Roll damping

Question 1

What is M_H in the roll damping equation?

Answer 1

Hydrodynamic moment with the “weak” damping effects of radiated waves

Question 2

What is M_A in the equation?

Answer 2

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

Question 3

How are the damping coefficients d_l and d_q found?

Answer 3

• 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.

Question 4

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

Answer 4

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

Question 5

How is the damping work achieved?

Answer 5

It is obtained by the damping moment

Question 6

what happens if the rudder movements are excluded?

Answer 6

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.

Question 7

Where is the reference point located?

Answer 7

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

Question 8

What is special about the height of the roll axis?

Answer 8

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.

Question 9

How can the roll eigenfrequency be found?

Answer 9

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

Question 10

With what tests can the damping coefficients be found?

Answer 10

roll decay test, forced roll test

Question 11

Explain roll decay test

Answer 11

measures decreasing roll motion amplitudes of an initially heeled modell

Question 12

Explain forced roll test

Answer 12

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

Question 13

Write down the roll damping equation

Answer 13

theta_xphi’‘+d_Lphi’+d_Q*phi’|phi’|+Ms = M_h + M_a

Question 14

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

Answer 14

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.

Question 15

What is the case for heave and pitch?

Answer 15

The ROAs have no or only very weak resonance peaks

Question 16

Equation of the roll period for dry cargo ships

Answer 16

T = (2pii)/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.

Question 17

How can roll motion in regular waves be suppressed?

Answer 17

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

Question 18

How can the damping part be estimated?

Answer 18

By strip theory or more complex numerical methods

Question 19

What happend to the rudder when roll motion occurs?

Answer 19

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

Question 20

What else can generate damping?

Answer 20

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.

Question 21

Explain the function of bilge keels

Answer 21

Fitted on all ships which has no additional roll damping devices.
Damping moment is found by:
Ms=21/2rhow^2Cdlh*R
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.

Question 22

What is a danger with bilge keels?

Answer 22

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

Question 23

Explain damping fins

Answer 23

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.

Question 24

Explain the different types of damping fins

Answer 24

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.

Question 25

What is the loading on the shaft dependent on?

Answer 25

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.

Question 26

What are the advantages of roll damping tanks?

Answer 26

• effective even if the ship is without forward speed

- considerably cheaper

Question 27

What are the disadvantages of damping tanks?

Answer 27

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

Question 28

What types of damping tanks exist?

Answer 28

• 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.

Question 29

How can the eigenfrequency of the tank water be found?

Answer 29

Using the one-dimensional stream filament theory.

dp/ds = rho*w’
w’=water acceleration

Question 30

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

Answer 30

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

Question 31

What else are the U-tanks used for?

Answer 31

stabilization of container ships by loading and unloading.

Question 32

What is the lowest natural frequency of a Flume tank?

Answer 32

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

Question 33

What are active rudders?

Answer 33

• 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