Gerenuk said:To find the center of gravity you would calculate
[tex]
\vec{x}_c=\frac{\iiint \vec{x}\mathrm{d}m}{M}
[/tex]
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.
The center of gravity of a 3D object can be determined by finding the point at which the object will balance perfectly in any direction. This can be done by suspending the object from various points and finding the point where the object remains level.
Finding the center of gravity is important for balancing objects in water because it helps to distribute the weight of the object evenly. This prevents the object from tipping over or sinking in the water.
The center of gravity of a 3D object is affected by the shape, size, and weight distribution of the object. Objects with a wider base and lower center of mass will have a more stable center of gravity.
Yes, the center of gravity of a 3D object can be calculated using the formula: x̄ = (Σmi xi) / (Σmi), where x̄ is the x-coordinate of the center of gravity, mi is the mass of each component, and xi is the x-coordinate of each component. This formula can be applied to the y and z coordinates as well to find the complete center of gravity.
The center of gravity of a 3D object can be used to balance it in water by ensuring that the object's center of gravity is directly above the point of support. This will allow the object to remain stable and prevent it from tipping over or sinking in the water.