Seakeeping Analysis

Why conduct seakeeping analysis?

Determine the motions of a design in conditions it is likely to encounter

• Is the vessel going to survive?

• Can the vessel carry out specified task or mission?

• Decide if motions are acceptable:Slamming, Deck Wetness, Speed Loss, Human Performance, Ride Control

• Decide which design is going to perform the best:Design selection, marketing

Seakeeping Analysis

Expected SeaConditions

Seakeeping Analysis

Expected SeaConditions

Resultant VesselMotions

Seakeeping Analysis

Expected SeaConditions

Resultant VesselMotions

compare SeakeepingDesign Criteria

Expected Sea Conditions

swell and sea breeze spectrum off Scarborough, 12 Feb 2000

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.1 0.2 0.3 0.4 0.5 0.6

frequency [Hz]

spec

tral d

ensi

ty [

m2/

Hz]

a) narrow b) broad

Multi-directional spectrum

Ocean Wave Statistics Methods

Wave buoys: Ideal source for wave statistics

There is significant data available from wave buoys - however it costs $ to obtain due to expense of collection.

Hindcasting:Use measured wind data to estimate waves produced using modellingtechniques.

Dependent on accuracy of models.

Remote Sensing:Satellite imaging of ocean surface - again $

Visual Observations

Hogben & Lumb (1967) compared visual observations with measured values from wave buoys.

H H

T T

T T

obs

Z obs

obs

1 3

0

106

0 73

112

/ .

.

.

===

Where :

period modal

period crossing zeromean

height t wavesignifican

0

3/1

==

=

T

T

H

Z

Visual Observations

Nordenstrom (1969) derived alternative expressions.

( )( )

( )

H H

T T

T T

obs

Z obs

obs

1 3

0 75

0 96

0

0 96

168

082

116

/

.

.

.

.

.

.

=

=

=

Visual Observations

For example Hogben & Lumb (1967) published comprehensive atlas based on 2 million visual observations from ships between 1953 and 1966.

Note: ships tend to try and avoid bad weather therefore vessels which cannot change course e.g. military craft and offshore platforms may encounter worse weather than shown by observations.

BMT Ocean Wave Statistics

BMT Ocean Wave Statistics

http://www.globalwavestatisticsonline.com/

You will need to use the following email address as the user name :

G.Macfarlane@mte.amc.edu.au

The password is currently 4RyHPsxn

Standard Sea Spectra

ITTC or Bretschneider "two parameter" spectrum.

Where:

Standard Sea SpectraIn coastal waters where the fetch may be limited the JONSWAP (Joint North Sea Wave Project) spectrum may be used.

Standard Sea Spectra

Simplified ITTC spectrum called the Pierson-Moskowitz spectrum is sometimes used, which has windspeed as its only variable.

Standard Sea Spectra

Vessel Motions

Expected SeaConditions

Resultant VesselMotions

compare SeakeepingDesign Criteria

Vessel Motions

Response Amplitude Operator (RAO)

Obtained from:

• Numerical predictions e.g. Seakeeper, Beamsea, HydroStar

• Towing tank experiments

Heave Amplitude RAO

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Encounter Frequency (Hz)

Hea

ve R

AO

(m/m

)

SEALAMTowing TankFull Scale

Pitch Amplitude RAO

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Encounter Frequency (Hz)

Pitc

h R

AO

(deg

/deg

)

SEALAM

Towing Tank

Full Scale

Encounter Frequency

As ships move through the water the rate at which they encounter waves is dependent on their speed and direction.

For a head sea the encounter frequency is higher than the wave frequency.For a beam sea the encounter frequency equals the wave frequency.In a following sea the encounter frequency is initially positive, meaning that the waves overtake the vessel, passes through zero and then goes negative which means that the vessel overtakes the waves.

Encounter Frequency

Bretschneider spectrum modal period 11secs,sig wave heght 2m at 0 knots and

10 knots head sea

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.5 1 1.5 2 2.5 3

frequency ( rad/sec)

zero speed

10 knots headsea

Motions

( )( )

( )e

z ee

zRAO

ωωζ ω

=

2( ) ( ) ( )z e z e eS RAO Sζω ω ω=

Using these RAOs the motions may be determined by assuming that the response function is linear with respect to wave height and that the principle of superposition holds. (The principle of superposition states that the response of a body to a spectrum of waves is the sum of the individual waves).

Thus if the linear response of the vessel is given by

then it follows that the motion response spectrum, Sz(�e), is given by:

where S�( �e) is the encountered wave energy spectrum.

Seakeeping Design Criteria

Why use criteria?

• to decide if the vessel's performance is acceptable

• easily compare different designs

What is important for a ferry design?

• passenger sea sickness

• speed loss due to motions

What is important for a patrol boat design?

• deck wetness

• ability of crew to keep working despite motions

Significant Motions

Hease Response Spectra

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

frequency hz

heav

e sp

ectr

al d

ensi

ty (

m*m

/hz

00 m=σ

�∞

=00 d)( eexSm ωω

0SIG 4Heave m=

Absolute Motions

centre of gravity

Position of interest, (px,py,pz)

Absolute Motions

Absolute vertical motion , sz, of a position (px,py,pz), due to heave, pitch and roll is given by:

s z p pz y x= + −φ θ

220 BAsz +=

AB

z =εtan

where: A z p pz y x= + −0 0 0cos( ) cos( ) cos( )ε φ ε θ εφ θ

B z p pz y x= + −0 0 0sin( ) sin( ) sin( )ε φ ε θ εφ θ

the amplitude and phase of the absolute vertical motion is given by:

Velocities & Accelerations

)sin(0 εω += txx e

)cos(.

0 εωω += txx ee

)sin(..

20 εωω +−= txx ee

Therefore velocity & acceleration transfer functions obtained by multiplying displacement amplitude by encounter frequency & square of encounter frequency

Slamming

Slamming

May cause:

• decelerations and local structural damage

• transient vibratory stresses (whipping) elsewhere in the hull.

Occurs when two events occur simultaneously:

• Re-entry of the ship's bow into the water after it has risen above the surface

• The relative vertical velocity between the ship's flat of bottom and the water surface exceeds a certain critical specified value.

Deck Wetness

Deck Wetness

This phenomenon may cause injury or drowning of personnel and damage to deck-mounted equipment.

Difficult to model accurately numerically, but some information may be gained from towing tank tests, eg. shipping of green or solid water

Occurs when:

• the bow of a ship is buried in the sea and throws solid water and spray into the air.

Speed Loss

a decision, by the captain, to reduce speed in order to reduce motions, slams, deck wetness, propeller emergence etc. to within acceptable limits.

a vessel travelling through waves will have a greater resistance due to its motions, and the resulting change in load on the propeller usually reduces the propeller efficiency.

Voluntary Involuntary

Added Resistance

Time

Res

ista

nce

Added resistance Raw

Calm water resistance

Resistance in waves

Propeller Emergence

Propeller racing occurs when the upper tips of the blades emerge from the water due to the motions of the ship.

The relative motion of the longitudinal position of the ship where the propeller is located can be utilised to determine the likelihood of propeller emergence.

The relative motion may be calculated by subtracting the local wave elevation from the local absolute vertical motion.

Propeller Emergence

Ship motions cause two undesirable effects of people onboard:

• Motion sickness

• Impairment of ability to carry out tasks in a controlled manner

Human Performance

The simplest human performance criterion

However it has been shown that the frequency of the oscillation is also important in assessing the impact on human performance.

Both Motions Sickness Incidence and Subjective Motions introduce a frequency dependence.

Vertical Acceleration

MSI has become a standard method for comparing seakeeping performance of different designs, particularly passenger vessels.

May be displayed in two forms:

• The percentage of people likely to vomit within two hours

• The time period after which severe discomfort (sea sickness) occurs

Determined by sequentially integrating the acceleration spectral density over 1/3 octave bands and then plotting against the standard curves

Motion Sickness Incidence (MSI)

The percentage of people likely to vomit within two hours

Motion Sickness Incidence (MSI)

0.1

1

10

0.1 1

Encounter Frequency [Hz]

rms

vert

ical

acc

eler

atio

n [m

s-2

]

2%

5%

10%

20%

The time period after which severe discomfort (sea sickness) occurs

Motion Sickness Incidence (MSI)

0.1

1

10

0.1 1

Encounter Frequency [Hz]

rms

vert

ical

acc

eler

atio

n [m

s-2

]

8 Hour (tentative)

2 Hour

30 Minute

Analysis limitations:

• Experiment subjects limited to young men - sea sickness incidence varies with age, sex and race.

• Statistically, tolerance to motions increases with time at sea, therefore ferry passengers are likely to be more susceptible to motion sickness than the crew.

• Additional influences such as vision, fear, odours etc. affect sea sickness, but their effects have not yet been quantified.

• Performance may be degraded before vomiting occurs.

Motion Sickness Incidence (MSI)

Analysis will give an indication on the ability of the crew to perform tasks

Subjective Motions (SM)

43.1

30ASM��

�

�

��

�

�=

g

s��

where: 30s�� is twice the rms vertical acceleration

A is a parameter which is a function of frequency which may be found from:

( )[ ] ( )[ ]22e log5.13log6.496.751.65-exp-1A eeee ωωω +−=

Subjective Motions (SM)

0

5

10

15

20

25

0 1 2 3

rms vertical acceleration (m/s^2)

Sub

ject

ive

Mot

ion

Moderate

Serious

Severe : necessary to 'hang on' all the time

Hazardous

Intolerable

Lateral accelerations experienced on board a vessel in rough weather may cause objects to topple and people to lose balance and stumble.

In a similar manner to subjective motions, lateral force estimators may be derived to ascertain the effect on a crew

Lateral Force Estimator

rms Lateral Acceleration m/s2 Motion Induced Interruptions per Minute Rating Level

< 1.0 < 1 acceptable

1.0 to 1.1 1 to 1.5 serious

1.1 to 1.25 1.5 to 2 severe

> 1.25 > 2 extremely hazardous

Limiting Criteria are acceptable limits for these various criteria which may be used to determine whether the vessel motions will be acceptable.

Limiting Criteria

General Motion Limit (significant amplitude) Location

Heave 2.0m C of G

Pitch 3.0° C of G

Roll 8.0° C of G

Vertical acceleration 0.4g Bridge

Lateral acceleration 0.2g Bridge

Specific task MSI 20% of crew Task location

MII 1/min Task location

Current design criteria for crew performance for naval vessels, after ABCD WorkingGroup on Human Performance at Sea (1995)

Probability of Exceeding Criteria

Assuming the probability density function of the motions is a Rayleigh distribution

Possible to evaluate the probability of exceeding critical value zcrit given the variance of the motion energy spectrum, m0z.

���

����

� −=>zm

zzz

0

2crit

crit 2exp)(prob

Author Ship type Slamming Wetness Propelleremergence

Verticalacceleration

Ochi andMotter(1974)

Merchant Probability0.03

Probability0.07

Shipbuilding ResearchAssociationof Japan(1975)

Merchant Probability0.01

Probability0.02

Probability0.1

Lloyd andAndrew(1977)

Merchant 120/hour

Aertssen(1963, 1966,1968, 1972)

Merchant Probability0.03 or 0.04

Probability0.25

Yamamoto(1984)

Merchant Probability0.02

Probability0.02 at FP

Probability ofexceeding0.4g at bridge= 0.05

Author Ship type Slamming Wetness Propelleremergence

Verticalacceleration

Kehoe(1973)

Warship 60/hour at0.15L

60/hour atFP

Lloyd andAndrew(1977)

Warship 36/hour avg. SM = 15

Andrew andLloyd(1981)

Warship 90/hour avg. SM = 12

Comstock etal. (1982)

Warship 20/hour 30/hour 0.2g RMS atbridge

Walden andGrundmann(1985)

Warship Probability0.03

Probability0.07

Seakeeper

Based on Strip theory of Salvesen, Tuck & Faltinsen (1970):

· Divide the ship into sections or strips

· Calculate the added mass, damping and restoring force at each strip

· Integrate the added mass and damping over the length of the vessel

· Put these values into the equations of motion and solve them.

Seakeeper

Strip theory assumes that· The ship is slender i.e. L>>B and L>>D

· There is no significant planing force. This implies low to moderate speeds for monohulls.

· The motions vary linearly with wave amplitude, which is usually valid for slender vessels operating in waves of small amplitude. However, extreme motions tend to be very nonlinear.

· There is no flow between strips, i.e. the motion is two-dimensional. Whilst this is clearlyincorrect, the results are surprisingly accurate.

· Viscous damping terms are negligible (a poor assumption for roll, but reasonable for pitch and heave under most conditions).

· The presence of the hull does not affect the incoming waves.

Seakeeper

Coefficients are determined by conformally mapping each ship section to a circle, then using the known analytical solution for a circle (Ursell, 1949). The values are then put back into the equations of motion which are decoupled and solved, yielding RAOs and phase angles for pitch and heave.

The mapping will not replicate the ship section exactly; the goodness of fit depends mainly on the number of terms used in the mapping equation. However, the more terms, the slower the computation.

Seakeeper uses a three-term mapping equation, known as a Lewis mapping. This is adequate for mapping most conventional hull shapes, though it will have difficulty with some bulbous bows and very high section area coefficients.

Seakeeper

Seakeeper - questions

· Mass distribution - what is the influence of changing the longitudinal radius of gyration?

· Number of mapped sections - what is the influence of changing the number of mapped sections?

· No transom terms - what is the influence of not utilising transom terms?

· Vessel speed - what is the influence of changing the speed of the proposed design?

· Idealised sea spectrum - what is the influence of utilising another form of idealised sea spectrum?

Seakeeper

Let’s have a go……