Hydrodynamic studies of sidewall hovercrafts

Gothenburg - Sweden

HYDRODYNAMIC STUDIES

OF SIDEWALL FOVERCRA FTS

by

CARL GISAEUS

Division of Ship Hyd±omechanics

Report No 49

Preface Sunuuary Introduction 1 Stability 2

2.1

General 2

2.2

Transverse stability 2

2.3

Longitudinal stability 8

2.4

Conclusions 10 Resistance 11

3.1

General 11

3.2

Theoretical background 12

3.2.1

Resistance and propulsion 12

3.2.2

Power requirements 19

3.3

Descxiption of trials 22

3.3.1

The model

22

3.3.2

The recording equipment 22

3.3.3

The trials

₂₅

3.4

Results

27

3.5

Calculations of full scale power ₃₃

3.6

Conclusions ₃₅

Seakeeping trials 36

4.1

Introduction 36

4.2

Discription of trials ₃₇

4.2.1

The model ₃₇

4.2.2

The recording equipment 41

4.2.3 The trials

42

4.2.4

Observations at the trials

₄₃

4,3

Results

₄₄

4.3.1

Quality of registrations

₄₄

4.3.2

Number of lags in spectra

₄₄

4.3.3

Calculated and observed values

46

4.3.4

Evaluations of spectra

48

4.3.5

Calculation of amplitude operator 56

List of symbols

Reference list

71

Appendix A

74

out at the Division of Ship Hydromehanics, Chalmers University of Technology, in the field of sidewall

hover-crafts during the period

1970 - 1973.

It is based on earlier work concerning air cushion vehic.=

les made both outside and within the Division., and. also

from experiencies gained from a scholarship that the author received from Lloyds Register of Shipping for studying fast marine vehicles.

As seakeeping stwlies using statistical methods has been given special attention at the Division for evera]. years,

it was natural

to

emphasize this aspect.

The work was carried out as a licentiate study by Carl Gisaeus under the supervision of: Professor Curt Falkemo.

Stability

Resi stance

In order to study the hydrodynamic problems of sidewall hovercrafts two models were built and tested at the

Re-search Station of Ship Hydromechanics at Lângedrag, about

10 ] west of Gothenburg. The following general

informa-tion was found.

By using displacing sid.ewalls and rigid seal arrangements a high stability is performed in both pitch and roll.

It is shown in chapter 2 how the stability is influenced by different parameters. Because of the high metacentric height, aspects on stability will not be decisive for the choice of distance between sid.ewalls, center of gravity

etc.

For a 1000 ton hovercraft geometrically identical to the

models studied, the initial metacentric height will be

about ₉ meters.

The tests show that it is possible to reach a lift to drag

ratio of about 13 with the model studied. Changing the

trim 1 - 2 degrees may give an increase in resistance of about 50% for the model.

The stiff seal arrangement used here is acceptable in calm sea operations, but in waves the increase in resistance

be-comes considerable. This is mainly due to the front seal

that should be designed more flexible arid. streamlined The

special design o± the rear seal allows the craft to trim when in operation, but gives a considerable hump resistance.

In calm sea operation the resistance is relatively indepen-dent of the airflow through the aircushion, but in waves this parameter becomes very important.

Seakeeping

a speed of 60 knots in calm water.

The tests carried out show that the sidewall hovercraft has

relatively good. seakeeping properties. The stiff seal

ar-rangement that is unattractive from a resistance point of view is attractive when operating in waves by giving a

res-taring moment while ploughing into a wave. With regard to

resistance it is however necessary to make the lower part

of the seals far more flexible. Generally it could. be stated.

that asects of the sea-behaviour as well as of the stability

of sidewalls are problems of second. order compared. to

resi-stance problems when projecting sidewall hovercrafts.

The calculations indicate that a 1000 ton vehicle may occa-sionally reach bow accelerations of about 2-3 g operating at

40-45 knots headsea in North Sea traffic. The corresponding

acceleration aft will be about 1 - 1,5 g. The motions

calcu-lated for pitch and roll show that high values could be ex-pected which is in agreement with observations made at the

An earlier economic study [Ref 1] carried out at the

Divi-sion of Ship Hyd.rodynaiics, CTH, indicated that sidewall

hovercrafts may be competitive with other kinds of sea tran-sportation systems in short and. medium range distances.. As distinguished. from the preliminary study, this investigation has been concerned with the hyd oinechanical aspects of side-wall hovercrafts.

For investigating the stability and the resistance a model was constructed and tested in the towingtank at the Research Station of Ship Hydromechanics at L.ngedrag.

The sea behaviour of sidewall crafts was investigated, by using

a bigger selfpropulsive model, that was tested in the open

sea outside L.ngedrag. Programs for evaluating the results

were developed and published separately [Ref 25].

The two models are geometrically identical and further

des-cribed in chapters

_{.3 and. 4.}

For those not familiar with sidewall hovercrafts some gene-ral information is found in appendix B.

The sidewall hovercraft may from a stability point of view

be

regarded

as an extreme variant of a catamaran. As the

catamaran has an excellent roll stability this may also be

expected from sidewall hovercrafts, In this case the prob-.

lem is however more complicated as a leakage occurs from the

air cushion between sidewalls and water. This gives a

down-ward heave motion because of the pressure drop which also increases the resistance through increased contact between

craft and water.

For pitching motions the catamaran is in general less stable than a corresponding single-hull ship, due to the slender

lines of the sidewafls. A sidewall hovercraft is also more

sensitive to pitching motions because of increase in

resi-stance when the seals dJ.p into the water.

2,2 TRANSVERSE STABILITY

The transverse stability is in practis solved for amphibious

crafts by dividing the cushion area into several compartments. For a sidewall hovercraft such an arrangement is not recjuired as the sidewalls may be designed to give a restoring moment.

The restoring

moment depends mainly at small

angles on the

change of displacement from the sidewalls. At larger angles

the center of pressure will move in relation to the center of

gravity, and. this will also influence the restoring moment.

The vertical position is given from the relation that an in-crease in lift gives a corresponding dein-creases in displace-ment from the sidewalls.

sidewall

Figure 22

Using the nomenclature in figure 2.2. the change in lift/length unit may be written

p(b - t) C

-)

51

cos cp0

The change in the cross section area from one sidewall

is

cos cp0 0 t/cos p0 =. h t

The change in lift = the change in displacement of the

sid.ewalls which gives

p(b - t) I - OS

P0

2 y t cos

p0

The heeling moment from the air cushion may be expressed

- o (g + b + h) sin

81

y is density of water.

: 'r

___

0

cx

oollc:scp.

oos(p0

cp) +

+ (g + h + Ah) sin

9 cos(cp0

-

cp)

--.

!j. (t2

+ 3

b)

X_.cp

dx

coscp

coscp.

g+h+Ah)

sinc0]

From the two sidewalls the resulting moment will be

b+t d.M5 2

_J

Y coscpo ö]. 2 2

cosp

2 o. cos(q - cp) 3 0. COS ( dIp

6

000s(p

-q)

dM=a3_d.MJ%._(t

+3b).o1J

.0

008 p

)

(g+ Ii +h) tanp0.o 81

If the moment is integrated all over the length, the following expression is valid for small angles

GM=

Ws.nip

W.q

+

3 b')

o

.p0.

p(b -

_{t)(g + Ii}

+Ah)

bt)(g

The initial stability expressed as the metacentric height (GM) is then

where W is the total weight of the craft

I.. GM

(t2

b2)

-.

p(b-

t)(g

+

h.ih)J

if

1(b - t) . _.+

a)

where a is the support from the sidewalls. Then

1 GM

= 1(b - t) . p(1

+a

.cp

-fluenced by different parameters a sensitivity analysis was

carried out. As a reference, data from the smaller model

were used.

1=2.35m, b=1.05m,

t_-0.05m,

p=36kp/m2

a

= 0.08, g = 0.09, h = 0.25.

This gives GM = 0.40 m.

As canbe seen from figure 2.4 the width between sidewalls, the thickness of sidewalls and the pressure have a

consider-able influence on the initial, stability GM. A change in

height from bottom of the craft to the water surface or the

lifting support

(a)

from the sidewalls has little influence

on the initial stability GM.

The results were controlled by servera]. tests carried out with different pressures and weights of the model.

As the possibility to variate the parameters is limited, the

measured variation in was in the interval 35 - 42 cm. At

large angles the air was leaking out under the sidewall, which caused a pressure drop and a downward movement.

When the craft is moving forward an additional restoring

mo-ment is gained from the sealing system. The influence from

2.3 LOITGITUDII'AL STABILITY

Regarding the longitudinal stability there will occur a re-storing moment from the change in displacement of sidewalls when the craft is trimming. The influence from the air cus-hion itself is of negligible importance in

longitudinalmo-tions. When the craft moves over the water surface there

will be an additional restoring moment from the sealing

sy-stem. The rear seal of the model was designed as a trim

plane, that makes it possible to maintain a specific trim condition even at changes in position of the centre of

gra-vity. L G - force of gravity T - " " pressure tt U _propulsion rear seal

I

From the figure it can be seen that the moments from the rear seal and the sidewalls have to balance the moments

from the propulsion and the air cushion. If an air

propul-sion arrangement should have been used the moment from the

propulsion would have been in the opposite direction. This

would of course also have influence on the weight

distri-bution along the craft.

The moments from the seals can not be calculated

theoreti-cally, as local speeds of water and. the surface wetted of

the seals are hard to estimate. The influence from the seals

is therefore better studied by mode]. tests. This is further

described in chapter 3.

water surface. However, when operating in waves the front seal gives an important restoring moment in pitch motions.

2.4 CONCLUSIONS

A sidewall hovercraft has a high transverse stability with a transverse metacentric height about the same as for a

catama-ran. A leakage from the cushion is more likely to occur at

small values of GM. This leakage causes a pressure drop which

influences the resistahce through increased contact between

craft and water. The .nitial stability is mostly influenced

by the width between the sidewalls, the area of floatation of the sidewalls and the pressure in the air cushion.

For a 1000 ton hovercraft, geometrically similar to the model,

the metacentric height will be about ₉ m. This indicates that

the motions of the craft will become rather stiff.

The design of the seals is of great importance to the

longitu-dinal stability. Rigid sidewalls give better contribution to

the stability than flexible ones. The special design that is

used for the model makes it possible to change the trim when

operating in a specific condition. This may be of advantage

when long distance vehicles are projected, because of the lar-ger flexibility in placing, for example, the fuel tanks.

3.1

GENERLL

Nost studies published about resistance of hovercrafts deal with amphibious vehicles that hover free from the surface.

Little is however

kno4

about the influence on the resistance

by for example surface contact, wave pumping effect, the seal arrangement and the cushion pressure.

For studying such problems a hovercraft model was designed and tested at the Division of Ship Hydromechanics, CTH.

3.2. TKEORETICAL BACKGRO1ThTD

3.2.1 Resistance and propulsion

As a surface effect machine is very much influenced by air resistance, the total resistance is more complicated to

cal-culate theoretically than for a corresponding conventional

ship. The total resistance for a sidewall hovercraft may be

divided into aerodynamic-, momentum-, wave- and. friction

re-sistance. These main categories may further be split into

different components, which can. be seen in the following

de-scription.

The aerodynamic resistance consists of one profile and. one friction component that may be expressed as

R =

C q S

a a a f

Ca = Coefficient of aerodynamic resistance

= Dynamic pressure from air

S. = Front area of the craft

If the craft is designed slender, the profile resistance will be very small and Ca will mainly depend on the

fric-tion.

As the air comes into the lift fan there will be a

horison-tal momentum relative to the vehicle. The speed of this air

is reduced to zero relative to the craft, and the force that causes this change of direction is known as the momentum

re-sistance. According to the law of momentum this component

may be expressed as

R. = v

a

Airflow

Speed of air relative to the craft.

The friction resistance may be divided into friction from

the sidewalls and friction from the seals. The friction

V

sidewall/

resistance from the sidewalls is caused both from the part

of the sid.ewalls that are submerged both inside and.

side, and. from the triangle part that just is wetted

out-side. The friction resistance may be expressed as

:Rf = L

ha. n

+ q,. L hb/2 2 Ci..

where q is the dyn.inio pressure of water

C is the friction coefficient of water

L is the length of air cushion

h is the part of the sidewalls that is wetted. on

a

both sides

hb is the part of the sideveiTh that is wetted just

outside

n is the number of wetted surfaces.

aircushion

Figure

3.1.

The friction resistance from the seals is very difficult to calculate theoretically, and is therefore normally estimated from experiments.

The friction resistance from sidewalls and seals increases

when operating in waves. This additional resistance is also

normally calculated from experiments, due to difficulties in estimating wetted surfaces and local speeds of water.

The pressure from the air cushion creates a hollow in the

water surface. The depression of surface will be smaller

in the front part than in the rear part, which gives a con-tribution to trim, because the surface has been exposed to

pressure for different lengths of time along the craft. Due

to the trim of the vehicle during acceleration, the lifting force gets a component that is directed opposite to the

mo-tion. This component is negligible at high speeds, because

of the decrease in trim, depending on the smaller depression of the surface.

The wave resistance may be divided into

- wave resistance from air cushion

- wave resistance from sid.ewalls

- interference resistance from sidewalls,

Wave resistance has theoretically been calculated by Chaplin ref [19] where different assumptions have been made about

in-fluence from sid.ewalls.

In ref [20] there is a suggestion to substitute the sidewalls

by two rectangular pressure fields. The pressure depends on

the submergance of the sid.ewalls. By this assumption it is

possible to get an expression for the wave resistance. For

investigating the components of the wave resistance and. the separate wave resistance of sidewalls from interference

re-sistance Plissov ref [21] has made a study at the Division

of Ship Hydromechanics,CTH. For the calculation Havelock's

where p where 64p2

T/20053

.

2!

VGB sin . 2 f_V

L"

Rytc=voyf

2 o

sin

28

2cós

)

u.n. 2

R is wave resistance from air cushion

wo

R is wave resistance

froni

sid.ewalls

V's

R is interference resistance from sidewalls.

w

-7/2

2

R =

,r.

2

j

.

cos3

8

d.8

is the density of water is the speed of the craft

is the wave amplitude far behind the craft

The wave profile at large distances from the body is derived from

I

z(x,

)

=

I

.[a(9)

cos J

(x cos 8 +

y sin.

8) +

-

Lc0s. 8

+ b(9)sin

_{[_V}

(xoos

8

₊

y

sin8)]

d.8

Loose

J

where

The wave amplitude is

Jf(e)j =

a28)

b)

if

a = a1

+ a2

b = b1

+ b2

where a and. are

the influence from the sidewafle and.

a2

and b2 represent the influence from the air cushion. The

wave resistance may finally be written

7/2

₂

R and have been calculated and computed by Plissov

in ref [21J.

For calculating the total wave resistance it is also ne-cessary to develop the expression above for R.

z.

Using the same nomenclature as in ref [21]'

b B

a

b

B L V

Fr=

g°

L'

L1

H=

4.

yO

be L1

H 3 e p L B

I

Fiire 3.2.

= pg

V =

giv

R wc

C=

_we

L..

The dimensionless coefficent for resistance C may then

we be written C we

Jt.psV2 (8D)2

1

peLoB(7toy)2

_v.B

"1

-

2

VOL

= 2

If the nomenclatu.re from page 16 is used, then

= 27,1

0 H

a

B 2P

_r

1 2F

_r

2

C may then be expressed

v2(8

p)

21"2

r.cos

3 2

.2

- poL.B(it.y)

0. sin 28

.21v.L\

Sin

I

_2cos8

ir/2

3n

/

C = G

f

cos

°

sine

(c

we 1

.2

1 2 o

sin

2 COS

For calculation of the integral, let

cos8=

x2 + 1. 2

_'v°B

sin8

sin

I 2

cos2)

.2(C2

_\..

° S.fl

I 10.8

cos 8)

TheC

is wc -C

1+x

1

4x2 (2x2)

(C1 x(i

+x2)2

+

0

Zdx

sin2 {c2 (i + x2)] .¼X

For practical calculations

this

expression was computed

and the results show good agreement with those from ref

[22] , which is obvious as

the

expressions for wave were

derived in similar ways.

As an example the resistance from the

air

cushion is shown

in uigire 3.3 with actual parameter values for the models.

As was expected the wave resistance is

increased when the

C '7O 0,02 0,01 -0,2 _0,4 0,6 0,8 1,'O - 1,2 Figure

.3.

3.2.2 Power requirements

The total power requirement for a hovercraft consists of power for creating and maintaining the air cushion and. power for the propulsion.

Lift power

A difficult problem is to estimate the air pressure at a

cer-tain condition. If minimum lift power is used the

resis-tance will increase due to increased contact between craft and water, and if a too large lift power is used, this will

I _I 1,4 1,6 Fr 0,06 - 0,05.0,04 0,03

-or

tip =

-a

where

is the chel coefficient and q

the dynamic

pressure of the incoming air.

The necessary power will then be

=J.c

PLs0tiP

fl

where

1 is the fan elTicency coefficient

Q is the air volume/sec

If -the dynamic pressure in the air cushion is negligible, may be formulated

Q. = C S

°Va

where CQ is an experimental coefficient S0 is the cushion area

p is the density of air

a

A representative value for C is 0.010 for sidewalls, ref

[i]. The lift power necessary may then finally be expressed

0 *

cause bad. operating economy0 If the fan intakes are

direc-ted. forward, the dynamic pressure may be utilized0 If the

pressure in front of the fan is free from losses, and. the

pressure increase in the fan is tip, the total pressure in

the air cushion will be

'k

(tip +

Prom the expression it can be seen -that -the power requirement

Propulsion power

The propulsion power may generally be written

R.v

PP =

where ii is propulsion efficiency.

±1-I-The power corresponding to aerodynamic drag is

P ='VoRt=--1.v .0.

a a

aT)

a a

1

-

2r

V3.

a

where Ca is coefficient for aerodynamic drag Sf is front surface of the vehicle.

The power corresponding to momentum resistance is

P.

_'R.

_s

_oC

\f2

1 T)pr

a

lrJ

a

.0

VPa

The power that correspond to wave resistance is

P _--.v R

pr w

The power that correspond to friction resistance is

P - .

v

R =

L..

'v-V.(Cf +ic)

j

.

sv

f V

11pr

=

. ..

p..

s.(c

+

C)

where C1. is the friction coefficient in water

is surface roughness correction

S is wetted area.

V

The total power may now be written

= PP

(excluding mechanical efficiency).

In reality, still more effect is required. as for auxiliary

3.3.

DESCRIPTION OF TRIALS

3.3.1

The Model

A model for measuring the stability and resistance

proper-ties was made. The principle is a plenum chamber, without

any peripheria]. jets. A detail that is special for this

model is the design of\the flexible seals, which allows the

centre of gravity to move without altering the trim. The

hull is built of two slender sidewalls, connected by a

bot-tom. The material is all marine plywood and the layout can

be seen in figure

3.6.

The seals are rigid with flexible materials along the edges.

Details of the construction can be seen in figures

_3.4

and

3.5.

The rear seal acts like a hydroplan which gives the

craft a proper trim. The lifting force is generated from

an axial fan, which gives a total pressure of 500 N/nL2 in

the chamber.

The model was towed in the tank of the Research Station.

[Ref 23]. Figure

3.7

shows how the model was connected to

the towing system.

3.3.2

The recording equipment

During the trials the following parameters were registered:

- speed - resistance

- pressure (in the plenum chamber) - depth

- trim

The speed was recorded with the normal. equipment of the

to-wing tank. The resistance was measured by strain gauges and

recorded photographically, which also made it possible to analyze how the towing force was applied.

/

Figure

3.4.

Figure

_3°5.

'I

-3__.

Ofi .d4'h ., I

,

-il

II

/ II

---.- II

II _{'I I,} I,

----.25Oo 35

3.3.3

The trials

At the testing different pressures, displacements, trim

con-ditions and. positions of seals were used. _Interesting

condi-tions were also studied with special regard to wave resistance by estimating the wave energy [ref 18],

The model was further tried in waves for studying the increase

of resistance, while using the specific seals0 Some pictures

Sreed = 2,48 ta/s

'5..-_555_

Fi

Sneed = 3,2 rn/s

'PS5. S -- r SS,S5 S

-'4

Sneed =2,26

/s

S'eed = 2,72

_/s

Spee1 = 2,12 rn/s

Sneed = 4,05 rn/s

3.4

RESULTS

When the pressure in the chamber was changed, resistance curves as shown in figure 3.8 were found.

The hump is easily distinguished at Pr =

_0.43.

As can be

seen the resistance is large when the pressure is too small.

(case 1). The differeixce in pressure between case 2 and ₃

is not great, which indicates that the added power in case

3 is not necessary.

-The influence from different positions of the rear seal may

be seen in figure

3.9.

The hump resistance is very sensi-..

tive to changes in the position of the rear seal, se also

figure

3.6.

When the weight of the model is increased, the result will

be as shown in figure

3.10.

The relation will roughly

be the same in both cases. In figure

3.10

it is possible

to see the difference in resistance when towing in calm

water and in waves. The result is discouraging, because

of the great increase of resistance in waves. This may

partly be explained by the special condition which made the

front seal cause an unnecessarily big resistance. The test

showed that it is of utmost importance to keep the front seal above the water surface as much as possible.

Regarding the depth it can be seen from figure

3.9

that this

will be too big if the rear seal is not in proper position, even when the centre of gravity has a midship location.

The trim curves show that the model has had positive trim

condition during all the trials. This is, as mentioned

be-fore essential if the front seal is not to plough water.

Furthermore, the course stability of the craft will be un-satisfactory at negative trim angles.

From the curves showing the angles of towing it is also clear that the position of the towing point has been chosen so that

a * cm /2 8 4,. a / 'S 18 0

j

if $ 0 / 2 3 4' $ 0 a a 4, a a 4 ,I frii .6 7i49 /c .4 a 7a44 c., a a ,, _a

The r.aiutance teats fare carried out in calm .ater and negliable influence froa find.

Iaigbt of model 92 k

Center of grcvit' from etero 1,15 Pocitionorrear coal

Trial 1 Preceure 305 Revolution of fan 1901 r cm /2 a 4, 0 a -a' . a a a- a a C I 8 -2 -4, if 8-4,. . . j-Trial 2 Preceure $55 N/rn2 Revolution of fan 2500 r Prerneore ₃₆₀N/rn2 Revolution of fan 2900 r

J 8

8 4, 4. 2 2 -2 -if

12 4 2 4,. -4.. a 6 4,. 4,. 4 3 4. . 2 0 . 3 4, ;; a

;

4 3 4. 3- 2 4,-a 4. 3

Cain eater and ne3linile wind

Trial 4

bight of nodel 92 kg

Cerier of avit7 fren stern _1,15

Position of rear ,eal 2

Presser. 555 N/n2

Revolution of fan 250u rpo

Trial 5

Tight of sodel 92 kg

Center of gzaeity fron stern 1.15

Po,itio of roar seal ₉

Pressure _{355 N/n2}

Revolution of fan 2530 r

Trial 6

bight of nodel 92 kg

Center of roviey f roe stern 1.25 e

Position of rear .eal ₃

Preasure 355 N/s2 Revolution .f fan 2500 rps

I

b 2a.'rn9 .auye 4 4, e

9

Ce, a a 4, a a /O4f T,-,C/ 6 C," /2 8

4, .2 a -q F 2 3 4, 3. 0 2 3 7 Th/a.' 9 2 7,-ia-,' lO

I 7;:,r

8 7w'y ap4r 0 Ce) a 8 4, .5 _{4, 3}

'

:8 -' .r

'

'%

it'

./ 6 7b.ewng ! 2 .3 q a jot CriodoutthofAarjlJ

Cole eater a.rnd no].iablo wind

Weight or nod.el 102 kg

Center of gravit7 from etern 1,13 n

Position of rear seal 2

Pr.ethr. 370

Revolution of ton 2850 n

Trial ned out of Ann

Trials in 2-3 n/s following wind, negliable waves,

Trial 8

Weight of model 92 kg

Center of avity fran stern _{1,25 a}

PoSition of rear sea]. 3

353

Revolution of fan 2500 r

Trial 9

Retgtt of nodal 102 kg

Center of gravit7 fran Stern 1,23

sitio, of rear neal 3

Treasure _{370 8/}

iovtutjo of fan 2850

Trial 10

Weight of nodel 102 kg

Center of gravjt7 Iran stern _{1,23 a}

Position of rear seal 3

Pressure 370 8/52 Revolution of fan _{2850 rn'} W'avaa _{t - 2,5 o 8. 0,10 a} 'p Drai/ a 4 .. ; 40 £2 a 4,

a realistic direction of the propulsion is obtained. The angle of towing varies of course considerably at the hump speed, but at realistic speeds of operation (Fr=l,4) the model has had a lift to drag ratio of about 13 with. a

neg-liable influence from the pressure in the cushion. From

figure 3.11 which is a comparison between theoretical. and.

measured wave resistance, it can be seen that the maximum measured resistance is twice as big as the corresponding

resistance theoretically calculated.. The difference is

mainly due to the fact that no regard has been made of the influence from the seal while performing the theoretical

calculation. A comparison with the total resistance shows

that wave resistance and friction resistance are about the same at hump speed.

The result indicates that an essential decrease in resi-stance during the starting period may be expected when the position of seals is changed in a suitable way during the acceleration, and that the hump resistance on the whole should get smaller if more flexible seals are used.

0o2

wave resistance from interference

bet-ween the sid.ewalls

Figure 3,11.

measured, wave resistance

theoretical total resistance

1.0

1.2

1.4'

o8

Oôi

oY

3.5 CALCULATIONS OF PBI1LSCALE POWER

In the previous chapter it was shown how to calculate the total power for the lift and propulsion of a sidewall

hover-craft. These equations are now applied to a 1000 ton design

operating at a speed of 60 knots.

The main particulars far the full scale vehicle are

accor-ding to ref 1: S0 = 1140 m2 d = 0,95 = 7770 N/rn2 S = 243 2 CQ = 0,010 1 = 51,8 m = 0,85

v =

31 rn/s

The formula for the lift power taken from chapter 3.2.2 then gives

= 11050 kW

which corresponds to a specific lift power of 11.1 kW/ton.

For calculations of propulsion resistance the aerodynamic, momentum and friction resistance are calculated according

to formulas given in chapter 3.2.1. With regard to the

mo-del used, the wetted surface was estimated more carefully

than what is possible by using these formulas. The wave

resistance may be calculated theoretically or measuerd at

experiments as a residual resistance. This is then scaled

according to Proude's law. The different components of re-sistance were R = 60.8 1O'N a R. =

50.0

103N 1 R.. = 219 . 1O3N

I

R = ₂₄₄ . 103N(exp.) w = 135

.

103N(theor.) w

The towing power P necessary is 14400 - 17700 kW. If the

propulsion efficiency is assumed to be 0.6 the power will

be

P = 24000 - 29500 kW

The total power is then

= + P, =

35050 - 40550

kW

which corresponds to a specific power of

35 - 40

kW/ton

3.6

CONCLUSIONS

The resistance tests show that the constructed model has a

lift to drag ratio of about 13 at Fr = 1.4.

The rigid sea]. arrangement works excellently in calm water. To get optimal resistance conditions for the specific model

the front seal must beheld out of water. The aft seal may

be used for trim even in operatiàns, and gives at the same time flexibility in chosing the position of the centre of

gravity.

Proper trim is essential for getting low resistance and ac-ceptable course stability.

At operations in waves there will be a considerable added resistance, which indicates that the rigid front seal is

not suitable from a resistance point of view. At least

the lower part of the seal should be more flexible. However, it must be stated that even with more flexible seals, the increase of resistance in waves will be considerable.

4. SEAXEEPING TRIALS

4.1 INTRODUCTION

To study the behaviour in waves a seagoing sidewall hover-craft model was constructed and tested at the Division of

Ship Hyd.roinechanics.

The behaviour of the vehicle may be evaluated in different

ways. As a considerable amount, of research has been done

at the Division using statistical evaluations of motions,

it was decided to use this approach. The seakeeping theory

used comes from KorvinKroukovsky [ref.15]. For the

eva-luations a special computer system was developed [ref 25]. As the fundamental theory is wellknown, it is not

4.2 DESCRIPTION OF TI TRIALS

4.2.1 Nodel

Prom the preliminary investigations of the design of the craft, it was considered suitable to build a model as

shown in figures

4.1 -.4.4.

This model was thought to

correspond to a 1000 ton ship operating at a speed of 60

knots.

The hull is constructed in plywood and the craft has

se-parate engines for lift and propulsion. For propulsion

15 kW was used and for lift about ₄ kW.

The sealings are of a rigid type with a special spring system for the rear seal which gives a suspension effect

to the craft (figure 4.2). The weight of the model with

ropulsion engine

\

.ca bearing engj.ne r

11v

I I

ii

,nnhri.,

4______L/_

_1L__...._

seal

/

H,

,

I

,'

I

-.tt-t.t-.

/

bottor

/

\.

_{/_-_seal}

9a /30

L

/

Qr lift Lap

0 I', 22a Pipur.e 41

bottoli

rigid, tube

Figuro 42

if

4.2.2 The recording equipment

The electronic equipment was supposed to registrate the motions of the model and the waves during the trials. The recording of waves was carried out from a service boat while the motions of the model were recorded by the model

itself. Coming ashore the tapes were analysed both

visu-ally and. by numerical calculations in a computer. The

following scheme illustrates the most important components in the recording and ev.luating process.

gauge.

Jr

vc0

1300 HZ

Pressure Pitch Roll

Gauge.

vC0.

2300 HZ

J7

Smiator

TaD e recorae Punch computer

'U,

Calou.lated value" AcC:. Fore Aft Figure 4.6.

vco

7350 HZ I

Pen

Recorder "Observed value" Waves vC0 730 HZ

V

Tace

1orier

Discriminator Gauger Gauge

'I;

The difference in pressure between the air cushion and. the atmosphere was recorded at a point shown in figure 4.1.

The pitching and rolling notions were measured by a gyro and the accelerations aft and fore were registered by

accelero-meters. The different signals were transformed. into

varia-tions in frequencies of a voltage controlled oscillator(VCO).

For wave registrations a gyro-stabilized accelerometer was

placed into a special buoy. A signal from the oscillations

of vertical acceleration was cabled to the service boat, where it was recorded on tape.

The records were transformed from tapes to punchcards and evaluated in a computer.

4.2.3

The trials

The model was equipped on land and then taken out together

with a service boat to the actual area. The service boat

was placed in the middle of the testing area and then the model was driven in special turns around the service boat.

Onboard the model motions, speed in water and revolution

of the fan were measured. From the service boat waves and

wind conditions were observed.

Every run was carried out at constant conditions.

Some-times swells were disturbing the registrations but as this was easily observed these registrations were eliminated from the records.

On some occasions incidents happened to the model and the equipment which made the recordings unsuitable for further

analyses.

All the registrations were carried out in the open sea

4.2.4

Observationsat the trials

To get a proper performance from the model the sidewalls must be submerged deep enough so that the propeller does

not come out of the water. Because of this the trials

were mainly carried out in a condition with the displace-ment from the sidewalls of about 1/4 of the total weight. The trials were therefore carried out at a maximum speed of about 13 knots instead of 17 which originally was

plan-ned. The higher speed was only reached at trials in calm

water. The best test condition was when the model had a

positive trim of about

_3°.

The behaviour in waves is characterized by relatively fast rolling and pitching motions compared to conventional

ves-sels. As expected the most violent motions were observed

at the trials in headsea. In side- and. following seas the

rigid seals worked excellently and the vehicle had

plea-sant motions. This was mainly due to the fact that the

frequency of the seal motions became low. The model could

be operated at full speed in headsea with a wave heigt equal

to that of the sidewalls. At slamming situations the seals

acted like a suspension and. prevented "plough-int1.

Because of the sidewalls and the water propulsion the hover-craft got an excellent xaanoeuverability and negligible

drift-ing. The unsheltered position of the fan machinery in the

front caused several stops during the operations when the

machinery was all wetted down. This occurred, however, just

in head.sea and hovering at zero speed when the air cushion caused a huge water-spray.

4.3 RESDIJTS

4.3.1 Quality of registrations

To get meaningful results from the experiments it is impor-tant that the registrations were carried out under station-ary conditions, which means that the direction and speed of the model were constant and also that the conditions of

mo-del and waves were constant duxing the actual trial. Those

parts which did not fulfill these requirements have been sor-ted out at the evaluations.

A control that the registrations fuilfilled the requirements

for normal distribution was made in a special program. The

control was carried out by a X2 test of the observed

popula-tion. It was shown that with a population of 1000 the

re-quirement of normal distribution was fulfilled.

4.3.2 Number.of lags in spectra

An investigation of the influence of lag numbers shows that the variation becomes rather small, which also can be seen from the example in table 4.1 (from figure 4.7)

Table 4.1 ROLL: M = 50

M= 75

M = 100 MO . 4,50 4,50 . 4,50 T 1,55 1,55 1,56 H2 3,71 3,75 3,77 Sm

w

em 3,44 3,77 .4,22 3,85 4,68 3,77 .

1256 17614 5(124 .6/A .7 5:46 8102 1.111168 1104 1.56 1.3816. 1.507? 1.69214 1.7584 1.1484 2 01191. 2.1352 2.2608 2. 3064 2.512 2.6376 2 71.32 2.81180 03.0144 03.14 3.7656 3.3912 3.51611 3.6424 3 33916 4.1)192 6.14411 4.2704 4.396 4.5216 4.6472 g4.77?.R 4.89114 S 024 5.1496 5.2752 05.4000 5.5264 5.652 5.7776 5.9532 6.0280

quencies in

rad/soc

scale)

and the vertical axis gives power density in

P4 Cl) (Cl C) * a . :

..

+ .711271 6.59287 .75 1.0 + 2.12100 9.71089 .62240 .767520 .222877 183717 115307 16(11411 .72692 .347119 171449 .271645 .21,1158 14968 .18197 42 10 Of. .796046 .115207 .171279 .21)044 .291.7 15 .620917 .404534 .309431 .5 12207 .4329 .597658 1.25556 1.25700 1.27751 2. 60891 4.1.7772 4.20609 2. 49584 1.94056 1.60997 .990599 .556396 .539931 .444279 .5119197 55023 .3472211 .274295 .196827 .160979 .138550 8.156430-02 6.396020-02 .044829 a 23911.98 1.111947 6. 1)0242 .707655 6. 55764 .75 1.0 +

+)

fl Cl) CD c )-J _E CD (TI CD

'-'

4') Cl, (P (:1 . 52 2.12053 9. 67339 .26366 .2 39487 .171984 .142152 .23 166 1 129328 .111)414 .2261152 .163715 .215115 1 1(4(4 16 .325871 10l441 .287517 .445641 .415393 .452311 .433 140 .84491.1 1.7114 1.54093 3.32637 * 47779) 2. 754 77 1.117949 1.17548 .640021 4942911 .535889 .5 14 393 .33575' .223449 .I62739 .117977 6. 3471185 F.-02 S .88950.02 5. 062320.0? 5.992730-07 9.6h427Efl2 8. 5 90 14 0-02 4. 05 94 10.0? I .635630-112 3.421850-07 3.676690-112 9 .7 1959 0-1)2 9.685,10-02 3.992650.82 9.166590-02 2480.12 1.84558 5.94141 .60 .75 Figure £4 Rolling Lag number Bias a.. .700566 2. 12872 6.49099 9.58057 1.0 + .749457 .IS. 4 C/) .18(1277 5J1 CD . .214769 .-. .269105 E .265785 CD CD .1911814 CD .76812 .7115971 .120301 .388415 .447660 CD 57448(, 1.111189 0 1.97529 9.41677 0 2.911544 52415 .7566 19 .519557 .472198 .289 171 .170161 9.76(41190.02 .4(59837 5.688820.8? .084056 6.752410-07 1.924830-02 l.a 172 10-02 .4)18758 1.599740.02 1.740740-0? 2.7fl0Il80fl? 2.4715500? I .9S09d0fl7 511117 002 2 .845780-0? 2.794410.11? 2.164070.112 2.0116810-02 1.705850-02 2.540780.02 2. 228 110_fl? 2.231270.8? 1. 98680 F-fl 2 2.139370.0? 2.0 1025F-fl? -1.799430.0? 1.406220-fl? xl -130.685 0(0) ,11114) 4.47054 -.272505 00 .7.02239 LAST 61.14 17.56 1.668030-02 WI ((2. 114 4.491.1.5 23.4987 T.P(1.F 1,416.0 1.55333 1.211755 141.112 .H3,144.H5.I16.H? I 3.110121 :4.75151 11.0294 11.6297 + .167467 .134913 .5024 .61.961.7 .8-47:133 31.0048 1.17277 1.33973 1.5077 1.67467 1.84213 . a 2.0096 . 0 2.17707 2.34493 . 2.512 . a 2.67947 . * 0.1(4693 3.11144 . 3.16187 3,34933 3.5166 3.68427 .13.85173 .0192 .181.67 .354 13 .5216 68907 .65653 iS 024 Ir. 19147 5.t.26'l 5.69387 5.86113 607438 6.19627 6.36373 .. 6.5312.

*

6.1.981.7 .. 6.81.613 .a 7.8316 .. 7.20107 Cl3 .. I') 7.36051 CD .. 7.531.

0 ..

7.7016?

.

1,7.87093 '8.0384 (Cl 8(1') ,S(Il) 4.47)454 .717615 RI) 91.6970 LAST 81.0 12.56 6.24612c0l UI) 114 4A911a9 73.2073 1.556317 1.28466 Hi. H2 141. 444 HA. H? 4.1)1711 9.1711.6 11.08117 11.6922 0 21 -13)). 6 85 R((l),RUI) 41.471)54 -.637177 nIl .11109 LAST 81.8 12.56 2.716380-02 MI) 3)2,444 4.49531 74.0978 -1.00.01.116.11 1.546145 1.29295 I$1.442.443.H4.85.H1..447 2.9707 3.71338 1(1.9173 11.5115 0 .25 + + .2512 .51124 .1516 1.0048 0 1.756 1.5072 1.7584 2. 0 096 ?.26U8 2,512 2.7692 3.0(44 3.2656 3.5168 7.71.8 4.1)192 4.7304 4.5216 4.7720 a 5.024 . a 5.2752 . a 5.6264 . a 5.7776 6.1)268 0 6.28

.

6.5112 .. 6.7874

.

7.11336 .0 7.2848

*

7.536 .* 7.1872 .* 8.0384

.

41.2896

*

8.5408 8.792 9.1141? 9.2944 .0 9.5456 .. I 9.7968 H a 10.0411 4)

. a

10.2997 Pi

-10.5504 0 16.8016 11.0528 m a 111.5562 0 1i.80A4 .0 17.1I676 12.3083 CD 2154.63 1.80615 6.09466 25 .5') a Ylgur. £6 Rolling 52 Lag number 100 side ou .25 .50 + S Figure £5 Rolling Lag number Bid. ceo

N

- lag number

NO - the area of spectrum

T - the average period

E2 - the average height

S - the maximum value in spectrum

max

We - the freqiency in rad/sec when maximum occurs.

max

The choice of lag number influences the confidence interval

for the spectrum. With a population of 1000 and a lag

num-ber of

_75,

which were used at the evaluation, the spectrum

value S will be within the confidence limits

0.675 - 1,34

S

80% of the time.

4.3.3

Calculated and observed values

By comparing the observed values with those calculated from a spectrum assuming a Rayleighdistribution, the accuracy of

the registrations may be studied. The observed values were

derived by analyzing curves from the recordings. (See figure

4.6).

It was shown that a good agreement was received in most cases when the registrations had not been disturbed by external

er-rors. Several evaluations were done from every registration

due to limitations in the computer-. A comparison between

different parts from a special registration is shown in the

Table 4.2

As shown from table 4.2 the agreement is relatively good for acceleration fore and aft, while- pitching and rolling

show significant differences between the two evaluations.

This depends on the fact that the spectra for pitching and. rolling have high values in the low frequency part in one of the registrations which gives a too large spectrum area

and characteristic values derived. from the spectrum. The

comparison with the observed values showed that the

spec-trum calculated from the last part of the registration ha;...

peried to be the best estimation for pitching and rolling in

this case.

Trial 71

Begirmig

End.

Pitch

2

Area of spec-trum(d.egree )-

1,84

_1,54

Average period (sec.). 2,1 _2,4

Average alue (degree) _{1,7 1,3}

Ro].l

Area of spectrum(degree2)

3,56

_2,25

Average period (sec.) 2,2

_1,7

Average value (degree) 3,2

3,0

Acc9 Fore

2

Area of spectruzn(degree ) 0,062 _0,056

Average period (sec.)

_0,45

0,43

Average value (degree) 0,46 0,46

Acc0 Aft

Area of spectrum(degree2) 0,016 _0,013

Average period (sec.)

0,56

_0,51

By taking calculated values from different parts of the

same registration a mean value may be estimated. This

was carried out for all the evaluations, but still the agreements between the calculated and observed values (average values) were not very good in all cases (table

4.3). Partly this depends on the fact that the spectrum

was not filtered enough. before the calculations of moments, and partly because a narrow spectrum was assumed in the

calculations, which not always was the case. To get a bet-.

ter agreement with the assumed Rayleigh-distribution in

such cases, the width factor

_Vi

-

was used.

4.3.4

Evaluations of spectra

When evaluating the spectra and the characteristic values related to it, it is important to ascertain that the spec-tra for different motions is riot influenced, for example, by drifting or by some low Ireq.uency periodical

disturban-ces. This may be the case it, for exanrple, the gyro is not

stable or the electronic equipment used is sensitive to changes in temperature.

5(w)

Figure 4.8

5(a)

/

/

Drifting Low frequency periodical

Table

4.3

The table shows observed values and. corresponding calculated

values from the spectra. (Observed. and calculated values, see

figure

4.6)

Trial Pitch Roll Acc. fore .Acc. aft

Obs. Caic. Obs.

Cab.

Obs.. Caic. Obs.- Caic.

31

2,8

2,4

4,1

2,3

0,32

0,38

0,24

0,30

32

3,0

1,8

3,2

2,0

_0,25

0,30

_0,17

0,16

33

2,7

2,9

2,1

2,8

0,43

0,47

0,22

0,26

34

2,3

2,5

3,0.

:

,7

0,34

0,23

0,20

0,13

41

1,2

1,0

1,.8

1,7

0,10

0,07

0,05.

0,05

42

0,9

1,2

1,6

1,9

.

0,10

0,07

0,05

0,05

43

0,5

0,8

2,1

1,7

0,12

0,09

0,06

0

44

45

51

5,2

_6,7

16,5

_13,0

0,96

1,22

0,32

0,34

52

4,0

4,9

16,2

13,7

0,99

0,90

0,36

_0,32

53

4,0

5,8

14,7

14,5

1,20

1,11

0,36

0,29

54

5,1

5,2

16,5

15,0

1,40

i:,35

0,33

0,30

61

6,1

5,9

_17,2

16,0

1,10

1,01

0,40

0,37

62

_4,3

_4,7

_16,3

_13,4

1,07

_0,94

_0,32

_0,34.

63

6,5

6,9

18,5.

_17,3

_1,14

0,96

0,36

_0,31

64

5,8

6,0

13,0

11,7

.

1,02

0,98

0,35

0,33

65

_5,3

5,1

16,4

15,2

0,92

1,04

0,37

0,32

71

_6,5

4,3

8,4

7,7.

1,08

1,2

0,53

0,52

72

_9,9

_7,9

_8,3

_6,5.

_0,99

0,60

0,58

0,20

73

6,9

5,3

16,1

14,0

1,03

1,15

0,50

0,23

74

6,5

5,4

15,0

13,2

0,90

0,96

0,47

0,21

75

5,0

4,7

20,0

17,3

0,65

0,60

o,40

_0,24

Waves As the registrations of waves were carried out from a buoy,

stationary spectra were received. At the registrations the

wave acceleration was measured and then transformed to wave

heights by dividing by

w4.

At low frequencies the values

could be somewhat unreliable due to this division. All spec-tra of waves that were evaluated from the trials show

maxi-mum values at

3.5 - 4.5

rad/sec (figure

4.10).

A comparison between a calculated spectrum and. corresponding theoretical Pierson-Noskowitz wave spectrum at the same sig-nificant wave height and average period is shown in figure

4.9.

The difference in spectra depends mainly on the fact

that the wave spectrum from the trial was not filtered enough in the low frequency area.

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a U) CDO6 1 * a (Si L90'..9 a * * * *

sponds to

w = 3.5

rad/sec. The maximum value is also lo-cated close to the maximum of the rolling frequency of the

model which is

_3.9

rad/sec, '

In figure

_4.7

rolling spectra are shown in the case of side

sea, and a. corresponding spectrum for head sea is seen in

figure 4.11.1. In side sea the rolling period of the vehiOle

corresponds to the period of the wave system, and. in head sea the spectrum, is moved to somewhat higher frequencies.

There was no response in the high. frequency part' of the

spectrum because the hull of the model does not react to

higher frequencies than about 6.-.rad/sec.-.

Pitch The evaluations show that spectra for pitch are' wider than

those for rolling, and have maximum values close to the

pitch frequency of the mode, which is

_3.5

rad/sec; At very

low frequencies the spectrum. has been disturbed by faults

which have been described earlier. As for rolling-there

- was no response for fiuencies larger than 6- rad./sec. In

figur 4.11.2 a spectrum for pitch is_shown for a head. sea'

case. ' - '

Due tO the great' addition to the spectra at .lowerfrequen-des- the values d.erived from the spectra must be multiplied

with, a width factor

Vi

'to coincide with observed

val-ues. -:

-Pressure The evaluations of spectra for pressure in side- and folio'

wing sea show a similar appearance as for rolling and

pitch-ing. In head sea, however, the spectra for pressure cover

a much larger area of frequencies...

A first maximum appears roughly at the' frequency of' the

mo-del and a second maximum at the frequency when the wave

-1111,142.114 7.1411.02

1452.24

c2144n1.

Figure 4.11

Roll, pitch and pressure spectra in head sea.

T,co.r1.w6.g . .67140*4 4.11416 6.29664 .66442 279*29 .0.U2.114 M0.U2.M4 .432445 3.45506 78.03.87 H1.147.U1,H4.145.141,.H7 .300544 3.78979 106.663 T.F7.F1.16.8 4.998*14 6.99872 11.1972 44.2204 *4.0954 T.FQ.F4.96.9 2.32494 .860240 1.58388 .543*28 o70.57414 21.6945 4.4309 4.70534 .663162 .548249 1141.142,H3,144.H5,H6,H7 .79 .90 H4,H2.143.H4.H5,H6,H7 1.31517 1.64396 2.63033 3.34052 .4 -9--4-_ .41141.1.7 .1811014 4.09644 4.37055 2.19288 2.78495 3.53601 I 4.6333) 5.09627 4147444 4.92941 4.2487 0 .25 .50 .75 1.0 .11*091 0 .25 .50 .75 1.0 I 1.?c(. 1.1.761.7 . .173157 .167467 . .467467 . . .120675 . J .334933 . 9 9 7.04207E-02 1 .5024 'Y 2.*12 .172.114 .3)4933 * 4.680350-02 I .669867 . (*3 2.91067 ID .27241.7 .5024 (D .1.1491* * -'.226D4R .669867 . 9 oq .-. 4.360i9E-02 .837333 . 3.950970-02 I0044 . * 1.71.14 .22141148 .837333 . '1 . E 3.445830-02 . 1.47227 . (9 1.0048 . (9 9 (13 1.17227 _. 3.487740-02 1.33973 . ID 4.1.0*31 . ID 1.33973 3.182790-02 i * 06.214 . * .14210*9 014.797 .197414 7.36853 4 1.22069003 . 7.536 ._ 8.0384 ID .' 4*4) 5.7846-04 I 8.20587 CD 0.1.2019 * .4114120 16.7467 . .174447 14.4211 .111699 ' 6.86643 19.7947 .

ii

.197227 21.1*; C) . * .4*249 22.11491 I . . R.i?1210P 023.4453 . #.,0914140-0P

When operating in head sea at a speed of 10 knots for example

the maximum mentioned above will occur at about 12 rad/sec.

The disturbances in the air cushion are caused by

encounte-red waves, which then influence the seals of the model. These

will also sway at a frequency close to the frequency of

en-counter.

In figu.re

4.11.3

a spectrum for pressure is shown in a head.

sea operation and here it is easy to distinguish a second

maximum at about 12 rad./sec.

Accelera- The evalutation of spectrum for acceleration show that

maxi-tion mum occurs for a correspond.ingfrequenCy as well as for the

spectrum of pressure. This is due to the fact that the

pul-sations of pressure in the air cushion cause motions in heave..

The maximum of acceleration spectrum. in the low frequency area

corresponds to the motions of the vehicle in rolling and

pit-ching and the maximum in the high frequency area is due to

vibrations in the model. This second maximum is related to

the special model which was used. at the trials.

For studying the acceleration that corresponds to the rolling and pitching motions of the vehicle the part of the spectrum

which appears in the lower part of the region is to be

obser-ved.

In figure 4.12.1 and 2 accelerations fore and. aft are shown

for the same test as the pressure shown in figure

4.11.3.

In figure 4.12.3 a spectrum of acceleration is shown in

foll-owing sea, and in his case no significant second maximum

ua,,1?.u4 MflIIP,Il4 1.AflcdcFo, 2.07225 A0q. R.2R97,r-D2 11.5822 558.97 - T.Ffl.F1.W6.fl T.O.F1.W6.0 I . 1.74P9 ..5flj4 .646578 4.47flA 1.71156 5.65141 .662667 .287919 67.147 _{$I.H2.H1.M4.Mc.H6.u5} . . Ht.H7.H7.M4,H5.H6.H7 l%(fl),AhiIl _{., .251415 .116766 .506875 .643668} .575857 .519797 1.19167 1.46263 1.89708 d.28624F-n7 -4.7ll562PO4 '.912Q1 .981974 2.1162 7.23157 80 _{o .pc .cn 75 1.0} 0 .25 .50 .70 1.0 8.00S7OF-flS _,__, t.AHT W1,R _{.4186107 .. 2.f.5R52P-05} .418106? . 1i5551r-fl1 11.4 1.27%2qF..flc . _0.811111 0 Cl) 1.60021r..0c 0.617111 . . Cl) R.56618r-04 U0.112.U4 _01.2SF. 8.%1500r-n1 .511916 110.790 j67447

*

-1.725fl4r-flS 01.756 * f4 4.81?cn-n4 '-... -1.1Q173r-fl4

T.rn.r1.w6.Q _{2.tIQ115 . ___} 1.ftA47rfl5_570n61E-05 1.67467 _E .71194l 7.80119 5.80104 .487904 A.56959r-07 02.017 . E 1.IOIIIF-04 I07..512

'

rs) D

H1.H2.I11.144.H5.Hl..H7 7.95067 2.610500r-n4 2.91067 . 1.,flRq4rfl1 .1l1191 .164719 .262782 313711 .47171%F. 7.14951

'

1.70153F-04 _j , 7.flflfl?l_fl1 .482862 .50914 04.768 .1.768 1.12176-fl4 o _{.75 .50 .79 1.0 .4.18667 .} (I) 1fl077SF-04 4.1866? 97920r07 ---+---.-+ -+- - 4.605 _CD 1,cI516F01 4.100935 CD .41866?

*

*

_-s

_{C!) l.fllSF.F-.flS 5.074} . _C) i.co47cr0l 5.024 . q6f.7QSIfl1 I °.6111 .. 1.19879F-.rlS 05.4476? 1.1AflA4F0I 09.44267 1.78071FAl 0i.70F. _ _,7.7191f10S 5.86111 1,BAASIF-fl1 c.Rh1 . . 5.d1d91Ffl1 0. .1.67467 4.71097F-fl9 6.28 6.78 .

-

0 9.648840-01 '... 1.650704-09 98.9355 Hood oos Q.ARl000flbI 1, 1c91sr.3

-

. 7.917q16.fl4 1.112486.04 -S.. 916.128 S . 1.847014.00 70.9155 019. 1653 10.047166.05 21.570? '5.074 * 1.759984_fis _{9.679fl *} 7.11197FQ4 '09.67915 019.9893 .. ?.IA4AIF-fli 70.9147 _Hood 1.816884.04 70.9147 .. 18,84 .. 1.402786-AS 77.4493 0 9145664.fl0 91.4401 (3 , 0

43.5

Caiculationof amplitudeoperator

By dividing the spectra for motions with the corresponding spectra for waves, amplitude operators may be calculated.

Every special condition regarding speed and heading towards the sea corresponds to a special amplitude operator for the

vehicle. To be able to use this operator for calculations

of motions in other wave systems it must be linear. This was controlled by. testing the model at constant speed and

direc-tion in different vave systems. By comparing the amplitude

functiorfs calculated, which then shouldagree,an acceptable

linearity was coiifirmed. .

In fi,ire 4. 1 3.1 an amplitude operator is shown. for pitching.

When the operators were calculated some filtration had to be

done due to errors in both wave and response spectra at low

-frequencies. This smoothing of the spectra was made by using

a function of second order in, the disturbed area. This

cor-rection has, however, only practical influence while driving

i.n head sea as the frequency then will increase.

4.3.6

Calculation of full scale response

To study the motions that may be expected for a 1000 ton-side-. wall hovercraft operating in the North Sea, some of the results were used for further calculations.

This evaluation assumes that the response of the vehicle is

linear, which seems to be .the -case according to the

evalua-tions carried Out. As the testing program became somewhat

smaller than the one originally..planned, it has just been possible to study the motions of the craft in a rather

mar-row range of speeds. The trials that were Oarried out

corre-spbnd to speeds between

35 and 45

knots in full scale, which

MO ,M2,M4 5.25908E-02 2.13128 T,F0,F1,W6,Q .986493 2.02738 HI ,H2,H3,H4,H5,H6,H7 .458654 .573317 1.68555 1.77728 0 + '=J 1.17227 1.33973 ' 1.5072 1.67467 CD 1.84213 2 0096 2.17707 2.34453 '.. 2.512 2.67947 2.84693 3.0144 ic 3.18187 CD 'd 3.34933 ( 3.5168 3.68427 p 3.85173 P' 4.0192 4.18667 o 4.35413 d 4.5216 d Cl) 4.68907 1 4.05653. 5..024 o 5.19147 I.j 5.35893 P. 5.5264 5.69387 5.86133 6.0288 I-' c-I-6.19627 6.36373 CD 6.5312 C) 6.69867 ) 0 6.86613 Q 7.0336 CD 7.20107 p 7.36853 ci- P 7.536 7.70347 7.87093 8. 0 384 8. 20 587 8.37333 8.5408 8.70827 87573 0 432 9.21066 9.37813 9. 54 56 9.71307 .* T(FULLSKALA. 3. 27 183 9 3. 9609 2 11458 .917307 .25 .50 .75 * * Figure A16 Reeponco Pitch 71.1 Bóau.fert .229327 1.47916 1.0 -I.--> 9.83248E-32 Cl) 4.60812E-31 2.06697E-1-9 CD CD 1.4-7576E--18 CD %._# 4.25466E-IB 3.09625E-12 Cl) 1.59640E-11 V CD 4.07597E-09 o

4.51-152E-08 1. 66854E-07 1.37584E-06 7.14281E-06 2.13664E-05 6 60661E-05 2.24035E-04 5 30069E-04 I .01310E-03 2.51868E-03 5 .000I4E-03 6 62227E-03 8.79 1141-03 I

12883E-02

I.09595E-02 9.45972E-03 9 99679E-03 1.38282E-02 2. 14102E-02 2,76201E-02 2 .73862E-02 2.55447E-02 .022016 .0176J6 I .67415E-02 i.57023E-02 1.34566E-02 1-.18252E-02 I

02913E-02

7 83923E-'03 4 .85361E-03 2.98191E-03 2 20053E-03 I .43201E-0-3 8.55371E-04. 5.89631E-04 5

1 3869E-04

4 37668-04 3.53294E-04 2. 96547E-04 3 83275E-04 5.68942E-04

OERAKNING AV AUPLITUDOPERATOR 1.0048 1.17227 1.33973 1.. 5072 1.67467 1.84213 2-. 0096 2.17707 2.34453 2.5 12 2,67947 2.84693 3,0 144. 3.18187 3.34933 3.5168. 3.68427 3.85173 4.0 192 4.18667 4.35413 4.52 16 4.68907 4.135653 5.024 5.19147 5.35893 5.5264 5.69387 5.06133 6.0288 19627 6.36373 6 .5312 6.69861 6.06613 0336 7.20107 7.36853 7.536 7.70347 7.87093 6. 03 84 8.20587 8.37333 8.5408 8.70827 8.87573 9. 04 32 9.21066 9.37813 9.5456 9 .71307 9.88053 a * * a * Figure A15

Amplitude operation Pitch

71.1

1.0 a

p4125.616

FARTYGETS FART I M/S? 75.67 RIICTNXNO UOT SJON? 71 69

101.156 55 15 2.69276E-04 2.69278EQ4 4.24673 0 0.25 0.50 0.75 + a a .958766 I 16498

A PiesonNoskowitz wave spectrum was chosen as a suitable theoretical wave system for the calculations.

0

Wave period in sec.

x Significant wave height in meters

Figure 4.14 Values used for calculation of theoretical

wave spectra.

By using a special program the Piersonoskowitz wave spec-trum may be calculated at different Beaufort numbers by us-ing the average wave periods and significant wave heights

for the route studied, fgire 4.14. By multiplying these

wave spectra with different operators the response was

cal-culated. In figures

4.15 -

4.18 examples from these

I 80 .02. 84 2.55722 78.1839 2717.13 T.F0.F1.86,Q 1.13576 1.76094 1.87744 .937947 1.59913 U0.I.12.U4 .60540 21.0299 T.F0,1.W6.Q 814.297 4 : uO,u2.u4 .123373 4.91959 T.P0.F1.86.Q 213.91 HI ,H2.H3.H4.H5.H6.H7 3.19826 3.99783 6.39652 8.12350 1.06559 1.87689 H1,H2.H3,H4.H5.H6.H7 ¶0.3144 1.98173 .947098 .778126 .994502 2.01106 H1.52.H3.H4.H5.H6.147 2.10002 .957639 .351245 11.7536 12.3933 0 .25 .50 . .75 1.0 1.55625 1.94532 5.71923 a.03o4a 3.1125 3.95288 5.01091 .7024892.58165 2.72215.078112 1.40498 1.78432 2.26553 0 .25 .50 .75 1.0

+ -+

0 .25 .50 .75 1.0 +---_+---+---+- t 1.17227 . 1.81089E-25 1.17227

.

1.33973 .5 4- + S 1.33973

.

1.5072

.'

1.17227 .5 7.476540-25 8.120830-14 1.33973 . p.. rJJ 0 0 0₀ 1.67467 .* CD ® 1.84213 .

''

2.0096

.'

2.17707 E 314*3 .. _a) s._.-2.512 . 'i.) 3.005940-13 1.256350-08 8.96957E-08 2.565940-07 3.046790-05 t.55444E-04 1.5072 _. 1.67467 .* 1.84213 . 2.0096 _.. 2.17707 . 2.34453 .5 a) J D I".) CD 3.76930E-20 1.766530-19 1.982260-12 1.415200-Il 4.080290-11 1.056490-07 1.5072

.'

1.67467

.'

1.84213 .' 2.0096 .5 2.17707

.'

2.34453 .5 p., (13 (1) ® 5.669700-302.657160-29 2.96061E-18 2.113790-17 6.09412E-17 2.113430-11 2.67947 . 6.007860-04 2.512 5.444560-07 2.512 .5 _1.089660-10 2.84693 3.405070-03 2.67947 6.695*40-06 2.67947 .5 _1.829790-08 3.0144 . 1.133540-02 2.04693 C12 6.280270-05 _2.84693 .5 2.017180-07 3.18167 . C) 3.34933 . 3.5160 2.216190-02 3.081990-02 7.069910-02 3.0144 .' 3.18*87 .5 3.34933 5 ₅(3 2.280020-04 5.94129804 1.678540-03 3.0*44 3.10187 .5 3.34933 .5. Cl] CD 0) 7.457260-07 5.042430-06 2.496260-05 3.60427 .1465*9 3.5168 .5 4.325920-03 3.5168 .. 7.406690-05 3.05173 .237266 3.68427 . S 9.34635E-03 3.60427 _2.152430-04 4.0*92 .348628 3.85173 1.917190-02 3.65173 . 6.835180-04 4.10667 .5*1603 4.0192_4.18667 . 3.477U6E-02 4.0192 _1.57741E-03 6.354*3 .829591 .058046 4.18667 . _2.975030-03 4.2I6 S 1.11385 4.35413 .107934 4.35413 7.081300-03 4.68907 1.12211 4.5216 5 .165879 4.5216 _l.36041E-02 4.85653 . 5.024 P 4.60907 1.16153 _4.05653 1.1607 5 _.107058 .213684 4.689074.05653 . _2.307950-021.770730-02 5.19147 . 5 .9026 5.024 . ₅ .233943 5.024 _2.098460-02 5.35093 . .63149 5.19147 . .195766 i 5.19147 2.760160-02 5.5264 . 5 .552964 5.35893 . .146663 5.35893 S _2.346920-02 5.69387 . .626404 5.5264 . .140031 5.5264 _2.445040-02 5.06133 . .823397 5.69387 .169004 5.69387 _{S 3.321830-02} 6.8280 . .94751 5.86133 . 5 .23665 5.86133 _5.07394E-02 6.19627 . .841*27 6.0288 . .284525 6.0288 _6.489810-02 6.36373 . S .696423 6.19627 .263235 6.19627 . * 6.376530-02 6.5312 .542*57 6.36373 .227197 6.36373 . _.os000 6.69867 .392645 6.5312 .183271 6.53*2 . 5.03042E-02 6.866*3 .337557 _6.866136.69667 ₅ .137961 6.69869 5 _.040001 7.0336 .29393 _7.0336 .122907 6.06613 . _3.765130-02 7.20107 . .233617 _7.20*07 .109034 7.0336 . 3.508630-02 7.36853 5 .190505 _{7.36853 *} 0.961370-02 7.20107 . * 2.987220-02 7.536 . .155273 7.509680-02 7.36853 . _{* 2.609180-02} 7.70347 . .112235 7.536 6.271670-02 7.536 . _2.256960-02 7.87093 3 8.0304 P' . * Piguxo £19 7.70347 6.619770-02 3.835660-02 7. 87093 gar* £18 .046106 2.76994EQ2 7.703477.07093 . _{PL61?. £17} 1.713070-02_1.05609002 0.20507

..

_ft..pon.i 8.37333 C17 . -P 8.5408 C!) .. PlieS 71.1 2.602080-02 1.735680-02 9.629780-03 0.0304 . 0.20507 8.37333 CD.. Iloepenso 71.1 1.630700-02 l.16095E-02 7.673270-03 8.0304 8.20507 8.37333 Cli: lIeupons. PLIeS 71.1 6.456370-03 4.743690-03 3.184320.03 8.70827 0 ... 6 6.350790-03 8.5408 0. 5 4.316570-03 8.5408 (D 1.831630-03 5IOr 8.87573 .. j* 5.316860-03 8.70627 - 2.891350-03 8.70827 0 _1.257610-03 9.0432 .* 4.368600-03 8.07573 *J1 2.455970-03 8.87573 .. %.J5 _1.092550-03 9.21066 _E '- 3.423690-03 9.0432 S

E..

2.044530-03 9.0432

.'

5 9.2781*0-04 9.37813 : 2.789590-03 9.21066 1.61921E-03 9.21066 S .* - 7.470700-04-9.5456 .* II 3.478890-03 9.37813 q . 9.5456

.'

II 1.333050-03 9.37613 .. fi 6.254550-04 9.71307

.'

0-. 5.029040-03 1.68371E-03 9.5456

.'

.p 8.059418-04 TCFULL6KA.A) 9.71307 .5 2.457390-03 9.71307 1.195740-03 3.76688 _3.53417 T(FULLSKALJ.) -3.29839