Seakeeping in Design

L E C T U R E m 1

S E A K E E P I N G IN DESIGN

L E C T U R E R : Tor Svensen, Det Norske Veritas Classification A/S

1. Introduction.

The primary use o f seakeeping theories is in connection with the design o f new ships.

Seakeeping theories used in combination with model experiments can play an important role in

the design process. However, it is important f o r the designer to have a good knowledge o f the

limitations with the individual theories and methods employed. I t is also important for the designer to know that possible design changes in order to improve seakeeping performance.are feasible. A common problem in the design o f commercial vessels is that seakeeping aspects are considered too late in the design process, after all the major parameters influencing seakeeping performance have been fixed based upon other considerations such as still water resistance. The primary area for use o f seakeeping theories in design are:

- Evaluation o f basic parameters such as motions and accelerations and comparison against criteria f o r cargo integrity, passenger comfort etc.

- Evaluation o f speed performance on a given route or selection o f routes for determination o f sevice margins and required main engine power

- Calculation o f hydrodynamic loads on the hull structure in a seaway and use o f this information in connestion with the structural design o f ships

The latter is becoming an increasingly important application as reliability based structural design procedures are gaining acceptance.

The following sections will discuss some o f the important issues relating to the application o f seakeeping theories in design.

2. Use and limitations of seakeepine models

The most common theoretical method for prediction o f seakeeping performance is the linear strip theory method. Despite the very substantial simplifications o f the actual physical realities that are made in linear strip theory, this method has gained wide acceptance in connection with

ship design. I n a survey o f ship model tanks to be published by the 1993 I T T C the following conclusions are presented :

Three-quarters o f the Institutions use 2-D strip theory or slender body theory only. Only about one-quarter use or have developed 3-D computations. The 3-D methods are used mainly f o r zero or low forward speed.

Three-quarters o f the Institutions use a frequency domain approach. The remaining one-quarter have a time domain capability.

It was not possible in this survey to distinguish between the methods that are routinely used and those that are still under development. I t should also be noted that some o f the institutions that are the most active in the field o f numerical seakeeping do not own any experimental facility and are therefore not included in the survey. However, the survey do present an interesting picture o f the present state-of-art.

When considering seakeeping in connection with design, the most important motions are absolute vertical acceleration and the relative motions at the bow. Vertcal accelerations are directly related to crew and passenger comfort and safety o f the cargo as well as the global structural loads imposed. Relative motions at the bow are more related to how well the vessel will be capable o f maintaining speed in heavy weather. The following comments are intended to point out how well current seakeeping theories are capable o f predicting the various motions and derived parameters o f interest in connection with design.

Vertical motions and accelerations: Good results from 2-D strip theory for most ordinary ship hull forms. Although the theory is limited to small amplitude motions, results show surprisingly good results f o r relative large amplitudes when compared with model experiments and fiill scale measurements.

Relative motions: Relative motions at the bow as well as the stern are not predicted well by linear 2-D theory. This is mainly due to the fact that the stationary wave field (the bow wave) and the dynamic swell-up due to the pressure field generated by the water entry o f the flared bow section are not included in the theory. In order to predict the relative motions at the bow with an acceptable degree o f accuracy it is necessary to include the non-linear body- boundary conditions in the prediction method. Such programs have been developed and are gaining acceptance in use.

Slamming: Slamming pressures are a flinction o f relative verical velocity and geometry. For deadrise angles less than 20 - 30 degrees, the maximum pressure will occur in the region o f where the jet is formed. Calculation o f slamming pressures necessitates the use o f nonlinear theories. The local pressures generated in slamming will normally not have any significant influence upon the global motions o f the vessel. As a result, the only practical way o f handling slamming predictions today is to first predict the vessel relative motions and subsequently use a non-linear boundary element or similar program for local investigations o f slamming. It should be noted that the heel angle at impact is an important factor when predicting the impact pressures. Accurate prediction o f rolling motion is therefore a requirement in connection with slamming investigations.

Global loads - vertical bending moment: Vertical bending moment is primarily a fijnction o f inertial loads and pressure forces acting on the hull. For large amplitude motions, linear

theories will underpredict the pressure forces acting on the hull during entry o f the bow section into the water. I n order to account for this it is necessaty to include incoming wave as well as the non-linear conditions on the body boundary. 2-D methods for time-domain modelling o f these effects are standard routines today, 3-D methods are under development, but are not yet part o f routine design procedures. Differences between linear and non-linear predictions o f vertical bending moment can be as high as 50-60 percent.

2-D vs. 3-D theories: Complete numerical solutions based upon 3-D theories with forward speed are still in their infancy. The major driving force behind the development o f 3-D methods is the prospect o f more accurate predictions o f hull pressures. This will give more accurate predictions o f local and global loads as well as added resistance in waves. Developments in computer power may result in 3-D methods playing an icreasing part in routine applications within 2-3 years f r o m now.

3. Seakeeping criteria

When using seakeeping criteria in connection with a design development or evaluation it is important to remember the following 3 basic requirements:

1. The criteria and corresponding responses must be relevant to the mission o f the vessel. 2. Criteria levels must be related to the actual task or mission o f the vessel.

3. The numerical value o f criteria levels must be based upon actual ship performance assessment.

For commercial ocean going vessels, seakeeping performance is principally addressed in terms o f :

Habitability: The ability o f the vessel to carry out a mission with a minimum o f

discomfort.

Operability: The ability to carry out a mission under all types o f weather

A third aspect o f seakeeping performance is survivability or seaworthiness. This aspect is usually not considered in detail by the designer and is generally assumed to be satisfied by adherence to appropriate classification rules, load line and stability regulations.

In practice the boundaries between habitability aspects and operability aspects o f seakeeping performance are vague and the two will always be considered together.

By describing seakeeping performance in terms o f physical parameters such as absolute and relative motions, accelerations, bow wetness and slamming it is possible to quantify

performance and subsequently evaluate performance in a rational and systematic manner. Limiting values for individual performance criteria have been derived f r o m full scale operational experience. These are:

Design limits: Absolute limiting values which are not to be exceeded in service

Operational limits: Limiting values beyond which performance degradation or

increasing likelihood o f vessel or cargo damage will occur Limiting values for operability forms the basis for voluntary speed reduction in service. Voluntary speed reduction or alteration o f course in service is in practice a highly subjective action by one ship's master based upon an observed degradation in habitability or operability. This subjective action is normally not reflected in the design analysis and limiting criteria are treated as absolute criteria in most aspects o f design analysis. This in itself may be a significant source o f error.

The enclosed figures present limiting values for selection o f the most common individual seakeeping performance criteria applicable to merchant vessels. The significance o f individual

criteria for some principal ship types are also presented. From the data presented, it is

significant to note that criteria limits vary considerably depending upon the source and the ship type. Only for vertical acceleration at the FP is there a reasonable agreement between the various sources.

4. Accuracy requirements

The uncertainty associated with establishment o f valid limits for individual seakeeping criteria are important to consider against the uncertainties in the seakeeping prediction method itself. It is often argued that uncertainties associated with the establishment o f limiting values are not significant when comparing characteristics o f two alternative designs. This argument may hold f o r naval vessels where mission effectiveness is primarily a function o f seakeeping

performance. For merchant vessels seakeeping performance is usually a trade-off against other factors such as still water performance and building costs. The absolute value o f each

individual seakeeping criteria limits can be an important factor in establishing a merit rating between alternative designs in techno-economic terms. Using a more severe limiting criteria will penalize a poorer seakeeping design more in terms o f loss o f performance. This may lead to the incorrect conclusion that a particular design is outside the limit o f a stated performance specification.

In order to illustrate the consequence for the design process o f errors in seakeeping predictions or in criteria limits, a case study is presented for a medium size container vessel operating on the North Atlantic Route. Details o f vessel and route are given in the enclosed table.

The effects o f introducing an error in the estimate o f the relative motions at the FP upon the limiting speeds due to deck wetness have been investigated for a range o f wave heights in the N o r t h Atlantic. The results o f this investigation for a maximum deck wetness probability o f 3% are shown in the enclosed figure. Similariy, the effects o f changing the limiting value o f individual seakeeping criteria have been investigated, and the results for vertical accelerations at FP and deck wetness are shown in the enclosed figure.

The results as presented show that variations in the predicted responses, which are well within the Hmits o f accuracy for present seakeeping theories, can result in dramatic reductions in the predicted speed for the vessel. A n overestimate in relative motions by 1 metre in this case represents an error o f only 12% with a corresponding reduction in maximum permissible speed o f over 3 knots in head seas in the range o f significant wave heights from 6 to 9 m. These results are clearly o f significant value in the design process. I f voluntary speed reduction at a

significant wave heiglit o f 7.5 m is unacceptable to a particular operator, then the designer will have to improve the seakeeping abilities o f the design by, for example, increasing the freeboard in the bow region. When using this type o f deterministic analysis o f extreme events it is clearly important that the seakeeping prediction method employed is capable o f generating accurate results and that criteria limits are stablished with a high degree o f confidence. However, in reality, a vessel will only meet such extreme event situations during a very small percentage o f the total operational time. The overall impact upon techno-economic performance may therefore be relatively small. This is in practice best examined by performing an operational analysis for the proposed design using a voyage simulation model. A n example o f such a model is the S E A W A Y system as already presented. In a voyage simulation model the vessel operation i modelled on a realistic trading route and the various factors affecting vessel performance in service are modelled in combination rather than on an individual basis. The principal steps in a voyage simulation is shown in the enclosed figure.

The environment is described in terms o f wind speed, direction, wave height, wave period and direction for predetermined segments o f a given route. This permits both voluntary and involuntary speed losses to be taken into account in the analysis.

Involuntary speed loss is defined as caused by Wind resistance

Added resistance in waves (short waves and ship motion domain) Added resistance due to steering (rudder motions)

Voluntary speed loss is a deliberate reduction in speed or change in heading due to exceedance of one or more limiting values for individual seakeeping criteria.

Long term or short term statistical weather data can be used in a voyage simulation analysis. In a design evaluation long term annual statistical data for the relevant routes are usually employed. This provides the most realistic basis for assessing the total economic measure o f merit for the design.

The selection o f operational profile (route) is clearly important f o r the results o f the analysis. The probability o f encountering severe weather conditions varies considerably between different sea areas with a corresponding variation in vessel performance. It is therefore important that the design analysis is performed using a realistic operational profile corresponding to the expected future service profile o f the vessel.

In order to illustrate the above points in some more detail and to examine the importance o f seakeeping characteristics and voluntary speed reduction against other involuntary speed losses, the container vessel described in the enclosed table has been modelled on a North Atlantic trading route vAth a typical roundtrip schedule o f 21 days.

In environmental terms the North Atlantic represents one o f the worst possible routes and both voluntary and involuntary speed losses and derived service margins for a vessel on this route will normally exceed values derived f r o m other routes, including a world-wide operating scenario.

Constant speed operation is assumed in the present analysis. When using constant speed as basis f o r the analyses a target schedule o f port arrivals is derived based upon this target speed, and the speed and power is adjusted continuously to give the correct arrival time. This method o f simulation reflects the normal mode o f operation where speed and power is increased during good weather parts o f a passage i f the vessel has previously been delayed by voluntary or involuntary speed loss during bad weather. The practical limitations on installed engine power are o f course observed during such simulation.

The enclosed table presents results f r o m the analysis o f involuntary speed loss showing that the vessel is not capable o f maintaining the required schedule despite having an installed engine power service margin o f 15 percent. For the complete roundtrip voyage the average involunatiy speed loss is 0.9 knots and for the Westbound Trans-Atlantic voyage 1.7 knots. Also enclosed are results f r o m an anlysis o f voluntary speed loss due to deck wetness using a 3 percent probability as the limiting criterion. For the Base Case the relative motions at the F.P. is marginally below the critical value for voluntary speed reduction. I n the subsequent cases the freeboard has been reduced, thus simulating an overestimate in the relative vertical motions at the F.P. The results cleariy show that a relatively large error in the seakeeping prediction will have a small impact upon the total speed and power performance o f the vessel.

M o r e important to note is the fact that involuntary speed losses contribute far more

significantly to the total loss in performance compared with voluntary speed losses. On the other routes that the North Atlantic this difference is even more significant.

It is clear f r o m these results that an error o f 10-20 percent in seakeeping prediction can be accepted at the design stage when considering voluntary speed losses and the total techno-economic performance o f a proposed new design. The larger contribution by involuntary

speed losses to the total economic performance clearly demonstrates that it is the accurate prediction o f added resistance which is more important in the design process.

A further comparison between speed losses due to environmental effects and speed losses due to deteriorative effects was carried out f o r the same vessel. A n increase in average hull roughness f r o m 125 [im to 300 f i m in this case represents a fiirther speed loss o f 0.3 knots. For a 5-6 year old well maintained vessel an average hull roughness o f 300 \xm would be a representative number. Further, more dramatic speed losses would cleariy take place i f the vessel also experienced hull fouling. A total speed loss in the range 1-1.5 knots due to environmental and deteriorative effects would therefore be an expected value for this type o f vessel on the N o r t h Atlantic route. In economic terms a speed loss o f 0.5 knots when

translated directly into lost cargo carried represents a total economic loss o f approximately $ 2 million over one year. This figure can serve as a guide when considering ways o f improving the seakeeping and overall techno-economic performance o f a new design.

5. Application of seakeeping theories in structural design

The conventional method o f using seakeeping prediction in connection with structural design is to perform an analysis o f motions and global loads (vertical bending moment and torsional moment). The vessel is subsequently "placed" on a regular wave giving the same global loads and the pressures on the hull resulting f r o m this wave are input to the finite element model. M o r e recent methods o f analysis also permit taking hull pressures directly from the seakeeping analysis in frequency domain and input to the finite element analysis. These are standard methods and will not be dicussed fiirther here. Instead it is relevant to show how seakeeping theories may be combined with modern probabilistic methods in the development o f rational methods for structural design

Probabilistic methods are used to determine the probability o f failure f o r a combination o f several variables and events. Computational methods determining the probability o f failure for a combinations o f several variables and events are today available through commercial

software. The software will schematically work as in the enclosed figure.

In order to apply probabilistic methods in assessing the safety against loss due to lack o f stability, the following steps are required to be performed :

1) Choose physical model to describe the relevant failure modes (limit states). 2) Model the uncertainties in a consistent way by probability distributions.

3) Choose statistical distributions types and distribution parameters for all uncertain variables. 4) Integrate probability distributions with the physical model in a limit-state function.

It is seen f r o m the above item list and scheme below that the physical model or limit state, describing when a failure occurs, is the primary item. This numerical limit state model f o r use in probabilistic methods may be both a purely experience based.regression analysis including the error information

or

it may be a physical model describing the dynamic behaviour o f ship motions with inherent uncertainties and model uncertainties. (Requires test results and analytical work).

Presently considerable research effort is spent in this area. However, to reach valuable results it is not only the computational methods that needs to be improved, but also the data collection and data analysis, forming a basis f o r the probabihty distributions. Experienced personnel can then join the physical models and decide on standard probability distributions for use in

reliability analyses.

The above model requires that hazards are identified and formulated in terms o f limit state functions. For different vessels there are different hazards or failure modes that need to be covered.

Combination o f load effects: Within each time scale there may be a set o f load components. For example, at the typical wave frequency it may be relevant to consider the horizontal and vertical bending moment and the local sea pressure acting on a plate field. For a description o f the distributions o f the combined load processes a formulation using crossing statistics is a convenient representation. The upcrossing rate describes the number o f crossings per unit time o f a specific level, and may be the basis for the required response distributions both f o r the fatigue and extreme value calculations. For a combination o f several simultaneous processes including nonlinear combinations, the outcrossing rate into the failure domain ( g ( X , t ) 0) contains the corresponding information (see enclosed illustration). For different types o f

failure, or load combinations, the crossing rate gives the distribution o f peaks that is used in the fatigue calculations and the extreme value ditribution used in ultimate limit state calculations

(ULS), The method can be apphed to Gaussian ( for example roll motion ) and non-stationary processes ( as f o r example lifting operations ). Non-linear load combinations may also be considered, as for example buckling under biaxial loading or the Von-Mises stress criterion. The exact solution may be approximated by simulation methods.

The numerical solution may be determined using a program such as P R O B A N (se enclosed illustration). The resulting outcrossing frequency is used to determine the probability o f failure during one specified storm, to be fijrther processed when determining the annual probability o f failure in the ultimate limit state. The same out-crossing fi-equency is used in determining the long term distribution o f stress amplitudes for use in the fafigue limit state.

The process f o r a typical application will consist o f the following steps:

- perform seakeeping calculations to obtain motions and loads transfer fijctions as well as the covariance matrix for the intended load effects

- define limit state fuction

- define wave environment for the analysis

- perform analysis using a probabihty integral solver program, such as P R O B A N - perform analysis on the resulting outcrossing frequency for determining U L S or

fatigue compliance with requirements.

Examples o f the most relevant application area f o r this type o f analysis is fafigue in side longitudinals o f large tankers, buckling o f bottom and deck panels or buckling o f L N G spherical tank shells.

Bottom Slamming Bow Flare Slamming Deck Wetness - r^ ^ n n Vert. Accel. Vert. Motion Roll AmpI. Prop. Emerg.

\ ^ ^ ^ ^

Large container vessel X X X X

General Cargo ship X X X X

Ro-Ro X X X X

Passenger vessel X X X X

Seakeeping criteria limits for merchant vessels

Ship type

Limiting criterion

Source

Deck wetness

High speed cargo vessel

Any

5 per 100 pitches

7 per 100 pitches

Aertssen (1968)

Chiho & Sartori (1979)

Slammmg

(bottom)

Gen. Cargo vessel, tanker,

bulker

High speed cargo vessel

High speed cargo vessel

Any

Any

Containership

Merchant ships

Merchant ships

Tankers

3-4 per 100 pitches

6 per 100 pitches

1 per 100 pitches

1 per 450-900 sec

3 per 100 pitches

Prob. < 0.01

Prob. < 0.03

Prob. < 0.03

6 per 100 pitches

Aertssen (1968)

Aertssen (1968)

SR 108 (1975)

Hoffinan (1976)

Chile & Sartori (1979)

Kim & Nakamura

(1984)

Ochi &Motter(1974)

Jomnee & Meijers

(1980)

Landsburg &

Cruikshank (1976)

Propeller

emergence

Cargo vessel

high speed cargo vessel

Container ship

25 per 100 pitches

1 per 100 pitches

50 per hour

(Prob<0.1)

Aertssen (1968)

SR 108 (1975)

Kitazawa (1975)

Vertical

acceleration at

FP

Merchant ship L = 125 m

L = 190 m

L = 260 m

High speed cargo vessel

Any

Any

Container ship

Merchant ships

jO.275 g rms

0.175 g rms

0.125 g rms

0.21 g rms

0.15 g rms

0.20 grms

0.215 g rms

0.2 g rms

Aertssen (1968)

SR 108 (1975)

Hoffman (1976)

Chih & Sartori (1979)

Kim & Nakamura

(1984)

Ochi & Motter (1974)

Limiting s p e e d s in head waves d u e to d e c k w e t n e s s for 1700 T E U container vessel. M a x i m u m probability of d e c k w e t n e s s = 3%.

Limiting s p e e d s in head waves for different limiting values of s e a k e e p i n g criteria 1700 T E U container vessel.

Ship speed

6 m 7 m 8 m 9 m

ROUTE : NORTH ATLANTIC - ROUNTRIP DISTANCE 7500 n miles SHIP TYPE : CONTAINER VESSEL - 1700 TEU

PRINCIPAL DIMENSIONS : L = 1 9 8 m B = 32.2 m T = 10.5 m OTHER PRINCIPAL DATA : 0 ^ = 0.577 C ^ = 0.812

PITCH RAD. G Y R . = 0.25 Lpp PROPELLER DIAMETER = 7.1 m TARGET SCHEDULED SPEED • 22 knots

CALCULATED VOLUNTARY SPEED LOSS DUE TO DECK WETNESS FOR VARIATIONS IN ESTIMATED RELATIVE MOTIONS AT F.P.

WESTBOUND EASTBOUND

BASE CASE 0 0

1 m (13 %) OVERESTIMATE < 0.1 knots < 0.1 knots 1.5 m (20 %) OVERESTIMATE 0.2 knots 0.2 knots 2 m (26 %) OVERESTIMATE 0.6 knots 0.5 knots

ROUTE : NORTH ATLANTIC-ROUNTRIP DISTANCE 7500 n miles SHIP TYPE : CONTAINER VESSEL - 1700 TEU

PRINCIPAL DIMENSIONS : L = 198 m B = 32.2 m T = 10.5 m OTHER PRINCIPAL DATA : Cb= 0.577 C ^ = 0.812

PITCH RAD. GYR. = 0.25 Lpp PROPELLER DIAMETER = 7.1 m TARGET SCHEDULED SPEED : 22 knots

INVOLUNTARY SPEED LOSS AND CALCULATED ACHIEVED SPEED

WESTBOUND EASTBOUND ACHIEVED SPEED 20.4 21.1 INVOLUNTARY SPEED LOSS 1.7 0.9

Basic Variable

U L

Libfary Limit States

Basic Variable ^

PROBAN

Failure Probabilities

z:

Sensitivity Measures

Importance Factors

Sensitivity Factors

6P 5P M

_6r

A^VOirTASIIESCAIICH

Experiements

Data gathering

Statistical

Distributions

Numerical model

of physics

G(x)

Probability

of total loss

^

Importance factors

Sensitivities

COMPUTING THE CROSSING RATE INTO FAILURE DOMAIN.

The out crossing rate :

V - | | ( G<0 n G+Ge<0 ) e . „ - <i'(Pd<o. o.<!a<o)||

G is the limit state function.

G is the velocity of the processes into failure domain.

The limit state in this case :

Where :

= Stress resistance level.

£7s, = Still water induced stress.

CTy = Vertical wave induced stress.

Gh = Horisontal wave induced stress.

0^,0 = Bottom slamming induced vertical stress.

C7f|() = Flare induced vertical stress.

Time ^ E v e n t s d e s c r i b i n g a n o u t - c r o s s i n g