21 NEI
7973ÂRCHE
24-ovGrcraft
eirci
t
t-o
.outhmton
by
T. K. S. MURTHY, PhD., MSc., MA., DIC., C.Eng.,
AFRAeS., MRINA
Hovercraft research 'jvas resumed at the University of Southampton in January 1967 and the
work sponsored by i/ic Ministry of Technology has largely been of a theoretical nature under
the broad heading of 1/le mOtiOnS and stability of a hovercraft over 't'a1er. Ami initial literature
survey revealed ¡liai very liti/e information was available in
1/lisarea cimid ii
t'as apparent rilar
a systematic mathematical stud
izay be s'oríhw/zile. Sue/i a study
lids
ills! been completed t'ìth
1/le publication of a linearised potential flow t/zeo,-' of the morions of a hovercraft in a seaway.
This work will he discussed present/v in some derail after giving a brief ourlimie of some
perìph-eral topics of a basic nature is/iicli itere first in vestigated during the period under review.
/-
(:kfZß.
Bibliotheek van
Ond eraf dei in9 er
ScheeOUWkW1t
Te'hnisclé HogeschOOCDet
D3CUMENTATÌE
DATUM:
1. Behaviour of Hovercraft over SVater
AFIRST
nected with a study of the mot!ons and stability ofLOOK was taken at some of the problemscon-hovercraft operating over water and some preliminary
notes have been set down in ref I (September 1967). On
comparing the influence of the free surface of ater on the motions of a hovercraft, with its effect on ship motions. lt was realised that there is an additicna degree of com-plexity (as illustrated on page II of the report; due to the
laws of cushion aerodynamics. sshich dictate a continuous interaction between the fluctuating pressure applied by the air cushion to the free surface and the deformation of the surface itself. This pointed to analogue simulation as the ideal method of solution of this prohlem. Assuming that
the behaviour of the hovercraft over land is known, a systematic method was proposed for the evaluation of the hydrodynamic part of the excitation (including the
damp-ing. added mass and added moment of inertia of the water) for inclusion in the equations of motion. lt was
established thtt it is possible to make some headway in
understanding the problem of the motions and stability of
a hovercraft over svater by considering its equivalent mathematical model, namely, a travelling pressure dis-turbance, provided the hovercraft is always cushion-borne and that no part of the hovercraft or of its flexible exten-sions contacts the water during any stage of the motion or
oscillations of the craft. In fact this is the basis for the
strict mathematical theory developed in ref 10.
Some results are given for a simple fluctuating rectangu-lar pressure (kid using two-dimensional theory illustrating how wave resistance and wave damping can he derived from considerations of energy in the outgoing progressive waves. lt appears that there are sorne exceptional speeds of motion at which the wave resistance of the main air cushion vanishes (a wellknown result) although the peripheral jets have a finite (if small) wave resistance at all speeds. Simi-larly, there are some exceptional frequencies of fluctuation
of pressure at which the damping of (h cushion vanishes
although there is a small amount of damping available
due to the action of the static pressure of (lie iir jets on
the water surface As two-dimensional theory has been
ii.iil, the liClil)lt(:fal jek are those loea(l it ((it how and
l i j ol H- t1_I.IiIrIiIa, ciiliioit.
S L'..'epsbuwkund
Technische Hogeschooì
Deift
The ss'aves generated by a stationary periodic surface
pressure within the cushion and outwards to infinity on
either side are derived and discussed in some detail. An interesting result has been derived, namely, that when a
hovercraft is osiliating. say in heave, the 'step" in the
elevation of the vater surface at the extremities of the
pressure field is of the same magnitude as that in static
hovering. It appears that the outgoing waves are
propa-gated about the undisturbed water level, whereas the datum for the "cushion wave" is the uniform depressed level appropriate to the instantaneous pressure. This step in the svater surface (although strictly true only in
two-dimension-al theory) is perhaps fortunate in the case o
hovercraft for the peripheral jets at the how and at the
stern can then operate with the design air gap even during oscillations.
The induced wave due to a uniform pressure field
mov-ing over the surface of water at a steady speed is also
derived and discussed. Some simple design criteria are
proposed for the avoidance of water contact of the boss' skirts and the central stability skirts.
hovercraft in }lcaving ",lotion at Zero Speed ahead
Ref 2 (1967) continues the study nude in ref I in respect
of a hovercraft in pure heaving motion at zero speed
ahead. The induced wave formations wïthin the cushion and outwards to infinity have been derived and discussed.
A quantitative measure of the hydrodynanile damping
coellicient sshich arises during the oscillations is derived showing its similarity to the resistance coeflìcient in for-svard motion. Wave steepness limitations to the theoretical values of damping are also discussed. Two-dimensional
theory has been used in this work together with an
assump-tion analogous to the Froude-K rilotï hypothesis, namely.
that the fluctuating pressure in the cushion affects the water surface, hut that tile deformation of the free surface does not upset t he ha la need opera t ion of the peripheral
jets. -1 his assoniption is. perhaps, not too drastic in view of
(lie possibility of the design air gap beingnia iritained dur-ing osci I la turns, as indica ted a hove.
Sta t ist ¡ciii kf 110(1 of I reil ¡et iii n of Mot jolis
A method for the statistical prediL-tiol of the motions
tif i niarinc crut ii geucil ojueI.ttliig iii a ss iiid-gvneratcd
iiíit'iilir
il'iujl
iir(
i Iil
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jI( .' I.I(l
IÌ(
Ii. LI.IPII ;ilit )IIi
Il.IiJI
)II t'4.i.tP IhII il Iiiic
I j ¡ 5IItI% II lt \' I IC \l)III t IC. I I i \j ('C I.
tI
I I U CIIItry IItiflS
)t nu lie
'r.ilI c;iu he it a vcry cìrIy s1gcf thcr dcsin by analytical nicth&is using
spccraI au;lIysiS tCClU1iLICS lì(l stListtcaI
thcry.
i hetcSp(flSe S'CCt rum fçi- thc ntt i"fls has hccn drived as a function of he vind speed ind fetch. tue craft speed and
heading re1atie tO 'VI 11(1. a nd a single pa rarnctcr
oh-cained fron theúry or I roni nlci 1ets, nanicly. the
naxi-mum tililt response in regtilar wavcs. The motions are
completely characterised by the statkticai properties of the response spcctruni.
The entire bask for the rrrosed method is the theory
of linear superposition. Ship motions such as pitching and
heaving n moderate seas arc usi;tl1y found lo he approx-irnately linear. Rolling is. howcvcr deuinitely known to he non-linear. although the superposition principle has been
verilied even in this case by sorne workers ¡n Japan.
Hovercraft are probably very prtne to
non-linearhe-haviour. mainly due to the uterm ittent contact ss'ith the free surface of water during oscillations and on account of the characteristics of the air cushion-peripheral jet sys-tem which is known to provide a non-linear damping. But assuming that the theory of linear superposition can be applied to the motions of hovercraft, this method of pre-diction may provide a useful working tool for the hover-craft designer as the effect of various hover-craft parameters on motions in the proposed area of operation under specified wind conditions can be assessed at a very early stage of the design on the basis of some simple model tests. A mathe-matical theory for the analytical prediction of the response functions in a regular seaway is proposed in ref IO (to be
discussed presently) and
if
these (or other) theoreticalresults are used, model testing, which is expensive and time-consuming, can be completely eliminated for a
pre-liminary investigation of the suitability of the proposed
design for the particular type of sea environment. The proposed technique is as follows. The sea environ-ment is assumed to be characterised by. say, the Derby-shire Spectrum for Coastal Waters, but the method could
be suitably adapted to the Pierson-Maskowitz or other
types of spectrum. The spectrum or spectral density
func-tion gives the spectral energy in a narrow band of
fre-quencies as a function of the frequency with the wind
speed and wind fetch entering as parameters. The spectral function takes a simpler form independent of wind speed or fetch when plotted against a function of the frequency containing these variables. This may he called the Reduced
Sea Spectrum. The area and moments of the reduced
spectrum have been calculated numerically with the use of a digital computer and tabulated. These tabulated
con-stants are used for the calculation of the area and mom-ents of the actual spectrum. The area and mommom-ents of the encountered sea spectrum may also be written in terms of those of the reduced spectrum by using operator rotation where the craft speed and heading as vvell as the wind speed and fetch enter in the coefficients of the polynomials
representing the operators.
An important (and doubtful) assumption has been made, namely, that the response curve is of the same shape as the familiar resonance curve of a spring and mass system with damping. 'This assumption was made because the solution cari then he obtained in closed form, as the standard equa-tion of the resonance curve as a funcequa-tion of stiffness and damping is well known, The statistical properties of the motions are very simply given in terms of the areas and moments of the response spectrum which can be calculated
ill I( IliI, )l 1h
,il,iil,itI ttiiisI.iiI.
'I,iiil
ilC,iu lC tiIil)14)y1l ti ill,tiiì iiacIicil
tsiilI vciy iii& l'ly.'I lie I55tiiIuliOIl tII,I( Ilic
respojisi' curve illi', hic
sanie paIlero us the resoiliilce curve ci1tÌt(itC a weaknessin this st tidy. I f (he response curve is plotted aga inst the frequency of encounter from theoretical or experimental
results, the of the ordinates at various frequencies
can he iìiItiplicd by the corresponding ordinales of the
encountered sea spectrum to obtain the response spectrum. A digital computer may have to he used for this purpose in the general case, hut hand calculation can he suflicicnt if a few discrete frequencies arc selected and the resulting curve smoothed. Much information about the motions can he gained Irom the niagiiitude of the arca of the response spectrum and this can be ohtained for various combina. -tions of wind spee(l/fctch and craft speed/heading.
This method is strictly applicable to unidirectional
long-crested sea. hut could probably he used with sufficient accuracy if the heading of the vessel is within ±45's of the direction of travel of the dominant waves (le within
±45' of the wind direction), The extension of the method to multi-directional short-crested sea is obvious.
The above method will give the short-term prediction of the sea during a period of the order of thirty minutes, For long-term prediction, the significant aspects of motion dur-ing the course of a season or a year may be calculated if the bivariate distribution of the frequencies of occurrence of wind speed and direction over a long period, such as
over a year. is available. Such a table can usually be
supplied by the Meeorological Office, lt is then only a
matter of calculating the motions corresponding to each : combination of wind speed and direction to arrive at the annual frequencies of occurrence of some significant as-pects of the motions.
4 Resistance
Refs 4. 5 and 6 (1969) deal with the wave resistance of a hovercraft with a cushion containing uniform pressure. The basic formula used for the calculations is that given
by Havelock, This formula has been derived independently
by a different method in the linearised potential flow theory to be discussed presently. The wave resistance of a drifting hovercraft has also been derived in closed form by a suitable transformation of co-ordinates in Havelock's
formula. This is of practical importance in hovercraft
operation since the wave resistance and sideforce can be used to advantage in the control and manoeuvrability of the craft. A rapid deceleration in an emergency may be
achieved by yawing the craft through an appropriate
angle and it is also possible to optimise the angle of
directed thrust for setting the course under cross-wind
conditions to make good a desired track. These results may therefore he useful to the hovercraft operator, The expression derived for the sideforce in drifting motion is slightly in error as it is taken simply as the component of the wave resistance in the lateral direction. This error has since been rectified in ref 10 where the component of the force normal to the direction of motion has also been
in-cluded. The side force prevents drift in much the same
way as wave resistance which retards forward motion.
Some quantitative results have been derived for the wave resistance of a uniform cushion with rectangular planform in drifting motion. It appears that the wave
resistance increases very sharply with the angle of leeway up to 300 with a further increase up to 600 or 750 when the craft speed is below the hump. On the other hand, t'ne wave resistance is not very sensitive to leeway angle at high speeds and, if anything, there is a decrease at 900.
26
It is instinctively assumed that hovercraft of the future travelling at very high speeds may well have an "all bow" configuration simTar to the "al! wing" aircraft for
super-sonic speeds. A theoretical expression in the form of a
definite integral has been derived in ref 5 for the wave
resistance of a triangular cushion. The maximum wave
resistance of a triangular cushion carrying a given total
weight increases. as may be expected. vih the angle of
entrance. The hump speed however decreases and the
power required which is
a product of the two also
in-creases with the angle of entrance.
1f, however, wavesteepness limitations are imposed on the induced wave,
the power required to propel a triangular cushion may be almost uniform over the entire region of wedge angles. Inthe case of a drifting triangular cushion, the wave
resist-ance does not greatly exceed that in longitudinal motion, whatever may he the angle of leeway. As a matter of fact,the resistance drops steeply at large angles of drift.
par-ticu!arly for blunt cushions. This is in sharp contrast to
the rectangular cushion (ref 4) discussed above, where the resistance increases sharply with angle of leeway.some-times by a factor of 8.0.
A theoretical expression for the combined wave resist-ance of a system of uniform pressure fìelds moving abreast
over the surface of water with an angle of leeway is
de-rived in ref 6. In applying this result to sidewall
hover-craft, catamarans and trimarans.
it has been implicitlyassumed that the distribution of pressure on the free
surf-ace is also uniform in each of the separate regions,
al-though this may not be the case in drifting motion due tothe circulation around the immersed part of the hulls.
Some formulae for the calculation of the interference
factor as a function of the pressure ratio and the
separa-tion ratio are presented so that ari optimisasepara-tion of these
parameters to suit
the service speed can be done for
specific design cases.
5. The Hull Form of a Hovercraft Cushion
It
is commonly supposed that the hovercraft cushion
contain5 air at uniform pressure, hut it is obvious that this condition can exist only when the flexible extensions en-closing the cushion are in intimate contact with or actually
enter the free surface of water. In the actual physical
situation where the air cushion is sealed by the peripheral
air jets or by plenum air, there is a reduction of pressure
immediately within and on the boundary due to viscous
entrainment of air from the atmosphere and the
genera-tion of trapped vortices within the cushion. A diffused
cushion is postulated in ref 7 with the pressure decreasing continuously from a maximum value at the centre (or over a central region) to zero at the boundary with a zerogradi-ent of pressure there in the direction of motion, as this
type of cushion used as a mathematical model for the
theory in
ref IO simplifies considerably the expressionsfor the potential and for the forces and moments.
The pressure distribution imposed by the cushion on the water surface, together with the planform geometry of the cushion, gives it a three-dimensional hull shape for if the surface showing the pressure distribution is inverted abovethe plane of zero pressure which may he taken to he the
load water plane, we have tIte body plan of the equivalenthull of the hovercraft. A parabola of the fourth degree is
shown ti) he adequate in the case of a rectangular cushion to provide the property of zeri) pressure and zero gradientof pressure n all directions at lite boundary. ihis type of
cushion selected with tite object of mathematical
xpedi-in (iv1!4)lii)1' ii) :iiitite (t'ty itt ref lU ¡111)1
obtain-n i ' i il i i i tI i 'l'ho nit Inni,! is ii, h jr.issIy
inconsistent with available information on the probable
shape of the pressure distribution in the cushion and also has the obvious advantage of giving the hovercraft a hull shape svith a deadrise and flare at the bow and indeed allaround the periphery svhich may he considered by the
naval architect as very suitable for a high-speed planing
vessel of the conventional displacement type.6. Two Fundamental Topics
Art attempt is made in ref 8 to determine the exact shape of the depression of the water surface created by the
urti-form cushion of a hovercraft and by its peripheral arid
central stability air jets in static hover over water. This isobviously of fundamental importance
n a study of the
motions hnd stability of hovercraft over water. It is shown . that a continuous form for the water profile can be derived by taking the surface tension of water into account. So far
. as the main air cushion is concerned. the uniform
depres-sion generally assumed for a uniform cushion pressure is
modified by anything more than, say.
I only withinapproximately half an inch from the extremities of the
pressure band, irrespective of its extent. This is on the
basis of two-dimensional theory. The depression at the
actual extremities is exactly one-half that over the major
part of the cushion svih a slope equal to k/2 times the
cushion pressqre
in head of water (feet), where k is a
property of the water related to its surface tension having
the numerical value of 110 per ft at 6OF. Results of a
similar nature relating to a compartmented cushion have also been derived. The method is also applied to pressure fields of very small length such as those due to the periph-eral and central air jets on the assumption that a uniform pressure is applied to the water surface within thebound-ary of the jets. An extension of the method is then made
to the case of actual air jets with the air impinging on the: water surface and flowing along it on either side of the
.stagnation line. A comparison of the results with those
de-rived by more sophisticated methods using conformal
transformation and ssith experimental results, shows that the simplified theoretical method outlined is probably ade-quate to explain the physical situation.The results derived above are not trivial as they have
an important application in the problem of the so-called
indeterminacy of the stable height of a hovercraft operat-ing over svater. The height of a hovercraft in static hoverover water has so far been considered an indeterminate
problem, but a solution is presented in ref 9.
lt appearsthat the solution is unique only if the air cushion of the
hovercraft is fed and sealed solely by the peripheral jets. If the cushion pressure is increased by auxiliary methodsof feeding, such as by the admission of air through the
central stability jets or by other means, the indeterminacyof hover height seems to persist. Two distinct cases
areconsidered in the above study. In the case of a hovercraft fixed svith its hase at an arbitrary height above the \vater surface, the cushion pressure developed and sealed by the
peripheral jets can he calculated n terms of the fIxed
height above water and the applied ntonicntum flti. rlSO,
if the cushion pressure is increased by other means of
feed-ing, the maximum pressure which can he sealed by the
peripheral jets with a given montent unì flux can he
de-ternuined.
I n the second important case of a hovercraft
free to hover, the height above water has been determined uniquely only in the case of the peripheral jet-fed cushion. Tite sia bu ity of the quasi-steady state is yet to he estab-I shied.
,\n iiickbenh,il
rt-ttIt shich has hecn di-riseit is that
titeand irivard tovards the
jet cxt oi the hase. This
re-eiìrait proper(y of the jct caii bc tiiidc usc of ¡ri the design of a re-circulation system in ordcr to conserve lift power. It is assumed in this study that the jet is thin enough to be considered as a "momentum line" and that the flow is inviscid. Under these conditions. the jet need not split and can flov along the (depressed) water surface without dc-seloping a stagnation line on tue surface. lt is demonstrated that if the cushion is fed and scaled solely by the
periph-eral jets. the jets will have to impinge the bottom of the cushion depression vertically at the point of seal in the
steady state. This is the basis for deriving a unique rejation-ship betsveen the cushion pressure. jet momentum flux and
the height of the jet exit on the base above the water
surface.
A generalised equation written down for the jet path in the air region. separating the cushion from the atmosphere. and in the water region. je along the depressed water
sur-face, shows that the momentum flux in the jet and the
surface tension of vatcr play identical parts in controlling the path.
7_ Potential Flow Theory
A linearised potential flow theory for the motions of a
hovercraft in a seaway is dev&opcd in ref lo (June 1970). This is. in a sense, the final and comprehensive contribu-tion to the subject during the period under review.
The hovercraft is assumed to he completely separated from the sater surface during its motions and oscillations. lt is also assumed that the cushior pressure/length ratio, the amplitude of oscillations and the maximum slope of the incident wave system are all small quantities and that the speed of uniform translation under a constant thrust ¡s moderate or large. It has been established that the free surface of water contained within the vertical projection of the cushion opening is the "effective hull" of the hover-craft and that the forces and moments on the hover-craft con-sidered as a rigid body can be obtained by integrating the fluctuating pressure distribution applied by the air cushion
over the disturbed water surface whose elevation and
slope are consistent with the pressure distribution itself as discussed above (see also ref 1). A fundamental parameter is the basic hull form of the hovercraft cushion also dis-cussed above (see also ref 7). The instantaneous pressure distribution on the water surface during the oscillations of the craft is expressed in terms of this basic hull form to-gether with its derivatives in the direction of motion and
the pitch and heave stiffnesses of the cushion with the
oscillatory displacements as parameters.
The analysis is developed in terms of the acceleration potential of the water in place of the conventional velocity potential as the former gives directly the surface pressure. elevation and slope of the water surface. This potential has been derived by means of Green's theorem with the
use of an appropriate Green's function in the form of a
source singularity distribution over the cquilihrium position
of the effective hull together with a line distribution of
sources and doublets (oriented longitudinally) around the periphery. In the case of a uniform cushion, the singularity
distribution is limited to that of doublets around the
periphery and in the case of the diffused cushion with the pressure reduced to zero at the boundary (and with the zero gradient there) the potential is given simply in terms of a surface distribution of sources.
The method is first applied to the steady motion of the hovercraft in calm water under a constant thrust yielding
an expression for the wave resistance in longitudinal
motion which ¡s identical with that derived long since by
27
Havclock and thus confirming the validity of the assumed
mathematical model and the particular choice of the Green's function for the derivation of the potcntîal. The
systematic derivation of the equations of motion has also
brought to light a result which will end the controversy prevailing over the years as to where exactly the wave
resistance acts on a hovercraft completely divorced from the water surface and whether the resistance would still be
sustained
if
the craft were trimmed level in forwardmotion. it is shown that the wave resistance is the force acting at the centre of gravity of the hovercraft irrespective of its attitude and that wave resistance does not in itself produce an overturning moment. Also, the steady trim of
the craft during uniform translation over calm water is
determined solely by the location of the thrust line. The
trim will be zero at all speeds if the thrust line passes through the centre of gravity. The wave resistance and
side force acting on a drifting hovercraft have also been derived in closed form. It appears that a hovercraft
com-pletely separated from the water surface can experience a
side force just as though it had a physical keel immersed
in the water and the quantitative measure provided for this quantity can be used in calculations relating to the
control and manoeuvrability of the craft under cross-wind
conditions.
-The restoring force and moment acting on a hovercraft forced to oscillate iii calm water have also been derived. The mean increased resistance due to the oscillations, the added mass and added moment of inertia and the damping
of water can all be calculated from the higher order forces
and moments which are, as may be expected. of a
compli-cated nature. But most of the results given in this work are
derived from the lowest order forces and moments ¡ri
coplanar motion in the longitudinal plane with freedom in surge, heave and pitch only. This restriction of the motion to a plane is not a requirement of the linearised theory, but
a consideration of unrestricted motion in all the six
de-grees of freedom will render the mathematical work very
cumbersome. The results presented
for motion in
thelongitudinal plane with freedom in surge, heave and pitch can be applied directly to beamwise motion in the lateral plane with freedom in sway, heave and roll.
Several useful results have been derived for the free
oscillation of a hovercraft in regular waves. The cushion
diffusion coefficient defined in terms of the firstmoment of
the gradient of surface pressure distribution in the direction
of steady motion is analogous to the metacentricheight of
the hovercraft on its cushion and this quantity appears to characterise the motions. A hovercraft can have a
sub-stantial surge displacement in waves longer than
the
cushion, but this can he controlled by increasing the
speed. On the other hand, the surge acceleration which is
probably very vital for passenger comfort is independent
of craft speed and there could he an appreciable accelera-tion in waves very much smaller than the cushion. This explains the familiar and uncomfortable "cobble stone"
effect even in choppy water. The pitch displacement
is
directly related to the surge and an expression for the
pitch response function in regular waves has been derived.
It appears that the heave displacement in the lowest order
is zero for a hovercraft cushion with a symmetric cushion, but when there is longitudinal asymmetry, there is a finite displacement and the heave response function in this case
has also been derived. The phase difference between the
maximum pitch and heave response (which, incidentally.
happen to be synchronous for hovercraft) and the arrival of a wave crest below the centre of gravity has also been
.4
IS % .iI(il. (L
'r ei Ii
Í,'r i sli,ìi e ¡u ii it. ev&u( laLluit'. S Ii
,nliits
cqi.ire roIcsioual advice Iront litciit Agents a n&l sdici(irs.have Iou 11(1 (ha t even before (h ros ' open (he scheme
to outsiders. ¡ can compile a hst of ten interes - echnica
projects for schools, mainly in the marine or assoc d
areas, and in consequence a varied 'menu" can he
sented. The scope is virtually limitless since t e 2.000
British schools known to he interested
this kind of
technology may be added those . e other European
and North American countrie
All is not plain saihi' , owever. ¡ have already noted
some reluctance the part of schoolmasters to pass on
drawings. r reason for this being that they wish to
calculated. The response functions can he used to assess the behaviour of the hovercraft in an irregular hut
long-crested seaway within the limits of applicability of the
theory of linear superposition. But, as already discussed above, this has to he done with caution since there is rio positive experimental evidence to show that hovercraft motions are not non-linear even in tle absence of water contact.
The question of compartmented cushions is briefly dis-cussed. lt appears that an arbitrary cushion stiffness can be
achieved by suitable compartmentation with the use of
lateral dividers. But ¡t has to be remembered that a differ-ential pressure in the compartments can increase the wave
resista nce.
When the speed of motion is such that the frequency of wave encounter equals the natural frequency of oscillation. there will he the usual condition of resonance and it may be expected that the motions may then be highly amplified although controlled by the aerodynamic damping of the cushion, even if no hydrodynarnic damping appears to be available in the lowest order If. in addition, the forward
speed and the frequency of encounter combine together in such a manner that their product is numerically equal to one-quarter of the acceleration due to gravity, a singularity of the potential of the water may arise and under these conditions of "double resonance", an adverse performance of the hovercraft may perhaps be anticipated.
Vhen the theoretical results presented in this study are confirmed (or corrected) by towing tank tests on hovercraft models or by full-scale trials of operational hovercraft, it may be possible for the hovercraft designer to optimise the craft parameters including the pressure distribution in the cushion in order to improve the performance of the craft. The body plan of a conventional displacement vessel is very carefully selected to suit the service conditions. In a similar manner the hull form of the hovercraft cushion
can be optimised by the use of lateral dividers and the introduction of auxiliary flows within the cushion. The
surge, heave and pitch accelerations will combine together in different forms at various locations in the hovercraft to determine the resultant acceleration at that point which is very vital to passenger comfort. This can be calculated from the results presented in this study which relate,
how-ahhiisv thi l,i
iii,iilr.IIilI,
iit'.Iit'íconìiìteiida hie motive ¡ nue which, iii thuc pic.ciIt Clin
text, tends ti) cm ca Le tite issue. Seeing Ihia t from (lue
year dot i flow no sa 1mg hydrofoil technology has
cxi . it follows that if tite boys arc Io he deprived of
e available knowledge they will take almost the same s an of time to get sailing and we could he faced with a kin f "travel Io I/te nearest star" proposition! How to live for '00 years (with travel at the speed of light)?
The aim is to se for a compromise where loud acclaim
is accorded to the said e -'i endahle motive but where the
boys really get up steam only r the first sailing craft
has been achieved by the plan of t " ortest distance between two points."
Hovercraft Research at the University of Southampton (Continued
frotti page 27)ever, to regular waves. The actual seaway is seldom regular and it is well known from towing tank tests on models and from full-scale trials that the responses are less severe in an irregular seaway. An upper limit to conditions in actual operation may therefore be considered to have been
de-rived and, if so, the study will have its useful practical
applications.
References
I. Muunv, T. K. S. Sorne Preliminary Notes on the Wave Damping and Wave Resistance of a Hovercraft Pitching and Heaving over Water (including Virtual Mass and Virtual Movement of Inertia). University of Southampton,
AASU Report No 271, September 1967 (54 pages, includ-ing four appendices).
i'slURmì, T. K. S. The Induced Wave Formation and the Wave Damping of a Hovercraft in Heaving Motion at Zero Speed Ahead over Calm Water. University of
South-am piouz, Department of A eronauutics and Astronautics, Technical Note No 2/67. 1967 (15 pages).
Muri-w, T. K. S. Statistical Properties o! the Motions of
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4 . Musnmy, T. K. S. The Wave Resistance of a Drifting
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4 figures).
MURTiiY. T. K. S. The Wave Resistance of a Triangular Hovercraft Cushion. AASU Report No 292, April 1969
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MURfliY, T. K. S. The \Vave Resistance of a Sidewall Hovercraft. Catamarans and Trimarans. AASU Report No 296, 1969 (15 pages; 6 figures).
Mutmmy, T. K. S. The "Hull Form" of a Hovercraft
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3 figures).
MURTHY. T. K. S. The Static Depression of a Hovercraft
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MURTHY. T. K. S. On the Determination of the
Hover-Height cf a Hovercraft over Water. AASU Report No
298, August 1969 (33 pages. including I appendix).
Mwsmy, T. K. S. A Linearised Potential Flow Theory
for the Motions of a Hovercraft in a Seaway. AASU
Report No 299, June 1970 (240 pages, including S append--ices; 12 figures).
