### -'

### -,-[ Lit

N-f-119

### Lab. v

### Technische Hogeschool

### A. HAD JIDA KIS

### Deift

-THE EFFECT OP SIZE ON THE SEAWORTHINESS OP HYDROFOIL CRAFT.

By A. Hadjidakis.

Aquavion Holland N.y.,, The Hague The pitching movenents and the vertical. accelerations of htdrofoil craft with surface-piercing foils are studied in a very simplified way to show the effect of size as a function of wave parameters,

and speed or Froude number.

ConsideratIons, are given to variations of static pitch angle, heave, natural

-frequency and damping rati' o, the latter based on a linearized equation of motion. The analysis indicates that at wave

lengths of 2/3and 3/2 of the length of

the hydrofoil craft, extreme values of vertical accelerations are to be expected, wnioh ciecrease rapidly with increasing

length of che craft, or decreàsing speed, which leads to the conclusion that the

seaworthiness increases with 'the length of the hydrofoil craft.

The seaworthiness of hydrofoil craft is sometimes doubted,
while the comfort offered to the passengers is often
con-sidered to be insufficient, when going ôn a seaway. The
purpose of this paper is to give in the most simple _{way}
some insight into the behaviour of iydrói'oil craft _{on'sea,}
and to determine the most unfavourable conditions, _{which}
are compared for craft o± different size.

This, of course., needs some explanation. The high _{cost }
in-volved in constructing big hydrofoil craft makes it

neces-sary to obtaili experience regarding seaworthiness,
stabil-ity and comfort as well as structural loadings and other
technical aspects, by means of scale models ör small _{}
proto-types. It is therefore desirable to prove that the resulta
obtained in this way can be interpreted for craft of greater
size.

To-day a hydrofoil craft does not present problems on
rela-tively smooth water. Its behaviour under unfavourable _{}
con-ditions is thus decisive for its suitability for passenger
transport at sea.

### AQUAVION HOLLAND NV.

### RIOUWSTRAAT 154

### SESSION 3

120Therefore it is necessary to gather thé existing knowledge which may contribute to a prediction of the properties of a big hydrofoil öraf t, based on the known performance and behaviour of a small craft, so that a projeòt for a sea-worthy passenger ferry can be started in full confidence. The following ôonsiderations and calculations havé been

formulated in a general way, making them valid br a large

number of existing hydrofoil systems. However, they are not valid for systems which cannot be compared to a spring-and-mass system. Thus they do not apply to hydrofoil craft with fully submerged foils, lacking a definite position of equilibrium relative to the water surface.

Their stability depends only on a human or electrOnic brain, controlling the lift developed by the different foils.

The behaviour in ä seaway of this latter category depends merely on the degree of intelligence of its governoi'... Furthermore only the most unfavourable conditions have been

considered. Going against the waves, the

verticalaccelera-tfons Were found to be critical and when going with the waves, this was the case with the maximum negative pitáh angle.

Both critical values depend on design characteristics of the different hydrofoil systems, as thereare: the lift reserve of the forward foils, the natural frequenoles for pitch and heave, the damping ratio, etc.

These design characteristics, being independeñt of size, will not be discussed 0in this paper.

The many purposely introduced simplifications of course create deviations. Thus it is necessary to apply the results only to two.or more craft of the sanie hydrofoil system,

differing essentially in a scale factor only, for it is only in that case that the deviations are in the same sense for all units, so that they will largely compensate each other.

121

_{A. 1-LADJJDAKIS}

The seaway.

The waves are assumed to be of sinusoidal shape, where _{the}

waveheight N is equal to G times the wavelength _{4} _{,} _{and}

G indicates the rate of steepness of the waves.

The craft's speed V forms an angle / with the vector of

the speed of wave propagation C . Then the forced frequency or excitation frequency of the forces, trying to disturb the craft from. its equilibrium position, is

where

The amplitude of the static pitch angle on a given wave pattern can be determined as follows:

A

### Pig.l

The maximum static, pitch angle is attaiñed in the position shown above.

Its value is:

### -=? s4/n.

### I coi

### J)

which can never exceed 77e'

Similarly, the amplitude of the static roll 'angle is found

### tobe:

### cc)

1117. (if### '"i)

The vertical movements of the centre of gravity of a hydro-foil craft can also be determined:

Pig.2 The dimensionless static amplitude of the C.G. la:

(4)

### lf=

### f coa.

('if### f

Both values are shown in Flg.'3 as a function of wavelength divided by craft length. The scales for Ç and Z./g re valid for G = 0.05 . Por other values of O' the scales have to be adjusted.

The roll angle. ÇO will not be discussed in more detaLL, because experience has shown that rolling is not a crltic. factor. Moreover lt can be treated in the same way as the pitch angle.

Plg.3 shows both the static pitch amplitude 'q and the

dimensionless static vertical amplitude of the centre of gravity as a function of the relative wavelenth*/eo4

If etc., then

but Zug shows an extreme value,

### whilefor

,1 3

and b. attains its extreme values.. The parameters on the crafts behaviour will

It should be noted that the values, of t1e 'excitation frequency resulting from eqC1), should be regärded with some reserve.

Practice has shown results to be sufficiently accurate when going against or with the waves,but when going along the waves

higher values of w are actually found due to the irregularity

of the seaway. See ref.(8).

A

etc.,

### 74/O

effect of .these be discussed later.0.0I YE

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-cmncQL COPI-DI77OVJ IP/a O 123:### A. HAD JIDAKJS

### SESSION 3

The Hydrof oil craft.

The seaworthiness of a craft might be specified as a combination of characteristics which guarantee safety and comfort for passengers and crew while travelling at sea. Some of those characteristics are:

static stability, dynamic stability,

constructional properties,

propermeans of navigation, and

lifé saving equipment.

Variation of size of a certain type of hydrofoil craft will not affect its static stability.

Constructional properties, proper means of riayigation and life saying equipment are (although very important) not to be discussed.

Hence the f ollôwing will be limited to the dynamic

sta-bility and its influence onthe comfortof hydrofoil craft..

Thé main factors whibh define the movements are:

### 1.

static amplitude (_{iread}

_{discussed}

2 excitation frequency

a natural-frequency, and damping ratio.

The motions of hydrofoil craft are defined by a number of basic equations. There is equilibrium when the weight of the craft equals the combined lift forces of the foils:

of a foil is proportional to dynamic coefficient, ánd submerged foil area, or:

### L=LV'CgP

ap,

A deviation in pitch from the equilibrium position creates an extra lift 4L which tries to restore tha craft to its original position. The restoring moment is called R

It will be clear that: .

### aL::

since### L. ::,

eq.(5)### R::mt

.further

### J::mê'

if the mass distribution can be supposed to be similar.. Thus the.natural frequency of the craft cari be calculated. The lift force

pressuré, -lift

(6)

### p/:

_{V7fr}

### (12)

### so

125

### A.HADJIDAKIS.

(7) or

In an analogous way the natural frequency for heaving motions be found to be.:

(à)

### =

### kw4/

The dimènsionless damping ratio in case of pitch

### dp is

the damping ti divided by the critical damping:### (9)

dp=

where N :: ,.e.

In this equation 1Dp is the damping force.

### (io)

### Dp=fpYZ4CTd

in which

_{Ce=}

. and ### w::

so N::

### ve'ri

The foil area P , contributing to the damping, is of

course proportional to the f oil area P (11) (Y:: VfP

It was already stated that and

### _____

### vrVl

Combining equations

### (5)

and (6). with (12) leads to:.

Cg.,.

Similarly it can be found that in case of heave

### db... i

### CPr

Consequently the damping ratio is inversely proportional to the lift coefficient and the Proude number for both types of motion.

This result might seem unexpected, the damping being proportional to speed,.-whlle the damping ratio is inversely proportional to the Proude number. The

explanation is simple, because ari increase of speed of 10% corresponds with a decrease of submerged foil area

3

### i

f AMPi.! TUDE### Of fORCEQ V/5AT!ON5.

### rok VRlOU

GREE### or DAt4P/N.

TIG,4 :;### e

£0127

### A.HADJIDAI(IS

Por similar hydrofoil craft of differing size, kw,. kw -andk are constant values. They may vary, however for different hydrofoil systems.

All elements iecessary to calculate- the motions of a hydrbf oil craft are now available if the craft may be

considered as a damped linearized spring and mass system. The dynamic amplitudes are then determined by the

equations:

### (15)

### !''°\/

### ('/-!/'+ 4 dp'

### w/4

16) 4

### y -

+ 4dh' W/-These equations have been plotted

### ui

fig.4 for various damping ratios.-It is. now possible to determine the vertical accelerat-ions at a certain point of thé craft. This point has been chosen néar the, bow at a distance from the center of gravity 'of lijf ,.no passengers-or-crew being expected to be carried at a mOre forward point. The resulting

accelerationshave been äalculated by adding vectorially

thé vertical acceleration caused by a variation of the pitch ., and the vertical accelerat10 caused by a

variation of heave Z . This is based oi the assumption that pitch and heave are entirely independent of each other, which, although not correct, gives very accept-able results, as has been shown by Prof. Abkowitz. See ref. 9.

Behaviour of the craft.

Concerning the course of a hydrofoil craft relative to the waves, experience.has shown two conditions to be of decisive importance for its seaworthiness.

The f.irst occurs if=O , i.e. on a following sea. In

Pig.5 Pig. 5 shows the influence of the orbital motion of water particles in a following sea. This orbital motion

creates a moment which tries to pull the nose of the craft dowfl.

As the pitch increases with increasing wave height, it will be clear that at a certain wave height the

combin-ation of a high valie of nagative pitch, cOmbined with the-orbital effect, makes the bow touch water.

This phenomenon introduces a braking effect which causes the craft to slow down, so this wave height represents the limit up to which the craft can remain foilborne on a followihg sea. The lift reserve of thé bow foils of a certain hydrofoil system evidently determines the limit-ing wave height.

However, ii fig. 3 he dynamic pitch amplitudes of two similar hydrofoil craft differing in size only, have been indicated as functions o± the relative wave length. The critical condition for the craft with th lower Froude number is seen to occur at a greater relative

-wave length.

Consequently, of two similar craft the bigger one (having the lower Froude number) will encounter its critical

condition on a following sea on relatively higher waves. When going along the waves i.e. when p=W/2 , a hydrofoil

craft Will attain its greatest roll igle

However, experience has shown that this is not a critical condition at all, therefore it will not be discussed in more detail.

When the craft is going against the waves, i.e. 1=ff' the pitch amplitude is not critical, because the o'bital moment will help to surmount the next wave, but the maxi-mum value of the excitation frequency is obtained.

Therefore this can be called a critical condition as far

### J-SESSION 3

128## j

### I-

### t

MAX. VERTICAL. ACCELPIRA 7/ON RT aOW Oft

### AQUAVIT [,.7i,,, - t2f. J

.30 k,,. AND UADUJS [.35.0Cm - 118 ft. J 45 kn.### F6

### e

### 1/

WAVI LIA?Nas vertical accelerations are concerned, these accelerat-ions being proportional to the square of the excitation frequency.

While discussing vertical accelerations,

### /

will furtherbe assumed

### to

be equal to_{if}

Applying the foregoing theory to an illustrating example, a comparison is made between au existing small hydrofoil draft (

### t

=### 6.73

in; V = 30 knots) and a designed biggercraft C

### t

### = 36

in; Y = 45 knots). Of the existingcraft, the natural frequencies for pitch and heave and the
damping ratio are known. With the aid of figs. _{3} and 4 a
curve could be obtained, indicating the vertical
accelerat-ion at the bow as a functaccelerat-ion of the relative wave length.
The natural frequencies and the damping ratio of the

de-signed bigger craft have been calculated according to eqs.

### 7, 8, 13

and 14, which made it possible to establiah an equivalent curve for the bigger craft.'Both curves are shown in fig. 6.

it will be noted that there are two critical values of the
relative wave length */1 _{,} _{where the vertical acceleration}
at the bow

### io1,

attains peak values. These critica], wave lengths correspond with_{2/3}

and ### 3/2

times" the craft's length.Contrary to what might be expected,'fig. 6: shows that crit-ical values of acceleration are not to be expected at a 'relative wave length of more than two. This means that

vert-ical acceleration deòreases with increasing wave length. In other words, the comfort ofthe small craft will be much better on waves with a length of 20.m and a height of 1 in,

than on waves with a length of 10 in and a height of 0.5 in.

Similarly, the big craft will be more comfortable on waves of 100 in length and 5 in height, than ôn waves of 50 in length and a height' of 2.5 m, although the comfort in the latter case is much better than the best that can be

ob-tained with the small craft.

In reality the wave pattern is never found to be so regular as the theory supposes it to be. On a seaway wave lengths vary considerá'bly, which tends to level off the extreme

ac-celeratiois. Purthermore small waves are always superimposed on thelonger waïes, which will tend to raise the maximum accelerations to be found. for values of '/g , higher than two. These'two effects have been taken Into account in the dotted curves, shown in fig.

### 6.

### SESSION 3

:JO

o

LEMGTH OP CPPT

### MAX. Y(TICA

ACCEL(R6QT/OM AT BOW

Of HYDgOPOIL CRRPr, POR CRITICAl. YAWU OP

Ì1L

P5 PUMC TIOPI OP &'

AT CV5TANT

LD

### or iokìi.

LENGTH OP CRAFT

### X. VLRTlCAL. RCCELERATION PT 3GW

_{OP N.YNCP1L CRAP}

AT 1.5

### A5 R

PUNCTIOM OP MILD. IC PIG, 8133

### A. HAD JIDAKIS

'As the behaviour of a hydrofoil craft in the most unfavour-able conditions is ' decisive importance for its seaworthi-ness and comfort, the critical accelerations at */,= 2/3 and

= 3/2 have been plotted in fig. 7 as' a function of craft length. This graph is valid for one speed only, i.e! 30 knots, which makes it possible also to show the variation

of the Proude number with the craft length. The vertical ac-celeration at the bow for

### */f.=

1 is also shown.0f these curves the one 'for */ = 3/2 is the most important, because the critical accelerations at 7t/ 2/3 occur at relatively" higher frequencies and can therefore be more easily attenuated or even eliminated by means of foi]. sus-pension or similar improvements.

The influence of the speed of the craft is shown in fig. 8, where the curve for */g = 3/2 has ben drawn for five dii'-ferent'speeds. Evidently the vertical acceleration is ap-proximately proportiønal to the square of the speed fora given craft length.

Hence 'it can be stated that vertical acce±erations decrease rapidly with increasing 'length of the hydrofoil craft, which means that the comfort, depending on the frequency

of variation of the accelerations (jerk), improveseven more rapidly.

Conclusioñs:

Assuming that the wave length and height are proportional to the lèngth of the hydrofoil' craft, in other words, that a craft of double length is running on waves which are twice as long and high, it may be concluded th9.t:

On a following sea, where maximum pitch is the critical factor, the seaworthiness is nearly unaffected by size. Actually the seaworthiness improves slightly' ,with

de-creasing Froude number., i.e. inöreasing length.

When going against the waves, vertical accelerations are critical, which, with increasing length of the'craf t, de-crease more than px'oportionally with the Proude number. Consequently the seaworthiness increases with the length of

the craft, the more so when the comfort is taken mio con-sideration.

List of Symbols.

angle of attack (effective),

8 = maximum span of. hydrofoils, = lift coefficient,

C = wave propagation,

= course angle relative to wave propagation, D = damping force,

### d

= damping ratio,P = submerged foil area (effective),

= submerged foil area, contributing to damping, = static roll amplitude (radians),

= roll amplitude (radians),

9 = acceleration f gravity, N = wave height,

### h =

index.f or heave, J = moment of inertia, k = design constant, L lift force, ( = craft's length, 7.. =wave length,= mass of the raft, N = damping,

= excitation freqiency, w,,= natural frequency, p = index for pitch,

static pitch amplitude (radians), = pitch amplitude (radians),

R = redressing moment (per radian),

O =density,

G = steepness of waves,

V = raft's speed,

W = relative vertical speed, Z. = static heave amlïtude, Z = heave amplitude.

135

### A.HADJIDAKIS

References.

i.) Buermann, T.M., Leehey, P. and. Stiliwell, J.J. "An Appraisal of Hydrofoil Supported Craft",

Trans. of the Soc. 'f Naval Arch. and Marine Eng., New York

### (1953).

### 2.)

Crewe, P.R., "T-he Hydrofoil Boat; Its History .ndFuture Prospects",

-Trans. of theInstitution of Naval Arch., london

### (1958).

3,) Bi1lèr, K.J., "Neue und noch gr6szere Tragflügelboote", Schiff ünd Hafen

### (1959), p. 802.

### 4-.)

Schertel, H. von, "Tragf1chenboote",Handbuch der Werften, Band II,

Schiffahrts-Verlag Hansa, Hamburg

### (1952).

### 5.).

Schertel, H. von, "Tragflüge1booe",V.D.I. Zeitschrift, Band

### 98, No. 36,

p.### 1955,

Postverlagsort Essen, Dusseldorf

_{(1956).}

Reinecke, H., "Tragflügelboote",
Schiffbautechnik, 8. Jahrgang, Heft 4,Berlin

_{(1958).}

Berentzik, H., "Vergleich der theoretisch errechneten Beschleunigungen eines Tragflugelbootes im Seegang mit den experimentell ermittelten Werteil",

Schiffbautechnik, 10. Jahrgang, Heft 7, Berlin

### (1960).

Heer, C.C., "Ergebnisse von Beschleunigi.mgsmessungen an einem 10-m-- Tragfliigelboot-Groszmodell lin natür-lichen Seegang der Ostsee",-Schiffautecbnik, 9. Jahrgang, Heft il & 12,: Berlin

### (1959).

AbkoWìtz, M.A., "The effect of Antipitching Fine onShip Motions",

Trans. of the Soc. of Naval Arch. and Marine Eng.,

DESIGN AND INrrIAL TEST OF CNR SUPERCAVITATING HYDROFOIL BOAT

### ÍCH-6

by GLEN J. WENNAGEL Vice Pres. (Affiliate Bethpage, Abstract:Dynamic Developments, Inc. Babylon, New.York, of Grumman Aircraft Engineering Corp.,

New York, USA)