Hydrostatics & Stability > Heel, Trim and Sinkage

To understand the input and output conventions of the hydrostatics and stability calculations of Orca3D, it helps to picture the model moving within a fixed world coordinate system (rather than the waterplane moving and the model remaining fixed).

This image shows a sailboat hull, with Z=0 at the bottom of the hull.

After running hydrostatics with a Sinkage of 0.5 meters and a Heel angle of 15 degrees, there are two options for graphically viewing the resulting flotation condition of the model:

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Add Plane(s) representing water surface: This option is convenient because the model is not moved in the world coordinate system, but it can lead to some confusion because it shows the boat remaining fixed and the waterplane moving. Note that the model baseline is still at Z=0, and that the plane representing the equilibrium flotation plane is not parallel to the Z=0 plane. The advantage of this view is that it's very easy to visualize the heeled waterline and the attitude of the model in this condition, and the plane can be easily deleted without worrying about having moved the model in the world coordinate system.

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Transform model to resultant condition: This option moves the model in a way that reflects how the calculations are actually carried out. The waterplane remains fixed in the Rhino coordinate system, and the model heels, trims, and sinks until it is in equilibrium. While this is more intuitive, you may not want to have your model move in the Rhino coordinate system every time you compute hydrostatics. But when interpreting the input and output data, this is how you should visualize the process.

When defining a flotation condition or interpreting the output data, we use the terms Heel, Trim, and Sinkage:

Heel: the heel angle of the vessel, in degrees, about the world longitudinal axis

Trim: the trim angle of the vessel, in degrees, about the world transverse axis (note that if there is heel, this is not the trim in the boat's axis)

Model Sinkage: the depth of the world origin below the resultant flotation plane, perpendicular to the resultant flotation plane. Positive sinkage is defined as the origin being below the flotation plane. This is sometimes referred to as "origin depth."

In the figure above, the vessel is in its original orientation. If we were to specify a Heel of 15 degrees, a Trim of 5 degrees, and a sinkage of 0.5 meters, the program would go through these steps to transform the model before computing the hydrostatics:

1.	First, the boat is heeled about the world longitudinal axis.

2.	Next, the boat is trimmed about the world transverse axis. Note that if the boat was heeled, this will not be the same as "trim" in the boat's coordinates; in other words, a trim inclinometer mounted on a bulkhead on the boat would not match this value.

3.	The boat is moved up or down along the world vertical axis by the sinkage amount.

The next figure shows the model moving in the Rhino coordinate system, from its original orientation to the equilibrium flotation condition. The center of gravity location (LCG, TCG, VCG) is specified by the user in the Rhino coordinate system. When Orca3D reports the center of buoyancy in the output, it is in the vessel's coordinates (as if the original coordinate system has been transformed along with the model). Thus the reported LCB may not match the input LCG, even though physically the two are vertically aligned in the equilibrium condition.