To further my study of how the centre of buoyancy shifts as a hull form heels I have constructed a set of animations. Each frame for each animation was generated to exactly locate the centre of buoyancy of the specific curve at the angle of heel being modelled. The centre of rotation used in each animation is the centre-base of each curve, however, this centre of rotation may not reflect the real world (see previous). The illustration is still instructive, but care should be taken when using these animations to assess form stability as a change in the centre of rotation would almost certainly have a great effect on the relative motion of the centre of buoyancy.
My animations model the 0 to 30 degrees heel of each of the following hull cross section curves: Parabola, Sine Curve, Square, Right Angle Triangle. For the parabola I have modelled three different scenarios that correspond to three different immersion depths.
Click on the thumbnail on the right to see a graphical comparison of the various curves (plus some extras for good measure).
Here is a key to the features you will see on each animation:
- On the parabolas and sine curve, this point indicates the location on the curve where the gradient of the tangent = 1. For the square and right angle triangle, this point is an arbitrary point on the hull. This point is typically related to the waterline at the maximum angle of heel (30 degrees).
- The axes (graduated at 0.5, 1.0, 1.5,...) - coloured blue.
- The line of symmetry of the curve - coloured black.
- The centre of buoyancy for the curve at this angle of heel.
- The line of curve being modelled - coloured black.
- A plot of all centre's of buoyancy for the curve.
One final point about the three parabola scenarios modelled. Each differs in that the 'tangent=1' point has a differing relationship to the waterline at the maximum angle of heel. One parabola animation demonstrates the parabola immersed such that the waterline at the maximum angle of heel passes through the 'highest' of the two 'tangent=1' points - 'Parabola > 1'. Another parabola animation demonstrates the parabola immersed such that the waterline at the maximum angle of heel passes through the 'lowest' of the two 'tangent=1' points - 'Parabola < 1'. The final parabola animation demonstrates the parabola immersed such that the waterline at the maximum angle of heel passes through a point midway between the two 'tangent=1' points - 'Parabola = 1'.
|Shape||Fast, Large||Fast, Small||Slow, Large||Slow, Small||Thumbnail|
|Parabola > 1||★||★||★||★|
|Parabola = 1||★||★||★||★|
|Parabola < 1||★||★||★||★|
|Right Angle Triangle||★||★||★||★|
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