Seakeeping Characteristics of Surface Effect Ships

In Celebration of The Republic of Indonesia's 50th Anniversary

REGIONAL MARTME CONFERENCE INDONESIA 1995

Developing Efficient Maritime industries within a Sustainable Marine Environment"

CONFERENCE & EXHIBITION

November 7- B, 1995 BPP TEKNOLOGI Building II, Jakarta Indonesia

SESSION B

Seakeeping Characteristics of

Surface Effect Ships

By

Prof. DR. -Ing. Heinrich Soeding

University of Hamburg

Germany

Organised by

Himpunan Ahli Teknologl Maritim Indonesia (IIATMI) The Association of Indonesian Maritime Engineers

and

Indo-PR

Public Relafio,ss

TCHSCE UVRSTE1T

taboratorium voor Scheepshydromochanica &zchlof Mekelweg Z 2628 t) Dettt seL 015 7FGß7 F 015 4B163

Seakeeping Characteristics of Surface Effect Ships

Heinrich Söding

Institut für Schiffbau, Lmmersieth 90, D 22305 Hamburg

Abstract

The effects of air cushion, fans and skirts on the motions of SESs in waves is

discussed qiaJitatively. A comprehensive method to compute motions and loads

of SES in waves is described. Its results are compared with exciting forces of an isolated air cushion model measured by Blume (1995). Further, computed and

measured motions of a real craft in natural waves (Ehrenberg 1995) are compared. The sensitivity of heave and pitch motions on various cushion parameters is shown.

A comparison between a monohull and a corresponding SES demonstrates the

superior seakeeping characteristics of the SES.

Fundamentals of seakeeping of Surface Effect Ships

In a typical Surface Effect Ship (SES; air cushion catamaran; Fig. 1) about

80% of the ship's weight is carried by the pressure within the air cushion between the two hulls; the rest is carried mostly by the buoyancy of the hulls, and a small

part by dynamic lift of the hulls like in a planing craft. The cushion pressure

corresponds, roughly, to about 1/2 m water column. Air escape at the bow is

minimized by an inclined front skirt: a membrane of fiber-reinforced rubber, pulled back by a number of triangular membranes arranged parallel to the midship plane.

At the stern, a bag inflated by a slight (5 to 10 cm water column) over-pressure

relative to the cushion pressure (Fig. 2) seals the gap between water surface,

wetdeck and side hulls. The purpose of the cushion is to reduce the resistance

and to improve the seakeeping of the ship.

In a rigid ship the relative motion between hull and waves generates pressure

forces on the hull which are largest at the bow, causing strong pitch motions. In an SES, on the other hand, the wave motion causes ship motions mostly by changing

the cushion volume between water surface and wet deck. This 'pumping action'

of the waves causes pressure changes which are nearly uniform within the whole cushion, except for short head waves which may cause longitudinal pressure waves within the cushion (so-called cobble-stone motion like in a truck driving on cobble

stones).

The nearly uniform cushion pressure oscillations due to wave pumping cause

mostly heave, no severe pitch motions. Small pitch motions are induced mainly by the change in cushion length due to varying immersion of the front, slanted skirt,

Fig. 1. Bottom view of an SES

by differences in longitudinal position between the cushion centre and the mass centre of gravity, and by forces transferred between aft bag and water surface.

The more important heave acceleration is caused mainly by cushion pressure

variations. The latter are

minimized by using fans for cushion air supply which

allow strong flow changes through the fans and even back-flow without strong pressure changes, i.e. fans with aflat pressure - flow rate curve, large cross section

and sma.11 length

of the air duct (to

decrease air mass effects). Further, most

SES seek to decrease cushion pressure changes by a ride-control system which

opens and closes valves to allow air escape depending on cushion pressure or ship acceleration. The effect of ride-control systems on motion reduction is, however,

relatively small, and

it has to be paid

for by smaller average cushion pressure,

causing deeper immersion and thus speed reductions, or additional propulsion and/or cushion fan power.

Even for constant cushion pressure, cushion force variations and thus heave

(and pitch) motions are induced by variations ofthe cushion length due tovarying immersion of the front skirt. These cushion length variations could be eliminated

by arranging the front skirt vertically instead of obliquely. However, this reduces

the longitudinal (trim) stability of the hull substantially.

If front or back skirt or the keel of the side hulls emerge from the water, cushion

air escapes, causing a pressure drop, vertical acceleration and speed reduction.

Thus the lower end of the front and back skirts should allow vertical motions to follow the water .surface, which changes its height relative to the ship in waves. This requires that thefront skirt is longer than necessary to reach the water surface in its mean position. For an SES in waves with speed ahead, the lower end of the

front skirt will bend backwards at the water surface. The aft skirt (bag) should,

typically touch the water surface, having a shape similar to a car tire on a road

(Fig. 3). Due to the roughness of the water surface, air will escape under the skirts

(mainly the aft skirt) even if the skirt touches the water surface. If the bag does

not touch the water surface, in case the water surface moves down relative to the

ship there will occur a cushion pressure drop due to an increased gap between

constant inner bag pressure, will then move the bag downward to close the gap

again; however, this occurs only after a

cushion pressucured,

which should

be avoided for reasons of speed and ride comfort. Thus, the normal operating

condition of the aft skirt should include a substantial touch length.

Because air is compressible, the air cushion behaves like a spring carrying the ship's weight over the water surface. If the frequency of encounter between ship and waves is similar to the eigenfrequency of the spring-mass system, large heave amplitudes occur. Typically this is the case for wave lengths ofabout half the ship's length and frequencies of i to 2 Hertz. Forhigher encounter frequencies additional

resonances occur, e.g. the above-mentioned longitudinal pressu1e waves.

The foregoing remarks show that relatively small changes in skirt design, draft,

trim condition and fans can change the motions of SES in waves substantially.

Thus a large numberof influences have to be taken into account to obtain realistic motion predictions of SES. Early computer programs for such predictions put main emphasis on nonlinear effects of the waves, but neglected many important linear effects, especially the skirt deformations. My prediction method, which is

used for a number of projects by different German shipyards and consultants, on

the other hand, deals with ail the above mentioned details quite elaborately, but

it disregards all influences which depend nonlinearly on wave height. A method

which is both nonlinear and detailed is not yet known.

Basis of the method

The method is an extension of the SEDOS program (Soding 1988). lt computes 6 degrees of freedom motions of twin hulls (SWATHs and katamarans), relative motions and sectional loads in hulls and bridge (connecting superstructure), using

strip theory to determine hull forces. Added mass, damping and exciting forces

are determined by a close-fit Rankine source method. Hull interaction is taken into account but turned out to be negligible for craft with speed ahead (F;, > 0.2). Forces on foils are included using half-empirical lift coefficients, the incident flow following from ship and wave motions including radiation and diffraction waves of both hulls. Schellin and Papanikolaou (1991) and Blume and Söding (1993)

showed that the results compare well both with model experiments and with 3d

calculations. In fact, a carefully developed strip method seems, at the moment, not surpassed by any other method with respect to accuracy for motions of high-speed craft which are always very slender.

In the following, extensions of this method to deal with SES are elaborated. They assume:

bag fan

cushion fan

ride-control valve

Fig. 2. Idealization of air cushion and skirts

- The

front skirt is a transverse slanted membrane. ii

is jflxibIe under

cushion pressure variations, but it is bent backwards, without inducing sub-stantial forces on water or boat, if the water surface is higher than the lower

edge of the front skirt.

- The aft

skirt is a bag consisting of an outer flexible membrane and n O

inner membranes which pull the outer membrane inward, subdividing it into

n + i lobes.

The aft skirt is filled by a separate fan drawing air from the cushion or from the atmosphere.

Air is pumped into the cushion by one or several fans with known stationary and instationary pressure/volumeflow relation.

- Cushion

air escapes only under the front and back skirts and through

ride-control valves.

The ratio of air loss under the front and back skirt is a given input value

('balance factor' /3). /3 may depend on the wave amplitude and on the trim

condition of the vessel.

- An

arbitrary number of ride control valves allows air escape through a cross section area ARC which, in regular waves, oscillates sinusoidally around a mean value. There is a known amplitude ratio and phasedifference between ARC and the vertical acceleration at the location of the respective valve.

The following deals with SES in regular small-amplitude waves of arbitrary

direction. From the transfer functions found in this way, the behaviour in natural

seaways can be determined in the usual statistical manner. At first, different

sub-problems are described in a logical order which, however, differs from the order (given later) in which the computations are performed.

In the following, amplitudes are meant to be complex numbers indicating real amplitude and phase of an oscillation.

Cushion pressure

Stationary cushion air flow

The cushion is subdivided into elements by transverse sections (Fig. 2). Zero-length sections are provided for. fans or ride-control valves. In way of the back

skirt short elements are generated automatically such that the cross section varies moderately (factor 0.65) within each element. The flow is treated one-dimensional (lengthwise) by considering mean values over the cushion element crc,ss-sectious. The mass conservation and Bernoulli's equation (for incompressible fluid) are

dis-cretized in the typical finite-difference manner. To solve the resui:ting equation

system, a simple forward sweep from element to element followed by a backward sweep is performed, giving as a result the stationary air velocity and pressure at the ends of each element. These are necessary for determining the mean shape of

the aft skirt and because they interact with the time-harmonic air motion. The

outflow at both ends of the cushion determines also the (time-averaged) gap size under front and back skirt.

Time-harmonic cushion air flow

Again a one-dimensional (lengthwise) flow is determined, using the same

ele-ment subdivision of the cushion. Equations to be satisfied are the mass conser-vation (for a compressible gas) and the (incompressible instationary) Bernoulli equation. The adiabatic state equation is used to relate air pressure to density.

A third group of equations relates the periodical changes of cushion cross-sections

(due to motions of ship, aft skirt and water surface) to pressure oscillations (see later). At the minimum gap between aft skirt and wate' surface, flow separation from the skirt is assumed; thus the pressure amplitude is zero there. The

bound-ary condition at the front end of the cushion (lower end of the front skirt) relates

pressure to outflow (and thus to mean air velocity) at the forward end of the first cushion element, considering both the periodic flow through the gap under the front skirt and the in- and outflow to the closed volume above the oblique front

skirt.

The resulting linear system of 3n + 3 equations (for ri cushion elements) is solved by Gauß's algorithm. Results are the complex amplitudes of air pressure,

of lengthwise air velocity, and of cushion cross-section at the ends of each element.

Aft skirt (bag)

Mean bag shape

Let us assume that the bag has n + i lobes and n inner membranes at which the outer membrane is pulled inside. The outer membrane tension is constant

Fig. 3. Bag shapes of model _cushion nonlinear system of equations is solved iteratively, using _{a standard routine, for} the following unknowns: a) n+1 outer membrane tensions; b) n directions (slopes) of the inner membranes. Two kinds _{of equations have}

io be satisfied: a) The outer membrane tension is related _{to the outer membrane curvature and the}

pressure

difference inside-outside (assumed _{to be known). The curvature distribution within}

each lobe determines, together _{with the outer membrane}

length f the

_{be, he}

distance of its endpoints. This _{distance must coincide with}

the distance between

the end points of the inner _{membranes and the two fixed}

end points of the outer

membrane. The position of the endpoints of the inner membranes follow from the membrane directions and the _{position of the fixpoirkts}

of the inner membranes. b)

Where an inner membrane is attached _{to the outer meniTbrane, the components}

normal to the inner membrane of the two outer membrane tensions must cancel.

Normally the lowest lobe will _{touch the water surface. This does not. contradict}

to the assumption that cushion

_{air flows out between}

water surface and bag,

because the water surface is rough, _{allowing simultaneously air outflow and the}

transfer of forces between water _{and bag. Within the 'touch area' between}

water surface and bag the bag has, approximately, no curvature. This corresponds tozero

pressure difference between inside and. outside. _{Thus, where in a previous solution}

the bag extends below the water _{surface, zero}

pressure difference is assumed for

the next iteration.

For the parts of the bag in front of the _{'touch area' the}

outer (cushion) pressure depends on the stationary cushion air flow and thus _{on the bag shape. Therefore} the nonlinear equation system is solved repeatedly, updating also _{the outer}

pres-sure on the bag in front of the 'touch area'. _{Fig. 3 shows examples}

of stationary

bag shapes determined in this way.

Periodical bag ¡notion

The outer bag membrane (as seen in a longitudinal cut) is _{subdivided into n}

approximately straight elements. A linear system of equations is established for the following unknowns: a) longitudinal and vertical coordinates _{of the endpoints of} each element (2n - 2 unknowns). b) n outer membrane tensions. _{(Here membrane} tensions are not constant within each lobe.)

5 kinds (a to e) of linear equations are to be satisfied. _{Considering first n}

element endpoint which is not endpoint of a lobe, motion equations for the two

half-elements at both sides of this endpoint are established: a) motion equation for the outer membrane mass in tangential direction. b) motion _{equation for the outer} membrane mass and the 'added air mass' in normal direction. _{The thickness of the}

'added air mass' is estimated. Considering lobe endpoints and the adjoining two

half-elements, we have c) a motion equation for the membrane mass in a direction

normal to the inner membrane. Here a part of the

inner membrane mass and

its added air mass must be included. Finally the following relations are applied

in linearized form: d) The distance between adjacent element endpoints must

be equal to the known length of the outer membrane element. e) The distance

between a lobe endpoint and the fixpoint of the inner membrane must be equal to the known inner membrane length.

As excitations for bag oscillations, unit outside pressure amplitudes at each pair of hall-elements around element endpoints are assumed. Thus the equation system

is solved for ri - i right-hand sides. For each solution the bag volume amplitude

is also determined.

Up to this point the interior bag pressure was assumed constant in time and

space, giving n - i 'Solutions O'. Now the results are corrected for an inside

pres-sure oscillation assumed to be uniform within the bag. Because inside pressure variations and negative outside pressure variations have the same (linearized)

ef-fect on bag shape, bag oscillations due to a uniform inside pressure variation of

amplitude i can be superimposed from the previous results forall localized outside

pressure oscillations, giving 'Solution 1'.

We consider now the mass conservation equation of total air volume inside the bag, which involves air inflow from the cushion through the channel and the aft

skirt fan, the bag volume change and the outflow through openings in the aft

skirt (mostly between outer membrane and side walls). This gives a (linearized)

relation between inside pressure amplitude, bag volume amplitude and cushion

pressure amplitude at the

channel inlet leading to the bag fan. This relation

is used to establish a superposition of 'Solutions O' with 'Solution 1' to account

for outside pressure variations accompanied by the correct, corresponding inner

pressure variations. These 'Solutions 2' are determined for n - i localized pressure

oscillations on the outer membrane and for a pressure oscillation at the bag fan

inlet. Finally, for each of these solutions (comprising the and z amplitudes

of the outer membrane element endpoints) the vertical bag motion at fixed (not

oscillating) longitudinal coordinates is determined, because this information is

required to couple the bag motion computation to the periodical cushion pressure computation.

Water surface deformation within the cushion

Mean position and oscillations of the water surface within the cushion should be known to determine cushion pressure amplitudes and cushion-dependent forces

1

3

-Fig. 4. Water surface deformation

due to a sudden pressure increase Ap travelling with speed u

Stationary waves due to stationary cushion ptessui

The case of vanishing or very low forward speed U is excluded. Things are

simplified by assuming a 2-dimensional flow in vertical longitudinal planes between

and under the two hulls. The flow potential is modelled as a superposition of the uniform flow potential Ux and Rankine (logarithmic) sources 2h above the free surface, where h is the discretization length. This satisfies automatically Lapace's equation and the large depth condition (velocity -k O). The radiation condition (no waves in front of the disturbance) is satisfied by the well-known method (Jensen, Sding and Mi 1986) of shifting sources relative to collocation

points by h backward. So only the free-surface condition

U7çrx

-

9Ç'z - U = O (1)

has to be satisfied numerically on the mean free surface z = 0. For the pressure p a unit step function is assumed. This gives results plotted in nondimensional form (independent on further parameters) in Fig. 4. For an SES a positive pressure step at the front end of the cushion is combined with a negative one at the aft end. The

aft end pressure drop must be taken into account even if one is interested only in

results within the cushion, because the non-wavy near field of the pressure drop

extends a considerable length upstream.

The higher pressure within the 'touch area' of the aft bag can be neglected

because the influence at the front and aft end of the touch area nearly cancel due to the high Froude number with respect to touch length.

Oscillating waves due to cushion pressure oscillations

Like for the stationary waves, a 2-d Rankine source model was used to

sat-isfy numerically the combined linearized free-surface boundary condition for the amplitude of the flow potential:

(iw. - U-)

_-

+ (iw. - U-) = 0.

(2)

Here the condition is satisfied not at collocation points, but in the average over

intervals between adjacent discretization points (typically 50 to 100) on z = O. The

by a backward shift of sources relative to the free-surface intervals, here by h/2. For r < 1/4 the same procedure is applied because results seemed not unrealistic; however, it is not clear whether the correct radiation condition is satisfied in this case. Due to the small influcence of waves induced by cushion pressure oscillations, the question seems hardly important.

The procedure is applied for a small field with unit pressure amplitude (being discretized much finer than its surroundings) to derive the relation between

pres-sure amplitudes at a point O to oscillations at points P. For later use the curve is

interpolated over f,he distance OP.

The water surface oscillation due to the incident wave is the most important

influence on cushion pressure oscillations. It is simply the sinusoidal wave motion. averaged over the breadth of the cushion.

Radiation waves (due to hull motions) and diffraction waves (due to the inter-action of incoming waves with the non-oscillating hulls) are held to be negligible; it would be no problem to include them if required.

Oscillation of cushion cross-section area

An equation for the amplitudes  of the cushion cross-section area at the ends of all cushion elements is required to determine cushion pressure amplitudes. Â

is combined from the following contributions: heave; pitch (other ship motions

have no effect on Â); incident wave; water surface motion due to cushion pressure

oscillations; bag motion due to cushion pressure oscillation at the hag and at the bag fan inlet. Nonlinear effects are approximated by applying the balance factor

3.

Within the 'touch area' of the aft hag, owing to the large 'stiffness' of the water surface for high speed of the craft and the 'softness' of the bag, amplitudes of the mean gap width between water and bag are assumed to be zero, and the motion of water surface and bag are assumed to be equal. Thus in the 'touch area' the

only unknown is the outside bag pressure (averaged over roughness elements of the

water surface). The latter is quite important both for craft forces and moments

and for bag motion in other bag areas. Thus, for the 'touch area' the air mass

conservation and Bernoulli's equation are substituted by equations  O and

longitudinal cushion air speed y = O (because in this region r is not coupled to other unknowns and thus arbitrary). This gives the correct outside bag pressure also within the 'touch area'.

Determination of cushion forces on the craft

To avoid missing data or unnecessary interaction of the above-listed problems, they are solved in the following order: Time-averaged water surface in the cushion; time-averaged bag shape and time-averaged cushion air motion (combined im an iteration); oscillatory bag motion for unit force loads at different positions; oscilla-tory water surface motion for a unit force amplitude; oscillaoscilla-tory cushion pressure distribution for three cases: unit heave amplitude, no waves; unit pitch amplitude,

no waves; and unit wave, no craft motions. Results are cushion pressure

ampli-tudes over cushion length and relative motiön. betwep craft and water surface

within the cushion for the above three cases.

To determine oscillatory forces on the vessel due to cushion pressure, the

pres-sure is integrated over the water surface within the cushion, including the water

pressure in the bag touch area.

The cushion air is, thus, treated as part of the

craft. Force contributions stem from the oscillatory pressure acting on the

time-averaged water surface and from the stationary pressure acting on the oscillating

water surface. Forces are first determined in a ship-fixed coordinate system and then transformed to the inertial system. Results depend not only on heave and

pitch, but on motions in all 6 degrees of freedom.

A special contribution stems from the obliqueness of the forward skirt: if the water surface is higher than the lower edge of the skirt, the forward integration

length for cushion pressure shifts forward, giving additional forces and moments. For the aft skirt no such variation of effective cushion length is assumed.

Oscillatory waves within the cushion have effect also on the side hull forces. To account for this effect, the waves are assumed to propagate (in a coordinate system not participating in the ship's forward speed) in transverse direction (i =

+900) like radiation waves produced by each hull and influencing the other hull.

Sectional forces due to these waves are the product ab of a = wave amplitude at

the hull section, and b = excitation coefficient of the section for transverse waves of encounter frequency.

All these cushion-connected forces due to unit motions are added to the matrix of motion-induced hull forces in katamarans without air cushion, while the forc'cs

due to a unit wave amplitude are added to the excitation vector of the

6-degree-of-freedom motion equation.

Comparison with model experiments

Blume 1995 measured exciting forces F and P and pitch moment M in head

waves on a model cushion (length L = 5.05 m) which had vertical plates instead of twin hulls as side boundaries. Front and back skirt

Fig. 5. Nondimensional longitudinal and vertical exciting wave force .nd pitch moment over wave length/cushion iengh. DoLs;

urcmcnt cf Bltr'

(1995,) circles: computation using the experimental data for cushion pressure, bag

pres-sure and cushion fan flow rate; asterisks: computation using pressures and fan

rate as in experiments for À/L 1.52.

(bag) were conventional except that the bag fantook air not from the cushion but

from outside. The model was rigidly fixed to the tank carriage. Fig. 5 compares

some ofBlume's results (black dots) for 5 rn/s model speed and the smallest of his

cushion fan rates with own calculations for the same conditions (circles). It turned

out that the results are very sensitive to mean water surface height at the skirts

and to the mean pressure difference between bag and cushion. In Fig. 5, asterisks

give computed results for a mean pressuredifference of 19 Pa (corresponding to the model conditions for )/L = 1.52), whereas in the experiments the nican pressure difference was, e.g., 26 Pa for À/L 2.03. The large effect of this difference is

shown in Fig. 5 as difference between circle and asterisk symbols at this wave

length.

The immersion of the skirts depends on the wave field generated by the cushion.

Using Fig. 4, it was estimated that the lower edge of the front skirt doe% not

emerge from the water even in the wave trough. Because in model experiments,in

front of the model the water surface is quite smooth, it was assumed that cushion

air escapes only at

the aft skirt (ß = 0).

Again using Fig. 4, the water surface

depression at the aft skirt was estimated to be0.0l SL below the undisturbed water surface. A value of 0.02L was used for computations of Fig. 5. For a wave length ratio A/L = 2.03, Fig. 6 shows resultsfor various values of this depression between

O and 0.025L. Especially the pitch exciting moment is very sensitive to the relative

1.0 05 F1/pgLB(A

.

0

00*

₀

**

101

5-o

F/pgLBA

*0 * * I s I s o f * _{* s} 0.4 o 0.2 1 2

3)/L

1 2

3)/L

M9/pgL2B Fig. 6. Exciting vertical

force and pitch morne at

depending on the nondi-.

mensional time-averaged

masured 3

depression of the

water

0 surface at the bag.

0.01 0.02

A/L

0.01 0.02

(/L

F/pgLB(A 10 0.4 measured o o o 0 0 o _0.2

-height between water surface and bag, which is decisive for

the 'touch length',

because for certain conditions the pitch moment

generated by the front and aft

skirt cancel.

Considering this extreme sensitivity, and taking into account

that some other

input values for the calculations could only roughly

be estimated (e.g. the dynamic

pressure/flow rate

ratio of the

fans), the coincidence between

calculations and

measurements seems reasonable except for longitudinal force amplitudes

which aregenerally larger in the measurements than computed.

Regarding the assumed linear increase of exciting fcrce5 with wave

amplitude, the measurements show that this assumption is not

unreasonable at least up to

moderate wave steepness 2A/A for a ratio wave length/cushion length

.X/L = 1.52

and .5 rn/s speed:

Comparison with

full-scale measurements

Blohm und Voß shipyard undertook measuring

trips with their

SES

Mekat-Corsair in different wave conditions;

simultaneously the wave spectrum was mea-sured (Ehrenberg 1995). Figs. 7 and 8 show spectra of vertical accelerations

at the forward perpendicular in head waves, both as measured

and as computed by

the above-described method. They will be further evaluated to fix the reasons

of

the differences. E.g. the difference near 0.2

Hz in Fig. 7 may be caused by the

wave-rider buoy being influenced by the wave system of the

SES or anothership,

or by a swell having a direction different from that of the

main seaway. In view

of the many uncertainties in measurements like this, and

comparing these results with other publications, Ithink the coincidence is encouraging.

Motion sensitivity study for an

existing craft

Results of non-dimensional heave transfer function ZA/CA

(full line) and pitch

transfer function OA/ICA (broken line) are shown in the following

figures. They

hold for an SES similar to the Blohm&Voss-bullt 29 rn long "Corsair" (Anon.

1989) without operation of ride-control valves. The abscissa

gives wave length

over ship lengh; left, middle and right graphs hold for bow, side

and stern waves respectively. Results for standard assumptions (speed 50 knots;

cushion pressure 6 kPa, bag pressure 8 kPa higher than atmospheric pressure;

cushion fan rate 55

2A/.\

0.0078 0.0130 0.0237

F/PgLB(A

0.58 0.56 0.46

F/pgLB(A

5.57 6.04 5.91

I 0.8 0.6 0.4 0.2 O S(max)=0.062 m2s H1 0.33 m

I

01 0.2

0.3 04 05 06

Wave Frequency [Hz)

Fig. 7. Comparison of power spectral

density (PSD) over encounter frequency (in Hz) measured on a 35m SES in head waves (Ehrenberg 1995), with computed

spectra (line with dots), for vertical ac-celeration at the forward perpendicular (right). Left: Wave spectrum

T .4 .2 as 06 04 1.6 0.8 0.6 0.4 0.2

Fig. 8. Comparison of power spectral density (PSD) over wave frequency (upper figures; seaway; in Hz) or encounter frequency (lower figures; vertical acceleration at FP; in Hz) measured on a35m SES in two head seaways (Ehrenberg 1995) with computed spectra (line with dots)

4 1,1 m 01 0.2

03 04 05 06

1.2 0.8 0.8 0.4 0.2 10 8 6 4 2 6 7 a 0 1 2 3 4 5 00 _{0.5 1}

₁₅

₂

₂₅

12 0.8 0.6 04

Fig.lO. Cushion air escape only under back skirt (ß = 0.0)

01

02 03 04 05 06

H, 0975 m 0 2 3 4 5 13 7 11' 1.4 1.2 0.3 0.13 0.6 0.5 0.4 0.2 o O

iii''

0 I o t O I 2 3 4 5 6 7 ß 1 2 3 4 5 6 7 5 1 2 3 4 5 6 7

Fig. 9. Noudimensional heave (full) and pitch (broken line) transfer function of

an SES similar to the "Corsair" in (from left to right) head, side and stern waves;

standard case (u 50 kuots, ß = 0.2, bag pressure 8 kPa)

0.8

0.6

0.4

16 1.4 ¶.2 0.8 0.6 0.4 0.2 o o 1.4 1.2 0.8 0.6 0.4 0.2 o 0

Fig.12. Speed 25 knots

2 3 6 7 8 12 0.8 0.6 0.4 02 o 1.2 0.8 0.6 0.4

Fig. 13. Touch length of bag assumed to be zero

1 2 3 4 5 6

Fig. 15. Double cushion fan pumping rate

0.2 o 1.2 0.8 06 0.4 0.2 ...-o

Fig.. 16. 1/3 of standardslope of fan pressure versus flow rate curve

3 4 5 6 7 8 08 o 6 04 0.2 o 1.2 r r . 08 0.6 o 1.2 'r- r T t r r / _... 1'... - - --O I 2 3 4 6 7 0 1 2 3 4

5 67

1.2 1.2 0.8 0.8 _0.6 .: 0.4 02 2 3 4 5 6 7 8 2 3 4 5 6 7 r r. r 1.4 0.8 0.6 0O

Fig.11. Most cushion air escape '.2

under front skirt (j3 = 0.8)

r _0,9 0.8 0.7 06 0.5

____

-2 3 4 5 S 7 8 0.9 08 0.7 0.6 0.5 0.4 0.3 0.2 0.1 o 2 3 4 5 6 7 8 09 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 o 8 1 0.8 0.6 0.4 0.2 0 o i 2 3 4 14. Touch length

Fig. zero and bag pressure reduced to 7 kPa

2 3 4 5 S 7 8 1.4 1.2 0.8 0.6 0.4 0.2 o O 8 0 1 2

3,4

1 2 3 4 5 6 7

r

m3/s; balance factor ¡9 = 0.2) are shown in Fig. 9. The same case, but neglecting

the periodical water surface deformation due to cushion pressure oscillations, gave nondimensional transfer functions differing by only, at maximum, 0.02.

Figs. 10 and 11, holding for ¡9 = 0.0 (air escape only at back skirt) and 0.8

respectively, demonstrate the substantial influence of this parameter which is in-fluenced by the (speed-dependent) trim condition of the craft and by the relative height of the lower edge of front and bag skirt; it may depend also on the roughness

of the water surface in front of the craft. Results for ¡3 = 0.5 were found to be

between those for 0.2 and 0.8 as expected.

For half standard ship speed (25 knots; Fig. 12), the steep

rise of transfer

functions with wave length is shifted to shorter wavelengths in head waves and

to longer wavelengths in stern waves. Fig. 13 (to be compared with the standard case Fig. 9) shows the moderate effect of decreasing the standard 'touch length' of the bag to zero. Fig. 14 combines this effect with a decrease of time-averaged bag

pressure to 7 instead of 8 kPa. 7 kPa bag pressure, while keeping the standard

'touch length' and 6 kPa cushion pressure, turned out to be impossible without

unreasonable upward deformation of the bag. Finally, Figs. 15 (doubled cushion

fan rate) and 16 (1/3 standard slope of pressure curve over cushion fan flow rate)

demonstrate the small effect of these changes, again contrary to the strong effect of these parameters on excitation forces and moments found in computations for the case of the model experiments.

Comparison between an SES and a rnonohull ship

To compare the seakeeping of SES with fast monohull ships, a monohull and

an SES were designed by Blohm and Voß shipyard with equal mass (loot), length (30m) and speed (3Okn). Vertical accelerations at the bridge were calculated for both ships in seways of different direction amid height. They were evaluated

us-ing the ISO standard 2631 both for vibration-induced human fatigue (maximum

sensitivity between 4 and 8 Hertz) and for motion sickness (maximum sensitivity

below 0.32 Hertz). Results (Figs. 17, 18) show that both with respect to motion

sickness and vibration fatigue the SES is superior: The tolerance limits given in

the standard are exceeded in waves of lower significant height for the monohull than for the SES.

References

Blume, P. (1995), Exciting forces caused by regular waves acting on cushion and

seals of an SES, Proc. FAST 95

Blume, P. and Söding, H. (1993), Numerical simulation and validation for SWATH

Ehrenberg, 11.-D., Linear calculation of seakeeping properties of SES, validation

with tank tests and measurements of the full-scale version, Proc. FAST 95

Jensen, G., Söding, H. and Mi (1986), Z.-X., Rankine source methods for

nu-merical solutions of the steady wave resistance problem, 16th Symp. on Naval Hydrodynamics, Berkeley

Scheffin, T.E. and Papanikolaou, A. (1991), Prediction of seakeeping performance of a SWATH ship and comparison with measurements, Proc. FAST 91

SZding, H. (1988), Computation of motions and loads of SWATHs and katamarans

in a seaway (in German), report 483 Institut für Schiffbau Hamburg

Anon. (1989), Air cushion katamaran SES "Corsair", a new kind of high speed

craft (in German), Hansa 126, 800-801 (similar: Schiff und Hafen 4/1989, 24-25)

1800 1800 2700 0 900 o.

Fig. 17. Limits of vibration-induced fatique (for 2hexposition time) in seaways of different direction (00 = stern sea) and significant height at the bridge of a 35m

SES (left) and a corresponding monohull (right) at 30 kn (Ehrenberg 1995)

1800 1600

a

Fig. 18. Limits of motion sickness (for 2h exposition time) in seaways ofdifferent direction (0° = stern sea) and significant height atthe bridge of a 35m SES (left) and a corresponding monohull (right) at 30 kn (Ehrenberg 1995)

900

075 i