/sec No0se right,

t Air te"Perabwr degrees C

At roýud t ta. e variationfr~stea§ai F) deprese F

Diwtano. from blade hime to feet ?IM stblade station Up,

10D

MAVTRArEVCEN 1205-3

*STMB 3ESCRTPTICN I.TNI?5- PO)TIVF SEV!M

Lateral control angle degrees Right

4, Hlade element area feet 2

Longitudinal control angle degrees Forward

Blade caord feet

Blade element drag coefficient none

, BFlade element lift coefficient none

Tail rotor coefficient of thrust

Coefficient of tail rctor torque non- Acceleratee

QTR dimensional rotor

Drag lbs. Rearward

F' Puselage drag force lbs. Rearward

D yliade element drag lbs. Rearward

East position

Grvound speed, "ast ft/eec

F!W Force - Left wheel !bs. Upward

FRW Force - Right wheel lbe. Upward

FTW Force - Tail Wheel lbs. Upward

SX Force due to main rotor lbs. Forward

FT T Force due to main rotor Ib!. Right

H Altitudie above the field feet ipward

HF k' titude of field feet Upward

HLW Height left wheel above field feet Minus aftertouchdown

PW Height right '*heel above field feet M4inus aftertouchdown

101

NLVThIN&.CK 1205-3

S!MBDL IRIPTION UNITS POSITIVR WSZ

RRW Heiht tail mi..l above field feet Mitnu aftertouabdown

SMosent of inertia of roto qosts slug.aft 2

as seen at main rotor

IX Momant of inertia about I axis slug-ft 2

Mlaes nwnt of inertia about 1710 2flapplag hinge slut-ft

½ Moment of inertia about T 4xie slug-ft 2

is Komnt of inertia about Z a=do slug-ft 2

L Lift lbs. Upward

La Rolling mowent about lb-ft Right wingplane X atis doam

5p Fuselage lift force lbs. Upward

4M Lift due to main rotor lbs. upwar

LR Main rotor rollinvg moMt, Ib-ft Puhes rightwing down

Lis Rotor hub rolling momet lb-ft Right windown

T*9 L, Rotor lift force bs.U

L*1i Made element lift lbs. upward

NPitching Momnt lb-ft Noss vp

Pitching soment about lb-ft Nose upplarr0 T Oda

Hab Umer

B mba mee eluae

V? Ftuela.t pitching Rm•ont lb-ft Pushe* nose

Mi Mss of aircraft slues

SLanding gear pitch ing .t lb-ft Phes noseup

AVTRLAI:VCEN 1205-3

feMZL. ~ r uj UNI "I P0SI TIVE M37S

MR Iffect of main rotor on lb-ft Pushes no&.pitching mcnnt UP

MPH Rotor hub pitching moment lb-ft Noe up

Blade element aerocOTwusc flapping ft-lbe Moves blade tipSmoment up, increase

N Engine rotational valooty RPM

GTound speed north ft/s9c

N Bank mo nt about planZaxb-ft Nose rit

N. Fueels e yT= moment lb-ft Pushes noseright

NP Main r.tor yw oent lb-ft pushes nos.right

N Effe3t of tail wheel onyOU moment lb-ft Pushes nose

rioht

.Ro,.ling rate red/s1c Right wingdown

p~t Pressure brake, left The-ftt2

p Preasure w&ake, rigtt lbs-ft2

P5 Static pressure at sea level in. uf Hg.

SLeft engine turque ft-lbs rpoedr up

SRight engine torque ft-lb Speed@ up rotor

QM Main rotor torque ft-lbs Speeds up rotor

•B Rotary brake torque ft-lbe 9peede up rotor

STail rotor torque ot-lb. Loads engine

4IT Tail rotor turbulence factor non-q djimns ional

NrVTRA 1rVC FN 120- 3

SYMTICT, y S, I R1!'IPTI" C, N UNITS 1V FI1 7 VFE SFNb

R 31 ft. Main rotor radius feet

P/C Rate of climb ft/sec Upward

U X axis velocity in air mass ft/sec Forward

U Speed in X bo(d axis direction ft/sec Forwardrelativ3 to a point on the ground flight

UPTR Tail rotor norral velocity ft/eec Positive tothe right

UP glade element relative velocity ft/sec Underside of blade

in air perpendicular to blade exposed to thespan (long) and to UT wind

U T Made elment relative velocity ft/sec Positive in*-y in air perpendicular to blade hover

span (long) axis and to rotorrotation axis

•W Wind speed in X axis ft/sec Wind blowson nose

Y axis velocity in air mas ft/8e6 to right

St eed in Y body axis direction ft/sec Flight torelative to a point on the ground right

VT Fuselage (total) airspeed ft/sec Always positive

Vn TDtil velocity of tail rotor hub ft/sec Always positive

VW Wind speed in T axis ftasec Wind blowsor right wing

W Z axis velocity In air mas ft/sec Down

WF Fuel flow lb/'r Drains tank

WG %.ned in Z Fbcd axis direction ft/sec Desoentrelative to a point an the groumd

W Induced airflow in Z body axis ft/sec Air blowsdirection down

(W ' Mean inflow velocity ft/sec Air blowsmean dovmuurd

(Wi) local inflow velocity ft/sc Air blows

loon AV

MV 'MA TFWVCKN 12-

5TrM1W)L M-$CRI.T01e N !,"N-LTS •TS1 TI 5E

-1MW p sed in , axi s f/@ee Wind bolev down

O Inflow dist•ibution facto- - F(y)

I Longitudinal force lba Forvard

Xa Total aerocdyrni forese b. Fomardin fuselage bod• I direction

IF Fselage longitudinal foroe lbs Forward

"Landn g•ar friction lb. Tomw d nose

T Lateral force lbs right

Ta Total a&roa nazde foroe in lb. rightfuselse Y direction

yB Di.t afl from f1sp hi•se to ft.bladde ce.. o 8.75 ft.

T7 fNel lateral foroes ls rilght

idTR etd fore& due to tau rotor lbT Poitivt torij~t

Z Helml farce lbs &mard

Stotal f e in fNselfe lbseZ directim

zlo Land'g gear earml f.-roe US Dmnwardi

a gle of attak deroes Relative Windfrom below x axis

lueelage angle of attack deo&iea Wind Oefrom be low x ax is

Tail rotor d.,o plax vvlociV doees Re lative wind

aigle from below I axis

9 AM n4g of attack dovege Wind comes frombelow blade x-7plane

NAVT1AXV-% 120 .,- 1

SYN¶rCL r.SCaIPTIoCN UNi TMIS P c I TIV FNSE

OF Sidea]ip an!ON degrees Relatlv" windfrom riet

0 R1I angle (instrv, ent) degrees a1a right

STail rotor mideslip angle degrees Relative wind

from right

Brlade flap *ngle at asnith degrees Blade tiphi1gh

Rate of change of blade element dog/sec Blade Tipflap angle upward

e Pitch angle of fuselag I aXis degrees Level - 0

U 900

Rate of change of Ealer anWle#9 rad/sec NoSe up(Pitch angle)

Pitch of tail rotor blade at degrees Positive 1hen3/4 point lediAg edge isdeflected tovardpylon

SAir density slugs/ft 3

* Rll angle of fuselage degres Positive ri1htwing down

* Rate of chanve of Euler Anrle,4 rad/sec Right wing(Roll ang).le down

Made -a. 1leMent inflow angle degrees Wind bums frabelow the unp-

pitchad bladepla.

STrue heading of fuselage X axis degrees North - 00

Zat = 90 0

Wind heading degrees Wind blowstoward th isheadlng

* Rate of change of Eulor axle 4 rad/sec Some right(Yaw angle)

2Rotor rotational velocit•y r@/eoc Conterolock-wise from top

1106

NAVTRAIIVCVW 1205-3

TM ELt r1 MSC PI P'71C N U NITS F()2iMI SF'NS!

S ?Tail rotor solidity/advance Non-

ratio parameter di1mnsionAl

Tail rotor velocity/thrust non-ratio dmensei..nal

AAR ft rotor rolling mment lb.-ft. Roll right

IFR Front rotor rolling moment lb.-ft. Roll right

7 ARH Aft rotor hub rolling moment lb.-ft. Roll right

Front rotor hub rolling moment lb.-ft. Roll right

77 Fuselage rolling moment lb.-ft. Roll right

LO Landing Gear rolling moment lb.-ft. Roll right

RA Rolling moment due to rough air lb.-ft. Roll right

4Fuselage rolling moment lb.-ft. Roll right

107

a. 5ID7L, ROTr,,R mmVCms

(i) FUJSKAGE L nTupA)rc8

~Qei~a Anie~fAtAao snW Sldw~lpj A&rI'+

40 + are÷,u tan W 0 an__ f. (W)u (6-1)

- ar .tan_)i v (6-2)

Fu ?useiame 4nmiltc Preassure

._ ,o r U2 .y2. (,.

D1ý a 5 (I.-r f ) f (a?)tf(19 .1~ 2.~5 (6.J4)

K•. a 0 for no externAl store$ aboard

a 1.0 wlth erternal stores aboard

Fumelft ift

- (91.125 [.309 + f( X, 5.633 q (4

Ki a 0 for no external stores aboard

a 1,0 vlth external itores aboard

"VT ( - f(W)(6-6)

(2) TAI '7VR A)iAMCS

Tall Rot-or tar,,1)e Faoto

ft(a) (6-.?)

ILVTRLZVCZN 3205-3

TR Tail Rotor Torque at Main Rotor Siaft

/q* 4 (R~R)2 Rr] 6.1 (6-8)

CTT, Tail Rota? Coefficient of Thrust

'-TT - A32 + B32; A3 w .0W8 f ( Rr) + '0211 r fSe)f (A.4(6-10o)

UPTRv Tail Rotor Norml Velocity (Nondimnsional)

. v- 36.06 r + 2.74. p6.)

A.. _Tani Rotar Solidity/Advance Ratio Parameter

0.. o.1945 A 34 0.1790 L (6-12)

A -3 f(.D B 34 f (46)

an,, Tail Rotor Disc Plane Velocity Angle

wl + 36.06 Q (6-13)

6p a U sin TR- (W + 36.06 q1 ) con a

Prx, Tail Rotor Sideslip Angle

p- 6.0ta(l V -. 36.06 .r+ 2.74) (6-14)(W +v 36.06 l)2

0 U2 + (V 36.06 q sl min PTR" (V.36.06 r + 2 .74p) con PTR

109

NIVTRALIEVCEN 1205-3

vT, Total Velooity of Tail Roteo' Hub

vT -v/u2 + (V :- 36.0o6 + 2.70p) 2 + (W + 36.06 •)2 (&15)

A. Tail Rotor Velocit!/Th~ut, Ratio

ita.o564 vTR f ( .O ) (6-16)

ens Pitch of Tail Rotor lade at 3/4 Point

*TR - 10.03 6e' - h.8 (6-17)

0 < ACI < 2.293

60/ - .1076R + .06760 a 1.77 + ABC Inputs

(3) wrmwO GaR

FIPW, Right 'Wheel Force

FRW .1,0 00 (m +(6-18)

Only when lriht wheel has tmohed down. OOthewise wo.

?,No iheel For"

jr.W a.10,9000(T (6-19)

Only vhen left wheel has tonched down. Otherwise zero.

FW, Tail 'ieel Force

F1W -2,.O * W (6-20)

Only when tail vheel haa touched dwin. Otherwise ro.

(14) 10NOITUMflL FORM

Xa3 Total Loagitadinal Foare

no

x&VThA DgvcV M5O-3

U ~ ~r Y, useiage L.ongit~udinal Far'oe

!12' -

XW -K [Ot5ZLO- 2*3 O + OEL KO(6.23)

Kua i UO 1.2.25 fps

(5) 8=131023

TastTO Side Faroe

~a I ThYR *hR*Z~(-a

yro' fucela. &ldo rues

YTRt side Forme D to TAU Rotor

y TRCr TA2 7aO15(6-86)

(6) WON YORCE

&;Total !Dmn Par"n

Z7, amelag. Effect

Z?- cIP 008at- N~ wins a009)

-W (w + F~ .m *~ (6m2

'ALRAEV .TA•i- 1205-3

(*2 hILL NO MPFNSS

Total R•illing Moments

af t TR 'h* 6 iIQ -, (545 +, + L m÷2•. (6-30) • "

LR, Main Rotor Rolling Moments

R -7.85 •y (6-31)

*• 6. 5 (T, - Fr) (6-32)

Fuselage Effect

-54(#)qU> 0 (6-.33)(8) P1¶ llH •fTS

Mat Total Pitch Moment

Ma - Is d* * MR + ,G * p + MM-

A %, -p11 (50.5) (6-3)

Horisontal Stabillser

klI korisontuL stabillser effects a'. canoelled due toincorporation into proper fuselage effects.

MR, Main Rotor Effect

MR - -7.85 F - .o*73L (6-36)

M,•, Landing Oear Pitch Moments

MW - 4,.38 (I' + FIX) - 18.99 F,• + 5.36 XW (6-37)

e112

N&VTRLWVCU 1205-3

r, Fuselag Pitch Momnts

My. ( 390 [.058 +f (ta) I+ I1 23.63 q (6-38)1- 0 fr no eteral star* aboard

S1 - 1,0 with eo t-rna1 sta-s aboard

(9) nw icmN., Total Yaw Nomnt

Na .-, -YTdx + NV + Ny + Nr - 36.06 .TR + N - Q

+*ITVA +N~t+ N + NW (6-39)

a

NO Nhoel Yaw Moment

With either or both main heols on grraund and tail mbeelon ground with tail ideel look off

k - 2200oo rK% (6.U. )

NI, uselage affects

?I a 4228.8 q fp) 64)

Nr, Turning owmnt Due to Turing Pate

-Nr - 102,762 !- q(61)

ii, Landn Gear Yaw oment

xW - 6.45% [Pw - PEL] XG (6-4i3)

(10) M ELEMNT AM•1XIICS

y. 00*. $in * Valms

In an equation contaning y,, cos and/or sin 9, tbeequation mnat be computed an war time as nwwessz7 toinclude all combinations* That is 3 tim. for y alm

6 time for sin * m/or coo t alom18 time for both y and sin *mad/or coo

113

KVT RACY 1205-3

Stations are distinguisded br subscripts "-7. Tkhs,

the 18 blaM .lomnt tAtirons ares denotOd 0-9.9,0-21.8, 0-28.1, 60-9,9, 60-21.8, *to.

TagnilVeoloi,

"UT (o. +YT VCs v +, +, U •t., (644I,)

Vertical V41oci•

up *w - w ~(0.0173) + (1,052 + y)

(q, Goo$ p sin +) (6•.45)

-ýe, 0U coo - V sin +) (.0173)

0g Inflow Angle

U

S -7 T (radians) (6-4~6)

M &iAnE of Attack

0 "a Pitch Anles D ep~e,.* - A*, " oo Big s , (6.40)

Ao 8 - ((asoB

A la f( )8 8 a

Bi af(80198*9 6 ) OF e -. 258 dog/ft.

,~, s~t~Of Atm ,bez.

po houena < 5

> 5

NAVAgRArEVCEW 1205.-3

S!¶t, Flapping Moment (Main Rotor)

N,3* -� [78.88 UC2 V76.9 L

"-T*9.9 C*9.9 T,-21.8 "L-21.8

÷ 56.50 TrL L (6449)

Main Rotor 5baft Moment

f (78.5 u U C - 73.02 U2 T CD ) (6-50)T F L *-q 9 T 4-9.9

* (190.0 U T U % 180.3 U2 T CD j

* (60.42 UT Up CLI -106.2 U2 T CDIf•-,2.1 -28.*1

S-5/6 1 %M, (6-51I)

Lq, Lj Rotor WZ Force.

L* 40~'[7.733 U`2T Cl 8.395 U2 T 'L r2.

S1.969 u2T 4 1 (6-52)T 1.48.1

5/- /6 ( L#*) (I + f(H) tf(Vt)] (6-.3)L14R

,C'(6.4s35 t2, - 6.872 U9 UP -9

# (93°4t 2 T CD* - 8.741 UT UP CLI1 1

115

NAVTRAIFWVD 1205-3

v T3. IC T- cL 6 UT UP CJT T

S 5/6 Z (.o173 L, coo, -D* •n ) (6-55)

FT, Rotor T Foroe

R 5--D * coo - . 3,,5 L,sin *1 (6-56)

", Coeffiol~nt of Lift ftuztion of a

,I*. k ki fGa.* i - 1, 2p 3p, 4p 5 (6-57)

2 UT " (fT6,O

,5~m57.3 (e. 0 *- &19*as 4ble sin4)(~

, 69 57.3 11 (&is hinmb,, Co.

as,q &I 1 blav Fla Arngle Fourier Coeftioients

go 0 60 m .10

49,7680092

248,800

116

MAV'TRA.MVCK 1205;-,3

-oý.0 60 o- ".ob180' 240 JOC.215,b6o

- a ('o.•,() -, ( 5.o5) (6-63)

,U K., PRot.or Ha Momnts., oc Nueela5 fin 0r, bl.

LMa -" w tw$ * TD e (6-464)

(W '~Lcl Il1f VJio

ai (W 1 ) (1an 010 0

- gin*) (6-66)

(11) TRLUSMTIOAT!OR&L A." o AIUR NAT

UG sin . . 1 dt (6.67)

Vo-0gk060,0.a..i -tto. lz] ft (6.66)

WO ' 00 4 " 6 "8 v - " (6-69)

N-006 *n 000 0 + sin3 # (TO SU~ WO 003 #j.J

-, - guy (Vo 0039- 0wo gu ) (6-70)

U.7

ATRA!zveKN 1205-3

i Iuaog 0. wi w*S (VO fin 4 WO 06

*0oo (V oo -G o sin f)

h UG gin 0 - 006 1 (V0 a *V 0 ) (6*Wo2)

VWi bloom fr * heaing (t48e) a wrl Wt!ve.

o �eotrioal ooqemmt f wind is ocwIdxexd.

s C . win (I - 1 -* 1860) ° (6-74)

IW' i n. 005e coo (Y - Tw '800)V- (I.'•;

+ si " gi Tw 1800) 3 (6-75)

Relative Ai•wY, Voeloc In k•,' A..

U a UO + tJ (6-76)

V , vo + Vv (6-47)

w. a 0 W I+ww (6-.70)

SLa d't (6•79)

KXX

dt (6-M8)

-,Y

re a dt (6-81)

NAVMhADEV(ME 10(-

Mear Inflow Velocity

(W -

Q9otr Vol ority

N or th and Ra, ostoi AltItude

N * N rtt

E - E d t

h 1- h It C'

Hieadinji LI ~e

I (r cos t' q sin *) sec rdnsj'sec.

T 5 7.3 /' Y dt degrees

c os t' - r iin rdq !e ýFN

0 r, 71.3 it rdegrees

Roll Angle

1, t d23/4 t degrees

(.)MASS A NTP INERT !A

Cene of Iravit Position (eet)~

- - ~' * ~ K- ~'MK, + I~j

O* MO~

r f

AMAv'rtVCF-W 1.205-3

b. TANJI7M R(W"T)R TEVI,',S

(1) FUSM~ACFE AEWDTJIMtCS

Cx,3 .Puselag Ansle of At~taak and Sideslip ingles

9 ~w - f (W (W)J(r1

A?-~ r -f(Wi.AV) f~)

q ,0 (V2 , - 3 3900 f(W) f (Wi AV 21238 r(w)f(.w AV (6-92'

LF Fuselage Lift

flyj, PiUDS104P ra.

PIua"1a Airgl..d

V vz (6-95)

j 1 IG .4f(H) - K1 l]K,~(8360 ,c-I.D0 (.025 +K,,,, K,,,

UG (6-97)

120

N(AVThAtEV(7E 1205-3

lAnding Gear Rolling Roment,

-Zw (K 2 4 - K3p)

(3) WN!()IUTN&L FORME

I& Total loongitudinal Fore*

I~f Fusel"g Lon~itundinal Fore*

IF - 0.986 D.y - 0.165 L7, (6-100)

(4) 311Z FORCI

T Total Side Force

F + Y 7 F AT RA pl (6-101)

TF fuee7lAge Side Foroe

Y. - ~( fp 1 ,) (t-102)

Za Total Ekmm Force

(6) VVM CLL M W-W

ZIP Fge~lage Effoat

7, 0.165 rý- 0.986 L? (6.-104)

Lo otal1 Rolli~w Moinnt

La& -7 'R*- R - M I (6..io5)

NAVTADZVCW 1205-3

-Zad * A'/W-1lO * .oi136 Q,0

"FRO17, R P Rotor Rolling mr,,nt(

-I " (O.LB) (FT FR)

-'Al a (7.65 (FT A) (6-107)

77s FUselage Rolling KOXcnt

F q qp)* af (C~r) t(py)) - KI,(6-106)

X1 to be determtned

x Total Pitcoh Mont

N za, * XFR * MAR * PIO " (6-109)

MnMARRotor Pitching Mouments

Hn - - •8.8 7 *16.46 LF2 (6-110)

No - - [8.377 A ' 16.,49 LAB) (6-111)

(9) TAl MOUT

wa, Total Taw Moment

122

NkAV7RATUrVCrT 1201ý3

NFR NAR Rotor Taw Moments

NFPlu ~ ootNF-qf•- Kt6. o L etr9n (~-!16Q

TrR

- r I1 q(6-i116'

- /4 ) VT

Ny, co u , sin T values

In an equation conta y. coo andt/or win To the

equation must be computeda u nMJ tilme as necessary toinclude aln combinations of the forward rotor. That Is3 times for y alone. Six tims for sin I 1ad/or co1 7alone. Eighteen times for both y AM• @In T and/or coo T.Stations are dstinguished by subcripts Y-y. Thus, the18 blade element scations for each rotor ar denoted (00s

"'R, (6o° -y) FR, (0o -y) AR, (600°-y) AR, etc. The subscriptFR or AR denotes forvw-d rotor blade station or aft rotorblade station

UT Tangential Ve1.ocity

U y - (e + yý1' * V coo I . U i V (6-1I8)

T

IMr&gVr,"Z 1205-3

p (?y) Local Vertical Velociy

con1-7

(ql cos I + r sin I)

-Ji (U cos V - aim T) (.0173) - 16.49 q,

P T-7 (RniLAN) (6-120)U-T"O T-y

M~e ngleof Attaok

1...Y (6-121)

o endO'- " -" ooeand 0' - Aing-le (6,..:22)

Su 2 12.6 T2 (6-123)?(I-7.3)1 ('7-7.3)+ (1-17)

"C'(*-17) # 23.1 U T2 ( -2 3. , ()

ofF CMp,j %, Rotor Mu*ft Momnta

12k2,

1 (1.? z "(T-73.)"

707?,P. 7 T 2 ?1, ) n•

12L)

NAVTRAPEYC•,: 1205-3

020 UT u 1•-2• )U,

f . 3r Cf( f(U) (6-1?5)4F " 2" 4m A'm)

AO0 AAR - - R f(V) .) + f(A )[ + 1000(A - A,- )]

AR 0O F 4F- 0 FR 0FR FAR 09Ai 0,FH

(U-126)

L tFR, LFR LAR Rotor (Z) Forces

LR 2,E. 2~UTCLL 7.8UT 'CLl~? *UT2CL L-iR -/07.5 u, TClj( %-7.3) +78UTcL( Y-17) + U T c.1)

CL-I??)

LFR " ½ ( FR ) [I + f(H) . f(VT)J i.o 1 (u) (6-12P)

AO 3AR

LAR = 1.19 L LFR A OS F- . f(U) . f(V) . f(A OS )

Sf(A 0 ) (Ln 1000 U 31 • O0+ I&A001a K Rs 1 2000 q,

(6-129)

K S - 1.0 when LFR-> L> kA

a 0 otherwise

A when c

"A >MAX- when >A

,XU - (6.5 x 10 . t(U)

125

NAVTRLADEVCGI 1205-3

D T n 0 , F XR Rotor (1) Forces

D av O[(7.43 UT2 - 7.5 EJTUPC7j ) (6-130)-D1- -3 . UT•.j(.r•

+ (4.38 UT2 CDj( _-17)FR - 7.(8 UTI FJa,-17)

+ ( .-37 T2D 231) - ITUP L( ,-2 -.1))

F , (.0173 pLcoo I - D @in ) (6-131)FR FR FR

S'AR F Y * 3o00•f(U) .-*f(v) . f(9) AI,

T TR Rotor () Frore

f Y (-DI coo I- .0173 • L' sin r] (6-133)YFR FR yFRIR

rFT AR F 300 f(9)). f(T). t(9) A., (6-13)

CL y. Coefficitnt of Lift

L - f I-) i a Is 2, 39 4x5 (6-135)

126

?iAVTRADEYCZN 1205-3

pr' Flap Angle, FR, ,

I IR 7.3(mas P coo I - ble m inYT) dog. (6-137)

ina 57 .39(alon inR - ba Co )dog/see. (6-138)

SW, a~s bl , Flap Angle Fourtar Coefficients

amP 0FR + P60ya+ P12oýR + NOpR+O MP2h% + 4O30FR 4#5502253

(6-139)

1 1P60,pR+\A2OFpR M P~hOFR - M300y~R

3FR 18L~,607

+ b1 * P (.390) - ia1.08q, (6-140~)

1 27

PAV'?RAIYCKn 1"05-3

144 0.5" P - 0.5 M 0,5 +. 0,5..b 7IR 60. A~ '120n 184% 'VOF

16 tOL

a] an(. 3w) - 1.028 p (6-1141)

-IM-AtA M7Wf M A Rot~or Rub PRoinnto on Fuselag.

"" . 610 Uls K.-A- (6-143)

Mm - -. 2125 1 o. too .T + LI 2 a5g (6.4.4)

*i a K B (6-1145)

Ws•, Local Infto Volooitr

(w)-7) (W)) mcoo in

(6-1459)

(12) TR•JILATIORL AnD LMMXA R RATE9ýt aU 1" Ormd"' Velocities

Co a I I X, tsi (0 - 9.5) ] dt (6-146)

To![a .Eo ~9. 5) sow* .Uar d~t (6-1148)

128

IFV72AIZrV M~5-3

0 ru Co 095 U(1)(oSA0g 0 )

vi TI (V G* 0 4 - V0 a" 0) (6-U~91~

b sin (s1 e, 5) -O (6&( . ) 5 sn +)

1V1M non from Tw saaedl (b..e) s tv~ns

TeVailea cawomt oft WLd ise 0erod

#,~ ~/~{l1(OF - 995)oa9e - *1o

V!1110 si (9.5) coo0) #(6 Io*

Relative Volooesi~ n ArL

.0 ~(6-M5%

w Ww

ft I V

AM

NAIVTRADV"'VN 12)cm 0

Yy

Nr a ) * a ,At (6-160)

)%an Inflow Velocity

00we- LY 2r 6-16.1•(mow)I YR 2 IrR2

,Rt ArUlar V.eocity

S .. (6-162)

'T OT 0 n * 'Al

Worth and Usot Positims. Altitude

N . / N dt (6-163)

-- / S dt (6-161)

h * / h dt (6-165)

V - (r co + ,•n * cv 0) foe (r - 9.5) ONS/3C (6--146)

v - 57.3 dt DZaR•

Pitch~ Angile

0 - cos 4-r • RIiS/SC 6-Mn7)

S- 57. a dt, 9m.5¶ DSMKM

Roll Angle

* S* ir' R.) fNS/SE 6-(e

-Rt

: O *. 4

dx, 1, du -enter- of 17revity Position~

dx - *)00 - .006P7 (M M f (YN'7N(-6

V/S7'OL LIRCTUF? (TILT,-WTMO)

1, 1UJFW?L&TR! US~r IN XC-1-MA ?FWATIONS

J:!ý"l Dfintionb Wing Npan

- ~Mean Aerodyinardoc (Thord

i t Incidence Angle Horizont~al ftAbiliser

:IV Inideno. Axgle - Wing

r Main Propellors n-1. 2, 3, 4 - Top View Left toRight,. looking fcrvard

q r~ianric Pr~e~mw - Mrse Stemm

qFM rynamic Pressure at Horizontal St~abilizer

QVT Itaiuic Pr.essure at Vertical Tanl

qw Trnaaic PrevuFA due to Power on Wi~ng Etfforts

.A n lade Plitc~h Angle - Main Propeller

To, 5 loaff.iciont of Thrust. at ~iing Mwa to Inflow'hvelocity

TIM Diameter Tail Potor

F IFU Bel1age

E Tner-tia of Main Frop.11er Ffladetv1 andlft

IflsArrtla of T&Ii IotorT Mfades a&M 3haft

J A~vmr-c. Rat'n MlainTro poll~r

RAVTRAMEVG"KN 1i205-)0wa

J TR Advance Ratio Tail Propeller or Rotor

Main 0 ropeller Moment (Initially Pitchina)

Nn Main Propeller Thrust Coaonent NorzI to Tn

N RPM - Main Propellern

SNom inal RPM - Main Propeller0

nt RPM -, Tall Propeller

Qn Main Propeller Torque Coefficient

5 Total Area of Wing

S Total Area of Main Propeller Disks

T Total Thrust of Main Propellers

Tn Main Propeller Thruit

Ti Tall Propeller or Rotor

TR TThrust - Tail Rotor

VB Total Velocity in Aircraft Bo Axes

VT Vertioal Tail

V Total Velocity in hind Stability Axes

W Wing

Tn Main Proreller Moment (Initially w--ai)

apAngle of Attack - ruselage

Angle of Attac - Horisontal %abiliuer

Angle of Attack - Wing

-F i9deellp Angle - Fuselage

0 TAde Pitoh Angle - Tail Rotor

A •Sideaolp Angle Wing

4E Dcwmrahl Angle

132

NAVRAMMF/N 1201"-3

______o T.)finition

e &ngular Accel~ration Main Propefler

I~rR Inertia of t~il rotA-r blades and shaft

2 TRknrular velocit~y tail rotor

FAII TRAkgular Acceleration 'rail Rotor

2. TILT V11 RG LIRC UFTi."rr SIM -IT &ON FET A TI 0N

a. AMMTNAQIC V&RIARLES

a a (6-170)

PFa tan-'(-11

VBWrR7

q *1/2 V 2(6-173)

p f (h

b. MAIN P1rPrLLFF APL'4MICC

*0 (1.w + a7) (6-1.75)

11n " ,Rco7I coo o vn( in w rCe1

+ xq'I sin 1. 2 q Cos 1 (6-176)

v n =v P aine (6-

n R

V * V cos A i. 4w yp ca irin i

n ni

1Y33

PIAVTRA!ZVCrs 12O

Jn oos n ( ) ( ) (6--In 0)n

60. vi fin i •(, (V" n

"Tn nB B j, J

C'Mn " ( nan(4-186)

a n

(J,) 2•T J(6--187)

.''I

n 0

41 22

), " 'n 77n183

-- L[ cot m in (614

n nF n n

1 cot*)Isi sin*n nf n* n. J

llý co J! (j i n6-185)n

G14ri d .0 n n(6..186)

n (q-)(..e* (6-187)0 2 o

n q- () e) 'N (6-18a)/0o n

0 0

n)

rl /041

rY r N n)2

0 r

n-l

P n-'l

(•= ) - I Z ) - A = )1 -[ aZ ) . £) 2 6 1p" a r•

14

(b -r sin V/(6-19L)

a n"w n,, Cop 'Dn co

n-1

(Air L I~ (Az 'Iy, f (,&z ) (az ) 6- 1915(AZa .a a3 Y2

P,1 P4 P2 p3

o1 Xa P4 p214 3

n-l1 n-l

(AM)P T Z tT,(coa 1.,) $pivot T (!eIn I*) 'Plvotp Pivot 1 n

Oil cc's s$in I +% coo sin I.

(N2 Cos 02Sin *1 c93 'i i 2 ( 9

CO COB1 co. * R1 co34i coo 14) 11~

*(N2 Copr Cos W * N 3 coi 'o 1, )03f 0t 2

n-1. nu'

w here 'I io )5T * T * 1.2T

135

N A VrR A:. EVC EN 12 Jc-I

( )"--x - (Xa ) I a a. 0 v"ap a p4 rL a p2 rI '

- n'coP) cos M. ( P n) co1 tvnalI ,-I

C. WIN£G AERODYNAMIECS

wp W- v lwU si I 1 * W cos iv (6-19$9)

p , - 199)

*u .+ V) V aV (6-200)

2 2T 1/2AV up + k' a- (62M

c T T/qw Sp (6-202)

qw:-q " *"/sp) (6-2C9)

2 2 2 , 112V " [ (6-204)

a - tan- 1 ((6-2on)- I l

Vw " 2 ,n (6-206)

3 2 ^022L~ ~ ~ 1-2:

L L L 'w

'L '1. * 1. *•'

0IF

0 6

.N&VRArFVF'<'N i 2'5-?

(Cj ) b ÷C 1 • c .

0 6SF mql

n w n4 * • "w zA n r

(cz) a c r - 0 L Cos (6-2131)

vc 1

(•.•) - -(c•) ' , • ( (C 8 ) o, (6.-2V?)v , , ( (6 - 21 6 )

a v 't) b S f (CT1 s 0 , (6-217)-(r 3 ff(c..) (62)

(A)- )b t( 5 )q, (6-220.)

d. V'MRTITL TARILIZER "XVTNArlC3

" - ' ,'. 8 R (6 - 2 2 24 Y JF pTR

NMV't¶A M2VCNM 1205-3

C X iR + lr (_2J1

p r

(hI.) . (,( (-•) q (6-225)v't

(.A,) C. I b• (, )q (6-226)

(-vtv

(tNa) - nS (C )q (6.227)v't

e. IPZDP,.I AI., !rAT.TLIZER .k•L"•UXAICS

'at c ' - (6-228)

T. t a t (6-229)T-t "'at t

"t ot t&

(Ara,) HS Dt Coo ( - a t) t &in t,( ta t)] s -- q (6-231)

(AZ) ,[+ c- t sin (it - a- )t). c (c.a)q (6-232)

(AM&) -S -( S b S (A a)K .a HS (6-233)

H13

f.TA.IL POC)R kJEI•l7TX~aCS

() a 90 * (a' • (6_23)

,'Rt"¥ t ., (6.-235)

1)8

NAMAU!VIN 1205-3

i TR- rrR )KTR(6-237'

Jh * 60 ) 1 R (6-21e)~TNTp

T~ l2 w2 )1/2 6-219)

IT. TR

c (B")2 (~2

p (L) ) E;

( r4) - TR CT6

Q( -IX) I c (6-24301

(AZ T '" (6-.244)

g..

139

NAVTRAr~tVCFZN 1205-1

(ý 8 e, t6.-2h9)L a?7 "

(Ma7 qSet C m-.C a .) (6-250)

(AN 8) F q SbC n P 7P(-21

'- CL , and C n also have effects irn the wing

"r~aodtyrI&Alcs.

h. T ILT W1140 ADMOA?? FOC N PWRATO

(1 1 Fort*g 'Iuatt.

SIMit ) q, (T n cos i v M - Y o 3 i

-[t~cc ( %)* 0 ii(it - )J Sq(-.ih~i H

D t t t - Sq -ý)Sq%'

NO(U* Vr) ms ag In 0

(2) Y ?oroe ISjuatkio

4 (-W, sine) qtn CY qq* *SqCY *py

a m(V + Ufr - WO) mg co 9 sin*

(3) Z force 3Quatiorn

C7 (f (C TS)J% * (-Tr, sin i-* N n c oo J3 coo

win(1 at) * CL C0(1 H ~)Sq (!-S I -T~

144 mVp t. - we Coe S Cos 4

140o

NAVRADFVCZW 1205--j

CVbSrt(C 's).)q

*+Tsin i~ N~ cu632 cos Ii.) -(+T sin~ *, N~ Cos :Cos )

2'' w N2 cwI - (3 s~ v.~~s3 3~

+ (4 +s ain j3.I N 6# sinp 5z (+N 2 sln P2 + N~ sin P,' 1?

- T si sE Msin)sn

P ~(5) Pit~C4 IUatico

Cm wcS( f ((Ts)) %w

~~~iTo *(coo Y xpvt'XT +n w)p , ot T nI ain yw pivot

Scon A, wir + N~ hcoo A, sin i.) a

-(N2 cots P2 sin *w N 3 coo 3~ aIn W) '2

* IC on 3 c oo IV~ H coo LCos V~ x I

+(N S 2 o 2 Co 0 N 3 con coo \,)x2 (Yni 3n

* (Mn coow3n

cooLi-* C n(it - at ] S (! H lcos at) CL q

t tS

s i n ~ i a -L c o n ( - a ) I q( ! H ) J I

D t t t t t t

MVMUAMMCI 1205-3

(6) Ta, qoation

C UbS~f(C T "S qw

.(Ti 000 iV - )L1 ows 93 an 1 ý- (T4 co0l NW - 40@4oi W)

-((r 2 cooe i - N2 oo0802 sinV - (T3 coo i - N3 oo&3 3in V1Y2

-("Ni An, N1 -i x (+N2 Sn 102 + 13 sin 0 3 )Z 2

4CJ(Tooaes0)Cos IV- N ipn 0 '

ri-i

0(

•,1 ¶7 . q1 (x%) coo - PI1a

No vi•plifioationa have been nis on the r4$ht sde of these ixequations. Torso ignored in msahanisation ae those with diagonal linethroug then. ftterua1 stores, roagh vir, or ladzing gear oonditios arenot developd in these equations.

NCOrM In equatlons 6-71? to 6-271 and equationa 1, 3-6 of the precedingforce and m~oment equations, kt k T) qw. I a Otnaxic rressure term

due to rPropoeller elipstream. C tI the cot-fficient of thrust due tothe in4uced wing velocity bV, ctrlbuted by tUhi •rop1ller slipstream,giving an Increaped iLft effect. With engi'nes off, (f(CTs) .*t 1Z I . x

and sq~aticxs 6-217 to 6-221 DecmeA force sod mzvwnt equations an vou4,jb e pected for let , ircraft. C It a f( V ) and depondertm vwin ttlt and wing nap angleOWS 1 L2