AD-774 431

A'R CUSHION LANDING SYST17M DROPDYNAMICS THEORY (MECHANICAL)

Frederick C. Bauer

Air Force Inst itute of Technology

Prepa red tbr:

Air Force Flight Dynamics Laboratory

December 1973

DISTRIBUTED 4,Y:

U. S. ODPARTMENT OF COMMERCE5285 P.;t Royal Road, Springfield Va. 22151

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DJC ~C~i C,2Ni1,L UATA - R & )

Air Force Institute of Tcchnolhi'' (AJ'rT/EN) UrclassifiLedWrigt -Ptteron A- 2. CFO0VP~14~gh-Pdteror~AF~Ohio 45433

Iý I'OAT TITiLE

Air Cjashion Landinp, System, Drop Dynamics Theoriy (Nechanical)

A CISCPt' T:vC NC ~LS (r),,- C1 t,pcI and 1nCIm,a,pe uiaiqa,

1i: F:ed::i;%C Bauer, Captain, USAF

6RE PC,R T oA TE 741. TOTAl- NO. 0; 1A~ i, NO Of' RCFS

*'*J I/AE/73A-1

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Aproe for publi rerL ~lease; 1AW AFR 190-171 .',': 7c rce' 11liv, t~"1i La',Or:itors:

JE11C.HX C~aipta;!, USAF 1b'right-PaL ter-Lon APOiiJo 45433Director o 1' orm~ o13 AVS'kAC.1

A rmecharieai aiialoi' Vertieal E~rAbsorption Xodel (VE.Ml!) iS developed Lopredict the dynanics of an Air Cushion Landinrg System~ (ACL.3) in clic verticaldime.nsion. Thiree d'o"reps ýf frie.-ddom and thus three primary modes of oscillationare investifvatcdi ht'aVC, Pitch and roll. Data t.rom Air Force Fligh~t DynamicsLatioratory LCSr:; Ot a tuLl-scale Australian Jindivik, drone are used to develop andverify the nod,! 1.

The VEX!! study dei~s trates that ',.e use of a mechanical analog, predi.ctionschcme for an xir-Cushir,n l-iirxing- SystoŽ:n has sufficient renit to warrant fulr-hcrinvest (t~M. It ShOWS t*-,at a lrrcanical. analog, mode)I can predict, Eystem responszewithin thp F-~ domain of thiree dea,.rces of freedon without c4o-dlegte of thetn~ume~rous ind vacvryint- trunk afid CUshion paramecters if tho m~cK-1 spring and dampe;Ircoefficient.! are provided. Ib':ý ncdeI, rcsponsae correlates with iinioivik test uata

much t-ett~er in pitch and roll than in '.'vave. Doth tt.ce pitch and roll nolra springand darmper c'~fce ar-ý ,horn to b,'f lintear in accrjJ,irdace? with i-odiel asz~u.-.pi icns,M Hodel resporisf in hs'avp is heavi ly dependient upon the -,odc da.2!piri 10 ratio ( -1ý ) andthe undamperl tiatural frequenicy ( Win ), L~it thoa results are ruascriab~le; that is'

r esponse frec.l;-ýncy coLi-:'latcs to Lezt data 2rid respon)TSe ipa'Žce is in th~eproper di~Antilt ;ctnsoi Lttrtcct n--riud. re 1;eaveod sprin,;coi:fficirnt i , shown toi hold to tije lineoir a;)b7(Jxi.CILi10. 'il' iri-ibili ty to ;-.itchrr;-n~.itudes exactly sugge-sts that tie 1,cave damper coemffieieLnL i- tv:ii-liricar.

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Air Cunhion Landinr Systeml j .. ..."L" EAir Cushion Revovery System -

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()

4.

AIR CUSHION LAIDING SYSTEM

DROP DYNAMICS THEORY (VEaHIANICAL)

T• liS

CAM/AE/73A-1 Frederick C. Bauer

Captain USAF

lt~wd cdwbNATIONAl TECHNICAL .. - LVINFORMA.ION SERVICE L

U $ DO.or'P ,ý of C"onmmfeeap,.1j Id VA 22151

A)Approved for public release; distribution unlimited.

"AIR CUSHION LANDING SYSTEM

DR3P DYNAMICS THEORY (MECHANICAL)

THESIS

Presented to the Faculty of the School of Engineering of

the Air Force Institute of Technology

Air University

by Partial Fulfillment of the

Requirements for the De.gree of

Master of Science

by

Frederick C. Bauer, M.S. (SM)

Captain USAF

Graduate Aerospace-Mechanical Engineering

December 1973

() Approved for public release; distribution unlimited.

GAM/AE/73A-1

P'ref'ace

This report is about a Vertical Energy Absorption Model (VEAM) for

an Air Cashion Landing System (ACLS) that was developed from full-scale

experimental tests of an Australian Jirndivik drone aircraft. The tests

were conducted by the Air Force Flight Dynamics Laboratory, Mechanical

Branch, and selected test cases were used to verify the predictive

capability of the model in its three degrees of freedom; heave, pitch

and roll. It is my hope that the results of this effort will find

practical use in the Flight Dynamics Laboratory and will help in the

advancement of Air Cushion Technology.

I wish to express my Gratitude to my academic advisor, Captain

James T. Karam, Jr. for the finesse with which he managed the "care andfeeding" of the student mind during the experience. His assistance a~nd

guidance were invaluable.

I am particularly grateful to Major John C. VaughN III, Principal

Scientist of the Mechanical Branrch, AFFDL, for his assistance throighout

the period of this study. A special note of appreciation is due to

Mr. James T. Steiger, also of the Mechanical Branch, who provided much

motivational and technical assistance. Without their aid this study

could not have been accomplished.

My children, Scott, K'mberly, and Tiffany, will never knew what

they contributed toward the conpletion of this study, and for that I

wish to thank them. My wife, Dorothy, knows, and with that knowledge

she remained a fortress oi patience and a fountain of understanding.

She is a special person, and I want very much to thank her...for typing

this thesis..,for everything.

0°ii

6JA M1 A• t I 1.,w,- ..

Contents

0PagePrveface . . .. . ... . ... • 0 it

List of Fisures . • . . . . . . ............. • • v

List of Tables ... . Vii . . • . . . , ... .* Vii

List of Symbols . . . . .. .. . . . . . . . . . . . . . viii.Abpt;ract 9 e e * 9 a o 9 e e @ # e * w a 9 o• * .... * •xi

I. Introduction * * * * * o. .a * a a e a a # o # a . I

Air Cushion Development ...... . ..... .. . IAir Cushion Concept and Definitions . 2 . . . .... 2Air Cushion Application ........ . ...... 3Background .......... * ........ * * . 4Purpose o . . • . . .* 9 . .e o .a s & . e * . a 5Scope . .* . . . . . . . o o . . . o. . . .e * a 5

11. Model Development and Theory . . .. ...... 6

The Jindivik Drone . . . .. o . , o o . . .a 6Test M&thod and Data . . . . . .. . ... 10The Vertical Fnergy Absorption Model (VEAM) . , . e a 12Model Assumotions . . 0 . . . . . , . * . . . . . * a 13Approach to Analysis . * . e * , * a a e o a 9 . , 13

Linearity of Sprints .. .. . . . . . . . . . . . . , 16

I III. The Model Equations of Motion o . . . . . . . .0 a . # 17The Force Equation ... e • . e o a .. .. 9 e . 17Perturbation from Equiliorium . . . .. . . . .o * 18The Heave Mode . . *. . . 0 * 0 w # .6 * * a * a 19The Roll Mode . . . . . . .& . . a . . . .* 19The Pitch M'ode . . . . . o s. . o o e o . 20Free Fall Analysis ... .. . . . , ..... 20Summary .. . . ... . . . . . . . . , , . * * a * 21

I'. Analysis of Jindivik Data (Theory) . . . . . .. ... 22

Analysis of Roll and Pitch rita . . . . . . . ..* 22Analysis of Heave Data ... . .o o e 23Results . . . . . . . . .. . . . . .a , . . . . , , 25

V. Analysis of the Spring/Damper Units (Theory) .. .. 28

General . . . ....... . .... . . . .. * * . 28Spring/Damper Unit Evaluation . . .a........ 28

VI. Analysis of the Vertical Energy Absorption Model .... 30

General. .. a - .a. .a s * * 9 @ * * e # * # 30Spxing Coefficient Comparison@ .* v * w # .a . . 30Model Roll Response . . . e . , . .# o .*Model Pitch Response . . . . .. .. .. . 31Model Heave Response ....... ... .. . o 34

il-i

VII. Conclusions and Recommendations . . . , . . , . . . . 41

(3) Conclusions* v * * : : : e e : : : : : : o : , 41Recommendations eee . , e ,, 42

Bibliography. * ..... , . .. . . , .e * e # a a . ., 44

Appendix As Analysis of Jindivik Data (Computer Solution), . 45

Appendix Bs Analysis of the Equations of Motion (ComputerSolution). . & . . .@a v . a a e .e a . a 65

Appendix Cs Justification of the Small Angle -and HorizontalDisplaceMent Assumptions in ritch and Roll . . . 82

Appendix Ds AFFDL Jindivik and Test Data . . . .e. # . .@ 86Vitae e e e e , e a a a e e * a a e & * e & % e 88

k II

C)

©

GAX/E/3Ai

List of Fijurs

Figure Page

1 The Lake LA-4 Aircraft with ACLS. ..... .. .

2 The deHavilland CC-115 Buffalo, with ACLS . . 2

3 An ACLS Trunk - Cushion Configuratior. T . . . . 3

4 The Australian Jindivik Drone with ACLS . . . .4

5 The Jindivik Drone in Test Configuration .& . . 8

6 The Jindivik with ACRS, Dimensions,and InstrumentationrW&.4. . . e * a e s & e # P 9

7 The Jindivik ACRS with Dimensions . . . . . .. 10

8 Schematic of Vertical Energy AbsorptionModel (VEAM) . . . . . . . . 12

9 Linearity of the Exponential Decay in Roll . . . 14

10 Schematic of Displacements . . . ..... . . . 15

11 Spring Linearity ......... .. . .# 16

12 A Spring/Damper Unit in Arbitrary Deflection . . 1?

13 The VEA. in Arbitrary Deflection (Heav :, Fitchand Roll) *. . . . . . . . . ..9 9 9.. .. 0.. . . 18

14 A General Underdamped Sinusoidal Response . . . 22

15 Heave Test Data . . . . ............ 24

16 Heave Data Analysis Coordinates . . . . . . . 24

17 Comparison of Spring Coefficients . . . .... 30

18 Model Response, Roll Test 58, Wing Tip Transducer 32

19 Model Response, Pitch Test 61, Nose Transducer • 33

20a Model Response, Heave Test 122, CC Transducer.* 36

20b Mode, Response, Heave Test 122, CG Trarsducer.. 37

20c Model Response, Heave Test 122, CG Transducer, e 38

20d Modcl Response, Heave Test 122, CC Transducer.* 39

21 Program DATANYL . . . . . ..*C . 48

22 Program DATANYL, Subroutine DECRE , . . . .51

23 Program DATANYL, Subroutine DATAPLT . . . . . . 52

24 Sample Output of Program DATANYL 4......

25 Data Analysis of ACRS on Jindivik Dronel TestRui, 55, Roll , . .. . . . .. . . . , . . . 55

26 Data Analysis of ACRS on Jirdivik Drone; Test~.~)Rn56 ol*. .. ... . • . . . . . • • . * *•5SRkm 56, Roll 56

V

GWI/AE/73A-1

I

27 Data Anaiysis of ACES on Jindivik Dronel TestRun 58, Roll . . . , . 9 . * . . .* * e s e * s 57

28 Data Analysis of ACES on Jindivik Dronel TestRun 59, Pitch * . *. o * . .* * a * a .* . 58

29 Data Analysis ef ACRS on Jindivik Dronel TestRun 60, Pitch . . . . . . . . . . . a a . . . . 59

30 Data Analysis of ACRS on Jindivik Dronel TestRun 61, Pitch *...a.,. * *.....a . 60

31 Program RISE . . . . . . . e . . . . . . . . . . 63

32 Vertical Displacement for Subroutine LOCATE. . . 66

33 Program MODANYL. *. *. a. , . @. * 68

34 Program MOIDNYL, Subroutines F and LOCATE. @ . 71

35 Model Response, Roll Test 55, Wing Tip Transducer 72

36 Model Response, Pitch Test 60, Nose Transducer . 73

37 Model Response, Heave Test 121, CG Transducer.& 74

38 Model Response, Roll Test 56, Wing Tip Transducer 77

39 Model Response, Pitch Test 59, Nose Transducer . 78

*4 hodel Rtsponne," 'avie. Test 123, CG Trn.cduer. . 79

41 Vertical and Translational Transducer Errors . . 83

"vi

List of Tables

Table Page

I AFFDL Jindivik Test Numbers . 1 .1.

I1 Results of Analysis of Jindtvik Data .o oo, 26

III Pioram RISE Free Fall Computations . . . . . • ° 27

IV linear Spring/Damper Unit Coefficients . . , , 29

V Zeta and Wn Conputations for Heave . . , , . . . 34

VI Program DATANYL- Input Data .. ........ 46

VII Program DATANYL- Output Data....... .. 47

VIII Program RISE- Input Data ..... .a. a . 61

IX Program RISE- Output Data . ........ 62

0

S~vii

GA,/AE/73A--

List of Symbols0Symbol Description Unit

b span of the ACLS trunk in

damper coefficient lbfreec/ft

CG center of gravity of entire vehicle

CP center of pressure of ACLS trunk

D displacement, angular or linear rad rr in

a logarithmic decrement dimensionless

Sdisplacement of CG from CP in

F FrcFl lt"

damped ni,.ural frequency cyc/sec

9gravitationi.1 constant ftlsec2

-&vertical axis measured from surface,Spositive down in

contact height above the surface; the inground effect condition of tne AZLS and thespring neu,ýral position of the VEAM in

vettical displacement height of the CG linear

transducer (AFFDL tests) in

equlibriumn (hover) height above the surface in

initial or release t'eight abc.ve the surfacefor drop tests in

vertical displacement height of the nnsetr'rnsducer (AFrDL tests) in

height above surface of any given dampedsinusoid peak (X) in

.J,., vt-rtical displacement height of the wingtransducer (AFFDL tests) in

L subscript identifier of the five spring/dc.mper units

moment of inertia of the vehicle slug-ft 2

viii

S= • -.---. •- •----- "• " •- ---- •- . - w-

, ... - ..... .GA•i/AE/7.3A-l

constant in the heave analylis of I and Wn. dimensionless

sprine coefficient lbflft

V length of the ACLS trunk betweenlongitudinal axis ground tauigent points

M moment fc-lbfI

mass of the vehicle slugb

; air -mass flow rate into ACLS 'ushi a lbm/sec

*t air r.•ss flov rate into ACLS tzunk ibm/sec

P,. ACLS cushion pressure Ibf/in2

atmospheric pressure 1bf/ln 2

T pe..od of sinusoioal oscillation see

t horizontal axit, time, in the modelf domain see

•o initial or &ctiiviacin time of the! model a 1Z see

T~x time in the model dozain of any givenT•",sinusoid peak ý X s ee

* horizontal axis, .,,in the free fall do-main see

"r-Irase time of vehicle for drop tests sec

"T"€ contact time of vehicle in free fall domainwhen reaches in 6round effect (IGE), at see

time in the free fall dc.aiAn of any tivtrsinusuid peak ( X ) Sec

(J' damped nr.tural frequency rad/f6ec

wJ, undamped natural frequency rad/sec

X longitudinal axis of the mndel, CGthrough nose vos;t ive

latera! axis of the model, CG throughright wing pusit've

I vertical avi.s nf the l, a;urcd frc Lhcequilitrium position through the CG downwardpositive

Z' contact heighc of u.zdel measured fram equilibrium In

k ix

GAI/AEI73A-l

the deflection height of each spring/damperunit measures from the model equilibri•mposit ion in

6 pitch angle due to rotation about the y axis tad

4, roll angle due to rotation about the x -xis Tad

4" phase angle of the general vndetrdapedsinusoilal res )onse 0Th

damping raLio dimens ionless

x

GAMIAE/7 3A-1

At stract

A mechanical analog Vertical Energy Absorption Model (VEAH) is

developed to predict the dyoamLcs of an Air Cushion Landing System (ACLS)

in the vertical dimension. Three degrees of freedom and thus three

primary modes of oscillation are investigatedi heave, pirnh and roll.

Data from Air Force Flight Dynamics Laboratory Tests of a full-scale

Australian Jindivik drone are used to develop and verify the model. As

part of the comparat~ve analysis of Jindivik data, a computer pronram

is developed that will analyze the peak data of an underdamped, second

ord.r, sinusoidal, response and evaluate the mode response characteristics,

damping ratia (I ), %mdamped natural frequency ( .0. ) as well as the mode

spring and damper coefficients. Another computer program is developed to

analyze the same response characteristics using the method of peak

overshoot and peak times.

The VEAX study demonstrates that the use of a mechanical analog

prcdiction acheme fik- att AiL-Cub'lion Landing System has sufficient

merit to warrant further investigation. It shows that a mechanical

(7• analog model can predict system response within the model domain of three

degrees of frcedon without knowledge of the numerous and varying trunk

and cushion parameters if the mode spring and damper coefficients are

provided. The model response correlates with Jindivik test data much

better in pitch and roll than in heave. Both the pitch and roll mode

spring and damper coefficients are shown to be linear in accordance with

model assumptions. Hodel response in heave is heavily dependent upon

the mode damping rat-io ( ) and the undamped natural frequency (uJn),

but the results arc re-asonablel that is, response frequency correlates

to test data and reeponse displacement is in the proper direction but

somtetimes of incorrect magnitude. The heave mode spring coefficient is

shown to hold to the linear approximation. The inability to match

magnitudes exactly suggests that the heave damper coefficient is non-linear.

(I

xi

1110

.. AIR CUSHION LANDING SYSTEM,

DROP DYNAMICS THEORY (M CHMNICML)

I. Introduction

Air Cushion Development

The Air Cushion landing System (ACLS) is a natural extension of the

alr-ad:, successful application of air cushion theory to Air Cushion

Vehicles (ACV) and Surface Effect Ships (SES). Bell Aerospace, a

Division of Textron, Inc. and a pioneer in this field, in concert with

the Air Force FlighL Dynamics Laboratory (AFFDL), has developed and

flight tested an ACLS on the Iake LA-4 aircraft (Figure (1) as early as

August 1967- These

tests proved that

/ an aircraft could

takeoff, land, and

L pround maneuver on

a cushion of air

H,,. cz z much in the same

manner as the ACV's.Fig. 1. The Lake LA-4 with ACLS Further, due to the

large surface

"ccntact" area of an ACLS, vehicle weight and landing loads were widely

.. tributed, rcsulting in I.V- f.Woop,,t pressures (approximately 0.5 3

psi). In certain cases this characteristic of the ACLS will motivate

abandoning conventional landing gear on aircraft for the air cushion.

The lcw footprint pressures free the ACLS equipped aircraft from a hard

surface run.way requirement and allow- routine operations on unprepared

surfaces, marsh land, water, and even obstacle strewn surfaces. In

cooperation with the Canadian government, Bell Aerospace is currently

testing an enlarged version of the LA-4 ACLS on a dc villand CC-ll5,

Fuffalo (Figure 2). Success of the Buffalo tests is expected to result

in an ACLS test series on the Lockheed C-130 Hercules.

0

%4

G1M/AEI73A-1

00

Fig, 2. The deHavilland CC-115s Buffalo$ with ACLS

Air Cushion Concept and Definitions

The operation of an ACLS is not the same as the ACV. The uniqueness

of the ACLS requires development of its own discipline.

The design and method of construction is in no way fixed. Many

configurations are under investigation (Ref 3126), but the one shown in

Figure 3 seems to be relatively standard. The shape and material of the

trunk has a significant effect on its capabilit:,.

The trunk is that peripheral portion of the system that contains

the air cushion. Usually an elongated donut shaped manifold of a nylon/

rubber material, it contains the flow of air around and into tne cushion.

The cushion is comprised of that volume of air inside the trunk

peripherys that is, the hole of the donut.

b~~~~~~~.t%%Af% L"&L8.I& ~ Lf.A~, O.U LV' C ZCI)OLXL.C "LAL JL&VW A.LI.V , Sibt:

cushion and a back-pressure relief valve in the trunk to reduce

springiness on landing. The trunk and the cushion together absorb the

vertical energy of a descending mass.

2

GAH/IAE/73A-1

0"Trunk _

" • • • Air Cushion

Fig. 3. An ACLS Trunk-Cushion Configuration

Early model and inexpensive trtnks are made of a non,-stretchable

material ha funcicEJos 1 iu- an inflatabl e beach ball which~ manan

the same surface area whether or not inflated. More sophisticated

C) trunks are made of a stretchable material. A trunk cannot be allowed

complete freedom of stretch or, like a balloon, it will expand under

pressure until fracture. An ACLS trunk must have limits, like a woman'e

girdle, which allows elastic expansion until it teaches the nylon thread

limit. Unlike a girdle, which has a 50% stretch capability, a Bell

Aerospace trunk will stretch up to 300% for its design shape limit. This

kind of trunk can be installed under tension, flush to the aircraft

undersurface, eliminatint the need for complicated, heavy storage doors

while maintaining a low drag profile when not in use.

Air Cushion Application

The Air Force, through the AFFDL, is showing great interest in

applying air cushion technology to drone recover:y. Most drones are in

the same size and weight class as the IA-4, so feasibility has already

been demonstrated. Present drone operations include surface launching

from a rail, dolly, or skid, or air launching from under the wing of a

(9 zmothership (C-130). Recovery methods include mid-air retrieval by

belicopter or parachute descent to the surface. Costs of support

3

GAM/AE/73&-l

operations and limitations an the ntubers of drones that can be

)handled simultaneously demand a better method. One serious proposal

is the Air Cushion Recovery System (ACRS). A recovery system differs

from a landing system in the senso, that it is designed for landings only,

and does not need the hiher power (Airflow) required for taxi and

takeoff operations. It can be constructed of less expensive non-

stretchable materials which can be stored in parachute fashion ready

for deployment at recovery. In a current test series, the AFFDL is

actively engaged in the dev'.lopment of an ACRS on an Australian

Jindivik drone (Figure 4).

_77/77

0

Fig. A. The Australian Jindivik Drone with ACRS

tackgro'md

The technology of the ACLS is in its infancy. Major research

efforts were the IA-4 program, the one quarter scale and the one tenth

models of the CC-115, and the current, full scale CC-115 program.

Throughout these efforts, the primary approach to development of a

Verttu=l Fn~rPy Absorntion Model (VEA9.) has been with the emphasis on

mass air flow theory (Ref 9). This approach was severely complicated

() by the number of variables changing simultaneously and the lack of

concrete informnation on many of the variables. It was the initial

4

GAM/AEI73A-l 7

Jindivik tests that suggested an alternate approachl drop test dataC))indicated that the Jindivik with ACRS was behaving like an underdamped,

second order system. In April 1973, the AFFDL decided in favor of

investigating a mechanical analog VEAM.

The mechanical analog promises a fast reacting prediction scheme

whirh is needed as a computer subroutine to be joined to a larger

aircraft simulation program that is being developed by the AFFDL Flight

Controls Division. the ACLS portion of the program, which must eventually

include forward motion with its asCociated aerodynamic aad braking forces,

is to predict the forces that the ACLS contributes to the overall

dynamics of the vehicle on landing. A real-time dynamic anAlysis is most

important in order to keep pace with other force inputs, such as pilotstick inputs, and to maintain a realistic simulation of vehicle response.

Purpose

The purpose of this study, under the sponsorship of the AFFDL,

Mechanical Branch, is to oevelop a Vertical Energy Absorption Model using

a mechanical system analog that will successfully predict the dynamics

of an Air Cushion Landing System in the vertical dimension.

The investigation is to show that a mechanical analog will predict

ACLS response even though the physical parameters of the trunk and cushion

are not known. If a mechanical analog is successful, and if the spring

and damper coefficients of the mechanical system eventually can be related

to the trunk and cushion parameters, then this m.ethod of analysis promises

a simplified design approach for the ACLS without the need to first design

and build expensive test vehicles.

Scope

The mechanical analog was developed solely from the full scale

Jindivik tests, and the model results are limited by the nature of those

tests. Results are confined to cases that are restricted to three degrees

of freedom; specifically, heave, pitch and roll. This feature is

VEAM. Not an explicit part of the analysis is the understanding that

G) the model was developed from a non-stretchable trunk of unique design.

Lxtension of the model to cases where a stretchable trunk is employed

Must be dons with caution since the energy absorption capabilities and

reactions of the two materials may vary significantly. The basic design

of the Jindivik trunk differs from the only other trunks tested to date

(the LA-4 and CC-I15), in that the cushion volume io smaller (in

proportion to trunk volume) than other trunks. The full effect of these

differences will only become clear after More tests with differeut

eonfisurt ions.•

6

11. Model Development and Theory

The Jindivik Drone

Tests on a full-scale Air Cishion Recovery Systri (ACPS) were

begun by the Air Force Flight Dynamics Laboratory (AFFDL) in February

1973 at Wright-Patterson Air Force Base. An Australian drone aircraftv

the Jindivik, was provided for the tests and fitted with a Sandaire

designed ACRS modified by the AFFDL. These tests motivated the

selection of the Jindivik drone as the b13sis for the Vertical Energy

Absorption Model (VEAM,•

The Jindivik was set in a test cell as shown in Figure S and

modified slightly to accomodate the tests. The forward hood was

removed to facilitate instrumentation and the landing skid was

removed for the ACRS installation. Weights were added to simulate thn

internal equipment, engine, and fu-l with care exercised so that the

total weight and moments of inertia of the test vehicle matched its

operational counterpart. rrimaty control of the Jindivik for the tests

was achieved through the single suspension point, chain and pully

assembly, attached directly above the center of gravity.

A planform drawing of the drone in Figure 6 locates tLe recording

instrumentation used in the AFFDL tests. Signals from this instrumenta-

tion eventually were recorded on light-sensitive paper by a Hioneywell

visicorder (Model 906 A) from which data vas reduced. rressures of the

trunk and cushion and the displacement of the nose, wingtip, and center

Of gravity were, measu--d on all tests used for develouiffeat of the VEAMModel.

Changes to the ACRS trunk design component fabrication$ and

installation were the cooperative effort of the AFYDL, Centro and

Goodrich. The trunk, depicted in Figure 7, was constructed from a

non-stretchable neoprene coated nylon of various weights. The lower

surface of the trunk cons'.sted entirely of brake tread made from

three-eighths inch tire tread material. The heavy brake tread results in

a weight penalty (one-half the weight of the entire trunk assembly), but

it did facilitate precise anguiar posi.ioning of Lie itik ,uwzzi vZv

optimum efficiency. Two Tech Development TD-530 ejectors were provided

7

CAM/Alt/734-l

'ge I

ii I

prd.- Ifur

t-ls aviaIIcp~

GAN/AS/73A-1

164.7 5 in

- etro gaiy(G

C.2 ~ ~ 1.2 Citrn.o AP

C Fit. 6. The Ji divik vith ACRI Di6son , an In* t u n pt r o

9-

GANIAE/734-1

-- - - - -- - --- 4.. .. . . .. . • 0 . ..- -...-

'7', t 1

inboard trunk attachment 10.0

outboard trunk attachment tread

tedLDimensinns inchesI

1 2 e~ l R1 2 .6 8 4 . 0

6J7R*-1, 6, 472.--- 17. .97R 17.& 16.4R9.5

10.,35. 2 JR

Fig. 7. The Jindivik ACBS with Dimensions

Cj9 for the portion of the tests used to develop the VEFM; cne provided

mass flow to the trunk and the other to the cushions

Test Merhod and Data

Vine AFFDL Jindivik tests were used to develop the VEAM. The tests.-• 4.. ed- ,-,-,, 4.. • ,.,* .o f . ii ,.,.•4 '•.-•.,, O@ tho m,.ido1 h0av0. Irtrh.wc S- bin Oh'S*.h- r' .-mods- -- -------.s.~~ain f h -- ~l heve p-r-

and roll, In pitch and roll, the analysis centered on perturbation about

the hover equilibrium condition, whereas in the heave case, the analysis

was of Jindivik osckllation dynamics after being released from a height

gre;.ter than hover equilibrium. The method of collecting data in tte

threo nodes influenced the analysis of each mode and the resulting model.

Roll Mode One winnl-tip was lowered to the surface and released at

time zero (t ). The wing-tip !inear transducers recorded vertical

deflections of the wing-tip as oscillations damped back to hover

equilibrium, A Mx1DuM roli angle was of the oroer of o oegrv3ts.

Pitch Mode - Resistance to pitch perturbation was sipnifican--

enough that the Jindivik could not be displaced eas!ly and released,

1.0

G/AX /7 3A-1

as with the roll case. Oscillaltions were introduced until the pitch

C) perturbations were of sufficient magrAtude. The linear transducer,

attached to the nose boc,• re•,.vrded vertical deflections of the nobe

boom relative to hover equilibrium. A maximum pitch angle of

approxim-ately 7 degrees was experienced.

Heave Mode - The magnitude of heave stiffness was large enough to

make it technically impractical to conduct perturbation testing. Thus#

the Jindivik was raised to a height and released. This teat method

required separation of the analysis into two regionss the first, the

free-fall from release until "contact" of the ACRS with the surface. and

the second, tht dynamic oscillations of the ACRS about the hover

equilibrium condition. Since the ACRS rides on a cushion of air,*contact" does not necessarily imply the physical meeting of the trunk

and the surface. Thus, "surface contact" has been defined as In Ground

ffecf (IGE); that is, the position at which the first distinguishible

rise in trunk or cushion pressure can be detected. Experimental

testing shBrs tr1ctnVmfK and cushion pressure rise wiLhin a fraction of a

second of one another, and can be considered simultaneous for the purpose

of defining ICE- Heave data was complicated by the fact that the heave

linear transdtuli.r could not be placed at the center of gravity due to the

fuselage, nor could it be placed directly abare the center of gravity due

to the suspension hoist. The sensor offset resulted in he&ve data

being affected by pitch and required analytical adjustment.

A aunvury of the AFFDL tests in its three significant modes of

oacilldtion and under various conditions is presented in Table I.

TABLE I

AFFDL JINDIVIK TFST NUMBERSused for the VEAM development

Test Vent Opened Vent Closed Flow Added Flow AddedNode Pc ct Pa Pc - unk Pcp-12.5 psi cp 30. 4 psi

S<0 ];c W 0 ic it -• -t

ROLL 56 55 58

ITCII 59, 60) 61

HFAVE 123 + 122 121

Jindivik balanced so that: CG is approxirmaLely over the trunk CP.

II

Tests were conducted in still ambient air in an enclosed test cells

K) and# 88 described above, were liMited to perturbations or vertical

descent (no forward velocity). Tbub, no aerodynamic lift or drag

forces nor brake drag f'trcp.'- were preetnt to coiaplicate force or mom~ent

The Vertical Enerygy Absorption Model (V7X~ .The model choser. for analysir is depictcd in F'igure 8.1

~.-Spring IL±-Damper K.-s/d itu .1

Fig* 8. Schiematic of Vertical Energy Absorption ModelI

Norr'ally, consideration of an objec%; in three dixnenuional tpace rebultsj

in six degrees of fre(-do (DOF'). Jindivik testing methods allowed a

reduct-ion to 10 DOF. The elimination of air f-Low over the wings and

fn~tvuird movement of the model during the initial teut series had the

effect of eliminating all forces in the horizontal ().,y) plane. Conse-I

quently, It is assumed that there is no lateral displacement, and that

all movement is confined to the vertical (Z) axis. Because there are no

lift and drag forces to create 6ideloads, 7av' is not present. Thus, tht

dynmicl~pertt~rbation study is limi.teti to the vertical mode (heavt%) and

the pitch arA4 rol.l lnode.¶. The axis system choseai, similar to a

conventional Euler system with Z positive down, has Its or~eit, at the

center of gravity and is fixed in spac-- with tht xpy plane par allel to

the surface uhen the center of gravity icr at the haver equiLittiurI

condition. V.).3 seemning complication to the &.6.9 Is required in ordex:

12

GAK/IAE/73A-1

to generalize the analysis and yet allow a changing equilibrium height

C) (relative to the sur-ace) as the mass flow into the cushion changes.

Model Assumptions

Objervation of the Jindivik oscillations in its three modes results

in data which gives insight into the character of the ACRS. One of the

first Jindivik dynamic tests conducted was the roll test shown in Figure 9.

The plot of peak displacements suegests an underdamped second order

xesponse, which motivated the selection of a mechanical analog model for

,e AC*S. The perio& ( T ) is approximately constant throughout, which

mXkeus the damped natural frequency ( WA ) constant. A semi-log plot of

the peak amplitude excursions from equilibrium demonstrates the linearity

of tCe exponertial decay. A complete discussion of this analysis iscý-n.ained 'A ctapter IVe

"bere is •-Angle effective spring and a single effective damper that

tesulta from e;'-i. mode analysis. With the assumption that the springs

and dampecs are linear and time invariant, it is possible to construct

spring/damper units (sid units), each a linear spring and damper in

I parallel, and dist.Ovute them as depicted in Figure 8. The rotational

roll sp-'Ing and damp,!r and the totational pitch spring ard damper are each

divided inr.o translational s/d units displaced at ay. assumed moment arm.

The linear heave spring and damper are represented by the combined effect

of the four peripheral s/d units and the center cushion s/d unit. The

constants of proportionality for the Jindivik are determined from the

expertwental data (Appendix A).

As is usual with lumped linear models, analysis requires the

concentration of mass at the center of gravity (point-mass assumption).

The plane surf -.e which distributes the s/d units at the proper moment arm

ts assumied massless. The center of gravity can be varied from the center

of pressure (also the Ceometric center of the trunk) by the distance •.

In the modelp thz center of gravity and the center of pressure are in the

same plane.

Approach to Analysis

() Nh~an the ).CRS vs (r..kt of Ground Effect (OGOh, it is inoperativel that

15, ple.svre8 *Z the tiz.,k and cushion are constant and no fozces or

13

0.0T ACLS/Jindivik/AFFDL

+20 )Test No. 55I I ROLL

GGn%0 (DE)E

OL

-10]

-20~_~

o 'o f'5 'o 25Time (see)

-7) K> ACLS/J ind ivik/AFFDLS0 Test No. 55

ROLLLo 1

0o Ib isp1 2b) 2•Time (sec)

9 - Upper Peaks

Fig. 9. Linearity of Exponential Decay in Roll

14

IA - -17

r moments are present. As the ACRS descends in free fall toward the

surface# it reaches the region (IGE) where reaction with the surface

causes a pressure rise in both the trunk and cushion,

The instant the ICE condition is encountered marks time zero (to)

for activation of the analytical model. This displacement corresponds to

the spring-neutral position (-c) as depicted in Figure 10.

release

i free fall distancecontact

hI hhhh eq

Q surface

Fig. 10. Sý-hematic of Vertical Displacements

Any further downward displacement causes reaction forces. Descent

of the model continues, compressing each spring (&Z ) until the combined

upward force of the spring/damper units (s/d units) supports the weight

of the model. This displacement is the equilibrium position (and

corresponds to equilibrium hover for the Jindivik. When the center of

gravity is displaced from the center of pressure, tl e Jindivik longitudinal

centerline will not be level with the surface. A non-zero equilibrium

pitch angle ( Oe, ) vill result so that for each s/d unitaZ. I (Oioment Arm) sin Oe, (1)

The equilibrium pitch angle is non-zero due to the combined physical

constraints of (1) the CG of the vehicle being aft of the trunk CP in

normal confipuration. (2) the a•.,tmprin rha.- ti ,.,--11 -. 4 ..* -

sprine coefficients are symmetrically placed relative to the trunk CP, and

(3) the assumption that the symnetrical spring coefficients are equal

Sin magnitude@

GAI/AE17 3A-

LinearitY Of Sprins

()The curves in Figure Ila illustrate that a linear approximation for

a non-linear spring is usually vali4 within a small perturbation of a

given position, in this cases equilibrium. Figure llb illustrates that

real spring phenomeni is not infinitely linear, but that non-linearities

are usually present at the extremes. For the VEAM, when it is above the

contact level, no forces should exist. At this extreme the spring

relationship F'=.x implies that -A o at displacements less than contact

(x?. )& At the other extreme, where the vehicle underbelly strikes the

surface, the spring relationship again terminates. It is suspected that

the spring goes non-linear prior to fuselage and surface contact (%.X)s

These two extremes define the limits of the domain for successful VEAM

operations.

Flinear model

linear shou~ld,approximation do

non-linear r modeldoes0 ! :-

X~q

Fig. 11. Spring Linearity

0I

! ! x ',O

III. The Model Equations of Motion

The Force Equation

In this chapter, the equations of motion that apply to the three

degrees of freedom will be developed. Each spring/damper unit P4

illustrated in Figure 12 will

+ LI contact result in a force with constants

equiblbrium of proportionality for displace-I _ . e dq eque--lon ment 5i and velocity Ci. for each

mode. The total force described as

-i (As Zci+ -C-i2 cL) (2)

where displacement is measuredki ci positive down from the spring-

neutral or contact position.

When the model is released from

surface the spring neutral positionp whichis defined as horizontal to the

SFig. 12. A Spring/Damper Unit surface, it will settle downwardin Arbitrary Deflection due to model mass and seek an

equilibrium position so that the forces and moments for each degree of

freedom at-3 exactly balanced. This equilibrium position can vary in

relation to the horizontal surface depending upon the relative location

of the s/d units to the center of gravity and the center of gravity to the

center of pressure of the trunk. Thus, at each s/d unit attachment

point 2 , if the variable deflection were defined as ti., then the total

force at each point would be

However, for any given model configuration, the forces and moments due to

the deflection A&. from spring-neutral to equilibrium are constant so as

to exactly cotun;'-eract '.he presence of the mass at all times. If the

deflection from contact to equilibrium were eliri.4£uted from an analysis#

the resulting :quations tepresent a dynamic forcc balance relative to

the equiuibritu condition i7here each s/d unit force contribution would be

represented by

17

GA•/4AEIMA-.

In this last eouatu.on, ýi represents the vertical deflection of each

C)/s/d unit attachment point from the equilibrium position ( i Zei ).

Perturbation from Eguilibrium

Analysis of the model in its three degrees of freedom starts by

considering the forces that act upon it in time (equation 4). The

forces remaining after model weirht is eliminated are dependent upon •.

and 3 . The model is given a positive deflection in heave, pitch and

roll simultaneously. Allowing that all angles are small (Appendix C),

zz

z

Fig. 13. The VEAM in Arbitrary Deflection (HeavePit,,h and Roll)

Figure 13 illustrates that the deflection at each s/d ,.nut location is

;6 z ¢, E)•,= + (4£-S) e (5)-, z- &e

The rate of deflection of each s/d unit point is the derivative of

C-) equations CS).

18

GAaI!AE/73A-l

(9 - (% cV

+ (6)1

Substitution of equations (5) and (6) into equation (4) provide the

necessary information for a force and moment analysis.

The Heave Mode

Summing all forces in the vertical direction, where the forces are

as previously described, results in

ZFZ= = Fi. (7)

Substitution of the complete s/d unit force equations (the combination

of equations (4), (5) and (6), into equation (7) and separating like

orders of heave displacement and pitch angle results in the heave mode

0 equation

+ z +(8)

where the effective spring and damper coefficients are

C =(9)

The Roll Mode

In a like manner, the roll equation develops from a sunruation of

moments about the longitudinal x-axis.

In this case, the physical symmetry of the trunk about the longitudinal

axis suggests that the corresponding s/d units are also symmetric; or• "• Z "- -,C~q - "C.a,ui

oplte = ,atst (11)C The complete s/d unit force equations are substituted into (10) and

19

CAI/AE/73A-1

the coefficients of like order derivatives are collected to give

2. Tx_ _ (12)

The Pitch Mode

Development of the pitch equation Involves a bit more algebra, but

the method is the same. Moments are sunmed about the lateral y-axis.

Y A O-FZ )+F.6-F U F4 6+ s (13)

and the complete s/d unit force equations are substituted. To the

assumption of the roll s/d units (equation 12) is added the more tenuous

assumption that the fore-aft s/d units are also symmetric, or

- = ." 3 (14)

Equations (14) are considered more assumptive due to the slightly

different volume between the fore and aft trunk sections (see the cross-

sectional areas in Figure 7), but the difference is considered negligible.

The complete pitch equation is

6 ~Y +' + +[~j~4~2 ~ (15)

+ A £4- Fz1JY+2a t 29S s14- Jyy L - -

Free Fall Analysis

The free fall case requires a separate analysis in a different

tme frame. After implementing the mode assumptions presented in

Chapter II, a free body diagram of the Jindivik Out of Ground Effect

(OGE) shows that weight is the only force acting on the system as it

falls in the vertical dimension. Time is measured from release and,

so as not to confuse with the time domain for the model IGE, free fall

i time is designated 1 . The height of the vehicle in free fall is

designated (t ) and follows the terminology presented in Figure 10.

20

CAM/E/73A-1 1It is measured positive down to maintain the same sign convention as

the model.

The equations which describe free fall with no initial velocity are

I2.Z a-V +(19) (16)(b)(c)

This free fall analysis is used in conjunction with the heave tests

as previously described, The values of the release height (kl) and thetime to initial contact (1-c.) are determined experimentally, and frocm

(16a) the height at contact ( L) is determined. Equation (16b) provides

another initial condition, the velocity at contact. These values, with

coordinate transformation, are then used in an analysis of the characteL-

istics of the equations of motioni.

Sum•nary

The complete set of equations to describe the model in its three

C degrees of freedom is the combination of equation (8), (12) and (15).

It should be noted that both the heave equation (8) and the pitch

equation (15) are coupled to one another if the center of gravity of the

vehicle is not at the center of pressure of the trunk, ie, & • 0 . This

is to say that a pure heave input motion will, in time, result in a

pitch motion that may remain even after the heave motion has damped out,

and vice-versa.

Solution of these equations of motion is the subject of the next

chapter, but it must be remembered that the dynamic analysis is in

reference to the equilibrium position of the vehicle. The equilibrium

position can vary according to the vehicle configuration and/or flow

rates into the trunk and cushion. In heave, the difference in height

between equilibrium and the surface is constant for any given test.

Program DATA11YL in Appendix A computes this value. For roll, the

equilibrium axis is parallel to the horizontal axis at all times due

to the fact that the trunk is symmetrical. Pitch is the same as roll

only if the center of Cravity of the vehicle is coincident with the

C) center of pressure of the trunk. For most pitch cases, where the CG is

behind the CP, an equilibriumi pitch angle ( Eej), relative to the

horizontal, will result. An expression for Ocj is in Appendix B.

21

IV, Analysis of JindiviIh D&ta (Theory)

Analysis of Roll and Pitch Data

The equations of motion developed in Chapter III can be related to

a standard form for linear, constant coefficient, second order

differential equations (Ref I1i44) where the coefficient of the

displacement term is equal to Qq% and the coefficient of the first

derivative of displacement is equal to Zf(0,. For example, in the

case of roll, these are written as

(17)

The parameters wl4 , the undamped natural frequency, and f , the

danping ratio, serve to characterize the differential equation and

thus the system. The solutions to the VEAM differential equationu of

motion (equations 8,12 and 15) are of the form

() where D(t) is angular or linear displacement as a function of time, to

is a constant, and W)J is the damped natural frequency. By definition,

'%O (19)The nature of the system being analyzed depends, to a large part, on the

S-. ,

14i . ,enerat Underdamped SiuodlResponse

u~nI

S14. GSinusoidal

22

C.AM•1AE/73A-1

value of f . For the case of this study where f < 1.0 , the system is

called "underdamped" and the natural response appears as in Figure 14.

The period of system response (T) is the time required to traverse

one full cycle, thus 'T' -tr - tp, 1/• :ps • From this, the

followt.ig relationship is established

Ad (rad/sec) V'iT = Z~ •', (cyc/sec) (20)

The period, which can be found from experimental data, leads directly

to a value for the damped natural frequency.

A description of the system as it damps to the equilibrium

position is available by comparing two adjacent peak amplitudes. This

comparison is called the amplitude ratio and defined as /C

Combining equation (19) with (18) for two adjacent peaks and solving

for the amplitude ratio gives

14 e (21)

The ....... '.. d'ccrcment 's) i4 vual Lu Lhe natural iogaritru o1 tne

amplitude ratio, and

Alternately, the damping ratio is

T = ( , r l - - J ( 2 3 ý

The proceeding analysis was computerized zo evaluate the system in

roll and pitch., to provide tvhe -mode Spr•ing and d_-=pcr coafficients,

and to plot the data. This proeran and its results are presented in

Appendix A.

Analysis of Heave Data

The initial analysis of Jindivik heave data indicated rapid

damping of the heave usude with another mode remaining. This is

illustrated in Figure 15. Evaluation of the data past the mode change

point indicated that the pitch mode characteristics now predominated.

Tczt reGilAtl• •ue.- Liiai the heave moce Camped out in about three

peaks (0 .75 to 1.45 seconds). With so few peak amplitude points, rhe

heave data was considered too sparse to analyze in the same manner as

pitch and roll. For 0h0s reason, an analysis based en percent overshoot

and rise time was -,elected to characterize the systemr,. This method of

23

ACRS/JINDIV lK,'AFFDLTest No. 121CP - CG

35I Heave mode damps out

"0- Pitch mode remains

30o I

25 equiblibrium

0

Time (sec)

rg.L ~ Ne.D* TestIV £ &bL iGL

0)i,-axis - for free fall

7-,t axis - for vEAH

-- --- --- --- --- --- --- --- - -- - -- - -release

free fall

S~,-.----model activAtion

S; .. . csurface

.pi - re, -

C) Fig. 16. Heave Data Analysis Coordinates

24

CAM/AFE7 U-1

solution, which is illustrated in Figure 16, accounted for the fact that

()• the model has both initial displacement and initial velocity at model

activation (surface contact).

Starting with the heave differential equation of motion (8)#Laplace transforms are used to find the solution

Z(t) -i tI,()(COSe Wz.t + K-i m )(4

,w e t K = 7 r + ( 2 5 )Sy using a trigonometric double-angle identxty, (24) can be simplified

to the form_(t_ -, '- e 5.rv (( t +.(26)

ZO"vhere 1/.( -• +.)CO L. / "1 (27)

Maximum overshoot/undershoot occurs when Sin (Ld t-+4,') + -. 0.

Thus, ______ t(r (87-. (28)

Equation (26) is differentiated with respect to time and solved in

order to obtain a general expression for peak time (tp) valid for anyresponse peak depending on the value of the integer (rx),

t f; (29)Equation (28) is solved for the damping ratio and equation (29) for

the umdamped natural frequency to provide two equations suitable for an

iterative solution on a computer.

Wip tp (a)

(b)te (i"±o + ZoaL.J') b

The program which acccz'plishes this, called RISE, is presented in

Appendix A.

Results

The results of the analysis of Jindlvik data from both prograins

DATANYL and RISE are presented in the following tables. Table 'I

I> characterizes the system for each mode for eaci AFFDL test, and

Table 1HI sw=erizes results that are peculiar to the heave mode only.

25

CMi1/AE/73A-1

TA BLE I- -

XI•5L'3 OF ANALYSIS OF JIh'DIVIK DATA

Program DATANYL

Mode Case Test Zeta Wn Mode CoefficientNo (rad/sec) kE CE

I I (ft-lbf/rad) Ift-lbf/rad/sec)

Pitch 1 59 .0436 6.66 80,394.76 1,052.36

2 60 U462 6.20 69,524.92 1,036.00

3 61 .0357 5.66 57,917r22 731.38

Roll 1 56 .0531 1.84 4,340.29 234.06

2 55 .0577 1.64 3,077 99 221.05

3 58 .0629 1.52 2,753.88 227.53

1ýrogram RISE

First Peak (Ibf/ft Vb-sec/ft)

Peave 1 123 .3482 15.22 17,769.30 813.04

3 122 .35331 16.61 21,163.15 900.29

4 121 .3771 15.4e 1C,381.59 895.57

.ve rage

,.,ave I T 123AV .2616 14,90 17,029.96 597.99

3 122AV .1822 14.67 1.6,508.26 410.06

44 !21AV .1799 14.24 15,554.68 393.02

CasesI - Ven.t opened1 - Vent closed3 - Flow added (6e c )

4 - Flow added (Oh a At)

26

- R~IAE/73h

• ITA1X III

PROGPAM RISE FREE FALL DATA(Jindivi' Tebta/IHe .e Mode)

Heave TPI Z0 ZODOT ZfILTest No (see) (in) (in/aee) (in)

123 0.220 -7.157 0,,2683 2.2-30

122 0.202 -7.267 0.2630 2.220

121 0.7190 -7.111 0.2173 1.980

0

2t

I

27

G&I4IAE/73A-1

V. Analysis of the Spring/Damper Units (Theory)

General

The analysis of the model equations of motion is completed by

computer solution, The computer analysis is presented in Appendix Be

Prior to implementing this solution# the spring/damper units must be

fully described,

$Mrin&/Daper Unit Eval uat ion

If it were not for the coupling terms Ln the heave and pitch cases#

the equations of motion could be solved with the mode charactezistics

only (I's and (jn's). The coupling requires knowledge cf the individual

s/d units.

In Chapter 11, it was -mphasiied that only one "spring"value and

one "damper" value could b- derived from the data of each mode. Analysis

of two of the modes# pitch and roll, resulted in torsional springs and

dampers, each of which no- can be transformed i-r.o a pair of hiatear

springs and dampers at an assunjed moment arm to satisfy the model

configuration. The moment arm chosen for this analysis is based on the

Jindivik ACRS tzunk (Figure 7). The tangential contact points of the

trunk and the surface with the xz and y-z planes define the points for

measurement of trunk length and width. Assuming trunk symtuetry, the

proper moment arms are half of the length (-&I/_) and half the width (b12).

In Chapter IV. the relations betwcere the mode characteristics end

the spring!damper coe-ffic'ents were established. The example for the

roll case is repeated here.

z,&I ~ ~ A.)rR ~ '~'(a)

-~ tjw,1 2 j/ ~(17)

Expreriions for the heave and pitch cases can be found by similarly

equati.g the coefficients of the differential equation, but the heave

and nitch spring!damper coefficients are functions of each other.

Simultaneous solution of the expressions res-ilt in a fo,.-n that is in

(C) telrms of the mode characteristics only. Thes• ares

28

9. TYY (31)

( '2.YT -w (32)

-Z (R ./ 7) 2

Z- fm (33)

M= ( W. - 2. 4, 4 (34)

Numerical solution of the s/d units is accomplished in program

MODANYL (Appendix B), the results of which are presented in Table IV.

TABLE IV

LINEAR SPRING/DAMPER UNIT COEFFICICNTS(from Program MODANYL)

Mode-Test No. Linear s/d Unitsland LI) Position ISpring Coefficients (K) Damper Coefficients

I (lbflft) (C)(Ibf/ft/sec)

H-122 1,3 1,174.8 6.9SP-61 2,4 639.1 52.9

R-58 5 17,340.1 772.4

H-122AV 1,3 1,232.9 13.0P-61 2,4 639.1 52.9R-58 5 12,623.1 274.6

H-123 1,3 1,804.9 16.7P-59 2.4 936,5 54.4R-56 5 9,434.6 599.5

.4-123AV 1,3 1,780.2 18.6P-59 2.4 936.5 54.3R-56 5 11,439.4 466.5

Note Is For the heave case, calculations are based on data acquiredwhere the CG was shifted above the trunk CP.

Note 21 For the heave mode, the first peak analysis was used forand L4n unless subscripted by AV, in which case the averageanalysis was used.

Note 31 Linear s/d unit values are based on the Jindivik Trunk,Figure 7, where £/1 - 53.85 inches and b//. a 17.6 inc|es.

29

G&M/AE/73A-1SI

VI. Analysis of the Vertical Energy Absorption Model

General

The Vertical Energy Absorption Model vis exercised on a CDC 6600

computer with the goal to duplicate the Jindivik test of Table I. The

model results, which compare favorably with the original tests and

with one another, are presented in graphic form in Appendix B with the

exception that the responses from a single test condition (flow added-

tests 58, 61, and 123) are included in this chapter in order to analyze

them more closely. A variable is present in these comparisons since the

heave tests were conducted with the CG approximately above the center of

pressure (CP) of the trunk, where as the roll and pitch tests vere in

normal configuration with the CG aft of the CP. The exact effect of the

change of the CG location on the heave data is not known.

Spring Coefficient Comparison

Before examining the model responses# it is worthwhile to compare

the mode values of the spring coefficients from Table II with earlier

experimental AFFDL static test results which are summarized in Appendix D.

These values are plotted in Figure 17 in a kind of histogram where the

abscissa represents the point cushion conditions of vent opened (VO), vent

nk ROLL n PITCH X HEAVE

4- 0

10-

V'0O VC0 <VCf Oordinate values x 1000

damCd ak vera pe40AFFDL static ro dDed Eam: ýv ~ Ca Revrae 1

Fig. 17. Comparison of .pring Coefficients

30

CAM/AS/7 3A-l

closed (VC) and flow added (FA). Although point conditions, the

(II) abscissa does suggest a scale of increasing cushion effectiveness (P. and

jr increasing). This suggests that the aynamic roll spring coefficient

and zt.i static roll stiffness are comparable. Thus, for an approximation,

the dynamic roll spring coefficient can be found from the easier and less

expensive static tests. Another advantage is that the static analytic

techniques are easier than the dynamic ones. The dynamic pitch stiffness

also shows reasonable agreement between the dynamic and static values and

does approach the static value.

The heave case shows dissimilar results. The first peak analysis

values appear to increase while the average analysis values show the

same decreasing trend with increasing mass flow as the static test values.

In both cases, there is a definite magnitude difference in the values

between the dynamic and static values of the spring coefficients for any

given test configuration. This fact suggests the presence of a dynamic

spring phenomencn that was not observable during the static testinge

Model Roll Resnonse

The test values of the damping ratio { and undamped natural

frequency WrL used to characterize model response are those in

Table II In all roll tests, I generally increases and W,, generally

decreases with increasing mass flow to the cushion.

In Figure 18 for roll test 58, the response of the model shows

excellent correlation to the test data in all respects.

Model Pitch R'.sponse

For the pitch tests, Table II, f 's show no decisive trend, while

WA 's, like the roll mode, show a decreasing trend with increasing mass

flow to the cushion.

Figure 19, for pitch test 61, generally shows good results except

it appears that the equilibrium axis of the response is angled slightlyto the equilibrium axis of the data. Referrinn mumentarily to Figure 30,

page 60 , in Appendix A, the equilibrium plots cZ> of the original data

show a definite increasing trend with time. The equilibrium height (11EQ)

() of each test was defined as the average value of these individuial

equilibrium positions. Back to Figure 19, it is the average equilibrium

31

GAM/AE/73A-1

0ri- w=b cc

r qr

'-14

I~i U

L 0I

00

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0

'-4

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0 0 0

301 SUw

33-

GAMIAEI73A-l - -

beight, a constant, that was used In program KODANYL to adjust the

original data to the same equilibrium axis as the model response so that

the two could be nompared. Thusp a slight deviation is introduced to the

plot. The magnitude of this deviation is equal to the difference between

the average equilibrium height and the actual equilibrium height at any

time.

Model Heave Response

The heave response requires several computer runs with different

initial conditions in order to evaluate. In Chapter III, the axis

chosen for the development of the equations of motion was based on the

equilibrium position. Experimental data showed that the equilibrium

longitudi.nal axis made an angle of about 3 - 4.5 decrees nose up from the

horizontal plane when the CG was displaced aft of the CP. When the

aircraft is dropped level with the surface, then an additional initial

condition in pitch is established where O n- - 3.0 degrees relative to

the equilibrium axis of the model. The first peak and average f's and

SL4's used to exanine the heave mode response are those calculated in

program RISE (Appendix A) and presented in Table V.

TABLE V

EA. &• N COW .rLAT!O(, Onq r.R v AvF(Program RISE, modified)

TEST 123 TEST 122 TEST 121Peak ZETA Wn ZETA j Wn ZETA .n

1 .3482 15.22 .3533 16.61 .3771 15.48

2 .2444 14.72 .1627 14.40 .1691 14.52

3 .1922 14.77 .1296 14.35 .0851 13.93

4 .1575 13.80 .1078 13.32

5 .1847 14.77 .2515 14.37

6 .1057 14.12 .0890 13.82

AveraCe .2616 14.90 .1822 14.675 .1799 14.24SValue.-.

34

GAZI/AE/73A-1

In the first two heave responses presented, the model is exercised

with initial conditions on heave only ( * 8 u 0) and thus no pitch

toupling develops. The results of these initial conditions are what was

expected from the Jindlvik tests when the CG was moved to a position

above the trunk CP. The fact that the Jindivik test data shows the

heave test coupling into a pitch mode su6gests that, during the actt%%l

tests, the CG was not exactly over the CP and/or the initial pitch

condition was not exactly level at contact.

In Figure 20a, the - and W from the first peak analysis are

used. The response correlates well with the first data point but is

too heavily oamped to approach the other data points.

In Figure 20b, the average values for - and Wrl are used. Even

though the response overshoots the first peak, a much better subsequent

response is achieved*

In the next two cases, suspected actual Jindivlk test conditions

are duplicated; that is, the model is activated parallel to the surfaces

which puts an initial condition on pitch, and with initial conditions

(D on heave. in these response examples, the model resembles normal

Jindivik confiuration where the CG is behind the CP.

In Figure 20c, the first peak analysis shows a degradation of

response to the first peak due to pitch coupling and a tendency for the

pitch mode to dominate the responsel that is, heave is not effective

after the first peak. It is obvious that the pitch peaks are nowhere

near the data points, but this Liay not be toO aerious. The per"Lod of the

pitch mode is constant and approximates the period of the data. This

means that the damped natural frequences (Wa ) do compare. In addition,

the peak amplitudes of the pitch response fit exactly into the data

exponential decay curve, thus suggesting a comparable logarithmic

decrement and pitch damping ratio ( ).

In Figure 20d, the same initial conditions as Figure 20c are used

but with the average values for -f and Wn. The degredation of the first

peak response actually assists toward matching the data point. Subsequent

response is much improved in heave, with the heave node matching or,

at least, moving toward all data points.

A closer inspection of the character of the heave mode is possible

with Table V which incluies a summary of I and L, 1, calculations frocu

35

GAN/A.E/73A-1

z 61j

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GLH/AE/73A-1

program RISE for all r&akso In all the Leave test Lases, the first peakvalues of f an., ti are sie nificantly tliher thasi the subseoquent values.

The subsequent valuer of Wo% are essentially consce-it. Equations (17b),

(32) and (34) imply that dhen & is constant# then the spring c.:efficient

is constant. -ne damping ratios ( $ ), on the other hand vary e.rratically,

sig•esting a non-lirear behavior. It can be seen trom equations (17a),

(31) and (33), that, given On, a constant, if -4 is non-linear, then the

damper coefficients are non-linear.

4

40

VII, Conzlusio.ns and Recomwuendat ions

Ccncl us ions

Fran the analysis in Chapter VI and with ths supplnientary response

curves in Appendi,- B, thW: Vertical Energy Absorpt-lon Model demonstrates

model response charactnristics in the rol'. and pitch modes that correlate

well1 to the Jindivik data. In the 1,eave .node, results are satisfactory,,

but more imaportant, the potential for continued development and more

precise prediction has beert demonstrated. The use of a mecchanlcal

analog; pred,.ction r'chem( for an Air Cushion Landing System has sufficient

merit to warrant furtAber investigation.

The linear assumption for both the spring and damper coefficients

made in Chzptvr TI is born out by analytic results and response curve3

in pitch and r-)1I. The roll mode is superior in this respect.

Heave response of the model is reasonable, but care must be

exercised in the selection of the proper damping ratio C')and

unidamped natural frequency C .For an anal- -ical ",ans of finding -1

C) ~and W~n . the method of averaging the values from a pealt time analysis

(program FtIE) provides good results. Reference the heave equation (8),

the terms on the right hand side indicate a coupling of the motion to

the pitch mode. The amplitudes of the heave response curves in Figures

20a to 20d do not match the data con~sistently as I' and Qv are -.raried.

Using the first peak values for Y' and Wn.- resuilts in a good rensuonse

rmatch at t*ý-e first data point (Figur-e 20a), but the excessive damping

ratio supresses the amplitude of the response at subsequent data poirts.

Using the average values of j' and WA.J,1, the response approaches thiL

subsequent data points Dut overshoots the first data point. 'Aihese

observations suCggest that the heave response is non-linear, Thcixc_

linearity is in the exponential decay curve of Figure 14 _r. i' 0'.ý t o

the product fo~rl . HIowever, from the summary of heave cn~az .tc 4 K*;!tics it,

Table V, it I.s shown that Wi is approxim~ately constant and is ap?,rOXJ1ZL(lY

equal to the average value of the heave L)q. With the conclusion that

teiI liudLd W"7 i.- is cuu1WL4X1, Ivt~i~t ji lbI~UL LU tCuAIluUit L'ivi LAI

dynamic heave spring coefficient (-?ir ) is constant (line..r) 11!jo. A

C) fuziher observatiorn is pos3ible. With a constant Leave Lif the

pioduct fuoq Is non-linear, then the non-linearity must be due to tile

4.

G&M/AE/75A-1

damping ratio (j). Translating this observation to the model, it is

now possible Lo Lonclude that the non-linearity in heave Is due to the

heave damper coefficient (C-E).

Of concern is the fact that the theoritical response peaks of the

remaining pitch response after heave had damped out did not match the

data in time (phase shift) even though there was correlation in period

and amplitude of the exponential decay. Since the heave mode has

violated the original model assumption of linearity, it is not possible

to form a conclusion about the phase shift of the remaining pitch rcsponse

without tirqt investigating the heave non-linearity.

In Chapter 1, it was noted that there are two categories of trunk

material, stretchable and non-stretchable. Since this model investigation

was based on data from an ACRS made of non-stretchable material, use of

the model with stretchable material trurnti must be accomplished with

caution. The exact effect of a ctretr1oble trunk on the linearity of the

sy.tc h .a•-a ctcr.. its is not 1-Mon at this t%-G; howe ver, th-e moel is

expected to operate co,-rectly if a proper expression for the spring and

( damper coefficitents are provided.

The schematic of the VEAM in Figure 8 visually suggests thar the

peripheral springs rerresent sections of the trunk and that the center

spring represents the cushion,. This is not the case. The model

r-equires a center spring (position 5) to account for the heave dynamics

in addition to the roll and pitch linear springs which are derived from

a torsional mode spring. This is illustrated in Table IV where the

linear s/d unit coefficients are sutmmarized from program MODAN0YL.

Recommendations

The following recoamendations are derived from this studyi

I. An investigation into the non-linear nature of the heave

damping phenomenon should bc rade. A non-linear heave damper

coeffiient should be formulated and incorporated int.o the

model to elininate the deficiency of the linpar a,••m•tit•-n.

These results should then be used to investigate the difference

in pbase shift between the theoretical curve and the experimental

() data of the heave response after heave damps out.

UA/AE/73A-1

2. A method should be investigated which would allow the prediction

of. the spring and damper coefficients directly from trunk and

cushion parameters so that this model can be used to investigate

the dynamics of arbitrary trunk configurations without first

building and testing on actual vehicle or scaled model.

0

£43

GAMIAE173A-1

Bibliography

1. Cannon, Robert H., Jr. Dynamics of Physical Systems. New YorkiMcGraw-Hill Booký Company, 1967.

2. Coles, A.V. Air Cushion Landing System CC-115 Aircraft. TechnicalReport AFFDL-TR-72-4, Part I. Wright-Patterson Air Force Base, OhioaAir Force Flight Dynamics Laboratory, May 1972.

3. Digges, Kennerly H. Theory of an Air Cushion Landing System forAircraft. Technical Report AFFDL-TR-71-50. Wright-?atterson AirForce Base, Ohiot Air Force Flight Dynamics Laboratory, June 1971.

4. Doebelin, Ernest 0. System Dvnamics, Modelint and Resnonse.Columbus, Ohiot Charles E. Merrill Publishing Company, 1972.

5. Dorf, Richard C. Modern Control Systems. Reading, MassachusettstAddison-Wesley Publishing Company, 1967.

6. Rodrigues, Anthony. Droo and Static Tests on a Tenth-Scale Nodelof an Air Cushion Landinr System (ACLS). Thesis for Master ofScience. Wright-Patterson Air Force Base, Ohio: Air ForceInstitute of Technology, 1973.

7. Ryken, John M. Desien of an Air Cushion Recovery System for theJindivik Drone Aircraft. Technical Report AFFDL-TR-73-xx.SWright-Patterson Air Force base, Ohio: Air Force Flight DynamicsLaboratory, 1973.

8. Saha, Hrishikesh. Air Cushion Landing Systems. Tullahoma,Tennessee: University of Tennessee, 1973.

9. Vaughn, John C., III and Steiger, James T. Vertical EnergyAbsorption Analysis of an Air Cushion Recoveryr System. TechnicalMemorandum AFFDL-Tri-72-03-FZ'-. iright-Patterson Air Force Base,Ohiot Air Force Flight Dynamics Laboratory, August 1972.

44

G IA.1•E73A1"

0

Appendix A

Analysis of Jindivi) Data (Computer Solution)

05

45

GAh/AE/73A-1

Prorram IDATANYLQ The prpgamm for evaluating the Jindivik ACLS roll and pitch data

according to the theory set forth in Chapter IV is called DATANYL.

Table VI describes the method for entering data into the program and

defines the symbols used, Table VII describes the output symbology and

units. Following Table VII is a listing of DATANYL, a single example

output from the line printer0 and a plot of the test data of each of the

roll and pitch tests of Table I.

TABLE VI

PROGRAM DATANYL-INPUT DATA

Data No. of Data Format Input SymbolGroup Cards in

___ Group

2 1 8F5,FI.0.3, N,P,Q,R,S,WL,U,NOTR,MAtSSEQ,TITLEA9

3 1-N F1G.3 T

4 I-N F1O.3 H

DEFINITIONS OF INPUT SYMBOLSF The number of sets of data (data groups 2,3, & 4)*

N Total ntnber of data pointsP The data point niember for the first positive peak (I or 2)Q Total number of positive peaksR The data point n=mber of the last positive peakS The data point number of the first negative peak (U or 2)W Total number of negative .peaksV The data point number of the last negative peakNOTR The inteiler nuinber of the Jindivik test runMASSEQ The moment of inertia (slugs-ft 2 )TITLE Enter "ROLL" or "PirCH"L T The time from t0 for all peaks in consecutive orderH The adjusted linear transducer heightsI data groups 2,3, & 4 comprise a set of data for each Jindivik testrun. Enter as many sets (F) :%s there are test runs to be analyzedon a singlp computer run.

46

TABLE VII

PROGRAM DATANYL-OUTPUTT DATA

Column Column DescriptionNumber Title

1 DTA The data point number for recorded positive andPOINT negative peaks in consecutive order

2 TIME The timhe occurrence of the positive and rngative(SEC) peaks

3 H The recorded heights or perturbations from(IN) linear transducers for CG, Nose, and Wing

4 T The period, measured between adjacent positive(SEC) peaks

5 FD The damped natural frequency ia cycles/second(CPS)

6 WD The damped natural frequency in radians/second(RPS)

7 HEQ The equilibrium height of the system in steady(IN) state

8 POSAR The amplitude ratios of the positive peaks

9 NEGAR The amplitude ratios of the negative peaks

The following values are averaged to obtain the final value used in the

remainder of the calculationst T, FD, WD, HEQ, POSAR, NEGAR.

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Program RISE

Q Program RISE camputes the iampinG ration (t) and undanped natural

..requency (Ln ) of the Jindivik h-ave mode using the method of percent

overshoot and rise time to the fi.-st peak (Chapter IV) and accounts for

an initial condition on velocity as well as displacement at model

activation. The free fall equations are included to provide values

required by the analysis. To check lit, ea'ity in heave, RISE can be

modified (lines 381-384) to allow computation of f and Wn at peak times

subsequent to the first peak. The program iL designed for use on the

teletype remote terminal. Table VIII provides thz method for reading

data into the program. Table IX describes the symbols and units for

output. Symbols in both Tables are in accord with Figure 16. Figure 31

presents a listing of the program RISE. A sutnary of all calculations

from program RISE can be found in Tables II and III of Chaper IV.

TABLE VIII

Q _PROGRAM RISE-INPUT DATA

Input Format Input SymbolStatement

Read 1I 5FI0.3 TAU TAUPI HI HEQ HPI

Read 4 2F10.4,215 ZETA WN N L

DEFINITIONS 3F INPUT SYMBOLS*

TAU Time of free fall (sec.)

TAUPI Time from release to the first peak (sec.)

HI Height of release point from surface (in.)

HEQ Equilibrium height from surface (in.)

HPI Height of first peak from surface (in.)

ZETA Dariping ratio - asstued or guess for iteration (N/D)

WN Undamped natural frequency - assurned or guess foriteration (rad./sec.)

N integer value of cyclv - 4 uoi £irt pfak

L Integer value of number of iterations desired

* Symbols are in accordance with Figure 16, Chapter IV.

61

TABLE IX

U• PROGRAM RISE - OUTPUT DATA

Output Output Output Definition UnitsStatement Symbol

Print 11 TP Time to first peak sec.

Zo Initial displacement from equili-brium, positive measured down in.

ZODOT Initial velocity at to in./sec.

ZPI Displacement of the first peakfrom equilibrium in.

Print 15 N The N value read in N/D

ZErA1 The first guess for ZETA N/D

WNI The first guess for WN rad./sec.

Print 13 ZETA The iterative solution for ZETA N/D

WN The iterative solution for WN rad./sec.

0

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62

CAM/AE/73A-1

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Analysis of the Equations of Motion

(Computer Solution)

65

GANIAEl73&-1

Provxa' MODANYL

The evaluation of the equations of motion of the Vertical EnergyAbsorption Model (VEAM) in its three degrees of freedom (DOF) isAccomplished by progran MODANYi. A listing of the program 13 prezCented

in Figure 32. Due to program volume, only the graphical results are

included in tbis study.

This program is designed to solve the VEAH equations with the use ofAFIT Subzoutine RKDES, a diffetential equation solver using , v riablestep fourth-order Runga-Kutta method. In addition, the mode -"Aings

and dampers are converted to linear spring/damper units with the

equations developed in Chapter V.

The total vo~rtical displacement as a result of movement in the 3

DOF of any arbitrary point in the plane of the model is comp.ted bySubroutine LOCATE. Displacement of any point (P) relative to the CC

could be accompl.ishcd by

LOCATE, but the model assumptionsSmall pri iir.nS' e . of Ch.• ptcr 1-1 P:•..it I ' _1tin6l

onie 1 the arbitrary point to the

PjZe horizontal plane (Z' a 0).

For this study, the three

C G- positions in the xy plane that

coincided with the locations of

the Jindivik linear displacement* - transducers were chosen for

output in order to compare with

Z the test data.

A subroutine called ANAILTFig. 32. Vertical Displacement plots the theoretical curve andfor Subroutine LOCATo hea

the experit-ental data points forcomparison, Since this plot routine is similar to DATAPLT of Appendix A,

a listing is omitted.

0'

GkM/AE/73A-1

The equatifnt of motion solve a dynamic force balance re-lative to theequilibrium axis. All initial conditions on displacement that are applied

to the equations of motton must be referenced to the equilibrium axis also.

Collecting data relative to the equilibrium axis is difficult since theequilibrium position changes according to test configuration* Therefore,

data is measured from a known horizontal such as the surface or the

spring-neutral/contact plane. For the purposes of these calculations, thespring-neutral or contact plane 13 chosen as the reference. A total

force and moment balance is accomplished and the equilibrium displacement

of the model from the spring neutral plane is calculated for each mode.The following relationships provide the means to reference the initial

conditions to the equilibrium axis.

Z + - (35)

(1 4)• • 0 for all times; that is, (37)

the equilibrium axis and the contact axis measure roll relative mo.

the horizontal.

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Appendix C

Justificaticn of tha Small Angle and

Horizontal Displac1r.;ent Assu".ption3

in Pitch and Roll

C

(.)

GAI/AE! 7 .1k -1

General

_ In LL-. r-lin text, si.plificatlons were made to the pitch and roll

onalysis that were barned upon the assumption that the respective angles

were small and/or the assu;.ption that the horizontal displacement of a

point during pitch or roll was negligible. Justification of these

assumptions in the tekt would have been unwieldy, and would have detracted

from the prii.%ry analysis. The roll mode has been chosen for this

detailed illustration because it has the maximum motion.

Geometry

Taie roll linear displacernent transducer was affixed to the Jindivilk

suspension fr.me a distance (L ) above the horizontal surface through

the :enter of grarity. A 'ire on inertia-reel frorn the transducer

was attached to the wing tip at painrt a. Figure 41 shows the wing in

defl•'ction fron equilibriu~n ( ). The transxducer recoro, a vertical

displacement (C)L ), Luz the attaclhniont point is constrained by the wing

and must sweep out the arc w-i. "'he wire, or.igirially of len-th (L ), is

-rtduced to a length (L-SO. Point a, attach•_d to th,. wire, must be or

arc t-t also, where arc t-t in ixprt of a circle centered

(Y') fYf- - L-hI

t

b 2 h

Fig. 41. Vertical Lnd TranulOtIon.al Tr-annducer E;rrorG

___)

ii' a'T| | |

/ GAk`1jAL/"/3A-l. Iat the transducer with radius (L-S). If the moverient were truly

vertical, theh point of artachment would be at a', but it is at position

a instead. This results in a vertical error (/A.i), and a horizontal

error ( Xk- i )

,Aal~ysis

An origin is created at the center of gravity with an x,y axis

def4r.ed for thi6 proble!n a'a illustratcd. Equ-t ions are then written

which describe the arcs.

For arc w-wl - 32- " (3S)

For arc t-t, 10( • ( L-- (39)

Simultaneous solution of these equations will yield the coordinates for

points a and f. From (3S), solve for X =-[(h;Yj- Z ] Z and substitute

into (39) to solve for _ I '

where LSaS2. (40)

K , 42 (41)

For the maximum roll case -

L.. - 14 ft. 168 in.

>/- 164.75 in.

22 in.

from which

bar 22.005 in.

4A ,005 in.

This calculation shows th,.t the vertical error is negligible.

Substituting , into equation (38) results in a solution for

Xo•t 163.268 in.

Point a translates by the anount A/ - 1.482 in. Thus, the

horizontal translation is only about 1% of the half span (b/2), and can

thus be considered negligible.

The method above allows a precise calculation of the roll angle,

also# vherek ~ 4 U-/

For roll, ( 7.68 degrees, which Lupports the small angle

assunption.

The pitch case follows the sa7e analysis except the half-spin is

-' 84

F replaced by tb, distance between the nose transducer attachment point

S.. and the center of gravity (166.51 in.), and the vjii-n vertical

displacement is 19.80 inches. The analysis shows that

19.8047 in.

Xo• i,5.328 in.

Ae- .001&7 in.

em= 6.23 degrees

Translatý.cn = 1.182 in.

vhich together support the original assumptions.

Although the above analysis used the displacement tranrducers as

the example, the same assuaptions hold true for the trunk. The x-

displacement changes magnitude but their relationships and the maximum

angles remain the same. The results of this analySis were used during

development of the ACLS model as describedi in Chapter II and in

subsequent calculations.

III

GAII/AE/73A-1

I App-enaix vi

AFFDL JiiAUvjk and Test Data

86

-- i

Certain data required in various computations was provided by

i k ) the Air Force Flight Dynamics Latboratory, ';cuhanical Branch.

1. Ejector Test Results

Equilibrium hover Vent Vent Flow Added Flow AddedConditions Opened Closed P,§. - psi PLZ:- - s P

Trunk pressure (Pt) 1.94 1.70 1.64 1.56 I

Cushion pressure ( Pc) 0.03 0.61 0.65 0.68

Trunk flcw ( r) lb m/sec 0.79 0.97 1.02 1.07

CuLshion flow (, ,) lbdsec UNK 0.0 0.46 1.32

Trunk footprint (Pr) '.238 612 579 565

2. Static StiffnessPoll (X)ft-lb/rad 4533.66 J3437.75 12864.79Pitch (Sp) ft-lb/rad 51,566.2 51,566.2 151,566.2 -

Heave (k.z) lb/ft 9000 8400 j7203

3. Heave Test

Drop Time, 1""c.... t- e....t... (eec) n _ _ - t0.0013 0.081

y. 4. Jindivik and ACRS

Momaent of Inertia (Jx-x) slug-ft 2 1190

Moment of Inertia (Jyy) slug-ft2 1810

Weight 1bf 2470

Trunk width in 35.2

Trunk length in 107.7

CP to CG Displacement (S) in 8.56

87

GAMIAE/73A--1

VITA

Frederick C. Bauer was born on 20 May 1942 in Maiden, Massachusetts,the son of Philip R. Bauer and Nita M. Bauer. Ile graduated from the

Units d States Air Force Academy 11 1963 with a Bachelor of Science

degree and a commiss 4 on z a Second Lieutenant in the United States

Air Force. In 1964, he completed Undervraduate Pilot Training at

i1,, Force Pc.zc, Arizona, f,:^- ,heh ho received his pilot

rating. While opcrationally ansIgned to Tactical Air Co,-,and (TAC),

Pacific Air Coxnand (PACAF), and the United States Air Forces in Europe

(USAFE) from 1964-1972, he has flown C-130. CH-3, 11-19, T399 and

UH-IP mission aircraft. In 1971, he received the degree of Hastcr ef

Science in Systems Ranage-ment from the University of Southern California.

Permanent addressi 4365 Antioch DriveEnon, Ohio 45323

A

This thesis w,ý. typed by Mirs. Dorothy T. Bau'ýr.

I.8