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 Sea Conditions
Seakeeping Analysis
Expected Sea Conditions
Resultant Vessel Motions
Seakeeping Analysis
Expected Sea Conditions
Resultant Vessel Motions
compare
Seakeeping Design Criteria
Expected Sea Conditions
swell and sea breeze spectrum off Scarborough, 12 Feb 2000 0.45 0.4
spectral density [m2/Hz]
0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.1
0.2
0.3 frequency [Hz]
0.4
0.5
0.6
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 modelling techniques. 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.
H1/ 3 = 106 . Hobs TZ = 0.73Tobs T0 = 112 . Tobs Where :
H1/ 3 = significant wave height TZ = mean zero crossing period T0 = modal period
Visual Observations Nordenstrom (1969) derived alternative expressions.
H1/ 3 = 168 . ( Hobs )
TZ = 0.82(Tobs ) T0 = 116 . (Tobs )
0.75
0.96
0.96
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 :
[email protected] The password is currently 4RyHPsxn
Standard Sea Spectra ITTC or Bretschneider "two parameter" spectrum.
Where:
Standard Sea Spectra In 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 PiersonMoskowitz spectrum is sometimes used, which has windspeed as its only variable.
Standard Sea Spectra
Vessel Motions
Expected Sea Conditions
Resultant Vessel Motions
compare
Seakeeping Design Criteria
Vessel Motions Response Amplitude Operator (RAO) Obtained from: • Numerical predictions e.g. Seakeeper, Beamsea, HydroStar • Towing tank experiments
Heave Amplitude RAO
Heave RAO (m/m)
1.2
SEALAM Towing Tank Full Scale
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
Encounter Frequency (Hz)
1
1.2
Pitch Amplitude RAO
Pitch RAO (deg/deg)
1.2
SEALAM
1
Towing Tank Full Scale
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
Encounter Frequency (Hz)
1
1.2
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 0.7 0.6 0.5
zero speed
0.4
10 knots head sea
0.3 0.2 0.1 0 0
0.5
1
1.5
2
frequency ( rad/sec)
2.5
3
Motions 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
z (ωe ) RAOz (ωe ) = ζ (ωe ) then it follows that the motion response spectrum, Sz(
e),
is given by:
S z (ωe ) = RAOz (ωe ) 2 Sζ (ωe ) 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
heave spectral density ( m*m/hz
0.6 ∞
m0 = S x (ω e )dω e
0.5
0
0.4
σ 0 = m0
0.3 0.2
HeaveSIG = 4 m0
0.1 0 0
0.2
0.4
0.6
-0.1 frequency hz
0.8
1
Absolute Motions
Position of interest, (px,py,pz)
centre of gravity
Absolute Motions Absolute vertical motion , sz, of a position (px,py,pz), due to heave, pitch and roll is given by: sz = z + p y φ − p xθ the amplitude and phase of the absolute vertical motion is given by:
s z 0 = A2 + B 2
tan ε z = where:
B A A = z0 cos(ε z ) + p y φ 0 cos(ε φ ) − p xθ 0 cos(ε θ )
B = z0 sin(ε z ) + p y φ 0 sin(ε φ ) − p xθ 0 sin(ε θ )
Velocities & Accelerations
x = x0 sin(ω et + ε ) . x = x0ω e cos(ω et + ε ) .. x = − x0ω e2 sin(ω et + ε )
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 Occurs when: • the bow of a ship is buried in the sea and throws solid water and spray into the air. 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
Speed Loss Voluntary
Involuntary
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.
Added Resistance
Resistance
Resistance in waves
Added resistance
Calm water resistance
Time
Raw
Propeller Emergence Propeller racing occurs when the upper tips of the blades emerge from the water due to the motions of the ship.
Propeller Emergence
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.
Human Performance
Ship motions cause two undesirable effects of people onboard: • Motion sickness • Impairment of ability to carry out tasks in a controlled manner
Vertical Acceleration
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.
Motion Sickness Incidence (MSI) 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) 10
20%
rms vertical acceleration [ms^-2]
10% 5% 2%
1
0.1 0.1
1
Encounter Frequency [Hz]
The percentage of people likely to vomit within two hours
Motion Sickness Incidence (MSI)
rms vertical acceleration [ms^-2]
10
30 Minute
1
2 Hour
8 Hour (tentative)
0.1 0.1
1
Encounter Frequency [Hz]
The time period after which severe discomfort (sea sickness) occurs
Motion Sickness Incidence (MSI) 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.
Subjective Motions (SM) Analysis will give an indication on the ability of the crew to perform tasks
SM = A
where:
s30
s30
1.43
g
is twice the rms vertical acceleration
A is a parameter which is a function of frequency which may be found from:
[
(
)][
A = 1 - exp - 1.65ω e2 75.6 − 49.6 log e ω e + 13.5(log e ω e )
2
]
Subjective Motions (SM) 25
Intolerable
20
Subjective Motion
Hazardous
15
Severe : necessary to 'hang on' all the time
10
Serious
5
Moderate
0 0
1
2
rms vertical acceleration (m/s^2)
3
Lateral Force Estimator 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 rms Lateral Acceleration m/s2
Motion Induced Interruptions per Minute
Rating Level
< 1.0
1.25
>2
extremely hazardous
Limiting Criteria Limiting Criteria are acceptable limits for these various criteria which may be used to determine whether the vessel motions will be acceptable. General
Specific task
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
MSI
20% of crew
Task location
MII
1/min
Task location
Current design criteria for crew performance for naval vessels, after ABCD Working Group 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.
−z prob( z > zcrit ) = exp 2m0 z
2 crit
Ship type
Slamming
Wetness
Ochi and Motter (1974)
Merchant
Probability 0.03
Probability 0.07
Shipbuildin g Research Association of Japan (1975)
Merchant
Probability 0.01
Probability 0.02
Lloyd and Andrew (1977)
Merchant
Aertssen (1963, 1966, 1968, 1972)
Merchant
Probability 0.03 or 0.04
Yamamoto (1984)
Merchant
Probability 0.02
Author
Propeller emergence
Vertical acceleration
Probability 0.1
120/hour
Probability 0.25 Probability 0.02 at FP
Probability of exceeding 0.4g at bridge = 0.05
Author
Ship type
Slamming 60/hour at 0.15L
Wetness
Propeller emergence
Vertical acceleration
Kehoe (1973)
Warship
60/hour at FP
Lloyd and Andrew (1977)
Warship
36/hour
avg. SM = 15
Andrew and Lloyd (1981)
Warship
90/hour
avg. SM = 12
Comstock et al. (1982)
Warship
20/hour
30/hour
0.2g RMS at bridge
Walden and Grundmann (1985)
Warship
Probability 0.03
Probability 0.07
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 clearly incorrect, 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……
