# How to calculate the moment of inertia for a half Ship

Discussion in 'Stability' started by Anum, Jan 27, 2017.

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### AnumJunior Member

Dear All,

I want to simulate the flow around a displacement ship hull with trim and sinkage. Only the half symmetric hull will be modeled. 2 DOF will only allow translational motion along the z-axis and rotational motion around the y- axis. The udf for dynamic mesh is given below.

#include "udf.h"
DEFINE_SDOF_PROPERTIES(ship, prop, dt, time, dtime)
{
prop[SDOF_MASS] = ; I know the mass of half of my ship
prop[SDOF_IYY] = ; This is moment of inertia for a half ship, i do not know how to calculate this value
prop[SDOF_IXX] = 1;
prop[SDOF_IZZ] = 1;
prop[SDOF_ZERO_TRANS_X] = TRUE;
prop[SDOF_ZERO_TRANS_Y] = TRUE;
prop[SDOF_ZERO_TRANS_Z] = FALSE;
prop[SDOF_ZERO_ROT_X] = TRUE;
prop[SDOF_ZERO_ROT_Y] = FALSE;
prop[SDOF_ZERO_ROT_Z] = TRUE;

I want to know how can I calculate the moment of inertia for a half ship (IYY) from the offset data?
(I know the formula for the second moment of water-plane area is ∫ B(x, z)x^2dx from –L/2 to L/2, where B(x, z) is the width of the water plane at the position (x, z), L is the length of ship and z is the draft)

Thanks in Advance

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### b1ck0Senior Member

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### HeimfriedSenior Member

To calculate the mass moment of intertia regarding to the y-axis (Iyy) you need other data than the offsets.

The Iyy of every (small) part of the ship has to be calculated with its own mass and its perpendicular distance of its centroid to the y-axis. The Iyy of the ship is the sum of all this Iyy parts.

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### Mermaid CoJunior Member

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