The discussion revolves around finding the center of gravity of 3D objects, particularly in the context of balancing a body in water to ensure it moves in a straight line when propelled. Participants explore the implications of weight distribution, shape, and external forces on stability and movement.
Participants express differing views on the factors influencing the movement and stability of the object in water. There is no consensus on the primary cause of the tilting or the best approach to achieve straight-line movement.
Some assumptions about the shape and design of the object remain unaddressed, and the discussion does not resolve how much to lower the center of gravity for optimal stability.
Gerenuk said:To find the center of gravity you would calculate
<br /> \vec{x}_c=\frac{\iiint \vec{x}\mathrm{d}m}{M}<br />
However it might not be relevant in the way you imagine. The shape of the object is very important for a stable position. I have an article that describes how the moment of pitch and rolling should behave for the thing to keep a stable position. Let me know if you'd like to read the article and the involved maths.
Moreover, turning one direction doesn't depend on the center of gravity either. Only the shape of the boat determines if it will turn. Of course if the center of gravity is too high, then the boat tilts, changes the shape of the part submersed in water and thus turns.
Basically if you want your boat to float I assume you should have a symmetrical boat and lower the center of gravity. By how much to lower is hard to tell anyway.