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1

AC

A STUOY DJ:"' THE HYOROOVNAMICS OF AC\I HIILLS

WI TH PART I Cl ILA R EMPHA S I S ON PLDUGH- I N

by

Rudrasena Aditya Prasad B.Tech

Submitted for the M.Sc

of Loughborough University of Technology

July, 19.78

Supervisors: Mr.D.Waters, M.Sc.,C.Eng.,M.R.Ae.S.,M.C.A.S.I.

Mr.E.Jenkins, B.Tech •• M.Tech.,C.Eng.,M.I.E.E.

~ by Rudrasena Aditya Prasad~ 1978

Loughborough University

of T~.:hnoiogV Library

Dlte ~~ Cla~s

I Ace. \ '1"\ ()S1 J 01 Ne.

~----------------------------------- ----------------------------------------------

SUMMARY

Since the major calm-water capsizes occurred in 1965/66,

much experimental work has been done to establish better

operational margins of safety. The general approach has

been to establish well defined limits of manoeuvrability

based upon available model and full-scale data. Mathematical

modelling of the ACV motion was used as a secondary approach

because the expressions involved are high in non-linearities . involving aerodynamic and hydrodynamic force terms of

similar orders of magnitude.

In this study, a numerical technique for the solution

of ACV non-linear equations is proposed and a two degree-

of-freedom model is built up using the digital simulation

language, SLAM. The simulation involved the use uf the

technique of storing values of the various non-linear functions

over a defined regime and then using these to provide updated

inputs as the craft changed its state •

. :An ACV overturn sequence is studied by developing,

simulating and testing of equations describing the roll and

sideslip motion of the craft. In particular, the equations

take into account stiffness and damping forces associated

with both the hard structure and the craft cushion system;

inertial coupling effects due to craft deceleration are also

incorporated; induced trim effects due to the position of

the cushion wave system below the craft is modelled and

suitable phase lag is employed depending upon the deceleration

of the craft.

A basic configuration craft is chosen based upon critical

design parameters such as hull depth, skirt depth, VCG height

and hull angle of inclination.Extensive numerical testing of this

configuration is carried out involving a systematic method

of variation of the critical design parameters.

Results indicate that it is good philosophy to design ACV

hulls with planing capability applied to all faces of the hard

structure. The results also allow a set of ranges to be

established for the critical design parameters, which, if adhered to will minimise the possibility of capsize for a craft

configuration of the type chosen for the studYe

ACKNOWLEDGEMENTS

The author would like to express his sincere thanks to

Mr.O.Waters for his generous advice and counsel throughout

the period of this ~tudy.

Grateful thanks are also giVen to Mr.f.Jenkins for his

guidance in the initial stages of the work and for offering

useful suggestions on the presentation of material.

Thanks also go to Professor D.J.Johns, the Director of

Research for his encouragement and to the Staff of the Loughborough University Computer Centre, especially to

Dr.B.Negus who helped overcome computational problems.

(iii)

TABLE OF CONTENTS

Summary

Acknowledgements

Table of Contents

Index of Figures

1. GENERAL INTRODUCTION

1.1. General Remarks Concerning Ploughing-in Phenomena

ii

iii

iv-

viii

1

1

1.1.1. The Mechanism of Plough-in and Overturn 2

1.2. Justification for Further Investigation 3

1.3. Necessary Approaches to the study and Associated Problems 4

1.3.1.

1.3 0 2.

1.3.3.

1.3.4.

1.3.5.

General Remarks on Stability

Critical Uesign Parameters

t.;raft Sensitivity to Critical Uesign Parameters

Problems Associated with the 1'10 d e 11 in g of ACV Motions

The Formulation of Equations Describing the Lateral notion of ACV1s ~Capsize

4

5

6

7

Mode) 9

Problem Solution 11

2. PREVIOUS AND PRESENT INVESTIGATIONS

2.1. Previous Investigations

12

12

2.1~1. notion Studies of Skirted Craft with emphasis on Plough-in 12

2.1.2. urag Forces ~ssociated with ACV's 16

2.1.3. The Hydrodynamics of ACV-Type Hulls 19

2.1.4. Studies Associated with the Cushion System 21

2.2. The Present Investigation 23

26

26

3. THEORY

3.0. Introduction

(iv)

3.1. uerivation of the Equation Describing the Roll l'lotion of the Craft 27

3.1.1. Moment due to Change in VCG Position 30

3.1.2. Moment due to Loss of Cushion Area 30

3.1.3. Moment due to Buoyancy Forces acting on the Immersed Hull structure 33

3.1.4. Uevelopment of uynamic Force Coefficients for Flat ~urfaces at High Angles of Incidence 41

3.1.5. uetermination of Centre of Pressure Location 43

3.1.6. Moments due to uynamic Forces acting on the Hull Face 44

3.1.7. Moments due to uynamic Forces acting on the Hull Top 47

3.1.8. uerivation of the Inertial ~oupling Moment 49

3.1.9. Derivation of the Holl uamping Expressions 50

3.1.10. uetermination of Lraft Inertia in Roll 60

3 e 1.11. Assembling the Holl Equation 67

3.2. uerivation of the Equation Describing Motion of the Lraft in ~ideslip 68

3.2.1. Aerodynamic urag 69

3.2.2. Lushion Air nomentumurag 69

3.2.3. llletting Drag 70

3.2.4. Induced Wave Drag and Wave Slope 70

3.2.5. Drag due to Hydrodynamic Forces acting on the Hull face 71

3.2.6. Drag due to" Hydrodynamic Forces acting on the Hull Top 72

3.2.7. Assembling the Equation Describing Motion in Sideslip 73

4. SIMULATION PROGRAM STRUCTURE 74

4.1. Subroutine HCVDATA and its Function Segments 74

4.2. Master Program ACVDYNAMICS 77

4.2.1. The INITIAL Hegion

(v)

77

4.2.2. The DYNAMIC Region

4.2.3. The TERMINAL Region

5. DISCUSSION AND ANALYSIS OF RESULTS

5.0. Introduction

5.1. Development of the Theoretical Model

5.1.1. ~uasi-Static Terms

5.1.2. Craft Dynamic Terms

5.2. ~imulation Program Development

78

80

82

82

84

84

91

106

5.2.1. Function Generation 107

5.2.2. Lhoice of Integration Algorithm 109

5.2.3. Problem ~onstraints 110

5.3. Model Performance 112

5.3.1. ~ensitivity to Variation of Initial ~tate 114

5.3.2. ~ensitivity to Variation of ~hape Parameters 116

5.3.3. Sensitivity to Variation of Fan Characteristics 124

5.4. Final Evaluation of Craft Design Parameters 127

6. GENERAL CONCLUSIONS AND RECOMMENDATIONS FOR -FURTHER lJORK

6.1. Major Conclusions

130

131

6.1.1. Conclusions on Model Perfo~mance 132

6.2. Hecommendations for Further lJork

7. REFERENCES

8. NOTATION

9 •.. APPENDICES

I. Evaluation of the Main Geometric Terms associated with the Buoyancy Forces Generated

135

137

141

146

by the Immersed Portion of the Hull 146

11. Lift and Drag Coefficients Associated with the Movement of a Flat Plate through a Fluid Medium at High Angles of Incidence 152

(vi)

Ill. Determination of Geometric Expressions Associated with the Damping of the Hull

IV. Determination of Geometric Expressions Associated with Added Inertia in Roll

V. Flowcharts and Listings associated with Program ACVDYNAMICS

VI. Flowcharts" and Listings associated with Program ACVDATA

VII. Definition of Main Computer Variables used in the Study.

(vii)

156

158

164

170

186

Fig. i~o •

1

2

3

4

5

6

7

8

9

10

11 a

11 b

12

13

14a

14b

14c

15

16

17

. 18

19

INDEX OF FIGURES

Description

Demonstration of Full-scale Plough-in Phenomena for SRN-6 Craft

Line Film Recording of the Capsize Sequence of a Model of ~RN-6 Craft

~asic Craft Configuration used in the ~tudy

The Main Forces acting on an RCV in a Heam-on Roll Condition

Uverturning of SRN-5 Craft - a Diagrammatic Sequence of Events

The Components of Drag acting on a'Hovercraft

wave Resistance for Different Craft Planforms Computed by Baratt

wave Resistance in Accelerated Motion computed by uoctors and jharma

Basic configuration Craft

Moment about the Trailing ~dgB due to craft weight acting through the C of G

Moment arisin~ from the Lraft ~ushion :Jystem (~ 11A)

Main Geometric uefinitions

1'10 men t due to 13 u 0 y a n c y For c e s (~A < ~ < J1 B ) l'loment due to Buoyancy Forces (I1 B < 11 < I -ex.) condition at which ~ = -!-~

l'loment due to Buoyancy Forces (~> ~ -oc)

Moment arising from uynamic forces acting on the Hull Face

Moment arising from uynamic Forces acting on the Hull Top

Moment arising from the Inertial Coupling t:.ffect

t:.stimation of ~ushion Volume (}1 .0 A) (viii)

Fig. IIJO. uescription

20 fan ~tatic ~haract8ristics - Linearised ~urve

21 uetermination of Uamping Contribution due to Hull ~ace

22 uetermination of uamping ~ontribution due to Hull fop

23 uetermination of the ~omponents of the ~raft Holl lnertia in Air

24 uetermination of the urag ~omponent acting on the ~raft due to uynamic ~orces Associated with the Hull ~ace

25 uetermination of the urag ~omponent acting on the Lraft due to uynamic ~·orces Associated with the Hull fop

26 Graph of Change in 'Primary Hump ~peed i- plotted against Craft ueceleration (g's)

27 Graph of Total Non-uimensional ~oment plotted against Craft Roll Angle

28 Graph repre~enting Terms affecting the Moment Contribution due to the ~ushion (Static Lase)

29 Graph of Lhange in Buoyancy and Total Moment Terms plotted against Craft Roll Angle for Pre-fransition and Aft-Iransition Conditions ~Static Case)

30 Graph of Change in Force Coefficient due to the Movement of a flat ~urface through a tluid Medium plotted against Incidence Angle

31 -llraph of ~hange in Moment due to t low Impingement on the Hull plotted against Sideslip Velocity

32 ~raph of Lhange in Damping ~oefficient due to"Flow Impingement on the HUll plotted against ~raft Holl Angle

33 Performance Curves for a Multi-wing Fan

34 Graph of Non-uimensional ~ushion Pressure Variation plotted against Craft Roll Angle

35 Graph Representing Terms affecting the ~oment Contribution due to the Lushion (Dynamic ~ase)

36 Graph of Variation of Wave Slope plotted against Lraft Speed

37 Graph of Variation of Craft Total lnertia in Roll plotted against Craft Holl Angle

(ix)

Fig. NO.

38

39

40

41

42

43

44

uescription

Graph of Total Non-uimensional urag Force plotted against Sideslip velocity

uutput Graphs used for a Comparison of Integration Houtines

l'lotion l..urves (see Legend)

l'lotion Curves ~see Legend)

l'lotion Curves (see Legend)

l'lotion l..urves (see Legend)

uetermination of Neutral Stability Line w.r.t Lhanges in VCG Height and Hull Angle of Inclination

45 Effect of Varying ~kirt Depth on the Position of the Neutral Stability Line

46 Effect of Varying Hull Uepth on the Position of the Neutral ~tability Line (Thin ~ectibn)

47 Effect of Varying Hull Uepth on the Position of the Neutral ~tability Line ~Thick §ection)

48 Motion Curve: Comparison Plot ~see Legend)

49 Plot of Craft Motion in Roll ~Demonstrating Motion Phases)

50 Plot of Craft Motion in Roll \Demonstrating the Effect of the Transition to Fully Attached Flow)

51

52a

52b

53

54a

54b

55a

55b

56

fllotion Curve: Comparison Plot

l'lotion· Curves (see Legend)

l'lotiofl Curves ~see Legend)

IYJotion Curves: Comparison Plot

rlotion Curves (see Legend)

Motion Curves \see Legend)

i'lotion Curves ~see Legend)

l'lotion Curves \see Legend)

Performance Curves: l'lul ti-wing the Fan Design Operating Point

tsee Legend)

(see Legend)

Fan - Shifting

57 ~lot of ~raft Motion in Roll \Basic Configuration Craft)

(x)

fig. No~ uescription

58 Plot of Craft Motion in Holl \Effect of Shifting the fan Uesign Uperating Point)

59 Graph of Variation of Cushion Pressure plotted against Craft Roll Angle - iffect of Shifting the fan uesign uperating Point

Basic Configuration Craft uata:

A1 Storage of Values of Induced Trim Angle

A2 storage of Values of Non-Uimensional Moment due to ~ushion

A3 Storage of Values of Craft Total Inertia in Roll for Detached and Attached flow Assumptions

A4 storage of Values of Total Non-uimensional Moment acting on the Craft

A5 ~torage of Values of Total Non-uimensional urag acting on the ~raft

A6 ~torage of Values of Moment Derivative -Damping Coefficients

A7 Input Data to Program ACVuYNAMICS.

(xi)

-1-

-.

1 • GENERAL INTRODUCTION

The evaluation of air cushion vehicle (ACV) dynamics

is going through a process of change mainly due to the fact

that air cushion technology is very much in its youth and

not enough research has been done to· cover all the areas

of: major concern.

Mathematical modelling therefore serves as a useful

tool in these early stages of development of ACV's as it

provides the designer with valuable insight into the principal

factors which influence the general behaviour of the craft

when subjected to va~ious initial coridiiions and constraints.

1.1. General Remarks concerning Ploughing-in Phenomena

In April 1965, an SRN-5 craft overturned in roll off

the coast of Norway and in May of the same year another such

incident occurred in San Francisco Bay. A third incident

was later recorded in 1966 off the British coast. On each

of these three occasions, the craft had developed yaw of

45 degrees or more at about 40 knots waterspeed; the

skirt plough-in and overturn finallt occurred at around la

knots waterspeed when travelling approximately beam-on

(reported in CAA paper on Hovercraft Stability and Control,

1975, re~ 1).

In all three occasions, the accidents were of a

plough-in tYRe associated with tight turns initiated at

high speed in glassy calm sea conditions.

-2-

1.1.1. The Mechanism of Plough-in and Overturn

The hydrodynamic mechanisms of plough-in and overturn

are intimately bound up with the presence of the skirt~

Usually, movement of the craft contrOl surfaces result in

some change of trim;.at high speeds, or in choppy conditions,

parts of the soft structure or 'skirt' tend to brush the

water surface. In some cases if the change in craft trim is

large enough, part of the lower skirt may collapse ~th a

. tendency to fold inwards or 'tuck' under the hard structure.

The effect of 'skirt tuck' is to cause cushion area to reduce

and the centre of pressure of the cushion to shift rearwards

resulting in a bow down motion.

If the motion is strictly in a longitudinal sense, the

craft rapidly decelerates and this deceleration is coupled

with a large nose down movement known as ploughing-in.

A multiexposure photographic recording of an actual

ploughing-in sequence is shown in Fig. 1.

In many cases, say in initiating a turn, there is a

tendency for the stern to break away so that large angles

of yaw rapidly develop well before the full turn is completed.

This is typic~lly characteristic of ACV motion and if skirt

tuck and plough-in ~ occurs, the craft is in many cases

unable to restore itself resulting in an almost beam-on

capsize. This phenomena has also been recorded on film

for an SRN-6 model and a multiexposure photograph is shown

in Fig. 2.

*.Hereafter, references will be indicated as superscripts unless otherwise indicated.

·-3-

1.2. Justification for Further Investigation

In the ARB special committee report on Hovercraft

Stability and Contro11 , an attempt was made to summarise

all the information available on Hovercraft capsize. The

report suggested that a theoretical research program of some

magnitude was necessary to establish satisfactory design

guidelines on which future hovercraft designers will base

their models.

Since the 1965/66 capsizes, a set of well defined limits

of manoeuvrability were established in order to ensure better

operational margins of safety; present day hovercraft pilots

are required to conform to these rules. However, this is no

justification for assuming that further accidents are

impossible and there are two main reasons to support this:

(a) if the skirts are damaged sufficiently for the ba9

internal pressure to approach that of the cushion,

then skirt stability is reduced and tuck under

could easily follow.

(b) secondly, much of the vehicle control is today still

left largely in the hands of the pilot. It is quite

possible that errors of judgement could be made,

especially in going through tight turns where proper

pre~ision control is required. In this mode, as

demonstrated before, a beam-on plough-in condition

could easily be initiated •

. It is therefore not only necessary to safeguard against

these conditions occurring, but primarily, if they do occur,

to ensure by proper design that the craft is capable of

r~storing itself.

-4-

1.3. Necessary Approaches to the Study and Associated Problems

1.3.1. General Remarks on Stability

In the design of any engineering system, there are

generally two approaches to the problem of dynamic stability_

The first and "oremost is usually carried out in the early

development stages of the system and this involves the use

of fundamental stability criteria to keep the general

structural configuration within certain specified limits.

Typically for ACV's, a VCG location range and a skirt depth

range will dictate agreat deal of the initial design approach.

Of course a secondary approach that has also achieved

wide application, is the use of feedback control to improve

the dynamic characteristics of the system if for instance it is

thought that the basic design has unstable tendencies built

into it. This will suggest for instance:

(a) . the use of motion sensors to detect any undesirable

changes in the operation of the system

(b) use of a controller to interpret the signals

coming from the sensors and using a

feedback law to generate a countera~tive signal

with the aim of combating the changes detected.

(c) the counteractive signal from the controller would

then be used to drive· force or moment generators

to return the-system to an equilibrium state.

In the case of ACV's various force and moment generators

like puff ports, multidiroctional rotors, rudders and skirt

lifting systems are generally used to contrel the motion.

-5-

The problem of ploughing-in however is sesn as a result

of basic design features and it was thought that preventative

measures could be sought by structural configuration changes

rather than by seeing the former as a control problem.

In any case, uhile present day motion controlling systems

for ACV's may be capable of enforcing constraints on the motion

in order to avoid a plough-in being initiated for instance,

their usefulness will almost inevitably be shortlived in

actually preventing a plough-in once initiated.

1.~.2. Critical Design Parameters

If there is to be any change in the basic design

philosophy applied to the ACV, it must happen while this

mode of travel is still passing through a relatively early

phase of development. An attempt uas made in 1975, by the

ARB special committee to supply a range of suitable values

fo~ the most critical design parameters affecting craft

stability1.

It appears that the most sensitive factors influencing

craft overturn are VCG height, skirt depth and hull depth.

Large VCG heights and skirt depths would obviouslY result

in a tendency for large angles of rotation to be developed~.

The hull depth is important from the point of view of providing

adequate buoyancy restoring forces should the craft develop

large angles of roll.

ACV plough-in is quite common both in the longitudinal

and lateral mode. No capsizes however, have been known to

occur in a strictly longitudinal sense. This is perhaps

partly because craft inertia is usually high in

-6-

the longitudinal mode and . partly because the hull

face of the craft bow is usually hydrodynamically designed to

give positive restoring momenE~ about the C of G.

As a result of these observations, it was believed that .craft

ability to resist capsize would be greatly enhanced by proper

hydrodynamic design ~ppli~d to ~ll faces of the hull structure.

This therefore introduces a fourth design parameter which

could possibly influence craft behaviour. in the capsize

mode and that is the hull angle of inclination, sometimes

referred to as the planing angle.

These four design parameters allows a basic craft

configuration to be defined and this is shown in Fig. 3.

1.3.3. ~raft Sensitivity to Critical Design Parameters

There are several approaches to the way in which the

craft sensitivity to change in the critical design parameters

may be assessed.

As the study would involve basic structural changes,

work with full scale craft would be almost impossible due to

the eitremely high costs of modification that would frequently

be incurred.

A second approach could of course be the use of scale

models to perform the required, tests. However, in this case

one is faced with the added problems of scaling the dynamics

of the cushion system especially the inertia and friction

associated with the skirt.

-7-"

A third approach which has also been favoured in this

study is the development and use of a mathematical model to

achieve the desired objectives. Naturally in mathematical modelling

it is necessary to be very careful about the way in which the

problem is formulated; it will be important to

constantly bear in mind the limits and assumptions made

regarding the- various .. expressions involved~ However, -0'

once the problem is formulated obtaining a solution is generally

a routine matter and a large number of cases could be evaluated

in a relatively short period of time compared with other

approaches.

1.3.4. Problems associated with the ~odellin9 of ACV Motions

Mathematical modelling of ACV motion presents an

interesting challenge to the engineer because the various

terms involved are extremely rich in non-linearities. The

problem is highly complex involving both aerodynamic and

hydrodynamic force terms of similar orders of magnitude and

motion of the craft can take place in six degrees of freedom,

in roll, pitch, yaw, sideslip, heave and surge.

Thus it is _not unusual to find that motion studies are

often simplified. A typi~al assumption for instance made

with vehicles having symmetry in the longitudinal plane is

that there is no coupling between longitudinal and lateral

motion as is done in the case of aircraft and ship motions.

Using a similar approach, the ACV plough-in and capsize

in roll when treated as a sequence of events, may be looked

~-------------------------------------------

-8-

upon as a series of unconnected motion ~hases. This is

demonstrated more clearly in some statements on the-observed

capsize sequence recorded in-the AR8 special committee report 1•

These are:

(a) initially, the craft is assumed to be on cushion

and operating sat~sfactorily

(b) the craft is put into some situation due to engine

failure, lift power reduction, skirt failure or

manoeuvring which results in leading skirt tuck-

under.

(c) following leading skirt tuck-under, craft hard

structure immersion occurs.

(d) following hard structure immersion, the capsize

occurs. It is also important to note that development ~f high angles

of yaw are also usually associated with (b) above. The above indicates two major regimes of study

and these are:

(1) to establish the onset of skirt tuck-under

(2) to establish the dynamic stability of the craft

with hard structure immersion and assuming that

skirt tuck under had already occurred.

In the case of capsize due to a turn being initiated,

skirt tuck under usually ensues during the transition from

tha initiation point to the time when a very high yaw angle

approaching 90 degrees has developed. This is observed from

the motion of the model in Fig. 2.

-9-

The modsl then enters a second regime, as indicated

in (2) above, uhere the hard structure begins to influence

the craft behaviour and where--the following motion is almost

beam-on.

Modelling the craft behaviour in the second phase of

the capsize sequence therefore need not include all the

degrees-of-freedom of the steady level motion. In fact

the ~otion during this phase is an almost pure sideslipping

and rolling of the craft coupled with some heave as the

craft leading edge sinks at high angles of roll.

It is seen from Fig. 2 that even at very much aggravated

angles of roll, the trailing edge of the model appears to

remain f.ixed in space at least vertically; this allows a further

reduction of the problem to that of a 2 degree~of-freedom

model describing roll and sideslip motion.of the craft at

least up to about ~O degrees of roll.

1.3.5. The Formulation of £ uations describin the lateral ~ion of ACV's \capsize mode.

It may have become clear that during the second phase

of an ACV capsize sequence, ~described above), the hydro-

dynamics of the hull mU9t necessarily play an important

part in determining the general behaviour of the craft;

this of course is in addition to the contribution from

aerodynamic and cushion forcing terms which are always

associated with the motion anyway.

-10-

Thus if the main forces and moments associatod with

the craft ltaking into account the Interaction of the hull),

could be estimated during this phase of the motion , the model

can be assumed to match fairly closely the condition of a beam-

on capsize.

Fig. 4 shows diagrammatically a general breakdown of the

main forces involved in a beam-on roll condition. It is seen

that it will be necessary to estimate the buoyancy of the

. immersed portion of the hull and this will act as a restoring

force. The action of water impingement on the hull face will

also contribute to the rolling moments and this will obviously

become aggravated as the craft Igunwale l moves below the ·water

surface. The hull will also have some damping associated

with it since energy is imparted to the water as the leading

edge portion of the structure sinks.

other terms in the equations must include the effects

'of stiffness and damping due to the cushion and the

destabilising effect of the VCG shift as the craft rolls.

Aerodynamic force terms will also come into play mainly as

orag terms in influencing the rate of deceleration of the

craft while in this phase of the motion.

The main coupling term between the roll and sideslip

equations ~ill be an induced downward roll due to the inertia

of the craft as it decelerates.

Non-linearities will come from geometric effects at

large angles of roll together with sudden changes in the

pressure distribution on the craft hull especially as the

-11-

-craft 'gunwale' s1nks below the water surface. Other sources

of non-linearity will be the ·effect of the changing cushion

volume of the craft on fan characteristics and from transitions

in the flow pattern around the hull as the craft speed changes.

1.3.6~ Problem Solution

Once the equations describing the roll and sideslip

motion of the craft in a beam-on condition have been

. formulated, it will then be necessary to apply some problem

solving technique in order that the craft motion may be

observed.

There are two basic approaches to the solution and these

are respectively by analogue simulation and by digital

simulation. However, analogue machines though. speedy, are

generally unable to handle problems where the non-linearities

are extensive. On the other hand, the digital machine has

the qualities of versatility and far less hardware to deal

with and will be favoured h~re.

This will of course raise the question of deciding upon

a suitable numerical integration technique and also the

development of a method of dealing with the non-linear

terms in the equations. Usually the task is to find an

accurate and reliable approach, which exhibits good stability

-properties without requiring excessive computer time.

-12-

2. PREVIOUS AND PRESENT INVESTIGATIONS

2.1. PREVIOUS INVESTIGATIONS

Studies so far into air cushion vehicle dynamics have

generally been accompanied by very little published material

as much of the work is usually done through commercial

or military interests. In particular, the availability of

material on the actual mechanism of ACV plough-in is severely

limited and therefore alternative means had to be sought in

retrieving the information required. Thus~it will be seen

from the following sections that a series of independent

studies were made on various aspects of the ACV in order that

.a more coherent picture may be built up illustrating the

state of the art.

2.1.1. Motion Studies of Skirted Craft with emphasis on Plough-in.

-Addition of 'flexible extensions' or 'skirts' to

ACV's not only enhanced the obstacle clearance capability

of the craft but also the wave riding capability. However,

as would be expected, along with these major advantages came

a series of problems, three of which have formed the basis

for further research and development.

2 by Crago as:

These were outlined

(a) ~ound skirt design consistent with the need for

it to adequately maintain its shape while at the

same time be pliable enough to reduce rough water

drag

(b) studies of the phenomena of plough-in and overturn

(c) studies involved with the reduction of skirt oscill-

ation and uear.

-13-

So it is seen that the plough-in phenomena right from the

start has been intimately bound up with the skirt system.

The plough-in phenomenon was first ·observed and studied

with SRN-1 craft as early as 1961 3• It was not given a great

deal of attention as this only occurred in the longitudinal

mode where resistance to c~psize is greatest. In the

case of SHN-1, a hydrodynamic bow had already been fitted

to cope with intermittent wave contact and this fortunately

gave the craft good restoring capability against capsize.

The earliest detailed study made of ACV plough-in and

overturn was carried out in the USA by walker and Rood 4

immediately following the SRN-S capsizes in 1965. . In this

report"it was suggested that with a small change of trim,

it was possible for water to attach to the fl~xible skirt

causing a hydrodynamic drag, a suction on the lowest part

of the skirt and a higher pressure rather higher up (See

fig. 5).

R. Stanton Jones records some work done on the effect

of reducing cushion pressure on craft heeling stability5.

It was found that the moment required to overturn an SRN-6

model reduced by up to 50% if cushion pressure was reduced

by only 20%.

In the Walker study4, an attempt was made to analyse

the effect of the forces on the skirt. It was suggested that the

net result would be to cause a downward pitching moment and

the subsequent collapse of the skirt. This would be coupled

-14-

with a violent nose doyn motion until the hard structure

contacts the water. As soon as the speed reduces suffici~ntly,

the skirt will ~edeploy restoring the craft to a full

hovering position once again; this phenomenon is popularly

known today as the tuck under and plough-in sequence.

Of course the skirt may not redeploy at all as in cases 5 where the bow contact is asymmetrical. R. Stanton Jones

records that the plough-in can proceed to a lateral roll

over, which, in actual full-scale incidents, has not reached

a completion until the craft has been moving sideways at

about lateral 'hump! speed. Thus two things can be

inferred:

(a~ In all the capsizes observed, the craft is travelling

approximately beam-on and this has been confirmed

in the ARB Special Committee report1

and (b) the critical region of capsize occurs when the

craft is travelling at around hump speed.

In 1968, Silverleaf in his review of hovercraft research

in Britain6 indicated that the lateral antisymmetric motions

of hovercraft in calm water had been analysed by using the

equations of motion for longitudinal force, sideforce, rolling

moment and yawing moment assuming zero pitch trim, small roll

-angle -and axes coincident with the principal axes of the

motion.

-15-

Obviously, this model l:Jill not --have been sui table for

the study of craft capsize which involves development of

relatively large angles of roll. Also, as the work was

done purely by analogue techniques, it is possible that

the many non-linearities of the motion could not have been

adequately represented •

. M.J. Saratt7 formulated lateral equations of motion

based on derivative notation widely used in aircraft dynamic

studies. However, this depends very much upon how the

solution to the expressions for these derivatives is approached

as they will·conta~n many non-linear terms and will therefore

be di ff icul t to sol v·e.

The general approach to the solution of ACV motion

equations has more usually been a numerical one. The

iequired data is accumulated for the particular regim~ under

study, and this information is then used for providing updated

inputs as the craft changes its stage in a simulation run.

Crag02 reported on dynamic studies carried out at SHC

where this principle was employed. As a result, time

histories of·craft attitude, speed and longitudinal deceleration

were obtained. This enabled a number of plough-in boundaries

to be calculated for zero yaw.

other reports written on this principle of motion study

only cater for specific cases. Fein et a1 8 studied air

cushion performance using BH-7 data as part of a computer

simulation. A four degree-of-freedom mathematical model

-16-

was used incorporating hydrodynamic experiments, aerodynamics,

propulsive forces and a control system. The equations for

yaw, sway, surge and roll. were integrated numerically using \

a computer program to provide time histories of the craft

motion. The program however was capable of simulating only

on-cushion condi ti o'ns andcalm-wa ter manoeuvres.

~ .'

2.1.2. Drag forces associated with ACV's

Another area which has stimulated great interest for

further research and development concerns the drag forces

associated with ACV's. The approach .has usually been

to separate the drag into major components and R. stanton

Jones lists theseS as:

(1) Air momentum drag

(2) Air profile drag

(3) water wave-making resistance

(4) water wetting resistance

(S) Increase of resistance due to encountered waves

A typical plot of the relative importance of the various

components is given in fig. 6.

Water wave-Making Resistance

It is noticed that the induced wave drag is a

dominant term influencing the total drag force acting on the

ACV and by far the majority of research work has been directed

towards a better understanding of the factors which have a

bearing on this drag.

Havelock9 was one of the first to treat the theoretical

problem of the wave resistance associated with a pressure

.1

-17-

distribution moving over water at constant speed.

Lunde 10 extended the theoretical treatment to cover

the case of an arbitrary distribution moving over.a finite

depth.

. 11 Baratt computed the wave resistance of rectangular

and elliptical pressure distributions. In deep water, the

main 'hump' on the drag curve occurs at a Froude number ~iven

by fR' = 1//Tf. In water of finite depth, this hump is shifted to a lower froude number, and for sufficiently

shallow water occurs at a depth/Froude number ratio equal

to unity.

The results obtained so far were based on the assumption

of a constant pressure distribution over the planform

and indicated that the resistance coefficient oscillates

rapidly at lower speeds (Fig. 7), a trend which is not

observed in experimental results.

fortunately, operating speeds of most craft are high

and this deficiency in the theory is generally of minor

importance. Houever, Doctors and Sharma 12 to some extent

were able to overcome this deficiency by introducing a more

'realistic' pressure distribution where a hyperbolic fall

off of the pressure at the edges was assumed. This allowed

further studies to be made for the cases of accelerating

craft and a typical wave drag plot obtained is shown in

fig. 8.

-18-

As to the computation of surface waves generated by

13 ~cVts, Hu and wang presented numerical results for craft

with rectangular planforms travelling at three different 14 speeds. Yeung computed surface elevations as well as

induc~d wave forces.

On several occasions, extensions to general trajectories

and to arbitrary time-dependent pressure distributions were

by now being inhibited by the computational complexities.

However, Haussling and Van Eseltine 15showed that a fourier

series approach lead to an efficient computatio~al scheme

for the analysis of wave resistance, side force, yawing

moment and wave elevations associated with ACV's.

A number of experimental programs were formulated to

check the above theoretical results obtained by Barat0 1

and Everest and Hogben16,17,18,19,20are the chief workers in

this field and the main question pointed out in these papers

is the resolution of the total drag acting on the ACV into

its components. Thus a short summary of the way the other

components are generally defined will be given here •

.8.!r r~omentum Drag

The momentum drag is that resulting from a change in

direction of the air flow, as 'the latter moves through the

c~shion system. The drag is in fact mainly made up of two

components usually referred to as the inlet and outlet momentum

drag respectively. The outlet momentum drag may sometimes 12 act as a thrust , depending upon the trim of the craft.

-19-

Air Profile drag

The air profile or aerodynamic drag is assumed to be

that resistance acting on a model if it were tested in a wind

. tunnel with engines not running.

Water wetting drag

This is usually referred to as water contact drag as

it is that due to any contact of the louer edge of the skirt

with the water surface. Spray drag is usually included in

this estimation as both have a very non linear nature and

therefore very difficult to predict. Everest 16 estimated

the water wetting resistance by eliminating it - using a

thin polythene sheet floating on the water surface.. The

technique however raises the .qu8stion about the tensile

forces on the sheet.

2.1.3. Hydrodynamics of ACV-type hulls

Very little theoretical work has been done on the

hydrodynamics of ACV hulls possibly because the hull shapes

in use today are too varied and possibly because it may be

considered that work done in other fields will be adequate in

providing information of the behaviour of a particular hull

shape.

However, experimental work has in fact shown that proper

hull design is vital to providing the craft with adequate

restoring capability in the event of a beam-on plough-in

(see Hefs. 4 ~ 21).

-20-

22 Shuford made a study of various planing surfaces and

found that an optimum planing angle of about 4-5 degrees

is typical. However it is expected that with ACVt s , this will be unachievable considering that some buoyancy must be

built into the hard structure and this usually implies steep

angles of hull incllnation.

It may also be possible for the surfaces of the hard

structure to be considered as flat plates. A relatively

large volume of work is available on the study of flat

bottomed planing craft which might therefore be of use~

• 23 24 Notably Shoemaker and Murray have made some worthwhile

contributions to the experimental study of the hydrodynamics

of planing surfaces.

Most texts on aerodynamics or hydrodynamics, notably

references 25 & 26, treat the theoretical study of flow "

i~pingement on flat surfaces using a two-dimensional approach.

However these methods will "generally be limited by assu~ptions

of small relative angles of incidence of the surface to the

stream flow.

On the other hand use of the 2-0 approach to the

theoretical treatment of ACV hulls is still justified as

the relative aspect" ratios of surfaces involved are generally

large (> 10) and therefore some extension to the theory will

have to be made to cover large angles of incidonce (>10 0 ).

Another approach which would also conveniently take into

account the bends at the top and lower edges of the hard

structure would be to use oonformal mapping techniques and

again olassical methods are found in most texts, notably the

-21-

uork of Prantle and Tietjens 27 •

28 The latter technique was used by Hogben reg~ding

the flow past a two-dimensional curved plate at a free

surface. One of the aims of the work was to make an

analysis of the flo~ past the rounded portion of the skirt.

Of course Hogben's work could be utilised in the aggravated

case where the skirt has tucked back close to the hull;

however, it is likely that the assumptions of a rigid boundary

and detached flow at the lower edge will impose too many

limitations on arriving at a suitbble solution.

A final approach to the prediction of the pressure

distribution around the ACV hull could be taken by adopting

the theory of SquirJ9 who considered the motion of a

simple wedge along the water surface. However the use of

this work will once again be limited by the assu~ption of

low trim angles and separation of the flow at the bottom edge

for all speeds above zero. It is thought that the flow must

detach at some speed since a point will be reached where it

will be impossible to achieve the proper formation of a wave

system.

2.1.4. Studies associated with the Cushion System

studies on the cushion system form a~other area which

has occupied a great deal of interest in the total research

and development of ACV's. Available material on the cushion

system may include studies on the fan, internal ducting and

-22-

the skirt all of which play an important part especially in

determining the heaving dynamics of th~ craft.

An important attempt to correlate the heaving and

pitching motion of ACV's with the cushion system was made

by Wheatley30. Ho~ever, his theory was based upon

restricting the craft to small motions. Important conclusions

made were that the stiffness of the cushion will be inversely

proportional to the daylight clearance at the bottom of the

skirt while the damping will be inversely proportional

to the flow rate.

Richardson 31 advanced the principle that the cushion

can be regarded as a suspension system similar in many

respects to that of a motor vehicle and essentially ~.

consisting of a spring and dashpot. This was later verified

in a report made by Wheeler 32 on research and development

of ACV's in Britain.

. Also the damping contribution of the cushion appears

to be intimately bound up with the shape of the fan

characteristic curve. It is therefore found that in most

theoretical work, linear or quadratic assumptions are made

in describing the slope of the fan characteristic curve

(see Ref. 33).

-23-

2.2. PRESENT INVESTIGATION

The present investigation involved:

(a) the theoretical development of a two degree-of-

freedom ACV modal describing the roll and

sideslJp motion in the beam-on leading skirt

collapsed phase.

(b) the simulation of the model using digital

techniques

(c) the subsequent testing of the model and the

final evaluation of the major craft design·

parameters.

The. equation describing the roll motion of the craft

was developed to take into account the following factors:

(1) static moment contributions due to VCG shift

and buoyancy of the immersed portion of the hard

structure

(2) dynamic moment contribution due to flow

impingement on the hard structure

(3) dynamic moment contribution due to inertial

coupling coming from the deceleration of the

craft

(4) damping forces due to the flow over the hard

structure at aggravated angles of roll.

(5) stiffness and damping contributions of the cushion

system.

-24-

(6) an estimate of craft inertia and added inertia

terms due to fluid displacement as the craft rolls

and (7) modelling of the induced trim due" to" the position

of the cushion wave system below the craft and

applying suitable phase lag to this system

depending upon the deceleration of the craft.

The equation describing the motion of the craft in side-

slip took into account the following factors:

(1) hydrodynamic drag forces associated with the flow

over the hard structure

(2) aerodynamic drag forces dUB to the air flow over

the craft

(3) cushion air momentum drag

(4) water wetting and spray drag

and (5) induced wave drag due to the cushion.

The simulation language SLAM, compatible with ICl , machines was used to model the motion of the craft. The

simulation of the model involved the use of the technique

of storing values of the various non-linear functions over

a defined regime and then using these to provide updated

inputs as the craft changed its state. This allowed fairly

accurate "solutions to the non-linear problem to be obtained.

A basic configuration craft was chosen as shown in Fig.9

and the following initial values were assigned. to the

major design parameters:

-25-

hB/B = 0.1

h /B = 0.1 5

hG/ B = 0.2

8 = 21 0

Extensive testing of the model which involved a

systematic method of variation of the above parameters

finally enabled a set of 'safe' ranges to be decided upon

for the major design parameters.

Also various aspects of the testing have brought out

some interesting features on motion characteristics for

instance the relationship of cushion damping with flow rate

through the fan which agree very well with previous.

b t · 30 o serva ~ons •

-26-

3. THEORY

3.0 Introduction

In this ~ection, the Hall and jideslip Equations des-

cribing the model dynamics are developed. It is considered

that inclusion of a Heave Equation in this initial study would

greatly increase the complexity of the problem as the dynamics

of the cushion system at large clearance heights (h> .058), is

extremely difficult to predict mainly due to non-linear cross-

flow effects. lt is thought that the effect of including a

Heave £quation will in general be to reduce the relative roll

angles achieved at least over the regime of rol~ angles considered

in this study and therefore the results using a 2 degree-of-

freedom model is likely to be on the pessimistic side.

five main assumptions are made based upon notes and obser-

vations made in ~ections 1 & 2 and these are:

(1) the craft is assumed to be in a condition where it is

travelling beam-on and possessing some initial pre-

determined sideslip velocity

(2) the leading-edge skirt in the beam-on condition is assumed

to be fully collapsed exposing a planing hull face

(3) the water flow is assumed to detach about the lower

edge of the hard structure at higher speeds, ~point p,

fig.4). A transition si~eslip speed is then defined

at which the flow becomes fully attached

(4) no coupling exists between the roll motion and heave

motion, or between sideslip motion and heave motion up to about 30 0 of roll. Thus for all purposes the craft

trailing-edge ~point U, Fig.4) remains fixed vertically . in time

-27-

(5) the trailing skirt is considered tb be rigid so

that for co~venience, body axes are set up about

the craft trailing edge and these axes coincide with

the space axes at the start of the motion.

3.1 DERIVATION OF THE ROLL EQUATION

The general equation describing rotation in any

engineering system usually has terms dependent on angular

acceleration, angular velocity and angle of rotation. If

the forcing function is given by some moment.Jt, the linearised

equation is of the form:

+ + !i. rJ -- . It • • • ••• (1)

where 1 , C and f

-28-

If cross coupling and added mass effects are included,

the expression becomes:

• • • ~ •• (3)

This expression is more easily formulated if the terms

on the right hand side are further broken down as functions

of one or two variables only.

Thus Equation (3) can be written in the form:

• • • • • • ( 11 )

Again ~he dashed term denotes derivative w.r.t ft and the coupling term (M 1) and the cushion forcing term (M 0 d) have been cp cp separated from the expression for total moment in Equation 3.

The dynamic equation written in this form makes it easier to

describe the roll motion of ACV's. However, although it

is possible to write this equation'o describing o

the rolling motion of the craft directly into a computer

simulation program, grouping the expressions derived

will be too cumbersome and lengthy.

Instead, the various terms are derived and put in a

suitable non-dimensional form, and a computer program is then

used to determine numerical values forO these terms over

a defined regime of study. This approach is discussed in

greater detail °in Section 4.

Section 3.1.1 - 3.1.3 inclusive involves the derivation

of the static moment terms and these are dependent on roll

angle (,£1) only.

-29-

Section 3.1.4 involves a brief study of lift and drag

coefficients associated with the movement of a flat plate

through a "fluid medium"Bt high angles of incidence as is

typically the case with a planing ACV hull.

Section 3.1.5 involves a short study of centre of pres-

sure location asso~iated with the movement of a flat plate

through a fluid medium at high angles of incidence.

Section 3.1.6 - 3.1.7 inclusive concerns the derivation

of the dynamic moment terms and these are functions of

both roll angle (~) and sideslip velocity (y).

Section 3.1.8 concerns the derivation of an inertial

coupling moment expression arising from the deceleration

of the craft after release from some initial speed. This

term is" dependent upon both roll angle (~) and sideslip

deceleration (V).

Section 3.1.9 involves the derivation of suitable

damping expressions for the rolling model. Two major areas

of contribution were identified and these are:

(a) that arising from the change in flow rate as the

cushion undergoes compression and expansion and this is

dependent upon both roll angle (~) and rate of roll (~)

and (b) the second term is that due to an induced incidence

" effect of combined sideslip and roll rate as water

impinges on the hard strutture, and this is~dependent

on "both roll angle (~) and sideslip velocity (~) of the craft.

Section 3.1.10 concerns the derivation of a suitable

ex~ression for the craft inertia and also an extra inertia

-30-

term due to added mass effects experienced as the craft:-rolls.

As a result, the inertia of the craft is dependent upon the

roll angle (~) of the craft.

Finally, in Section 3.1.11 the full equation describing

the roll motion of the craft is assembled based on the

various terms already derived in Sections 3.1.1 - 3.1.10,

inclusive.

3.1.1 Moments due to change in VCG position

ALL i v-From Figure to , the moment about 0 is given by:

= ••• ••• (5)

Non-dimensionalising by dividing throughout by LlB,

gives:

MOG [~ hG tanp J cosp LJrB = + B = cosW + hG sin,0 ••• ••• (6) 2 B

3.1.2 Moments due to Loss of Cushion Area

It will help at this stage tb"consider the contribution

of the cushion from a stri~tly static point of view,

although the expressiqns derived are not actually

incorporated in the model. A more rigid study is

made in Section 3.1.9 where the effects

of compression and expansion of the cushion are taken

-31-

into consideration.

It is assumed that the cushion pressure remains

constant and that cushion area is red~ced due to

leading edge skirt collapse. The effective plan area thus

has a reduced beam, shown as OP' in Figure 11a.

3.1.2a Case for yi

-32-

= -t

3.1.2b Case for [5> -liA

In this case, the effective cushion is reduced even

further as the crait rolls through angles greater than -A.

Thus the leading edge of the cushion is moved further inboard

as the craft rolls, shown by the movement of point M in

Figure11b.

The effective beam OM is given by:

B. h S.1 OM = s~n Assuming once again that the pressure force acts at

half the effective beam, the moment about 0 is given by:

= [ ~2 SI"nfJ] ••• . ... (10)

Using Equation (8), Equation ·(10) can be

non-dimensionalised by dividing throughout by WTB.

Thus:

= ·2

.[~J • • • • • • • • • (11 )

-33-

3.1.3 Moments due to buoyancy forces acting on the

immersed hull structure

The theory for both the detached and the attached flo~

cases will be derived in this section. Some of the geometric

terms associated with the buoyancy forces are derived

in Appendix I and these will be referred to from. time to time.

Definitions:

(See Fig.12) Let:

5 ~

~A 4

~S ~

(See Fig.13) Let:

T ~

V ,;~

. 3.1.3a Case for _ < ~A

h S/ S 1· - tanS

tan -1 hS/ S S

tan -1 [:S + :S~

(Stan~ hS) cos~ S S Ttan~ cos~

· ... • •• (12)

• • • • • • '(13)

• •• • • • (14 ).

• 0 • (15)

• •• (16)

There is no contribution of buoyancy from the hard

structure.

Thus:

= o • • • • • • (17a)

and the non-dimensional quantity:

= o ••• " . . (17b)

-34-

Figure.13 shows craft immersion at an angleji, CI1 A

-35-

moment, a relative density term «(reI) is defined given by:

('reI MT

= L.S.h S

= ~;r/9 (19) L.S.h S • • • • ••

D i vi din g E q u a t ion (1 8~ t h r 0 u g h 0 u t by LJ T San d sub s tit uti n g

Definition (19) gives:

=

= _1.'&. 1 6 .(rel hs/ S • [

T2 J [ T l tan(S-0) • 3V + tan(8-0~

• • • ••• (20)

3.1.3b(ii) Attached flow case (Fig.13)

. . If the flow is assumed to remain attached as could be

the case at low speeds, the area under consideration ought

to be that given by b. PMN and not b. PXN as assumed for the

detached case.

But: . b. PMN = b. PXM of- A PXN

Thus only the extra contribution of APXM need be

considered here as APXN has already been taken into account

in the provious section. The area of interest therefore is

as shown below.

~36-

Thus the moment contribution due to APXM is given by:

• • • ••• (21c) •

Non-dimensionalising Equation (21q by dividing throughout

bYWTB and using Definition (19) as before gives:

= .1. L5! . -L.. 6 I'rel hB/B

T 1 ... (22) tan~J

The total moment contribution due to buoyancy assuming

fully attached flow is found by summing Equations (20) and

(22) giving:

• 0 .. ••• •• (23)

-37-

3.1.3c Case for n> ,08 figure 14 shows craft immersion at an angle ~ degrees

to the water line (11 > ,08)' the latter crossing the hull structure in two points M and N.

3.1.3c(i) Detached "case

In evaluating the buoyancy terms as the top of the craft

becomes immersed below the water line, the assumption is

made that flow separation occurs along the line PXin the

detached case (fig.14a). The angle ~ is as defined in

figure 14a. It should be noted that as the craft sinks'

deeper, (i.e ~ increases), a point is rea~hed where PN and

PX coincide and 0(= (~ -¥5),(see fig.14b).

A new assumption is then made that separation occurs

along the line PN as _ increases further (see fig~4c ).

Definitions:

Let: W ~ h8Ls+ hS/ S .. . . • • • (24) tanj1

0( ~ h

sLs • • • • • • (25) 5 - lJ

In this case, the immersed portion of the hull under

consideration is the area PXNQ (fig.14a). This can be divided

along PN and represented by triangles PXN and PNQ.

~PXN .

f-r 0 m A pp end i x I • 2 • 1 ., the are a 0 f t his t r i a n g 1 e i s

-38-

given by:

=

The moment arm (OU) is also found in Appendix I.2.3

to be given by,

=

.6. PNQ

iBLlt C"OSff +

2/3 {8T~ tan (

=

where

1t Case for g1 > 2" -0(

A' =

-39-

~ tw . ~'[A'+ S' J frel B/B

. [ 3lJ + cos~

• • • •

2T 1 tan{d. +~ )J

••• (27)

As 'mentioned before, for y1 > (1-0

-40-

at the lower speeds, the area under consideration ought

to be that enclosed by PMNQ (Fig.14c).

But: Area PMNQ = APNM + A PNQ

The contribution of Area PNQ has already bean considered

in Section 3.1.3c(i) for ~> H-ex). Thus only the extra

contribution due to Area PNM need be considered here.

From Appendix I:

Area pNM =

The moment arm due to a PNM is given by:

ApNM hs

+ ~(BS -t:~Ji)'( = sin~

Let: G ~. S - ~ ... - •••• (30) tan The moment contribution due to area PNM is then given

by:

= +

Non~dimensionalising Equation (31) by dividing

throughout by IJTB and using O'efini tion (19) gi ves:

~l°B 1 .&. . --L. C' = - 6" • • • • •• WTB Irel hB/B h .

. [3hs/~ 2G. Sino

-41-

The net moment contribution of Area PMNQ is found by

summing Equations (29) and (32) and non-dimensionalising

by dividing throughout by WS;-

Thus:

1 - '6 ~ .~[ C'+5']

(reI hs/S • • •

where C'is as defined in Equation (32)

and 5' is as defined in Equation (29).

• • •

3.1.4 Development of Dynami c Force Coe ff icients for 'Flow

over Flat Surfaces at High Angles of Incidence

As much of the dynamics of the craft depend upon the

(33)

lifting 'properties of the surfaces presented to the stream,

it is important that realistic expressions be used for the

various lift and drag coefficients associated with these

surfaces.

The surfaces presented to the flow possess properties

of high aspect ratio (>10), and high angles of relative

incidence (>15 0 ). This has therefore dictated a 2-Dimensional

approach to the problem and this is outlined in greater detail

in Appendix 11.

In the extreme case where the surface is set broadside

to the stream, the force coefficient assumes a maximum value

of about 2.025 •

-42-

Ctc -

Diag.3

for the case shown in uiagram 3,

Total force coefficient

lift coefficient

drag coefficient

CN ~ 2·0

C ~ 0·0 L .. C ~ C

D N

CL and Co are defined perpendicular and parallel to the

stream flow respectively.

ixpressions were developed in Appendix 11 for surfaces

at both positive and negative angles of incidence and three

constraints were used,

(a ). CN:j. +2·0 (for all positive angles of incidence)

(b) C {-O·1 (for all negative angles of incidence) deN

(c) .-1! "'" 1t ( for small angles

-43-

::: Sir )] ... (36)

3.1.4(ii) Negative ~ngles of Incidence

---"-~. Oiag.5 Expressions for these coefficients were found in Appendix 11

to be given by:

Cl = o • 1 4 [ e 1 0 T{{l - e ltfolcosf • • • • •• \37)

as in t:.:q~34) I,; -0- cL:Tanf • • • • • • \38)

dCl [ 1011f ;:lint) -e Y: (ltCO¥ - ~if}t3 B err = 0·14 e .• (10ncosr- • • • • • • (39)

3.1.5 Centre of ~ressure Location

It is difficult to predict the movement of the centre of

pressure on thb craft hull as the incidence angle changes,

though, it has been shown that the value stays around the

quarter-chord position at least for small angles of incidence29

•

To simplify expressions describing the hull dynamics which

are derived in the next two Sections, the quarter-chord assumption

was made for all cases studied. fhe further implications of

this assumption is discussed. in greater detail in Section 5.1.2a.

I .

-44-

3.1.6 Water Impingement of the Hull ~ace

The moments due to water impingement on the hull face

will be derived in this ~ection. tigure 15 shows the force

components to be considered and PC is treated as a section

of a flat plate of length L making an incidence angle of (8-~)

with the stream flow. The assumptions made for derivation of

force coefficients and centre of pressure position in Sections

3.1.4 and 3.1.5 apply here.

3.1.6a Case for p < PH

There is no contribution from the hull and therefore,

3.1.6b Case for @A < ~ < ~t.l

from Fig.15,

A

(B-~) PCX =

.: .. PC PX

= ~int8-~)

= {BT} ~in~8-~)

= .. 8(TF)

'where(TF)~ T ~in~8-.0) • • • ••••

The area ~SH) presented to the flow is given by:

,sH = L.(PC)

= L8(TF)

(40)

-45-

Also from ~ection 3.1.5, the centre of pressure location

is assumed to be at the quarter-chord position,(point T in

fig.15).

TC = tB(Tf)

Hence the moment-arm due to the drag forces (JT) is

given by:

JT = tl:l(TF). Sin(8-~)

. = tlBT)

I"loment arm due to the lift force lDJ) is given by:

DJ = 01'1 + I'IX + XJ hS

+ ~ + f(BT) = sin~ fan lan~B-~) ,. .," .. Let (T1 ) ~ ~ T ~41) .. Sin + T~ • • • • • •

DJ = B.[CTI) + f( TF,~

The lift force is given by:

LH = !rW"U:,~,CLH . (42) · -- • •• CLH follows the definition given in Equation 34, where:

-~(8-~) 0-2(1 - e ).Cos(8-~)

The drag force is given by:

Substituting for CO H using Equation 35, gives:

= • • • · -.

-46-

The forces due to skin friction is small compared with

LH and OH and will be neglected here. Thus, the total moment

due to the hydrodynamic forces acting on the hull face is

given by:

.

= ~}f' U:LB2.( TF). CLH{~ TI) + 0' 75 (Tf ~ - [O.25(T)Tan(8-j1~ ••• (44)

Non-dimensionalising ~quation 44 by dividing throughout

byWrB and substituting lquation(B) forWT on the right hand

side gives:

2 2 -tPw Uw LB ( ) r 2. TF .CLH

Pc L.B . {

- [oe25(T) Tan~8-J6)]

+ 0'75(Tf l] - [0'25(T) Tan(S->1B} • e • • • •

3.1.6c Case for ,0>}ifB

For ~ > ~lj' water impinges upon the whole of the hull

face so that,"

PC = PLl

t4S)

Thus the lTF) term in lquation ~44) is substituted by

hS/B and by induction, the moment expression is found to be: SinS

• CLH" {~TJ) + 0. 75:~~~] - [0. 25( T) • Tan\ 8-,11~}

o • .. • • • • • l46)

-47-

~imilarly, the non-dimensional moment becomes:

- [0' 25 (T) Tan (a-pH} •••

It should be not~d that it is possible for incidence

angles to go negative at high roll angles and hence the-

following constraints on CLH are observed:

••• ~47)

From £q.~34) (for 8 ~ ~)

3.1.7 water Impingement on the Top structure

In cases where roll angles are large (~> ~ti)' water

impinges on the top structure, and this increases the over-

turning moment acting on the craft.

from fig.16:

OH' =

= (SW) ,definition (24-)

OQ' = 8

R'Q' = RQ = 8(1-w)

"The area (3 T) presented to the flow is given by:

Assuming the centre of pressure to be at the quarter-chord

position, (see Section 3.185), the force will act at point K,

-48-

where,

RK = iRQ

The arm due to the lift force (DC) is given by:

OC = OR + HC

he + hS -+ RK.Cos.0 = Sinj!)

tJ + 0·75(1-W).Cos~ = Cos~

The arm due to the drag force (CK) is given by:

CK = HK.Sin~

= 0.75 RQ.5in~

CK = 0-75 B( 1-W). Sin~

The lifting force on the top structure is given by:

L.T = ••• • • • • (48)

CLT follows from the definition given in t::quation (34j,

where,

CLT = 2· D (1··--it~

e 2 ).Cos~

The drag force is given by:

=

Substituting for .COT using Equation (35) gives:

• • • •••

Again it is assumed that the forces arising from skin

f~iction will be small compared with the normal pressure

forces acting on the hull top and is neglected here.

(49)

-49-

Thus the total moment arising fr6rn the hydrodynamic forces

acting on the hull top is given by:

=

(LT". DC) + (D T • CK)

o/wU~~B2(1-1J).CLT{[~~S~ + O.75(1-1J).CO.~ I +' [O.75C.1-IJ). Sin~. ran~

which reduces to,

• • • t50)

Non-dimensionalising Equation 50: by dividing by IJrB and

making the subs ti tution for IJ T on the right hand side given

by £quation ~8) gives:

• • •

In this case, no constraints are put on ~LT regarding

incidence angles achieved as ~ will always be positive for

the water to impinge on the top structure.

3.1.8:Derivation of the Inertial coupling Moment

As the craft decelerates from some initial speed, there

will be a force generated at the C of G due to the inertia

of the former; AS the resulting moment is dependent upon

the dynamics of the motion in sideslip, it is here referred

(51)

to as a coupling moment. It is required to derive an expression

for the moment about 0, the trailing edge of the skirt.

from figure 17, the inertial force at the ~ of G parallel

to the water line is given by:

-50-

FI -M T ...

~-.- --~--

= • y

where MT is the total mass of the .. and y is the craft deceleration

2' also OG Jh G

2 = + tj 2

=

=

The moment arm (GK) is given by:

GK- OG.Sin(¥-.£1)

=

The moment about 0 is given by:

frlCPL MT

.. GK = .y •

lJT ... GK = - .y. g

Non-dimensionalising tquation ~52) by dividing throughout

=

3.1.9 uerivation of the Koll uamping Expressions

It is expected that the major contribution to craft

damping in roll will come from the Ipumping' effect of the

• • •

craft

~53)

-51-

cushion and from the dynamics of the hull.

3.1.9a Cushion uamping

As the craft rolls, the cushion volume will change. ~ince

the cushion system i~ not a perfect seal," this will result in

some amount of leakage through the skirt. accompanied by

changes in flow through the fan. It is assumed that leakage

through the skirt will be negligible and that"the fan will

respond instantaneously to any flow demand; this will result

in a change in pressure rise across the fan and consequently

the craft cushion pressure will change.

3.1.9a~i) Estimate of Change in Cushion Volume

as Craft Rolls lCase for p1

It is assumed that althoug~ the leading edge skirt has

collapsed, it still operates as an effective seal as shown

diagrammatically in Figure 18.

The cushion volume per unit length is taken as the

area enclosed by OQPl.

But area UQPL = A POQ +" A POl

Consider 6.POl

let APOL = A(1)

It is seen that this area does not depend upon the roll

angle ~ and is therefore a constant.

Consider 6.POQ

PQ = hS - (!:is) Tan~

Hrea POQ = A(2) = -KBS).[hS - (8S) Tan~J

The Lushion Volume (V)

V = L [A (1 )

= L[ k1

-52-

is given by:

+ A(2)]

+ k2 - ~82~2 2 .:l

where:

Tan,O]

k1 = 11(1)

k2 = ~B~hs

• • • • • • (54)

The change in cushion volume w.r.t time can be written in

the form:

dV dV • .2if dt = d}f dt.

Equation (54) is then differentiated to give:

dV (ft=

2 2 2,,( ri{ ~L.! ~.5 ~ec p • ? • • • •

3.1.9a(ii) Estimate of Change in Cushion Volume

as Craft Rolls tCase for .0 > PAl

· ...

from figure 19, the cushion volume per unit length is

given by area OLM.

Now OM' =

LM =

=

Area DLI'I =

=

The Cushion Volume is given by:

V =

= + h 2]

t Ta~;0 • • • • • •

(55)

(57)

-53-

where =

uifferentiating Equation l56) w.r.t time gives:

hS 2

dV 2 cosec2~ % ....... = -L.t.B B • • dt

3.1.9~liii) ~xpression for the Moment arising

from Cushion Forces \Dynamic Case)

• • • • • • l57)

It is necessary to define some of the fan characteristics

for a given KPM, in order to obtain an estimate of changes

in cushion pressure.

Let the fan design operating pressure = PT o Let the fan design operating flow rate = Qo

let the duct diameter = dc

Also, assume that the characteristic curve can be linearised

and that. any pressure rise will be accompanied by a propor-

tional decrease in flow rate. This allows a simple relation-

ship to be developed relating total pressure rise across

the fan to its flow rate and is given by a curve with a 450

slope as shown in figure 20. The equation of the line will

therefore be given by:

PT = k1~ + C • • • • • • • l58) -PT

where: k1 0 = ~

C = 2PTo

The assumption may also be made that the total pressure

loss in the cushion system is approximately equal to the . .

dynamic pressure 34a , (~fouJ). This assumption is typical for

small craft where air flow is made to pass direetly into the

-54-

plenum area. thus encountering a sudden -enlargement.

The mean duct velocity, Ud.!_ will be proportional to the

volume flow Q, where,

=

This then allows the total pressure rise across the fan to

be related to the cushion pressure by the equation:

PT = Pc + -!(i ~d

= - Pc + k Q2 2

2

• • •

where: =

• • • (59)

14-A 2

d.

jubstituting Equation (58) in Equation (59) gives:

• • • • • • (60/

Also by ignoring any additional flow under the trailing

skirt, the following equation can be written down:

Q =Q + dV o dt •••

,; .. (61) where: (~~ is the change in flow rate

Que to craft roll and is related by the expressions given in Equations (55) & (57).

~ubstituting Equation (61) in Equation (60) yields the final

expression for the cushion pressure (pc)' where,

or

p = c

p . = c + lSDL)2

P~cr£ • • • • • • 0 • (62)

-55-

In the dynamic case, this expression for Pc is substi-

tuted in the equation for the moment contribution due to

the cushion derived in ~ection 3.1.2.

Case for !1 < @'I\

Substituting Equation (62) in ~quation (7) gives:

Case for 0> 01\

Substituting ~quation ~62) in tquation t10) gives:

• • •

It should be noted that the correct expression for

••• ~63)

(64)

&~ must be substituted using either of Equations (55) or ~57} depending upo~ the roll position of the craft.

3.1.9b Oamping of the Hull

A certain amount of damping will come from the hull as

a result of the induced incidence effect arising from combined

sideslip and roll rate. The hull face and hull top are treated

as fl~t plates, as befo~e,:at relatively high angles of i··

incidence to the stream flow o

-56-

General ~olution

o Oia9·6

Consider the movement of the surface shown in uiagram 6.

Let the veloci ty of the stream flow. be l.J...> and l.et the angular

velocity of the surface about point 0 be w \positive downwards).

rhe velocity (w) at the 'centre of pressure of the surface

perpendicular to the stream flow is given 'by:

• • • ,I • • • • • • ~65)

The induced angle, e, is given by,

E = w = U

-57-

tram uiagram 4,

Differentiating this expression w.r.t gives:

dCN· cor + Cw -~inf·r ::: dCl .

dCN '" dCl 1

V = CN = df3 + Cl" Tant· cor ••• • •• (67)

The moment about o is given by:

M = N.X 2

~ -tr u; .S. eN .(;s + X1

-58-

XH, = B J S2 + • • • (70)

where, h (TG) A B S Sin8 + S.Cp_s8 ~71) • • • • • •

XH2 = x H 1 • Cos ( 8 - ¥') - .... • • • ~72) where: ¥'is as defined in App 111.1.1.

The incidence angle, f, is given by,

f = (8-}1) .... • •• ~73) Substituting £quation (73) in ~quation (57) and then

dCl making the relevant substitutions for CL and df given in

Equations l34) and ~36) respectively yi~lds the expression

for CN

for the hull face, where,

This simplifies to,

_ -~(8-~) CNH"" = It e ••• • • • l74)

Equation ~68) applied to the hull face may then be written

as:

= • • •

where the various terms on the right hand side are as

defined in ~quations t59) - l74).

[;ase for ~ ~ .fltj

for ~~"~~, water impinges upon the whole of the hull

face. The wetted length is then given by,

~75)

(TF) = hs/s SinB

-59-

. _--_ ..... _. • • • ~ 76)

lxpression l76) is substituted ~n Equations \69), \70)

.q' I I and l72) to give new terms ~, xH1' XH2 for this case ~see

Appendix 1I1.1.2).

I::..qua tion l 75) is· then of the form,

=

Also, it is possible for incidence angles to go negative

at high angles of roll. This is the case when 15 > 8. In this ....

case, the relevant expression for CNH is derived from

Equa tions'. ~ 37) and l39) giving,

• • •

3.1.9b(ii) Damping due to water Impingement on the Hull Top

figure 22 demonstrates the induced incidence effect

applied to the hull top. This will of course only come into

play when 11 > ,f1B.

The area presented to the flow is shown in Section 3.1.7

to be given b~,

Sr = L8(1-W) • • e • • • (7S)

where: W is as given in Definition (24)

The arms xT1 and xT2 measured w.r.t the trailing edge

of the craft is shown in Appendix 111.2. to be given

respectively by:

-60-

= + 2 (4W.Tan,0) •••• (79)

t:I = 4' (3+W) • ••• • •• ~80)

The incidence angle,Y'~ is given by,

• • • • • • • ~81)

,.. By induction, the expression for CN T can be obtained

using Equation (24) where,

-!!.Jf eNT = ite 2 • ••• • •• (82)

Equation (68) applied to the hull top is then of the

form:

= • • • (83)

where the various terms on the right hand side are as

defined in ~quations (78) (82).

3.1.10 uerivation of Expressions for Craft Inertia in .Holl

The craft Toll i~ertia will con~ist mainly of two terms,

(a) that due to the rotation of the craft about

its trailing edge in still air~

(b) an added masq term due to displacement of

fluid as the hard structure comes into

contact with the water.

These terms will have an additive effect on the total

craft inertia in roll and they are treated separately in the

forgoeing sections.

-61-

3.1.10a Craft Inertia in Hall associated

wi th I'lotion in ::Itill Air

In general, for a given craft weight, the inertia term

will change as the craft dimensions change. It was found

that a good estimate of the light hovercraft inertia in roll

could be obtained by making the following assumptions:

1. t".ngine

(a) Mass of engine (ME) = 30% MT-(b) The engine is fitted on the centre line and

represented by a rectangular block (dimensions

as given in Fig.23).

(C) C of G position at point x.

2. ~rew

(a) Crew mass (MC) = .30% Mr. (b) Crew mass is treated as lumped masses and the

craft takes a crew of two, symmetrically displaced

at n·3B from the centre line.

3. Hard ~tructure

(a) Mass of hard structure (M H) = 40% MT. lb) The hard structure is likened to a rectangular

block with dimensions as shown in fig.23.

tC) C of G position at point Y.

It is required to find the inertia about 0 where 10 is

given by:

I o =

=

IG + MT(O~)2

+ 2 ~2

MT(h G + '4)

.. . .

-62-

10 = IG + MT~2~hG/B)2 + ~

where: . 2

IG =.2, MrK

a _ •

The components of ~MTK2 are as given below.

from ~ig.2:S:

= o • 3", T • 2 ( 0 • 3 B ) 2

•••

••• \84)

••• (86)

+ [ o· 25 + ,,( h 8/ B ) 2.J 1 12 J

-.. _ •• (87)

3.1.10b uerivation of the Hdded Inertia ~xpression

General ;)olution

o

Diag. 7

Consider a mass of fluid mv being displaced as point P

rotates about 0 with angular acceleration ~(Diag. 7). The

force required to accelerate the mass is given by,

-63-

• • • • • • (88)

The moment about 0 is given by,

• • • • • • (89)

mvr2 is in effect an added inertia term, where,

• • • • • • t90)

Case for PH < 11 < .0 8

1. uetached Flow assumption (see ~ection 3.1.3b(i»)

from tig.13, for the detached case, the area under interest

is APXN. From Hppendix 1.1.1, this is given by,

A PXN = 1.'(8T)2 (91a) Tant8-#) • •••

. ~ mvpXN _ ! (8T)2 - fw L • Tan t 8-J¥) • • • • (91b)

From Hppendix 1V.1.1, the distance of the centre of

area of A PXN from 0 is gi ven by:

OZ' + 2 '

T • • • • (92)

Thus using Equation (90), the added inertia term due to

area PXN can be written as,

• ••• (93)

. where mVpXN and Ol' are as defined in Equations (91b)

and (92) respectively.

2. Attached Flow assumption (see ~ection 3.1.3b(ii)

The area under consideration is that given by APMN (fig&13).

-64-

tjut APMN = APXM + APXN

From Hppendix 1.1.2 area PXM is.given by,

= 1.. .uw.2 2 Tanl • • • • ••• (94)

~umming Equations (91~ and (94) and multiplying by I'wL

gives the expression for the total mass of fluid displaced.

Thus,

= ••• ~95)

Define rab as the distance of the centre.of area of

4P~N from the trailing edge of the craft. from Appendix Iv.1.3

rab is given by,

\

2 + T ... ~ 96) :z B jh3 V + T ( 1 ,_ 1 '0 2 3'. t . Tan~8-J1) 'f8"i1'W Thus the total added inertia for an attached flow assump-

tion is given by,

= • • • • .& •• \ 97 )

'where, mVPl"ilN and rab are as defined in I:.quations \95)

and \96) respectively.

Case for 11 > 0t:j

Again the form of the expressions involved here will

depend upon the assumptions made for the detached and

attached flow cases and these have already been treated in

~ection 3.1.3c.

-65-

1. uetached Flow assumption (see Jection 3.1.3c(i))

Case for Eo -C( > Rf > P 2 t:i

From Figure 14a, the areas under consideration are given

by ll. PAN and ll. PNQ. From Appendix 1.2.1,

=

,t. The mass of fluid displaced is given by,

= (BT)2

-~ fwL - -Tan (ex +.0) • • • • .... (98) Also, from Hppendix 1.2.2,

=

The mass of fluid displaced due to APXN is given by,

= • • • (99)

From f\ppendix IV.2.1, the distance of the centre of

area of A PXN from 0 is given by,

\

DU' 8 j(~ + 2T )2 T2 (100) = 3" lan(o;+~) + • • •

Also, from Hppendix IV.2.2, the distance of the centre of

area of A PNQ ·from 0 is given by,

OF = j(OH}2 + (FI;i)2' • • • • • • (101)

where: OH = f:m+ Cos a( 1-!J)[COS~ 2L3Sino

-66-

Thus the expression for the added inertia term is given

by,

= • • • ~102)

where the terms on the right hand side are as defined

in tquations (98) - ~101) inclusive.

Case for ~> ~ ~

In this case, ~PXN is non-existent and therefore only

APNQ contributes to the added inertia term in the detached

flow case~~se8 Fig. 14c).

• 2 (103)· .. IpNQ = mVPNQ·(OF) . . . , • • • where mvpr~Q and (or) are as defined in Equations (99)

and (101) respectively.

2. Rttached Flow assumption (see ~ection 3.1.3c(ii))

All cas e s (gf >