An investigation of the roll stiffness characteristics of three flexible skirted cushion systems

AN INVESTIGATION OF THE ROLL STIFFNESS CHARACTERISTICS OF THREE FLEXlBLE SKIRTED CUSHION SYSTEMS

by

rECHNISCH~

flOGESCHOOl

l.l~lF1 LUCHTVAART- EtJ RUlr.HE\}MRnECHNIE~

61 DliIOTH::S;

Kluyverweg 1 OELFT

..

AN INVESTIGATION OF THE ROLL STIFFNESS CHARACTERISTICS

OF THREE FLEXIBLE SKIRTED CUSHION SYSTEMS

by

P. A. Sul1ivan, M. J. Hinchey and R. G. De1aney

Date Submitted: October, 1976

March, 1977

UTIAS Report No

.

213

..

..

Acknowledgements

The work described in this report was, in the first in stance , made possible through the provision of eqllipment and f'acilities by the National Research Council of Canada, through its Negotiated Development Grant Program. The Transportation Development Agency sponsored the particular research project through contract number D-500-203-l, as part of its general program of

inves-tigation of air cushion technology. The untiring assistance of

Mr

.

J.

Brandon

..

This report presents experimental data on the roll stiffness characteristics of three flexible sldrted air cushion systems. The systems examined were: (i) an open loop and segment system reserrbling HDL designs, (ii) a multicell system reserrbling early BertinjSEDAM designs, and (iii) a recently developed mul.ticell known as a Flexicell. The results show that, whereas the loop and segment skirt behaves in a relatively straightforward manner, the multicell systems are subject to certain phenomena which could have important consequences in practice. The most noticeable of these phenomena is a loss of restoring ability or hysteresis in the roll up portion of a roll down-roll up cycle. For the Bertin type multicell this hysteresis is sometimes so large as to completely eliminate the restoring moment of the cushion. The available evidence indicates that the hysteresis is, in some cases, associated with a buckling failure of the air cells which generate the roll stiffness. There is also evidence which suggeststhat

the ability of the cells to support loads in the cell walls is also a possible

hysteresis mechanism. Comparisons indicate that the maximum stiffness generated

by the FlexieelI is roughly twice that of the multicell when corresponding system parameters are approximately equivalent. Thê report describes an approach for presenting data in a manner suitable for sealing to full size designs. Also presented is a roll stiffness theory for the multicell which was found to be very useful in the data interpretation.

1. 2.

3.

4.

6.

CONTENTS

Acknowledgements

Summary

Table of Contents

List of Symbo1s

INTRODUCTION

THEORETICAL BACKGROUND

2.1 Application of Dimensiona1 Analysis to Hovering

Cushion Systems

2.2 A Theory for the Multice11 Skirt

2.3 Avai1ab1e Theory for Loop and Segment Skirt

DESCRIPI'ION OF F ACILITY

AND

EXPERIMENTAL PROCEDURES

3

.

1 illIAS Cushion Dynamics Faci1ity

3.2 Instrumentation and Data Reduction

RESULTS

4.1 Pre1iminary Tests

1~.2

Results for Loop and Segment Skirt

4.3 Results for Multice11 Skirt

4.4 Results for Flexice11 Skirt

DISCUSSION

AND

COMPARISON WITH THEORY

ii

iii

iv

v 1

3

3

11

15

17

17

19

21

21

22

24

28

30

5.1 Theory and Experiment for the Multice11 Cushion

30

5.2 Hysteresis Mechanisms

33

5.3 Towards a Comparison of F1exice11 and Multice11 Skirts

3).j.

CONCLUSIONS

REFERENCES

FIGURES

APPENDIX A - DIMENSIONAL ANALYSIS:

REVIEW OF BASIC IDEAS

APPENDIX B - VOLUME FLOW MEASUREMENTS FOR THE CUSHION DYNAMICS

FACILITY

APPENDIX C

-

EXPERIMENTAL DETERMINATION OF CENTRE OF PRESSURE

SHIFT

APPENDIX D - DETERMINATION OF SLOPE OF FAN CHARACTERISTIC

APPENDIX E - LISTING OF COMPUTER PROGRAM FOR MULTICELL ROLL

STIFFNESS THEORY DEVELOPED BY M

.

HINCHEY

35

37

List of Symbols

A _ref base area of hard structure of vehicle

Ac cushion footprint area

Af cushion feed area from plenum supply box

B beam width of vehicle

CA feed area coefficient, defined in Eg. 15 of Section 2.1

Cc cushion footprint area coefficient, defined by Eg. 28 of Section 2.1

CD discharge coefficient for orifice flows

~

CM cushion rolling moment coefficient, defined in Eg. 13 of Section 2.1

CpC cushion power coefficient, defined in Eg. 17 of Section 2.1

C

QC cushion volume flow coefficient, defined in Eg. 14 of Section 2.1

C

RC box pressure coefficient, defined in Eg. 16 of Section 2.1

CSC fan slope coefficient, defined by either Eg. 18 or 19 of Section 2.1

h hovergap on smooth flat surf ace

HSC denotes hard structure contact with the ground

N fan rotational speed

n number of cell pairs in multicell cushion theory, Section 2.2

p _{air power of cushion flow}

p statie pressure

Q cushion volume flow

w

gross weight of model

Cl _{roll angle of cushion system}

p atmospheric density

Sub scripts

b denotes conditions in the plenum supply box

c denotes conditions in the cushion volume or volumes

e denotes conditions at roll angle

ex

= 0

1. INTRODUCTION

The effective development of many applications of air cushion tech-nology is hampered by the almost total lack of comparative data on the

suspension characteristics of typical flexible skirt systems. This situation is further complicated by tbe fact that, whereas much of the development to date has taken place in Europe for predominantly marine applications, Canadian applications tend to involve movement over a variety of types of land, ice and snow. The work described i.n this report is part of a program of model tests aimed at filling this need through the evaluation of representative commercial skirt systems together with the presentation of the data in a way which is suitable for the application to the design of a full scale vehicle for 'over~ land application.

The evaluations described in this report are mainly statie roll stiffness characteristics obtained in hover over a smooth flat surface. This is clearly only a first step, since in practice the typical operating environ-ment of an air cushion vehicle is much more complex than th at used in the present laboratory tests. Nevertheless, it appears that much of the data to be presented below is not available in the open literature, so that i t

represents baseline information obtained under laboratory conditions suitable for assisting the designer i.n his choice of skirt system. In addition to providing this baseline data, an important objective of the present program was the identification of any background areas which would require additional investigation. In the course of the test program several such problem areas have been identified.

were:

Three flexible skirt systems we re chosen for evaluation. These

(i) An open loop and segment system related to the Bri tish Hovercraft Development Li:m.:i.ted (HDL) designs,

(ii) A resistance orifice stabilized multicell system reminiscent of early French Bertin/SEDAM concepts,

(iii) A multicell concept developed in Canada by Jones, Kirwan and Associates specifically for overland operations and known as the Flexicell.

The c:haracteristic feature of the open loop and segment skirt is the complete absence of compartmentation, The system relies on ground contact and segment collapse to provide roll stiffness. The segments also provide a seal in the presence of ground irregularities. In the present tests, two cushion feed

systems were examined, one directly through the base of the hard structure and the other horizontally into the loops, as shown in Fig. 1.1. The multicell

system used a total of

8

separately fed conical cells each having an

8

0

taper, together with an outer skirt having four compartments as shown in Fig. 1.2.

The Flexicell system used in the present tests, which may be regarded as a development of the multicell concept, has a total of 18 resistance orifice fed cells, designed with a cross-section which changes from circular at the base to rectangu1.ar at the level of the hard structure (Fig. 1.3). No outer

skirt is used and a hinging arrangement is incorporated to reduce snagging on overland obstacles. The work in the present report places special

The primary facility used in the program was the UTIAS cushion dynamics rig, which is capable of testing cushions up to 2.44m x 1.22m in planform and about 300 Kg gross weight in hover on a flat surface • A feature of this f acility is an infinitely variable fan drive for the air supply system which allows a wide range of pressures and volume flow rates to be obtained. Furthermore a wide range of effective fan characteristics can be simulated. However, some data was also obtained on the UTIAS

circular track test vehicle Vampire 1, which is 4.2m x 2.03m in planform and weighs up to about 900 Kg.

The bulk of the experiment al data presented in this report shows the effect of various design parameters on the restoring moment produced by the cushion system as it is rolled through an angle

a.

Some of the design parameters investigated include:

(i) All up weight,

(ii) Installed power or air flow rate, (iii) The shape of the fan characteristic,

(iv) Alteration in cushion feed are as or geometry, (v) Different skirt materials.

The test program undertaken can be conveniently grouped into a number of series:

A: Statie roll stiffness tests on the nrulticell system as equipped with skirt material type I.

B: Statie roll stiffness on the open loop and sègnent skirt with material type I.

C: Statie roll stiffness tests on the Flexicell skirt system equipped with material type lIl.

D: Tests on the multicell system as equipped with skirt material type II.

E: Tests as for series A and D, but with material type I. F: Additional roll tests on the Flexicell system as equipped

with material type lIl.

The skirt materials were all elastomer coated fabrics, but of varying thickness and composition. They were respectively:

I: Supplied by Jones, Kirwan and Associates, 0.009 ins. thick and

7

oz./sq. yd. ('blue' skirt).

II: Uniroyal Fiberthin 0.018 ins. thick and weighing 18 oz/sq. yd. ('white' skirt).

lIl: Uniroyal Fiberthin 131 at 0.020 ins. thick and weighing 21 oz./sq. yd. ('black' skirt).

It should be noted that, in addition to a skirt material change, the other major reason for undertaking the test series D, E and F was that the infinitely variable fan speed drive was not ins'talled in the cushion dynamics facility

until af ter series A, B and C had been concluded.

Finally, it has been observed that some of the results obtained in the present program may be open to question. Rowever, we believe that the data given here and their interpretation are realistic representations of the behaviour of typical cushion systems that would be found in controlled laboratory tests. Considerable care has been taken wi th the acquisition and interpretation of the data. To give the reader some feeling for the level of attention to detail for which we have strived, we have included in this report a number of appendices describing in detail some of the more routine test procedures adopted here. Appendix B, which describes routine volume flow measurements, is typical.

2. THEORETICAL BACKGROUND

2.1 Application of Dimensional Analysisto Rovering Cushion Systems

There are two major advantages to be gained by presenting all data in a suitable nondimensional form:

(i) The number of variables which have to be investigated is reduced, (ii) A rational basis is obtained for sealing the results of model

tests to predict full size vehicle behaviour.

The basic idea is to use the well known Buckingham II-theorem to replace functional relationships bet ween dimensional variables by appropriate nondimensional groups. In many areas of engineering knowledge, custom and experience has established certain nondimensional groups as being particularly useful. Typically, the value of the Reynolds Number is well established for predicting viscous effects, the Froude Number is widely used in ship tank testing, and so on. Unfortunately in air cushion technology, although particular nondimensional groups have been proposed (see for example, Trillo, Ref. 1, p. 32, or Fowler, Ref. 2) there is not yet a widely accepted practice. Because an approach is proposed here and

because, as will be shown, complications in the interpretation of the experiment al data have been encountered, it is essential that the basic principles of dimen-sional analysis be clearly appreciated. It is with this objeetive in mind that we present in Appendix A a short review of the most important features of

dimensional analysis.

The first step in the application of dimensional analysis to cushion systems is to determine the appropriate variables required. To do this, i t is helpful to examine a specific cushion system. We choose for convenience a system comprising two conieal cells fed from a common plenum supply b'ox, as box shown in Fig. 2.1. The system is resistance orifice fed, so that 'the feed area into the individual cells is an important design parameter.

Consider the behaviour of the cushion at roll angle

a

=

zero. The

v~j.ables involved are the f'ollowing:

(i) The vehicle gro&s weight

w.

(ii) A parameter representing the vehicle size, taken here as the base area of the hard structure Aref" or the vehicle beam width B. (j.ii) ~he resistance orif'ice areas Af'.

(iv) The cushion volume flow Q at

a

=

0, ~.

(v) The plenum box pressure Pb' at

a

=

0, Pbe. (vi) The cushion pressure Pc at

a

= 0, pce. (vii) The effective hovergap h, at

a

=

0, heo (viii)The system operating power P.

Not all of these quantities are independent; it is easy to show that only certain ones can be arbitrarily chosen and hence be regarded as independent.

Firstly, the particular fan system installed will have its own pressure-volume flow characteristic, so that there will be a given source law

(1)

USually this will be expressed as an en:q;>irical curve fit such as

(la)

It is assumed that the fan operates

at

constant rotational speed N. Similarly an orifice flow law will relate the difference between box and cushion pressure t:.p

=

Pb - P _{e ce} to the flow rate

where ReD is the Reynolds nurnber of the flow through the orifice based on an orj,f'ice dimfmsion • I f the orifice is a sin:q;>le plate type without downstream. deflector s, then i t is well }çnmvn that

Q == C (Re

)A1

2t:.P

e D D P

where the discharge coefficient CD is constant for practical values of' ReD

.

(.R.e,:Ó

>.>10

3) •

This suggests that, for the type of orif'ice-deflector combinations used in cushion systems, we assume Reynolds number independence and put

(2)

Simi1ar1y, the discharge ~ under the edge of the cushion will be governed by an appropriate 1aw, which should also be Réynolds number independent:

A fourth equation is derived from t.he hovering condition, which requires that the integral of the ground board pressure equal the weight W. Here this is simp1y expressed as

where Ac is the footprint area of the cushion. This footprint area will be effectively determined by the choice of skirt geometry. Finally the system design power is of considerable practical interest. Formally this can be expressed as

P "- 'I)

Q

p e be

where T} is the overall efficiency of the fan system expressed in terms of the fluid energy flow out of the plenum box. Since the efficiency l) is a function of many factorswhich are not of immediate concern here, we simp1ify by considering only the fluid power Pf:

Hence there are a total of five equationsconstraining the relationship between the eight design quantities. The selection of independent variables must be done such that it is compatible with these constraint equations.

Now consider the behaviour of the cushion syst.em as it is rolled through an angle

a.

The pressure in the downgoing cell will increase and in the upgoing cell will decrease subject to the condition that the integral of pressure over the footprint area remains equal to the weight W, provided that the skirt does not support any weight when parts of i t are in contact with the ground. The volume flow through the downgoing cell will decrease and that through the upgoing cell will increase. Their sum, the volume flow through the plenum box, will not usually equal the zero roll value Qe'

Consequently, i t is, in principle, important in describing the effect of the fan on the cushion system to include the effect of the shape of the lift fan characteristic in addi tion to specifying an opera:ting point through Eq. 1. Tt will now be assumed that the pressure Pb does not change by a large amount as the cushion rOlls, so that the fan characteri stic can be approximated by a straight line. This in turn means that specifying the

operating point (Pb, Q at a

=

0) and the local slope dPb/dQ completely

specifiesthe characteristic. The experiment al data to be gi ven later shows that this assumption is valid.

For practical skirt systems based on multicell concepts, other parameters may be important. For exanqlle, for types (ii) and (iii) in Section 1, there will be additional bleed areas either direct to the outer skirt in type (ii) or to the central area in type (iii). In this case the number of design variables is increased by one and the number of nondimen-sional groups required is also increased by one. In the multicell skirt

~yPe (ii):. the relative heights of inner and outer skirts is also an

important design parameter (see Fig. 2.2) since it can be shown to critically affect the roll stiffness characteristic. Also material properties mayalso be important. For example, if there is significant elastic deformation of the cells in Fig. 2.1 associated with the effect of internal pressure on the hoop strain, then the effective cushion footprint area Ac depends on Pc, possibly in the form

A ~ A [1 + Ep ]

C co c

where E is a parameter over which the designer has some control. If, as

appears from the data to be presented later, the skirts may have some capacity to carry vehicle loads directly, other parameters controlling the material properties may be important.

The arguments for other skirt systems will follow much the same pattern butthere will be some differences. Typically, for the loop and

segment skirt the major feature is that there is no compartmentation and no resistance orifices, so that Pb

=

pc.

We comment brieflyon the choice of independent parameters. Generally speaking, it is widely considered that direct use of the zero roll flat surface hovergap he does not have much practical significance since it is rarely uniform over its periphery, owing to skirt wear and the presence of irregularities in the typical operating environment. A satis-factory alternative is to quote volume flow rates Qe directly. Also, for resistance orifice fed systems, the box pressure at zero roll Pbe or the box pressure ratio Pbe/pcemay be more useful than quoting feed areas Af, since for some cushion systems the feed areas '00 indi vidual cells rray be adjusted to obtain uniform cell pressure at zero roll angle. Typically the end cells in the multicell system may require larger feed areas than the central cells (see Fig. 1.2). For some comparison purposes the flow power, given here by the product PbeQe' may be an important choice of reference quantity since for those systems that deliberately use resistance orifices there is an associated power penalty. It is also necessary to choose a reference dimension and reference area. Since our objective is the

comparison of skirt systems of different geometries, the reference quantities must be independent of the particular skirt system. For all stiffness charac-teristics, the obvious referencE;! length and reference area are the width and area of the base of the hard structure B and Aref respectively. In the present tests Aref =

aB2.

We now undertake the dimensional analysis. In forming the dimen-sionless groups it is only necessary here to choose three reference quantities having independent dimensions. Obvious choices are the gross vehicle weight W, the beam B and atmospheric density p. We can use these to form reference groups to nondimensionalize all other quantities. For example, cushion pressure can be referenced to W/B2 . However, it is possible to choose

alternate references which have a slightly greater physical significance. For example, referencing cushion pressures by the quantity W/Aref gives a number which should be close to unity since the cushion pressure is determined largely by these quantities. In general, the latter pradice will be adopted.

We now apply the II-theorem to the simple two cell system of Fig. 2.1. We have typically basic fundional relations for the rolling moment

such as

(6)

This choice is consis·tent wi th the constraint equations, provided the fan size is chosen correc·tly. For a given skirt geometry, the choice of Band W fixes Pce through Eq.

4.

The orifice flow law, Eq. 2, then fixes Pbe

since Af is given. This implies that a given point (Pbe' Qe) of the fan charaderistic is specified so th at a fan size is specified. However, the fan characteristic slope can still be arbitrarily chosen. Another choice consistent wi th the specification of a fan characteristic is

(7)

Here Co and Cl are coefficients of a linear fit to a given characteristic. Again, choice of Band W fixes Pce. Choice of

Qe

fixes the hovergap through Eq.

3.

Also, given a fan characteristic the choice of Qe fixes Pbe so that in turn the orifice flow law specifies Af. A third choice is the combination

(8)

Again, Pce is specified so that the orifice flow law (2) reduces to an

equation for Pbe in terms of Qe. The fan charaderistic also determines Pbe in terms of Qe so that we have two simQltaneous equations for Pbe and Qe. still another choice is

since, as we have noted, the overall design power is an important performance index. For this case, choice of Pe and Pbe specifies Qe and since Pce is dictated by W and B we have Af determined from Eq. 2. This is a similar choice to that expressed in Eq.

6

since a fan size is specified.

In the gener al case, if additional parameters (such as the difference between the inner and outer skirt heights) are present,we will have additional quantities in the moment equation, such as

...

)

(10)

Forma! application of the II~theorem replaces Eq. 10 by

...

)

(11)

where Zl'and Z2' etc., are the nondimensional replacements of zl' z2' etc. Equation

9

can also be replaced by

We will define nondimensional coefficients in a slightly different form in order to take advantage of physical understanding of the processes involved. All pressures will be referred to W/Aref and velocities will be referred to ~2P _re f/p =~2W/PA _re f· We therefore define CM:! = M _WB == moment coefficient

(13)

C QC == Qe

r;:f

2WA ref = flow coefficient (14 ) CA Af

=

_A ref

=

feed area coefficient (15)

C

RC

=

PbeAref

W = box pres3ure coefficient (16)

C_pc

=

PbeQeYAref Pc

W3/2,J2

=

power coefficient

(11)

12A

f dPb

C_SCA

=

A _{ref p W dQ} re

_I

c e

=

fan slope coefficient

(18)

An alternative fan slope coefficient is

In many ways this is more useful than CSCA since it depends solely on the fan characteristic.

It follows immediately from the definitions gi ven above that

(20)

(21)

Also, i~ as in the case of loop and segment skirts, Pb we then have

Pc so that CRC ::: 1,

(22)

In any case the main point to note is that the constraint equations 1 to

5

imply that only two of the basic cushion coefficients CQC, Cpc, CRC and CA can be arbitrarily chosen. Also either CSCA or CSCB can be used to represent the effect of fan characteristic.

One important parameter not discussed to this point is the craft 1ength to beam ratio. Cutts (Ref. 5) has suggested that the cushion flow coefficient CQC be modified to include the effect of this ratio by including a factor which accounts for the fact that the cushion air escape area is proportional to the perimetric length of the skirt. This is a useful idea

since it should permit the comparison of performance of vehicles having differing p1anform ratios. Cutts has chosen to define his LAC by

LAC ;:;; f C QC

with f

=

unity at the commonly encountered 2:1 ratio of length to beam. Since the present tests were done for a length to beam of 2:1, CQC :;::: LAC here.

We now make two remarks in connection with the objective of seeking appropriate scaling laws. The first point is that it is possible to check the scaling 1aws by using one model of a given size and feed area geometry by simply examining the effect of gross weight W. If the quantities CA and CSC are fixed, then provided no additional quantities Zl and Z2 are i.mportant, two curves of roll stiffness CM = f(a) obtained for two different weights Wl and W2 should plot on the same curve provided both Pb and Qe are adjusted

so that CPC 11

=

CpC 12, or so that CQC 11

= CQC 12

. Failure of the two sets of data to fall on the same nondimensional plot indicates th at addi ti. on al

variables have to be controlled; not that the use of CpC or CQC is inval.id.ated. It is to be noted that, although, for design purposes, there may be arguments concerning the ap~ropriate choice of the core quantities CQC, Cpc, CRC, CA' for testing of scaling the choice is immaterial. Equation 15 shows that, if in a given test for scaling

(23)

It should be noted that it is possible to derive a simple formula relating Cpc, CQC and CA if a simple form for the orifice flow law is used. Considering the two-cell system used in the derivation of the nondimensional coefficients, we have the total volume flow at roll angle

a

=

0 given by

(24)

where CD is the discharge coet'ficient for the feed orifices, assumed to be the silP,Ple plate type.

Sim11arly the power P is given by

,

I

2(Pbe - pce)

p

=

~~e

=

CnAfPrê/

.

p (25)

Now elim;inate Pbe from Eq. 25 by appropriate use of Eq. 24 to obtain

P la Q [Q2p

+

p ]

2C2 A2 ce .

D

l'

(26)

Introduce the nondimensional coefficients Cpc ' CQC~ CA to obtain

C

=

C

[C~c

+ p ce

~

-J

PC QC C2 C2 W

n

A

(27)

Now since the vehicle is hovering,we have Pce

=

W/Ac where Ac is the cushion footprint area, y.sually less than

At.

If we de fine

(28)

w4ere Cc

<

1 usually, we have the relation

- ·2

J

- l

CQC 1

Cpc - _{CQC C2 C2} +

C-D A c

(29)

This is a particular case of the general ;Law that for a given skirt system or geometry, which fixes Cc

A ;ü:m "lar relation for C

RC can be obtained

(30)

Since in the experiments to be described both Pbe and Qe were measured, clearly the formula (29) can be compared with the experiment al data to ascertain if the flow at

a

~ 0 is following a simple orifice plate lumped par~eter type of behaviour, as is assumed in Section 2.2.

In concluding this discussion of sealing it must be emphasized that we have limited ourselves to hover over a smooth flat surface. When forward motion involving vehicle dynamics is to be included certain skirt properties will clearly become very significant. To take but one example, when motion occurs over wavy surfaces, either on land or on water, the inertial properties of the skirt material will clearly determine the effeetiveness of the cushion seal as it passes over these irregularities. If this is the case, then the nondimensional group rr Aref/W, where rr is the skirt weight per unit area, ~ust be scaled. However, detailed analysis of the sealing requirements in these more generalized conditions is beyond the scope of the present report. 2.2 A Theory for the MulticelI Skirt

A theoretical model for the multicell skirt (type (ii) in Section 1) has been formulated. It is similar in many respects to the theory developed by Jones (Ref.

6);

however, the present theory is more complete. The model is basically a very simple lumped parameter type using one dimensional orifice flow laws; however, computation of results is complicated by the geometry of the system when it is rolled. In particular, for a typical conical cell i t

is necessary to identify three skirt-ground geometries; (a) regulating, (b) transitional, and (c) shut-off. In the regulating mode the cell does not

contact the ground plane, whereas in the shut-off mode the cell contacts the ground plane at all points. In the transitional configuration only part of the cell perimeter contacts the ground. These ideas can be seen in Fig. 2.3 where both the downgoing cell and the outer skirt a.re in transition, and the upgoing cell is regulating.

The following major assumptions are made:

(i) The flow into and out of each cell is governed by simple orifice flow laws; that is, internal flow effec'ts are ignored.

(ii) The cell material behaves as an inelastic membrane sa th at it cannot support any weight.

(iii) The shape of any portion of a cell not contacting the ground plane remains conical; any portion of the skirt contacting the ground plane lies flat on the ground plane and forms a perfect seal in such a way that the pressure support area is defined by the ellipse of intersection of the ground plane and the fully deployed cone.

(iv) The outer cushion is not compartmented in rollor in pitch. (v) The restoring moment generated by a cushion in roll is due

solely to the dif'f'erences between the pressures in the upgoing cells and downgoing celIs.

(vi) The forces arising from the momentum of the air escaping f'rom the cushion can be neglected.

Consider now the action of a simple cell pair. For a typical down-going cell the flow into the cell must equal the flow out;

where the symools are defined in Fig. 2.3. This can be rearranged to give

Similarly, for the upgoing cell we obtain

Note that Al = A

2 for a two cell system.

Conservation of mass flow for the outer cushion gives

2(p - P )

~P

box 0 _ C A ~ = F

(:1)

=

0

p d a p

-a

Since the air pressure is solely responsible for supporting the vehicle, f'or n cell pairs we have

(4)

where Gdc' Guc and Go are the f'ootprint areas of the two cells and the outer skirt respectively. The pressure-volume flow relationship as specified by the fan system supplies a f'if'th equation. For computational purposes the fan characteristic was represented by aquadratic Pbox = Co + CIQ. + C2Q.2 where Co, Cl,C2 are fit coef'f'icients ~d Q. is the total system flow, at roll angle

ex

>

O. Note that in Section 2.1 when

ex

=

0, Q.

=

Qe and Pbox

=

Pbe'

The fifth equat10n is

f

2P

C A ~ d a p a ëp o p

=

0 (5)

If a roll angle

a

and a mean hover height hv are specified, then

analytical formulaecan be derived for the flowareas AI O, .A20 and A~ from the

standard formulae for conic sections:

(6)

(7)

(8)

These formulae are complicated and will not be inciuded here. As noted above

they will take different forms depending on the flow regime in which the cell

is operating. Similarly expressions for the footprint areas c~~ be derived

from the geometry

F(9)

-

G dc f4 (a, h ) v

=

0 F(lO)

-

G uc f

₅

(a, h ) v .. ::;;, 0 (10) F(ll)

=

G - f

₆

(a, hv) ~ 0 0 (11)

The values of the discharge coefficients Cdl' Cd2 and Cdo are taken to be those for standard circular orifices at high Reynolds number namely

Cd

=

_{0.61. The values of discharge coefficients CdlO ' Cd20 and Cda are not}

so easily determined since in gener al they will be a function of the roll

angle

a

and skirt taper angle~. For a given cell, the local discharge

coefficient will vary around the perimeter from a maximum on the upgoing

side to a minimum on the downgoing side, since the effective local slot angle

varies around the perimeter. For simplicity the valu~ corresponding to a

two-dimensional slot having walls at

90

0

to the mean flow direction namely

CD

=

0.61 was used in the calculations. This was believed to be a good

approximation since for small. roll angles

a

apd smaJ.l skirt taper angles

the effective slot angle should not be too far from 90°. In gener al for the

upgoing sidè of the cell the effects of ~ and.

a

tend to cancel. Thl.s is

where most flow occurs.

The theory was modified to allow inclusion of end effects which must be present in a finite length cushion system. As can be seen from

Fig. 1~2 the value of Aa for the two end cell pairs will be greater than

that for the centre cell pairs. The value of Aa for the end pair was computed from the skirt geometry and the extra area was distributed uniformly over

Once a solution to the above system of equations is obtained for a given s~lected roll angle ex, the restoring moment generated by the cushion is easily computed

pG.e - P G . e

C ; dc dc dc uc uc uc

M WEQB . (12)

where .edc and .euc are the effective moment arms for the cell forces relative tq a chosen datum.

Solutions to the system of equations are obtained on a computer for a given ~le ex by using a Newton-Raphson technique modified to include a convergence criterion on the norm. That is, given a system of kalgebraic equations for k unknowns~

as ;

cOl(X_j ), j = 1, 2 to k the iterative procedure adopted W&S in the form

'\0

~O

A._a Pbox PdC

(dF.

f

~ ; Puc _'

~+l

=~ - M

~

F

(~)

J Po G uc G dc G 0

~

where ex is th~ iteration number, and M is a scalar multiplier chosen to millimize ~ Fi at each step. The Jacobian J ;:::;> (àF:JOxj) was derived

explici tly from the alge braic relations. The computer program is gi ven in Appendix E.

The theory presented by Jones (Ref. 6) differs from the present one in four major respects:

(i) To simplify the c omputati on , only that portion of the curve of rolling moment as a function of roll angle corresponding to complete shut-off of the downgoing cells is considered. In this limiting case the number of equations to be handled is reduced and their form is considerably simplified.

(ii) End effects are not included.

(iii) No allowance is made for variation of heights of the outer skirt relative to the inner skirt, that is Llli

=

0 in Fig. 2.2.

(iv) The supply pressure Pb is fixed so that no effect of the slope of the fan characteristic is included.

These simplifications allow the equations to be solved by a graphical tech-nique.

Figures 2.4 to 2.7 show typical computations of roll stiffness characteristics. In Fig. 2.4 two curves are included corresponding to two different gross weights but with the same value of power coefficient

CPCe = 0.06. The two curves are virtually identical, and this provide,s both a good demonstration of the sealing arguments given in Section 2.1 and a check on the accuracy of the computations. The curves display a character-istic two-slope behaviour. The first slope corresponds to the downgoing cell acting in the regulating zone while the second slope corresponds to the downgoing cell shut-off. Figure 2.5 shows the effect of CpC on roll stiffness at a given CA. The effect of increasing Cpc is to increase

significantly the maximum rOlling moment that can be generated by the cushion; however, the initial stiffness of the curve dCmlda at ex

=

0 decreases. Figure 2.6 shows the effect of increasing CA at constant pressure coefficient CRC' Again as CA is increased, the initial slope dCmlda

Iex:::()

decreases; however, the maximum value of CM changes only slightly. This suggests that CRC is the critical parameter which controls the maximum moment generated by the cushion system. Figure 2.7 shows the effect of CSC at fixed CPCe and CA, and here the interesting feature is the increase in maximum stiffness

associated with an increase in the (negative) slope of the fan characteristic. The data in Fig. 2.7 is for CSC in the range (0

>

CSC

>

-500) where csc

=

0 corresponds to a constant pressure source, while-CSC ;--500 approximates a constant mass flow source. The maximum stiffness varies by a factor of about two between these limits, so it clearly indicates that CSC is a very important design parameter.

2.3 Available Theory for Loop and Segment Skirt

The simple geometrie theory that is available for the loop and segment skirt was compared where appropriate with the experimental results. lts main features are summarized below. In this theory, the cushion system is assumed to rotate in roll about the tip of the segment on the side opposite to that which is rolled down. Since the cushion pressure is the same every-where, the restoring moment arises solely from a lateral shift of the centre of pressure relative to the base of the vehicle.

Fromthe geometry in Fig.

2.8,

and using the approximations that can be made since the roll angle ex is usually small, we have

(1)

Here cp is the angle that the outer edge of the segment makes with the ground when ex = 0, and BW is the width of the cushion footprint at a

=

O. Note that certain effects have been omi tted on the grounds that they are small. Typically if the cushion rolls about the tip of a segment, then there is an increase in footprint area which would normally be accommodated by a variation in mass flow and hovergap on the upgoing side.

The maximum CM is given by

(2)

where Lf is the segment length as defined in Fig.

2.8.

To complete the theory it is necessary to ascertain the angle cp from a knowledge of the skirt geometry. Burgess (Ref. 12) has described a simplified method for computing

cp

given the segment geometry and loop and tie lengths

1t

and

Lr

respectively. His method is reviewed briefly here. Consider first a force balanee on an individual segment. Forces are resolved normal and parallel to the upper surface DC of the segment, so that using the notation shown in Fig.

2.9

we have:

Normal: T sina + FT si~

=

pd cot8 Parallel: T cosa + pd

Here T is the loop tension and FT is the tie force. The geometrie quantities are defined in Fig.

2.9.

Since T

=

pR where R is the loop radius, we have

cott3

=

cot8 - R d sinx

1 + R d cosa

An additional equation is obtained by taking moments aboutC

d

sina = 2R cot8

From geometry, the following three conditions are obtained

LL

=

R(rr/2 -

a

+ w)

~ sin)' + ~ si~ = R( cosa + sinw)

(3)

(4)

(5)

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

._-LH cos{ :;; Lf/cose + Lt cosf3 + R(cosw - sira)

These constitute 5 equations for 5 unknowns, cx, f3, R, w, {. The quantities LL, LH, LF, e,

Lr

and d are all known. These equations can be solved by an

appropriate numerical procedure, or by a graphical technique described by Burgess (Ref. 12). Finally, since the points A and B are located on the hard

structure , the angle the line AB makes with the ground at roll angle cx :;; zero is known. Let this angle be Eg. Then (see Fig. 2.9),

cp

e

+

E - (

g

This theory was applied to the results described in Section 4.2.

3.

DESCR~PTION OF FACILITX AND EXPERIMENTAL PROCEDURES 3.1 urIAS Cushion Dynamics Facility

(8)

The test model or 'vehicle' is a box supplied by air from a fan system through a soft, flexible duct as shown in Fig.

3.1.

The dynamic head of the air flow entering the box through the duct is eliminated by an

appropriately placed baffle, so that the box acts as a reservoir of qud.escent air for the particular skirt system which is attached immediately below it. The equivalent or effective fan characteristic is then the mean static pressure in the box as a function of the ~.r.olume flow through it into the skirt. The flexible duct through which the air is supplied is attached to the point of least motion of the box, na.mely its top centre.

The box and skirt system hover over a smooth flat surface , the 'table', constrained by the harness system, which, for the present tests, is set up to allow the box to move freely in heave and roll (Fig. 3.2). The constràining mechanism or harness uses ball bearings in both angular and linear motion ·so that frictional effects are negligible, and is attached to the box at points close to a horizontal line through its centre of mass

(Fig.

3.3).

Although the experiments discussed are the effect of rolling moments, air cushions usually heave as they rOll, so that in order to properly simulate acÜon at constant weight, the model must be free to move in he ave .

The air supply system used a standard industrial type centrifugal fan fitted with backward facing blades and driven by a 15 hp three-phase AC induction motor. Inlet air was drawn from the laboratory so that the air temperature and atmospheric pressure we re accurately known. Two controls were available to allow precise setting of the required box pressure and system volume flow rate. These were an inlet flow choke and a spring loaded vee belt drive which allowed the fan speed to be varied continuously while the fan was running. However at the time the test series A, B and C were undertaken the fan could only be changed by changing pulleys and belts.

Two mechanisms were used for imposing a rolling moment on the cushion. The first comprised a cart holding a known weight, which is driven across the top of the box by a 10 turns/inch lead screw. This can be seen

in Fig. 3.2. Counterbalance weights attached to the harness arms through a cable and pulley system compensate for the effect of weights added to the moment cart, s 0 that the weight remains constant at the nominal value.

Compensating weights were also used to correct for the varying weights of the different skirt systems as they were used in the tests. With this system all tests were conducted by moving the cart and weight out from the geometric centre of the box to a point at which the cushion rolled over to hard structure contact. This was done for bath outgoing and return movements of the weight to check for hysteresis in the roll characteristic.

The travelling cart system, although convenient to operate, was ;found to have one major disadvantage. Since the test weight was mounted on top of the box, for a given position of the cart along the lead screw, any increase in roll angle causes a slight increase in the rolling moment imposed on the system. It was found that above a certain roll angle

a,

the multicelI system generated a roll stiffness which was comparable to and sometimes less than the minimum stiffness requirement imposed by the cart rolling moment increase associated with increasing

a.

When this occurred, a very small movement of the cart would cause the cushion to roll through large angles, usually down to hard structure contact (RSC). Test series A, B and C used an appropriately placed spring balance to counteract this effect. Rowever, for series D, E and F, the travelling cart system was replaced with a sector arm system. This had the advantage of imposing a rolling moment which was indepen-dent of the roll angle

a,

but its major disadvantage was that, in a given roll experiment, as weights were added to the sector arm to increase roll moment, compensating weights had to be added to the counterbalance. Although this wa,s awkward to operate, it did not affect the results, provided small increments were applied at each step increase in roll angle. The sector arm system is shown in Fig.

3.4.

As noted earlier , the tests were normally conducted on a smooth flat horizontal surface which was fixed relative to the vehicle supporting frame. Since the box was fixed to the harness system at the height· of the centre of mass, this implied that for most tests the skirt systems when in ground .contact would be forced laterally across the ground as the vehicle rolled. In order to ascertain if the sliding frictional forces so generated had any significant effect on skirt rolling moments, some tests were undertaken using what is subsequently described as a rolling board. This was simply a flat sheet supported directly under the skirt system and on the table by means of a large number of tubes aligned so as to allow the sheet to roll wi th the skirt system. This wa.s found to very effectively eliminate skirt-ground contact frictional forces.

It is to be noted that a full scale vehicle operating under realistic conditions would in general operate at neither of the two conditions simulated in the present experiments. Rowever, it is felt that,if little difference between the results obtained by the two methods is found,then it is reasonable to argue that the results should apply to a full scale vehicle.

The equivalent fan characteristic for the present system, that is, the variation of box pressure with system volume flow,was typical of most air cushion installations, that is, it had dp/dQ,

<

O. Fjgure

3.5

shows typical system characteristics. A feature of the variable speed fan drive system was that it enabled artificial simulation of a wide range of characteristics which we re unrelated to the basic characteristic of the instalIed fan.

3.2 Ins"trumentation and Data Redudion

At the beginning of eaeh run, laboratory temperature and pressure were no"ted. During the run, the following items were monitored as a function of roll angle:

(i) Roll angle, (ii) Heave height,

(iii) Distanee of motion of test weight,

(iv) Statie pressure in the feed box at a number of stations, usually

5

or

8,

(v) Statie pressures exerted on the table at suitably loeated positions under the eushion or individual eells as required by a part.ieular design,

'-(vi) Fan speed,

(vii) A statie or dynamic pressure whieh was related to volume flow rates.

The box heave heigh"t and roll angle were measured using Shaevitz linear and angular displacement transdueers respeetively, and the output was displayed on a digi tal voltmeter. Ini tial detailed ealibration followed by periodic spot eheeking showed that the calibration factor remained constant to better than

±

0.5%. In one case when a shift of about 1% was noted, this was traced to slight looseness in the mechanical clamp system. The resolution of these deviees is also excellent, usually better than that of available calibration apparatus, whieh in the case of the displacement transducer was a vernier micrometer capable of measuring to ± .001 ins. The fan speed N was measured digitally by mounting direc"tly on the fan shaft a disc with holes drilled on a cirele of given diameter. This :system interrupted a light beam aimed at a photosensitive cell, and the pulses were processed to give a direct readout on a digi"tal counter. In general, for a given var,iable speed drive and inlet vane setting, N was found to vary less than ± 0.2% within a run and from run to run.

Two methods of measuring mass flow were used in the present tests. For series A to C, "the procedure adopted was an outgrowth of an earlier program. of examination of the flow in the duct. Pitot traverses in the rectangular duet along three parallel lines in each of the two principal directions as shown in Fig. 3.1 had established that the volume flow in the duct would be correlated accurately in with the centreline velocity through a correction factor which was between 0.785 to 0.780 for the available range of inlet choke vane settings. The advantage of this method was that the volume flow was ascertained just upstream of the point at whieh air was fed intothe box, so that it minimized the chances of introduction of error caused by leakages.

For tests in series D, E and F, a second calibration was required beeause the ducting was changed. The opportunity was taken to install a

system which would be easier to calibrate, and which would yield more accurate measurements at low values of volume flow. This second volume flow measurement system was basically a calibrated fan inlet, in which the static pressure drop across the inlet was used to provide a direct indication of mass flow on a micromanometer capable of being read to 0.01 ins H20. The inlet itself was calibrated against an ASME standard orifice plate installed downstream of the fan. One complication was that the ducting geometry downstream of the fan prevented installation of the settling length of completely straight pipe upstream of the orifice plate, as required by the ASME standard (Ref. 7). Past experience at urIAS has shown that the upstream settling length as specified by the ASME is quite conservative so this was felt to introduce no significant error. However, a check on the accuracy of the orifice plate estimate was made at one volume flow rate by taking detailed pitot traverses in the inlet. These traverses gave agreement between the two methods of inlet calibration to within 0.87%. As noted in Section 1, the details of this test are given in Appendix B.

The rolling moment generated by the cushion for a given roll angle is usually expressed in terms of a movement of the centre of pressure on the ground board expressed as a percentage of a suitable reference length, normally taken to be the beam width of the vehicle. This convention is followed here; in fact, the moment coefficient defined in Eq. 13 of Section 2.1 is precisely this quantity. To complete the specification it is necessary to choose a reference point on the vehicle. One obvious choice is the centre of mass of the basic vehicle, since the equations of vehicle dynamics normally make use of centre of mass fixed coordinates. However, the magnitude of the centre of the mass height above the cushion will differ from vehicle to vehicle, so that we will adopt the convention of specifying the shift relative to a point directly below the centre of mass which is at the base of the hard structure . The method used to determine CM is described in detail in Appendix C,

All data has been presented in terms of the coefficients in Section

2.1. .An important aspect of the present program was the use of the infinitely

variable speed drive and flow choke to allow precise setting of volume flows and box pressures in order to examine certain aspects of the scaling laws discussed in Section 2.l.. These tests were:

(i) To test for the importance of additional parameters in scaling, that is, to find out if any of the additional Z' s in Eq. 11 of Section 2.1 are required to scale up results.

(ii) To examine the effect of fan slope coefficient by setting Csc equal to zero.

For the first test the procedure adopted was that outlined at the end of Sec'tion 2.1, namely, for fixed CA and

9sc'

,

tests were undertaken at two gross weights, Wl

=

72.6 kg and W2

=

140.6 kg, and the flow choke and variable speed drive were usedto adjust both the Pbe and Qe so that the quantity epC was the same for both weights. If the nondimensional plots of CM as a function of

ex

are the same for the two different weights, this suggests that no additional scaling coefficients are required; this is point (i) above. For the experiments in which the effective slope coefficient CSC was set to zero, the quantity Pb was held constant as the roll angle changed. Basically the procedure adopted was to monitor the average box pressure when a rolling moment test was underway. As the applied rolling moment was increased, any

change in box pressure was removed by an appropriate incremental adjustment of the fan speed. Physically, this is equivalent to using a very large air supply fan.

Considerable care had to be taken in estimating the local fan slope

dp/dQle for calculating CSC' since i t is well known that estimating a slope

from an experiment al curve ha ving an even modest amount of scatter can produce

very large errors, unless appropriate care is taken. The most effecti ve procedure

for avoiding this error source is to obtain a large number of data points for the curve, then use a least squares technique to fit an appropriate mathematical expression to the cUNe, which can in turn be formally differentiated. One difficulty faced in adopting this approach in the present tests was that a wide range of fan speeds and flow choke settings were used in obtaining the exact

volume flow and box pressure requirements for sealing tests, so ·that relatively

few data points were available for any given combination of ehoke set·ting and

fan speed. This difficulty was circumvented by using the weil known fan sealing

laws to eliminate explicit dependenee on the fan speed N, and thus build up a

sufficient number of points to enable accurate curve fits to be made. This is

described in Appendix D.

4.

RESULTS

4.1 Preliminary Tests

(i) Repeatability of Data - In general, we have found that the statie roll

stiffness curves obtained on the cushion dynamics facility were always repeatable to a high degree of accuracy, even when the cushion system was showing unexpected

or apparently anomalous behaviour. An interesting example is given in Fig. 4.1.

This shows results for the multicell system with the 'blue' skirt; two points should be noted. The first is that the roll characteristic exhibited a hysteresis

phenomenon, in that the rOlling moment obtained during the roll-down or 0: increasing

portion of the cycle. to hard structure contact (HSC) was always higher than the

moment obtained during the return or roll-up portion. This pattern appeared

consistently in all of our tests for all skirts. It is a true hysteresis

phenom-enon, since

JCM(O:)da

is a nondimensional work term, and the work required to roll

down to HSC is greater than the work supplied by the cushion in the roll-up portion of the cycle.

The second point is that Fig. )+.1 shows two successive tests of roll

stiffness taken for the roll down portion of the curve. The repeatability is

clearly very good, even the sudden decrease which occurs at about 0: =

5

0 is

reproduced. Later tests also showed that the return portion of the curve is repeatable.

(ii) Use of Local Slope to Define Fan Characteristic - One condition on the use of a nondimensional fan slope characteristic CSC as defined in Eq. 13 of

Section 2.i was that during a typical roll experiment, the box pressure and volume

flow should not vary significantly from their values at zero rOll, so that the characteristic could therefore be assumed to be linear. Figure 4.2 shows the

pressure and volume flow variations during typical roll cycles for both a multicell and a Flexicell skirt. It is clear that the variation in pressure and flow are both sufficiently small to allow the use of a local sJ ope concept.

One interesting point to note is that for the multicell cushion, the box pressure decreased as the cushion rOlls, whereas for the Flexicell, the box pressure increased. This has an interesting consequence which is discussed later.

(iii) Range of CpC Used in Test Program - The quantities CpC and CA were chosen as the basic reference parameters for expressing the cushion flow characteristics. Particular emphasis was laid on selecting a range of CPC which was representative of the values used on full scale vehicles. Unfortu-nately, very li'ttle data is available. Two cases are given below to indicate the expected range.

Data supplied by Jones (Ref. 11) indicated that the Roverjak HJ-15 towed raft operated at about Cpe = 0.011. Trillo (Ref. 1, p. 80) notes that for the BRC SRN6 about 150-300 HP is used by the lift fan at a 17500 lb. AUW. Assuming a fan-duet efficiency of about

50%,

this corresponds to the range 0.02

$

CPC

$

0.04 approximately. In the present test program the ranges of Cpc used was between 0.01 and 0.1, with particular emphasis placed on the range 0.01 to 0.03.

4.2 Results for Loop and Segment Skirt

(i) Geometry - Figure 4.3 shows the geometry of the loop and segment skirt system used in the present tests, together with the geome'try of a skirt system tYl'ical of those used in HDL vehicles (Ref. 10). The scale has been adjusted

so that the outside ségment length is the same for both skirts; this gives the relative magnitude of both the loop length LL and the segment att.achment cable length

Lr

for the two. The description of the HDL geometry was received some time af ter the skirt used in the present tests was manufactured_ Both systems employ a

90°

included angle segment but the HDL skirt has greater loop and segment attachment lengths • In general the indications from the tests are that variation of both segment and loop length does not greatly affect the major characteristics of the skirt.

Two methods of feeding the air into the cushion were used, the first was direct through the base of iie, hard structure and the second was through holes directly into the loop area. These two are shown in Fig. 1.1. In the following figures, feed areas are quoted as :fractions of reference area which is here

2.97rril-

and the segment attachment length is quoted as a fraction of the segment length. The segment length forthe present skirt was 25.4 cm or

o

.208 of the nominal vehicle beam.

(ii) Results - In the resultsthat fOllow, a vaJ.ue of Cpc has been quoted in addition to values for CQC, although as noted in Section 2.2, strictly speaking, Cpc

=

CQC for the loop skirt. The difference here arises because the box

supply pressure differed somewhat from the cushion pressure owing to losses across the feed orifices. Also the notation RSC given in some figures indicates the point at which the plenum box or 'hard structure' contacted the ground plane.

Figure 4.4 shows the effect of varying CPC (or CQC)' As shown,

increasing Cpc results in an increase of both C.P. shift and roll angle at HSC. The feed for both cases was through the loop. Note the sudden increase in

stiffness immediately before HSC. A possible explanation for this increase is the following. As the downgoing edge of the vehicle hard structure approaches

ground, the slot formed between the downgoing edge and the ground regulates the flow into the cushion through the downgoing loop. This reguJ_ation results in a reduction of the total cushion flow and an increase of box supply and down-going loop pressure. The local increase in loop pressure would explain the increased stiffness ~hown. One would expect the effect, if it is due to regulation as discussed above, to be more noticeable for a higher CPC (or CQC) because the supply pressure available to the downgoing loop would be greater. This appears to be the case in Fig.

4.4.

For the lower Cpc curve in Fig.

4.4

notice the loc al changes of slope or nonlinearity between 3°:s.a ~ 5°. These are believed to be associated with the impingement of the loop feed-jets onto the loop-segromt join regions shown in Fig.

4.5.

The impingement causes skirt deformations and periodic separations of adjacent segments. This separation was observed during these tests. They result in local flows between segments

and local losses of loop pressure. The nonlinearities do not occur when feed is through the base. It should also be noticed that the curve for high CPC in Fig.

4.4

shows some indication of a dead band effect at CM

=

O. This is to be

expected for the loop and segment skirt, since increasing CpC increases the clear air gap and the angle through which the skirt has to roll before segment-ground contact occurs.

Figure

4.6

includes an estimate of the roll stiffness as predicted by the theory described in Section 2.3. The agreement between the theoretical

estimate and curve B4 is reasonable. Figure 1+.6 also shows the feed hole position effect. The feed for the curve B5 was through the base whereas for the curve B4 i t was through the loop. Skirt deformations associated with jet impingement for loop feed probably cause some of the difference in initial

slopes. Note the characteristic sudden increase in stiffness for loop feed near HSC. No such increase occurs when direct feed is us€d. This is as one would expect, considering that the regula ting effe cts of the downgoing edge orifi ce and the partly compartmented loop do not occur when feed is direct. Figure

4.7

shows the variations of box pressure with roll angle for the cases considered in Fig.

4.6.

The increase ip box pressure near HSC, for the loop feed case

only, supports the regulating explanation for the sudden increase in stiffness noted above. Figure

4.7

also shows the variation of mean cushion height as

a function of roll angle. There is a considerable drop ,which is to be expected, since the roll stiffness arises directly from the collapse of the segments on the downgoing side, while those on the other side remain deployed.

Figure

4.8

shows the effect of varying the segment tie length

LT.

For both curves, feed is through the loop, and the nonlinear effects associated with jet impingement can be seen. Apparently varying the segment attachment length has not affected the segment-to- surface exterior angle cp as the average slope of each curve is almost identical. However, the CP shift and roll angle at the end of the initial slope (up to change of slope near HSC) are affected. Also increasing the segment attachment length from zero to 0.2 LF decreased the equilibrium height of the hard structure above the table to 91% of its original valu~. This height difference explains the effects on CP shift and roll angle which occur.

Figure

4.9

shows the effect of varying CSC' The only noticeable difference between the two curves shown is that there appears to be less jet impingement effect for the more negative CSC' The equilibrium flow for the lower CSC is

1.55

m3/

sec whereas for the higher CSC it is

1.08

rn3/sec. This difference in flow could explain some of the effect shown.

I