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# how to do water buoyancy

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Hi I''m making a game similar to wave race, but I am having trouble with the physics. Unfortunately the search feature is down on the forum. Does anyone know the clear formulas for calculating boyancy? Do you know of any examples of this working? Many thanks Chris O''Shea

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The upthrust of the water on the object is calculated from the mass of the volume of water displaced. Therefore the simplist method would be to find the upthrust based on the depth of the object and mulitply by some suitable constant. If you''re just doing waverace style jetski''s this might be accurate enough. Beyond that and you''ll have to calculate the submearged area and take that into account..

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I''ll second OrangyTang''s suggestion. That should be perfectly sufficient for a basic wave-race-like game. You could even add some simple heuristics to add a bit of instability if the boat is sitting at an angle (e.g., if the angle is small it tends to spring back to sitting vertical, but if angle is large the boat may flip over).

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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As an idea that is part-way between the above suggestion and a proper simulation, just treat the hull of the boat as a volume that has a rectangular plan-form (looking from above) and a triangular cross section (looking end on). The volume is then trivial to compute.

As to the stability. If you want to go further than Graham''s suggestion, you could work out the pressure on the hull of the boat at different points, noting that pressure of a liquid (in a regular gravitational field) decreases logarithmically with height. The pressure per unit area is the force applied at that point. So, if the boat is not sitting level in the water there will be an imbalance of forces. As Graham suggests, at small angles this will tend to right the boat but at larger angles this will tend to capsize a boat.

Cheers,

Timkin

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