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What is M_H in the roll damping equation?

Hydrodynamic moment with the "weak" damping effects of radiated waves


What is M_A in the equation?

Moments by roll damping devices that are considered to be time dependent, fex active fins or water motion in roll damping tanks


How are the damping coefficients d_l and d_q found?

- The damping moment is used to find the d_l (linear damping coefficient) for small roll amplitudes
- d_q (quadratic roll damping constant) is found by considering the harmonic motion with a critical amplitude.


What is the case of linear approximation of roll motion of a symmetric ship (small roll and wave amplitudes)?

The equation of the roll motion is only coupled with sway and yaw.


How is the damping work achieved?

It is obtained by the damping moment


what happens if the rudder movements are excluded?

There will be no restoring moment for the DOF sway and yaw so their eigenfrequency would be zero. The only motion with an eigenfrequency > 0 is the roll motion.


Where is the reference point located?

Not in keel point, but in the same height as the roll axis because it will make the sway amplitude equal zero.


What is special about the height of the roll axis?

Can be seen as the height of the common centre of gravity of the ship mass and the hydrodynamic mass due to the sway motion.

since the COG of the hydrodynamic mass is said to be approximately at the water line, the roll axis can be assumed to be in the middle of the waterline and the COG of the ship mass.


How can the roll eigenfrequency be found?

w = sqrt(stiffness coefficient/ mass moment of inertia) = sqrt(GM*mg/I_xx)


With what tests can the damping coefficients be found?

roll decay test, forced roll test


Explain roll decay test

measures decreasing roll motion amplitudes of an initially heeled modell


Explain forced roll test

Based on the application of a time-harmonic exciting roll moment of known frequency and amplitude


Write down the roll damping equation

theta_x*phi''+d_L*phi'+d_Q*phi'|phi'|+Ms = M_h + M_a


What is the result of modifying the axis of the roll motion?

The roll motion will be decoupled from all other degrees of freedom and the mass moment of inertia including the hydrodynamic part which will get a min value. The ROAs for the roll motion will have significant peaks in all combinations of wavelengths, encounter wave angles and ship speed, for that the encounter frequency is equal to the roll eigenfrequency.


What is the case for heave and pitch?

The ROAs have no or only very weak resonance peaks


Equation of the roll period for dry cargo ships

T = (2*pi*i)/sqrt(g*GM)

The roll period tends to infinity (in calm water) when the roll amplitude tends to the angle where the righting lever is equal to zero.


How can roll motion in regular waves be suppressed?

The amplitude of the damping moment must be equal to the amplitude of the exciting moment


How can the damping part be estimated?

By strip theory or more complex numerical methods


What happend to the rudder when roll motion occurs?

The inflow to the rudder will have an angle of attack: this induces a transverse force on the rudder which damps the roll motion


What else can generate damping?

The hull: similar damping as the rudder if the hull has a wide immersed transom stern. Due to cross flow of a rolling ship with forward speed and the flow spearation at the transom stern, a lift force at the stern will be induced. Approximated the same way as the rudder daming moment.

The main part of the damping moment results from the lift force from the immersed transom stern effect. The lift force is proportional to the cubic of the transom stern width.

Daming mechanisms are usually too weak and monohull ships require additional devices to increase daming.


Explain the function of bilge keels

Fitted on all ships which has no additional roll damping devices.
Damping moment is found by:
where w is the relative transverse velocity between the ship hull and the surrounding fluid when no bilge keel is installed.

The effect of the bilge keel does not depend on the forward velocity of the ship and the loading on bilge keels (tilting moment) does not depend on the roll motion, but the heave motion. Bilge keels are necessary for the case of low or no forward ship speed. Large bilge keels increases the ship resistance.


What is a danger with bilge keels?

They can contribute to the excitation of a roll motion in rough sea conditions


Explain damping fins

Installed at each side (port and starboard), not far from the midship section and the bilge. A single fin of double area whould have similar effect as two. Two fins offer a greater safety against the total failure of two. The fins rotate around an axis normal to the hull surface. The created moment around the x-axis is in 180 deg phase shifted to the roll velocity.


Explain the different types of damping fins

retractable and non-retractable. Non-retractable fins are built much lighter and are installed more often in small systems. They have small fin length so that they do not go beyond the largest width of the ship and to prevent the damage when docking.

Retractable once have slender fins that are folded before berthing(docking). The motion is achieved by a hydraulic system.

Large lift coefficients can be achieved because of lage angle of attack of the main part of the fin. The effectiveness of the fins increase with the increasing forward speed. This is why the angle of rotation must be limited to small values for ships with high forward speed to prevent high values of the lift coefficient and an overloading of the shaft and bearings.


What is the loading on the shaft dependent on?

The angle of attack, not the angle of rotation.

The angle of attack is influenced by the heave and pitch motion and the wave orbital velocity.


What are the advantages of roll damping tanks?

- effective even if the ship is without forward speed
- considerably cheaper


What are the disadvantages of damping tanks?

- much higher weight
- more space to install the tanks
- reducing of metacentric heights
- disturbing noise


What types of damping tanks exist?

- U-tube tanks: 2 vertikal tanks on port and starboard side, which are connected to each other with a double bottom
- Flume tanks: rectangular tanks with free surface over the entire width of the ship. They need more water than U-tanks and also more space. These tanks damp the ship roll motion over a wide range of frequencies due to the breaking waves inside the tank.

In both cases the tank is partially filled so that sloshing can occur. The phase difference between the wave and the sloshing water in the tank will be 180 deg. Ideally, the ship remains at rest, and the waves only excite in the tank water. The tank water thus forms a vibration absorber.


How can the eigenfrequency of the tank water be found?

Using the one-dimensional stream filament theory.

dp/ds = rho*w'
w'=water acceleration


What is important to consider by the design of U-tanks?

Ensure that the tank natural frequency is higher than the largest natural roll frequency of the ship, and then to delay the tank water motion during operation.

The tank water motion can be controlled by throttling of air motion (relieve the air into the atm or


What else are the U-tanks used for?

stabilization of container ships by loading and unloading.


What is the lowest natural frequency of a Flume tank?

The frequency of waves which have the length of twice the tank width b.


What are active rudders?

- active controlling of the rudder
- active controlling of the thrust direction of the Voit Schenider Propeller
- Damping moment can be easily controlled and adapted to the roll velocity
- non-forward speed roll damping device