Motions and Added Resistance due to Waves of Surface Effect Ships (SES)

to Waves of Surface Effect Ships

J . Moulijn

Report 1169-P October 1998

Symposium on Fluid Dynamics Problems of

Veiiicles Operating near or in the Air-Sea

Interface, to be held at the Royal Netherlands

Academy of Sciences (KNAW), Amsterdam

TU Delft

Delft University of Technology

Faculty of Mechanical Engineering and Marine Technology Ship Hydromechanics Laboratory

AC

/323

(AVDTP/9

NORTH A T L A N T I C T R E A T Y ORGANIZATION

R E S E A R C H AND T E C H N O L O G Y ORGANIZATION

BP 25, 7 RUE ANCELLE, F-92201 NEUILLY-SUR-SEINE CEDEX, FRANCE

RTO MEETING P R O C E E D I N G S 15

Fluid Dynamics Problems of Vehicles Operating

Near or in the Air-Sea Interface

(Problèmes de dynamique des fluides des véhicules évoluant dans ouprès de

1'interface air-mer)

Papers presented and discussions recorded at the RTO Applied Vehicle Technology Panel (AVT) Symposium (organised by the former AGARD Fluid Dynamics Panel), held in Amsterdam, The Netherlands, 5-8 October 1998.

Motions and Added Resistance due to Waves of Suiface Effect Ships

Joost C. M o u l i j n Delft University of Technology Ship Hydromechanics Laboratory

Mekelweg 2 2628CD Delft THE NETHERLANDS

Summary

This paper presents a computational method for motions and added resistance due to waves of Surface Effect Ships. The computed added resistance only includes the added resistance of the air cushion. This added resistance component was believed to be the largest. The results of the computational method are compared to experimen-tal results of M A R I N and to results of new experiments which are carried out at the Ship Hydrodynamics Labo-ratory of Delft University of Technology.

The computed motions and cushion excess pressures agree well with the M A R I N results. The computed added resistance is however much smaller than the added resis-tance that was measured by M A R I N . This discrepancy was the major reason for the new experiments.

The aim of the new experiments is to get insight into the magnitude and origin of added resistance of SESs. The new experiments are still in progress at the time this pa-per had to be delivered. This papa-per presents therefore only some first results of these experiments. The new ex-periments show that the added resistance of the air cush-ion is not large. The new results for added resistance are reasonable agreement with the computational results.

1 Introduction

Up to now Surface Effect Ships (SESs) or air cushion supported catamarans were mainly operating in sheltered waters. In these days however both naval and civil oper-ators show an increasing interest in large SESs sailing in open seas. The seakeeping of m SES is quite different from the seakeeping o f a conventional ship. SESs appe;u-to have a large speed loss when sailing in waves. The design of large SESs requires therefore an accurate pre-diction method for inotions and added resistance due to waves.

A Surface Effect Ship is a hybrid of a catamaran and a hovercraft. An air cushion is enclosed by the side-hulls, the deck, the water surface and flexible seals at tlie bow and stern. Figure 1 presents a longitudinal cross section of an SES. Most of an SES's weight is carried by the air cushion. The remainder is carried by the buoyancy of the hulls. Some air will leak from the cushion through gaps under the seals. This leakage flow is compensated by a system of fans. Most SESs have a bag-type stern seal; a bag of flexible material which is pressurized at a slightly higher pressure than the air cushion. The bag is open to the sides where the seal plenum is closed by hulls. One or two internal webs resti-ain the aft side of the bag, thus dividing the bag into two or tiiree lobes. The bow seal of SESs is usually of the finger type; a row of loops of flexible material which are open to the cushion side. Several authors presented studies on motions of Surface Effect Ships. Kaplan and Davis[l] presented one of the first papers on motions of SES. Kaplan et al.[2] devel-oped a non-finear six degree of freedom motion program. Doctors[3] presented an extensive overview of the hydro-dynamics of hovercraft and SES. S0rensen[4], Steen[5] and Ulstein[6] published extensive studies of the high frequent motions of SES; the so called cobblestone

ef-fect. Nakos et al.[7] showed that these high frequent

mo-tions are caused by acoustic resonance of the air inside the cushion. The cobblestone effect causes SESs to have a poor ride quality. The present paper does not deal with the cobblestone effect.

Only very little literature can be found on the topic of added resistance due to waves of SESs. Faltinsen et al.[8] presented a comparative study on the speed loss and operability of a catam£iran and an SES in a seaway. They did not however include the added resistance due to the air cushion. The result of the study is that the SES has a slightly larger speed loss than the catama-ran. Elrrenberg[9] states however that an SES has much less speed loss in waves than a comparable catamaran. Kapsenberg[10] measured a large added resistance due to waves. He also showed that the usual quadratic

rela-Paper presented at the RTO AVT Symposutm on "Fhdd Dynamics Problems of Vehicles Operating near or in the Air-Sea Interface", held in Amsterdam, The Netherlands, 5-8 October 1998, and published in RTO MP-15.

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Figure 1: Longitudinal section of a Surface Effect Ship

tion of added resistance with wave height does not hold for an SES.

The main goal of the present PhD research project is to investigate how one can accurately compute the mo-tions and added resistance due to waves of SESs. This paper presents results of a new computational method for motions and added resistance due to waves of SESs. These results are compared to the results of experiments that were carried out by Kapsenberg[l 1] at M A I ^ N . The computational results are in good agreement with the M A R I N experiments as far as motions and cushion pres-sure are concerned. The large added resistance due to waves that was measured at M A R I N does not however follow from the computations. New experiments have been canied out at the Ship Hydromechtmics Laboratory of Delft University of Technology. These experiments give new insights into to the origin of the added resis-tance due to waves of SES.

The next section presents a description of the new compu-tational method for motions and added resistance due to waves of SESs. Section 3 describes the new experiments that were carried out at Delft University of Technology, Section 4 presents and compares the computational re-sults, the experimental results of M A R I N and some new experimental results.

2 Computational method

This section presents the computational method for mo-tions and added resisUince due to waves of Surface Effect Ships. Up to now the rnethod is only suitable for head and following waves as only heave and pitch motions are considered. The effect of surge motion is neglected. Nev-ertheless most of the theory is presented for six degrees of freedom.

Consider an SES sailing in waves at a forwttfd speed U. The vessel carries out small oscillatory motions which are superimposed to the translatory forward motion. These

small motions are defined by a small translation vec-tor ?7 = {7]i,7]2,V3V ^ small rotation vecvec-tor H =

(774,7?5, r/s)"^. The six small displacements, r / i , . . . , r^e

(i.e. surge, sway, heave, roU, pitch and yaw displacement) are the achial unknown motions that have to be solved. Next to these unknowns two additional unknowns occur: the excess pressure in the cushion plenum, pc, and the excess pressure in the stem seal plenum, ps. The excess pressures are assumed to be constant in space, so acoustic effects of the air inside a plenum cannot be resolved.

2.1 The equations of motion

The motions of the SES are assumed to be small. Then the equations of Euler for the motions of a rigid body can be linearized to the following system of differential equations:

6 ,2

E ^ ^ i ^ l J ^ = ^ i i = i , - - - - 6 (1)

k=l

where Mjk is the is the fc*'' component of the row of the generalized mass matrix, Fi , ^ 2 , ^ 3 are the forces

which acts on the vessel in a;-direction, y-direction, and

2;-direction, and - ^ 4 , ^ 5 , Fe are the moments which act on

the vessel ai-ound tlie x-axis, j/-axis, and ,z-axis. Each force is split up into the following components: a gravi-tational force, a propulsive force, a hydromechanic force, a force due to the air cushion and a force due to the seals. The propulsive force is balanced by fiie resistance of the vessel. The hydromechanic force is computed by means of a three-dimensional panel method. The force due to the air cushion follows from integration of the cushion excess pressure over the deck. The forces due to seals foUow from the appropriate seal models.

2.2 The equations for pc and

Next to the equations of motion two additional equations for the additional unknowns pc and ps have to be

formu-lated. These equations follow from conservation of mass for the air in a plenum and the equation of state of the air in a plenum. The equation of state is taken to be the isenü-opic gïis law. Figure 1 presents the system of plena and the air volume fluxes of an SES. The equations for and Ps read:

one-dimensional analysis leads to good results:

'^P^ (Qdn) _ Q{out)^ _ ^

(2)

Vs dps KiPs + Pa) dt

dVs

where Vc is the air cushion volume, Vs is the stern seal volume, Pa is the ambient pressure and k, is the ratio of specific heats of air; k = Cp/c„ « 1.4. Furthermore

Q("I) ^ ^ g( m ) ^ i^ j i^ i ^ jg jj^e Qf through

the cushion fan find the leakage flow from the stern seal, and Q(°"'' = Q'^°f'^ + q ' f f ^ which is the sum of the leak-age flow under the bow seal and the leakleak-age flow under the stern seal. The cushion volume Vc depends on the heave and pitch displacement of the vessel, the geometry of the seals and the wave height in the air cushion. The stern seal volume K depends on stern seal geometry.

2.3 The fan system

The air volume flux through a fan into a plenum, Qt™) is approximated by the linearized steady fan charac-teristic. Durkin and Luehr[12], Sullivan et id.[13], Masset et al.[14] and Witt[15] show that fans respond in a dyn;unic way to oscillating back pressure. Sulli-van et al.[13] show that flie dynjunic behavior of the fan has a damping effect on the heave motions of a hovering box. Moulijn [16] also showed that the fan has an impor-tant effect on the overall motions of an SES. Nevertheless all computational methods for seakeeping of SES, includ-ing the present method, use static fan characteristics. This is due to the absence of information on dynamic charac-teristics of lift fans.

2.4 Air leakage

Many authors (see for instance Nakos et al.[7], McHenry et al.[17], Masset et al.[14]) consider air leak-age to be important and highly non-linear. Nevertheless, air leakage is often linearized or even neglected. Steen [5] showed the importance of air leakage for the cobblestone effect. Ulstein[6] carried out extensive Jiir leakage com-putations using a non-linear panel method. He found fliat the following formula which follows from a stationary

Q {out) ciAi '2Ap

(3)

where q is flie leakage coefficient which depends on the local geometry of the orifice, Ai is the leakage area, A p is the pressure jump across the orifice and p is the density of air. The leakage areas under the seals follow from flie seal models. The leakage area under a seal is highly non-Unear in the local relative wave height. When the relative wave height at the seal is large, the seal will touch the water surface so the leakage area equals zero. When the relative wave height at the seal becomes smaller a leakage gap wifl occur suddenly, and afterwards grow linearly. This process cannot be captured by a linear formulation.

2.5 The stern seal

This subsection presents a brief descriptions of flie stem seal model. A more complete description can be found in reference [18]. Lee[19], Steen[5] and Masset et al.[20],[14] presented similar seal models. The following assumptions underhe the stern seal model. The model is two-dimensional in a longitudinal plane. This impfies that the wave height is assumed to be con-stant in transverse direction. Therefore the se£il model is most suitable for head and foUowing waves. The gravi-tational and inertial forces that act on the seal canvas aie neglected. Ulstein[6] developed a seal model which in-cludes the inertial forces. He found that inertial effects are important for high frequent inotions. When the seal does not touch flie water surface air will leak from flie cushion under the seal. This air flow wiU result in a dy-namic pressure distribution under flie seal which wiU re-duce the air leakage gap. Lee[19] neglected this pressure distribution. In the present model and in the models of Steen[5] and Masset et al.[20],[14] a simple stationary one-dimensional modeling of the leakage flow is used. The seal canvas is assumed to have no bending stiffness; it only transmits tension.

For a given bag configuration the following parameters determine the bag geometry and the tension in the seal canvas: heave displacement, pitch displacement, cushion excess pressure, seal excess pressure, mean wave height at the seal and mean wave slope at flie seal. When flie bag geometry and tiie tension in the seal canvas are known, the seal volume and seal force can be computed easily. The seal may either touch the water surface or leave a leakage gap. In the bottom case the cushion pressure is larger than the seal pressure, which results in the concave cushion facing part of the seal.

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2.6 The bow seal

The modeling of the finger-type bow seal is much more simple than the modeling of the bag-type stern seal. When the local deck height at the bow is smaller than the height of the seal, the lower part of the fingers is simply bent backwards at the water surface, and no air will es-cape under the seal. When the local deck height is larger than the height of the seal, the seal wiU leave a gap above file water surface, and air wiU escape from the cushion plenum. The bow seal model is also two-dimensional (in a longitudinal plane). Again the me;in wave height and wave slope at the seal are used. The seal is represented by a flat boundary which roughly coincides with the fore-most pai t of the fingers which actually closes the cushion plenum. The part of flie seal that is bent backwards at the water surface is neglected. The frictional forces that act on flie bow seal aie neglected.

2.7 Hydromechanics

This subsection presents a brief description of the solu-fion method for the hydromechanical problem of an SES saiUng in waves. A more elaborate description of the method can be found in reference [21].

The hydromechanical problem is solved by means of a three-dimensional Rankine panel method. The water flow is assumed to be incompressible and non-rotational, so potential flow theory can be used. The boundary condi-tions on the free surface and on the hufls me linearized around the undisturbed flow. This leads to a Kelvin free surface boundary condition which includes some extra terms due to flie presence of the air cushion, and a Neu-mann hufi boundary condition. The hufls and a part of the free surface are paneled with flat quadrilateral pan-els. Each panel has a constant source an dipole distribu-tion. The tangential derivatives of the unknown poten-tial which occur in the free surface boundcU"y condition

follow from analytical differentiation of a bi-quadratic

spfine approximation of the potential. N£ikos[22] also uses tills spline scheme, but he also uses a quadratic sin-gularity distribution on each panel. When the boundary value problem is solved, the pressure and the wave height can be calculated. The hydrodynamic forces which act on the hulls follow from integration of the pressure over the wetted part of the hulls.

The unsteady hydiomechanic problem is solved in the frequency domain, thus avoiding a complicated time step-ping algoritiim and saving much computational time. The motions have to be solved in the time domain because of flie non-linear cushion and seal dynamics. Therefore the tiieory of Cummins[23] and OgUvie[24] is used to

trans-form the frequency domain results of the panel method to file time domain.

2.8 Added resistance due to waves

The added resistance due to waves of a ship is the time averaged resistance of the ship when saifing in a seaway minus the resistance of flie ship when sailing in calm wa-ters at the same speed. For convenience it is henceforth caUed added resistance. Most autiiors consider the added resistance of SESs to be large. Three components which contribute to the added resistance are distinguished:

1. the usual added resistance of the hulls, 2. the added resistance due to sinkage, 3. flie added resistance of the air cushion.

The usual added resistance of flie hulls is caused by flie diffraction of the incident waves and tiie radiation of flie waves due to the motion of the vessel. This added resis-tance component is also experienced by normal ships. It can be computed for instance by the method of Gerritsma and Beukelman[25].

The added resistance due to sinkage is basically an in-crease of the steady resistance of the hufls. When an SES sails in a seaway, the amount of air leakage increases be-cause the ambient waves be-cause large leakage gaps under the seals. This results in a decrease of the mean excess pressure in the air cushion, so a larger part of the SES's weight has to be carried by the buoyancy of the hufls. The draft of the vessel wfll therefore increase, which leads to a greater resistance of the hufls. This greater resistance is parfly caused by an increase of the frictional resistance due to the larger wetted area of the hulls. The rest of it is caused by an increase of the wave making resistance. The resistance of the air cushion follows essentially from the foflowing equation:

R'"'= Pc • {Cb - Cs) • Be (4)

where pc is the cushion excess pressure, Cb is flie wave height at the bow seal, is the wave height at the stem seal and Be is the widfli of the air cushion. Some ex-ü'a terms which account for the momentum of leaking air should also be included. Then the added resistance due to the air cushion follows from:

R'•^^.^ = i?(''«)(m waves) - i?(»")(calni water) (5)

where the over fining denotes that the time averaged value should be used.

The added resistance due to the ah- cushion should be by far the largest contribution to the total added resistance. Only a small pm t of the weight of an SES is cmied by the buoyancy of the hulls. These hulls are usually very slen-der. The usual added resistance of the huUs should there-fore be small. Kapsenberg[10] showed that the added resistance due to sinkage is relatively small too. He in-creased the RPM of the fans in order to compensate for the larger air leakage flow. This resulted in a reduction of the added resistance by only 6 percent. Therefore the major part of the added resistance must be attributed to the air cushion. The present computational method only computes the added resistjmce due to the air cushion. The computational results do not however indicate a large added resistance due to the air cushion (see Section 4). The other components are not likely to be large either. Therefore new model tests have been carried out in order to get more insight into the magnitude and origin of the added resistance of SES. The next section describes the new model tests. Section 4 presents and compares the computational and experimental results.

3 New model experiments

This section presents a description of the new model ex-periments. The new experiments are still in progress at the time tliis paper has to be delivered. Therefore only a first part of the results is included in this paper.

The goal of the new model experiments is to get more insight into the magnitude and origin of the added resis-tance due to waves of Surface Effect Ships. An attempt is made to measure the three added resistance components that were distinguished by Section 2.8: added resistance of the hulls, added resistance due to sinkage and added resistance of the air cushion.

3.1 The model

The model was partly derived from the target vessel of the HYDROSES project, a large collective research project on seakeeping of SES. This enables comparison to the experimental results of Kapsenberg[26] that were car-ried out at M A R I N . These experiments <'ire a pai t of the HYDROSES project. Table 1 presents the basic dimen-sions of the model. This model will be refeired to as DUTSES.

The air cushion plenum and the stern seal plenum are both pressurized by axial fans. The fans are mounted di-rectly on the model. The RPM of the fans is conti oUed by a Computer. This ensures a very stable RPM of the fans.

3.200 m Lc 3.000 m ^plates 0.549 m 0.745 m Be 0.525 m To 0.100 m 220 0.050 m Pc 300 Pa Ps 306 Pa

Table 1: Main dimensions of the DUTSES model

The fans iire kindly on \om from M A R I N .

A flexible membrane is mounted on top of the air cush-ion. This membrane is Ccdled diaphragm. A diaphragm can be used to obtain a correct scaling of the stiffness of the air cushion. Kapsenberg[26] presented a paper on this diaphragm technique. Moulijn [27] also presented a more elaborate discussion on the topic of scaling of air cushion dynamics. In the present experiments the main purpose of the diaphragm is to prevent very large pres-sure amplitudes which might lead to a negative cushion excess pressure. When the cushion excess pressure be-comes negative the seals will collapse, and air from out-side the cushion will flow into the cushion. This is not a very realistic situation, which is effectively removed by the diaphragm.

Two versions of the model are tested. The hulls of tiie first version are very slender; in fact they are only 12mm thick plates. The forces that act on these plates are very smafl (in head and foflowing seas). Therefore the forces that are measured during the testing of this version can be attributed ahnost entu-ely to flie air cushion. This enables a measurement of the added resistance of the arr cushion alone. This version of the model has almost no buoyancy. Therefore it is tested in a captive setup, where the model is connected rigidly to the carriage. Otiierwise tiie model would capsize. This version of the model wifl be refeiTed to as the model with plates.

The second version of the model is equipped with more reahstic hufls. The difference between the results of this version and the version with plates provides an indication of tiie added resistance of the hufls. The second version of the model is also tested in a free sailing setup. An indication of flie added resistance due to sinkage can be obtained from free saiflng cahn water test with a reduced fan RPM. This version of the model wifl be referred to as the model with hufls. The results of the model with hufls are not included in this paper, as the experiments were stifl in progress at the time fliis paper had to be deflvered.

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3.2 Experimental setup

The experiments are carried out at the #1 towing tank of the Ship Hydromechanics Laboratory of Delft University of Technology. This tank is 142m long, 4.22m wide and about 2.30m deep. The carriage is suitable for speeds up to 7m/s. A hydrauhcally driven flap-type wave maker, which can generate both regular and uregular waves, is installed at one end of the tank. The carriage can be equipped with an osciflator for forced oscillation experi-ments.

The model with plates is subject to two types of ments: wave force measurements and osciflation experi-ments. The model with hulls is subject to fliree types of experiments: wave force measurements, oscillation ex-periments and free saiflng exex-periments. During the wave force measurements the model is connected to the car-riage by the two legs of the oscUlator. The forces in the osciflator legs ai^e measured and the model is restrained in it's mean position whfle it is towed in waves. During flie oscfllation experiments the model is also connected to flie carriage by the oscillator legs. Again the forces in the oscillator legs are measured. The model carries out an imposed oscillatory heave or pitch motion whfle it is towed in cdm water. During the free sailing experiments flie model is free in heave and pitch, whfle the model is towed in waves.

During the experunents several variables are measured. During captive experiments the vertical and horizontal forces in the osciflator legs aie measured, while during free saiflng experiments flie heave and pitch displacement and the resistance are measured. Next to this the hori-zontal and vertical seal connection forces are measured. Furflier, the excess pressures in the cushion and stern seal plena, the flow through the fans and the wave height close to flie bow and stern seals are measured. Finally the ref-erence wave is measured.

4 Presentation and comparison of

the results

This section presents and compares the computational and experimental results. First it presents computa-tional and experimental results for the HYDROSES target vessel. Then the computational and experimental results for flie DUTSES model are presented. Finally fliis section presents a discussion of the results for added resistance.

Lpp 153.00 m Lc 144.00 m

B 35.00 m

Bo 26.00 in Pc 11.11 kPa

Table 2: Main dimensions of flie HYDROSES target vessel a: 0.6 1 1 1 kA = 0.01 kA = 0.05 kA = 0.10 kA = 0.16 experiment + 1 1 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 wave frequency [rad/s]

Figure 2: Heave RAO of the HYDROSES target vessel

4.1 The H Y D R O S E S target vessel

The HYDROSES target vessel was designed as a car/passenger ferry by FINCANTEERI in Italy. It served as a shidy object in flie HYDROSES project. Table 2 presents the main dimensions of the vessel. It is equipped with a free-lobe bag-type stern seal and a finger-type bow seal. The flft to weight ratio of the vessel is about 0.85. The vessel's speed is 45 knots, and it safls in head waves. In flie experiments flie model was equipped witii a di-aphragm in order to obtain a correct scaUng of the air cushion dynamics. The computations were carried out on f u f l scale. A l l results are presented on fufl scale. Figure 2 presents computed and measured heave Re-sponse AmpUtude Operators (RAOs) as a function of flie wave frequency. The RAOs follow from a harmonic anal-ysis of the computed and measured time signals. Results for several levels of wave steepness are shown. The com-putations and experiments agree well. The effect of the non-Unear cushion dynamics on the heave RAO is not very large. They manifest them self most proininentiy as sinkage and higher harmonics, as was shown in a previ-ous paper by Moulijn[I6].

Figure 3 presents the computed and measured pitch RAO as a function of tiie wave frequency. In the higher fre-quency range flie computations and experiments agree

0.6-/ 1 ' kA = 0.01 ƒ 1 KA = 0.05 / I kA = 0.10 / I kA = 0.16 - - ••

/

\

Figure 3: Pitch RAO of the HYDROSES target vessel

1 1 1 l<A = 0.01 1 1 l<A = 0,05 l<A = 0.10 _{* *} I<A = 0.15 - - • e x p . fore + e x p . aft X / X \ 1 1 1 02 0.4 0.6 0.8 1 w a v e f r e q u e n c y [rad/s]

Figure 4: Cushion pressure RAO for the HYDROSES target vessel

well, but in the lower frequency range the computational results are larger than the experiments. It is not clear whether the computational method over predicts the pitch resonance, or whether the resonant frequency is shifted. This discrepancy is probably caused by the relatively harsh hneai'ization scheme of the hydrodynamic prob-lem. The effect of the non-linear cushion dynamics on the pitch RAO is negligible.

Figure 4 presents the computed and measured RAO for the cushion excess pressure. The pressure was measured at two locations: one at the fore side of the cushion and one at the aft side. The computations and experiments fire in good agreement. The effect of the non-linear cush-ion dynamics on this RAO is larger, but still not really significant. In the high frequency range the experimental results are somewhat larger, while in the low frequency range the computational results are greater. The latter discrepancy is caused by the large computed pitch mo-tions which cause air gap modulamo-tions under the seals. The Hehnholtz resonant frequency of the air cushion is

l(A = 0.01 kA = 0.05 l(A = 0.10 l(A = 0.15 e x p e r i m e n t 0 2 0.4 0.6 0.8 1 w a v e f r e q u e n c y [rad/s]

Figure 5: Quadratic added resistance operator for the HYDROSES target vessel

located in the high frequency range. This resonance is very sensitive to for instance the behavior of the fan, and is therefore difficult to predict computarionally (see ref-erence [16]).

Figure 5 presents the computed and the measured added resistance divided by the wave height squared as a func-tion of the wave frequency. M A R I N measured added re-sistance values up to two times as laige as the calm water resistance. In the case of conventional ships tiie added resistance is proportional to the incident wave height squmed. The scattering of the experimental results in-dicates that this relation does not hold for an SES. The measured added resistance is negative in some cases. The computational results are much smaUer than the exper-imental results. There even does not seem to be any correlation between the computed and measured added resistance. The computational results also indicate a non-quadratic relation of the added resistance with tiie wave height, although the scattering is much less severe. The discrepancy between the computed and the measured added resistance was the reason for the new experiments.

4.2 The DUTSES model

This section presents preUminary results of the new model experiments. These results are also compared to computational results. The experimental results have not been analyzed thoroughly yet. Nevertheless these results give some interesting new insights into the topic of added resistance of SESs. A l l results are for the model version with plates, and are presented on model scale. The model is towed in head waves at a speed of 3.72 m/s.

Figure 6 presents the measured and computed RAO for tiie wave force in heave direction. It displays results for

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3 4 E wave frequency [racJ/s]

Figure 6: Heave force RAO for the DUTSES model

2 3 4 6 6 wave frequency [rad/s]

Figure 7: Cushion pressure RAO for the DUTSES model

several wave heights. The correlation is not fully satisfac-tory yet. The scattering of the experimental data indicate that the heave force is quite non-lmear m the wave height. The computational data appear to behave in a much more hnear way. Generally the correlation is better for higher waves.

Figure 7 presents the RAO for the cushion pressure dur-ing wave force experiments. The cushion pressure was measured on two locations: at the fore side of the cush-ion and at the aft side. These results are shnilar to the results for the heave force.

Figure 8 presents measured and computed quadratic op-erators for the added resistance of during (captive) wave force experiments. Both experimental and computational data indicate that the added resistance is not proportional to wave height squared. Contrary to the results for the HYDROSES target vessel, the results for the DUTSES model are of the same order of magnitude.

The computations do not include the usual added resis-tance of the plates. This added resisresis-tance should be small

experiments + calculalions

2 3 4 5 6 wave frequency [rad/s]

Figure 8: Quadratic added resistance operator for the DUTSES model

exp. A = 0.02 exp. A = 0.04

3 4 5 wave frequency [rad/s]

Figure 9: Quadratic added resistance operator for plates of the DUTSES model

as the plates are extremely slender. It was measured dur-ing wave force experiments without cushion pressure. Figure 9 presents the results of these experiments. The added resistance of the plates appears to be relevant when compared to the total added resistance as presented by Figure 8.

The added resistance of the air cushion can be calculated by subtracting the added resistance of the plates from the total added resistance. This way of computing the added resistance of the air cushion unpUes that interaction of the air cushion with the plates is neglected. The added resistance of the plates was assumed to have a quadratic relation with wave height. This assumption is approved by one of the .A = 0.04 measurements(A is wave am-pUtude). The other A = 0.04 measurement does not ap-prove a quadratic relation (see Figure 9).

Figure 10 presents the thus calculated experimental added resistance of the ah- cushion. The results are not di-vided by wave height squared. The calm water resistance

A = 0.01 A = 0.02 A = 0.03 A = 0.04 5 1 1 1 1 1 experiments + calculations r 1 1 1 1 1 — l l l l — 1 — I 1 1 1 4 + 3 + 2 1 - s .

A

Figure 10: Added resistance of the air cushion; the experiments follow from the total added resistance minus the added resistance of the plates

of the vessel was about 27 N . The computed and mea-sured added resistance of the ak cushion are in reason-able agreement. The magnitude is about the same, and the trends do also agree.

The added resistance due to the ak cushion can also be calculated from the horizontal seal connection forces. The resistance of the air cushion follows from:

i?<"'^) = -F^s - F^b -Pc-Ad- ?/5 (6) where F^s is the horizontal stern seal connection force (positive in forward dkection, hence the minus sign), F^b is the horizontal bow seal connection force, Pc is the cushion excess pressure, Aj, is the deck area and 775 is the pitch displacement angle. The added resistance of the air cushion follows again from Equation 5.

Figure 11 presents the added resistance of the air cushion, where the experimental results were calculated from the seal forces and the cushion pressure. Again the results are in reasonable agreement. The results of both meth-ods for calculating the experimental added resistance of the ah- cushion agree quite well (compare Figure 10 with Figure 10).

4.3 Discussion

This section presents a discussion on the topic of added resistimce. There is an obvious difference between the experimental results of M A R I N and the new experimen-tal results. There are however many differences between both experiments.

The model was free in heave, pitch and surge during the M A R I N experiments, while the model was rigidly con-nected to the carriage during the new experiments. The

cushion pressure amphtude is much larger during a wave force experiment than during a comparable free saihng experiment. Therefore one might expect to find a larger added resistance during wave force experiments. This is not however the case.

The M A R I N model has reafistic side huUs instead of plates. I f this is the reason for fiie large added resistance, the major part of the added resistance should be attributed to the huUs. This is not very likely as file realistic huUs are still very slender.

The added resistance was measured m two quite differ-ent ways. The M A R I N model was self-propulsing by means of model water-jets. The added resistance was determined from a propulsion increase of tiie water-jets, which follows from a measurement of the flow through flie water-jet. In some cases an extta towing force was added because flie model could not reach tiie desired speed. The DUTSES model is always towed. The added resistance foflows from an increase of the towmg force. This metiiod is, according to the author, more simple and more reUable than the mefliod adopted at M A R I N . The M A R I N results might be affected by a decrease of flie efficiency of the water-jet propulsors.

The large speed loss of SES might also be caused by a decrease of flie thrust of the water jets. This would ex-plain the large added resistance measured at M A R I N . It would also explain the statement of Ehrenberg[9] that an SES has much less speed loss in waves flian a comparable catamaran, as his experience foflows from an SES which is propulsed by means of surface piercing propeUers.

12-10 A = 0.01 A = 0.02 A = 0.03 A = 0.04 1 1 1 1 1 experiments + calculations 1 1 1 1 1 + + 1 1 1 1 1 + + 1 1 1 1 1 + + + • " + + + + + + 1 1 1 1 1 + + + 1 1 1 1 1 + + 1 1 1 1 1 + 1 1 1 1 1 + + + 1 1 1 1 1 + + 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 wavs frequency [rad/s]

Figure 11: Added resistance of the air cushion, the experiments follow from the seal forces and the cushion pressure

5 Conclusions

The results of the computational method that was pre-sented by Section 2 are in good agreement with the ex-perimental results of M A R I N , as far as motions and cush-ion pressure are concerned. The computatcush-ional results for added resistance are however much smaller thm the added resistance that was measured at M A R I N . New ex-periments, which were carried out at Delft University of Technology, lead to a much smaller added resistance which is in reasonable agreement with the computations. There were however many differences between both ex-periments.

At this stage it is not possible yet to say i f SESs have a large added resistance. It can however be concluded that the added resistance due to an air cushion is relatively small. The added resistance of the hulls and the added re-sistance due to sinkage will follow from the experiments that are in progress at the time this paper is written.

Acknowledgments

I would hke to thank the Royal Netherlands Navy and M A R I N for their financial support of my PhD-project. M A R I N is also acknowledged for providing the experi-mental results for the HYDROSES target vessel, and for providing a lot of equipment for use in fiie new experi-ments.

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