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FhSim
3.1.0
Marine systems simulation
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Collaboration diagram for Wind force:Wind force and yaw moment on a vessel from Fourier series in the apparent wind angle. The apparent wind is the wind velocity minus the vessel velocity in the horizontal plane (the vertical velocity is not used). The angle \( \psi \) is the angle from the vessel x axis to the apparent wind, in (-pi, pi]. For each of x, y and n, a coefficient is
\[ C = A_0 + \sum_{i=1}^{N} A_i \cos(i\psi) + B_i \sin(i\psi) \]
where N is the number of values of the FourierA array of that direction. The force and moment are then
\[ X = \tfrac{1}{2}\rho A_F |v|^2 C_x,\quad Y = \tfrac{1}{2}\rho A_L |v|^2 C_y,\quad N = \tfrac{1}{2}\rho A_L L |v|^2 C_n \]
with \( A_F \) the front area, \( A_L \) the lateral area, \( L \) the characteristic length and \( \rho \) FluidDensity. The moment about x and y is \( (z_p Y, z_p X) \) with \( z_p \) = VerticalPressureCenter, and the vector is rotated to NED with the quaternion. Without 360DegData, Y and N change sign when that angle is negative (the data are then used for angles 0 to 180 degrees only).
| Name | Width | Description |
|---|---|---|
| VelocityNED | 3 | Velocity of the vessel in the NED frame |
| WindNED | 3 | Wind velocity in the NED frame |
| QuaternionNED | 4 | Orientation quaternion of the vessel (body to NED) |
| Name | Width | Description |
|---|---|---|
| ForceNED | 3 | Wind force in the NED frame |
| TorqueNED | 3 | Wind moment in the NED frame |
| AngleNED | 1 | Apparent wind angle \( \psi \) in radians from the vessel x axis (horizontal part) to the apparent wind velocity, negative when the z component of the cross product x axis times wind velocity is negative |
| DragCoefficient | 3 | The coefficients \( C_x, C_y, C_n \) |
| Name | Width | Description |
|---|---|---|
| ProjectedLateralArea | 1 | Lateral projected area \( A_L \). Required. Unit not stated in the code |
| ProjectedFrontArea | 1 | Front projected area \( A_F \). Required. Unit not stated in the code |
| CharacteristicLength | 1 | Length \( L \) in the yaw moment. Required. Unit not stated in the code |
| VerticalPressureCenter | 1 | Height \( z_p \) of the pressure centre in the roll and pitch moments. Default 0 |
| FluidDensity | 1 | Density \( \rho \). Default the air density of marenv (1.2) |
| 360DegData | 1 | The Fourier data cover the full circle: do not mirror Y and N. Default false |
| FourierA0x | 1 | Constant term of \( C_x \). Required |
| FourierAx | N | Cosine coefficients of \( C_x \). Its size sets N for x |
| FourierBx | N | Sine coefficients of \( C_x \). Same size as FourierAx |
| FourierA0y | 1 | Constant term of \( C_y \). Required |
| FourierAy | N | Cosine coefficients of \( C_y \). Its size sets N for y |
| FourierBy | N | Sine coefficients of \( C_y \). Same size as FourierAy |
| FourierA0n | 1 | Constant term of \( C_n \). Required |
| FourierAn | N | Cosine coefficients of \( C_n \). Its size sets N for n |
| FourierBn | N | Sine coefficients of \( C_n \). Same size as FourierAn |