Nonlinear motions of fast ships and the effect on operability

NONLINEAR MOTIONS OF FAST SHIPS

AND

THE EFFECT ON OPERABILITY

J.A. Keuning

Report No. 930-P - May 1992

MARIN JUBILEE MEETING, lI -.

15 May, Wageningen

Deift UnIve,lty of Technology

Ship Hydrornechanics Laboratory Mekelweg 2

2628 CD beIft The Netherlands Phone 015 - 7868 82

SESSION II

DYNAMIC BEHAVIOUR

AND

NONENCIATHRE

a113 = signifIcant amplitude

af = vertical acceleration forward

g = acceleration due to gravity

Fnv' = volumetric Froude number

V/Jl'

Fn Froude number

v/Ji

L = ship length B

=beam

fi deadrise angle À wave length pitch' amplitude heave amplitude a = wave amplitude INTRODUCTION

In the last decades the interest in fast

marine vehicles shows a continuous

growth. Typical appliòatioñs a these

NONLINEAR P)TIONS OF FAST SHIPS AND THE EFFECT ON OPERABILITY

ir. J.A. iceuning

Ship Hydrcmechanica Laboratory

Del! t University of Techìtology

ABSTRACT

In the design practice of present days design frequent use is made of optimisation techniques based on operability analysis.

Given a known set of operational criteria with respect to motion amplitudes, velocities and accelerations and a statiaticäl des-cription of the environmental circumstances the "downtime" of the vessel under consideration may be calculated. This involves a large number of motion calculations for which generally spoken linear theories are being used being it 2-D striptheory methods or 3-D diffraction methods.

Fbr fast monohulls this may yield to eronous results, because the motions and in particular the vertical accelerations tend to become strongly nonlinear with increasing forward speed and rela tive motion amplitude.

A comparison between an operability analysis of a design

variation using both linear and nonlinear motion calculation

methods' will be shown.

kinds 'of high speed vessels are among

others:

patrol craft, combattant ships,

pas-senger ferries and pleasure

boats.-Traditionally the operation of.:these

kind of vessels was constrained t the

more or less

sheltered areas with a

moderate wave climate, due to the high motions and/or' accelerations expe-rienced by cräf t moving with high f br-ward speeds in waves.

The combination of high forward speed and an acceptable or even comfortable level of accelerations aboard the ship

proved to be a difficult problem.

Therefore all-kinds of so called "ad-vanced" concepts have been developped, each with their -own benefits and def

i-cuts. Compared to the relative simple

rnonohu'Ïl all these concepts proved to be

more expensive and more complicated and therefore there still remains -a role to be plaid by the fast monohuil.

Improving the operability of the fast mono-hull meaned improving the

seakeep-ing behaviour of the concept, lin partic-ulär in head waves.

To be able to perform an optimieatonof the design in the design stage it is 1m-, portant to have an adequate motion

pre-diction tool available!

Cenerally spoken two, models are availa-ble now adays:

- Most commonly used in particular in optimisation procedures is the linear

model. Not only is this model well

proven and extensively tested, it also combines great accurracy with ease of handling, ie. short run times on

com-puters.

- Less frequently used, but gaining in importance, are nonlinear models

de-velopped during the last decade..

These tend to predict important

cha-racteristics of fast monohulla in a

seaway, such as vertical accelera-tions, much better, but are generally

complicated, the simúlations in the

time domain demand big computing. power and for 'optimisation purposes they are very time consuming. A short

'descrip-tion of both models will be. presented

hereafter only to outline the differ-ences of importance in this paper. For more. complete discription referen-ces made to the literature.

LINRJR DRL.

A general accepted tool for calculating. the motions of ships moving with a f or-ward speed is the so called strip theory approach. In 'this approach the ship is devided in a large number of cross sec-tions, yielding a division of the ship

in essentially two dimensional "seg-ments" which are considered to be cilin-drical with constant cross. section in lengthwise direction.

For each of these "segments" the hydro-dynamic reaction forces, ie. added masa and damping as well as the wave exciting forces aré being calculated using linear potential theory. Use is being made of conformal mapping techniques to trans-form the actual cross sectional shape of the ship and the potential due to the oscillatory motion to the unit circle or of a 2-D diffraction theory solving the boundary value problem on the oacillat.-ing cilinder in the free surface.

Since the theory is in principie 2-D in-teraction bétween the different segmenta are not considered. Forward speed

ef-fects howver are being taken into

account by introducing corrective terms in the equations containing the distri-bution of the added mass and damping over the length of the ship and their

derivatives. The theory is amply

described by among others Tasai

[11,

Gerritsma and Beukeiman [21 a.o.

A linear model however lends it self

very weil for calculations of the mo-tions in a irrguiar sea characterisized by a given wave energy spectrum: once

the transfer function is known the

response in a variety of spectra may be calculated using the linear

superposi-tion principle. This may weil explain

the popularity of linear models in

opti-misation routines. Typical reStraints

however of this calculation method are: linearity: forces and motions are li-nearly dependent on the wave amplitude moderate forward speed

small motiöns amplitudes, actually the calculations are carried' out for zero

amplitude of motion.

siendér hull forms and' no big changes

in hull geometry in the region above

and below the waterline in contact

with the watet in the relative motion. Some of the constraints, mentioned are not very stringent. For instance the

restriction on the forward speed.

Blok and Beukelman (31 took the parent

model of the High Speed Displacement

Hull Form Series of MARIN. This is a

high speed round bilge hull form,

showing resemblance with the Marwood

and Bailey hull form. They calculated

the heave, the pitch, relative motion

at the bow and the added resistance of

this model at high forward speed and

compared these with measured results.. The speeds investigated were Fn = 0.57 and Fn 1.14. A typical result of their

calcUlation is found in Figuré 1 and

Figure 2.

o

o

'Figure. 1. Heave transfer function head

seas. From (31.. MODEl. 5 Fn. 1.140 VERSIOII I 2 FIT EXP CLOSE

----'VERSIOU 0 MAR54 0.5 10 .5 1.5 I.0 't 0.5

They performed the comparison between calculated and measured results for a variety of -models which were all tested

which was not to be expected since the so called version 2 included additional terms thought

to be of

importance in particular at high forward speeds.

o o

Figure 2-. Pitch transfer function head

seas. From E-31.

Thereafter the linear approach has also been used extensively for the calcula-tion of the mOcalcula-tions of planing craft in waves. To show the applicability of this method the results found by Beukelman [41 will be -presented here. See Fig. 3. He compared the results of motion mea-surements and calculations for a hard

chine planing hull at high speed in

regular waves and found good correlation in heave and slightly less satisfactory agreement in pitch. Considerable discre-pancies however did occur in the results

of -the vertical accelerations at the

bow.

Results tended to detonate when

the environmental -condition grew worse-, ie for the higher seastates. This- is an

important aspect when predicting the

limits of operability which normally

spoken will be associated with more- or less extreme motions.

t

0.8 0.6 0.4 0.2 o I I - 0 0.4 -0.8 l..2

ñ;7.

Figure 3. Heave - transfer - function of planing hull. From [41,.

NONLINEAR MODEL

The motions of fast: monohulls in waves and in particular the vertical accelera-tions may be strongly nonlinear. This

nonlinear behaviour has already been de-monstrated during many years by various

authors.

For instance Van den Bosch -[5)

investi-gated the motions of -the Clement Series 62 parent hull form with 12.5 degrees of deadrise in head seas and compared these-with the motions of a systematic deriva-tive of this model with 25 degrees of deadrse. The frequency distributions for the vertical bow accelerations are presented- in Fig. 4 and 5 respectively From these figures the difference

between the two models may be -seen and in particular the- deviation from the Rayleigh distribution-. This- deviation is most evident for the model with the smaller deadrise angle.

MODEL S

Fn U40 CLOSE_{MARIN EXP}FIT

at MARIN.

Blok and Beukelman concluded that the application of the linear strip theory yielded quite reasonable results in par-ticùlàr for the heave and pitch mot±on even at the highest speed. Results of the reletive motion and the added resis-tance due to waves was generally spoken less satisfactory. Generally spoken the

so called ordinairy strip theory

(version 1) yielded the best results, Za/ca

1.2 1.-0 Fn 0.724 CALCULATEE

-MEASURED MIDEL NO.3 0.5

Vt?:

1.0 15 I.5 1.0 X .5 o-o-5

The nonlinear character of the system of a fast monohull moving in waves may be found amongst others in the change of reference position of the craft due to its high forward speed.

ti 30

0

20 10

I::

00 80 60 40 20

0 2

4 6 8 1012 14 16 1820 920

af rn/sec2

Figure 4. Frequency distributions of bow

vertical accelerations for 12,. 5

degrees deàdrise. From [51

io:

o

Figure 5. Frequency distributions of bow vertical accelerations for 25 degrees deadrise. From [5].

It is known that fast monohulls at speed have a considerable change in their re-f erence position known as "sinkage" and "trim". These are caused by a change in pressure distribution over the length of the model when compared to the assumed

hydrostatic pressure distribution at

zero forward speed. This is an obvious deviation from the procedure followed in the usual linear ca]culation routines, where the stili water zero speed water-une of the ship is used as the ref e-rence position around or rather at which

all, the forces, moments and

displace-ments are being calcùlated.

00 80 60 40 20 o »20 af rn/sec2

i

i

The, result of this is not Only f ond in a change of geometry, je waterplane area and shape, curve of cross sectional areas etc. The equilibrium situation of the craft at speed may not be obtained by considering static buoyancy forces only with the craft at its high speed

reference position, a discrepancy

between weight and displacement does

otherwIse occur one which can not be

handled by usual linear theory.

Other important phenomena introducing

nonlinearities are:

-' the pressure distribution over the

bottom of the 'craft due 'to its high

forward speed.

nonlinear added mass and damping. The

frequency dependency.':of the' added mass

and damping appeared to be of minor

importance when compared to the

changes herein due to the change. in,

for instance, the actual' geometry of

the craft in contact with the water

when performing motions with non small

amplitudes of motion Relating the

added mass to the actual momentaneous

waterline beam of the ship by using

Wagners frequency independend equation proved to yield' a significant

improve-ment, in the predicted motions and

aòcelerations.

nonlinear wave forces also due to the large motion amplitudes. in the f re-quency range of interest when

consid-ering fast monohulls in head waves

these forces are dominated by the Froude Krilof f component.

Taking the actual volume of the craft 'at its momentaneous submergence due to

the combined effect of momentaneous

motion amplitudes and wave elevation

appeared to be of prime importance

when calculating the wave f orcés.

Compared with this effect the dif

frac-tion part in these 'forces is of minor

importance.

COMPUTER PROGRN.

Based on both mathematical models compu-ter programms have been developped by the Delf t Ship Hydromechanics Lab: - The program called SRAWAY is based on

the linear strip theory. The program has been developped by Journée [61. it has been extensively used and tested

ma variety of

applications, among which the calcülation of the motion of fast monohulls, as presented by

Beu-kelman. The program runs on a PC.

MOD.84

-

ic----i--_

L/2aii3=i1i.4

MOD:85 ß

25.0°

Ffl27

-L/2aiaihs.4

'

0 2

¿ 6 8 10 12 14 16 18:20

Runtime for a monohull at 5 different speeds and a variety of headings is in

the order of 15 minutes on 80386

ma-chine.

The program FASTSHIP is based on the nonlinear mathematical model, it has been developped using the orginal work of Zarnick [81.

It is a time domain simulation pro-gram. At the Laboratory the program lis

run on a CONVEX. Typical runtime on

that machine for one particular speed at head seas in one particular

spec-trum is about 10 minutes. The program has been validated using tank results

of different planing hulls, for

in-stance the parent hull forms of the

12 .5, the 25.0 and the 30.0 deadrise series as described by Keuning '[7].

A typical result of this comparison

may be seen in figure 6.

t

5 10 15 20 25 30 DEAURISE

Figure 6. Measured and calculated' verti-cal accelerations as function of deadrise angle. From [71.

APPLICABILITY OF LINEAR AND NONLINEAR PDELS IN OPERABILITY ANALYSIS.

As indicated before the avaIlability of an adequate motion prediction tooÏ is essential when performing an

optimisa-tion with respect to operability of

('fast) monohulls.

Equally important ii the availability of a set of limiting criteria for the ope-ration of

the ship at

sea. For faSt monohulis the Dutch authorities 1ssued a set of cr.terIa related to the signif

i-cant values of the vertical

accelera-tions at the bow and rnidShp. These criteria are:

- Significant Vert.acc. at bow < 0.50 g - Significant Vert.acc. at i/2L < 0.35 .g Using these criteria an optimisation has been performed by Beukeiman (91

of a

design of a patrol boat for the Dutch

coastel waters. The results of this

study will be used to demonstrate the necessety of using non linear

mathemati-cal models.

In an effort to optimize the operability of the craft the effect of the beam of the craft has been investigated. This was done by increasing the beam of the parent ship with 0.60 m and decreasing it with the same amount. This resulted

in the following three -ships:

25.00

4.80

74.00

28

2.00

The operabiiïty has been calculated

using the given set of criteria and the scatter diagram for the Dutch coastel

waters. Both mathematical models have been used, ie the linear model and the nonlinear model.

The typical result of the calculation is

presented in Figure 7, in which the

solid line presents the result of the linear calculation and the dotted line the result of the nonlinear calculation. The difference between the two is

ob-vious and may be largly attributed to the decrease in deadrise of the vessel with increasing beam, which inevitably

leads to an increase in the level of

vertical accelerations. This effect is not properly accountéd for- in the linear model. The change in parameters used may even more mask the influence of the de-crease in deadrise because the beamier boat has almost 20% more displacement compared to the narrow, high deadrise

ship.

Uptill here only the significant values of the vertical accelerations have been used as a criterium of operability. But what if the maximum values of these

ac-celerations are the determining factors in the Safe operation of fast monohulis?

length

m

25.00 25.00

beam

m

6.04 5.42

displacement m3 93.20 83.60

deadrise degr. 22 25

'P

-

LINEAR THEORY

D FASTSHIP MAXIMUM FASTSHIP SIGNIFICANT

I I I I

Figure 7. Operability of planing hull as function of beam.

In this respect a closer look has to be given to the criteria determining the limits of operability of fast monohulls in a seaway.

Generally spoken all ships perform spe-cific tasks where they are designed for, which impose specific criteria

deter-mining their limits of operability.

These may be related to heave, pitch and roll amplitudes and velocities or acce-lerations. More often than not they come in the shape of limits on significant values of the amplitudes of the motion

(or velocity/acceleration) under consid-eration. These will not be assesed here. From a real scale investigation aboard a variety of fast monohulls at sea

per-formed by the Deif t Ship Ilydromechanics

Laboratory it appeared that generally

spoken not the significant values of the vertical acceleration was the limiting factor for the operability of the ship

but the height of

the maximum values encountered. Professional crews tended to imply a voluntary speed reduction at the exceedance of one maximum vertical acceleration or slam, irrespective of the prevailing level of the significant vertical accelerations at that time. The criteria set forward by for instance

the Dutch authorities are "transfered" to significant values of the vertical accelerations because that was the usual

and well known way of setting criteria. The transverse however is based on the

assumption of dealing with a more or

less linear system, which implies a

ratio of 2 between the significant

value and the maximum peak value with 1/1000 change of occurrence.

As may be seen from Figure 6 in which both the significant and maximum values of the vertical accelerations have been plotted this fixed ratio is not valid for bow vertical accelerations of fast

monohulls and, in addition to this

this ratio is deadrise depended. So if the given criteria on significant verti-cal accelerations are "transfered back" to maximum accelerations at the bow and midship, being the actual limits of ope-rability which may not be exceeded, the criteria become:

max acc at bow < 1.0 g

max acc midship c 0.7 g

Using this criteria in the results ob-tained by the nonlinear calculations the operability reduces even further with

some 15%.

cONcLUSIONS

Both linear and nonlinear models are

being used for motion prediction of fast monohulls in waves. Since linear theory is not capable of taking into account the effects of high forward speed and changing geometry of the craft

perform-ing non small motions in head seas,

optimisation using these theories may yield eronous results.

REFERENcSs

Tasai, F., 'On the damping force

and added mass of ships heaving and

pitching', Reports of Research Institute for Applied Mechanics,

Kyushu University, Japan 1960.

Gerritsma, J. and W. Beukelman,

'The effects of beam on the hydro-mechanics characteristics of ship hulls', 10th ONR Symposium, Boston, June 1974.

[31 Blok, J.J. and W. Beukelman, 'The

high speed displacement ship syste-matic series hull forms', SNPIME,

Trans., Vol.92, 1984.

[4] Beukelman, W. , 'Semi planerende

vaartuigen in zeegang predictie

inzetbaarheid', Report 658-O, Ship Hydromechanics Lab., TU Delf t.

[51 Bosch, J.J. v.d., 'Test with two

planing boat models In waves', Re-port 266, Ship Hydromechanics Lab., TU Deift 1970.

[61 Journée, J.M.J., 'SEAWAY Deift',

User Manual of Relea8e 4.00, Report 910, Ship Hydromechanics Lab., TU

Delf t 1992.

(71 Keuning, J.A. ,Non linear

mathemati-cal model for heaving pitching of planing boats in irregular waves,

Ship Hydromechanics Laboratory, TU Delft 1992.

[8], Beukeiman, W., 'Predictioñ of

ope-rability of fast semi-planing ves-sels in waves', Report 700,, Ship Hydromechanics Lab., TU De]f t 1986.