Hi

I am trying to create simplistic model for boats floating in water in Unity using PhysX but i am not understanding how to get it work properly.

I use a single rigid body with a centre of mass as the red dot. Its below the ship's mesh as i read having a lower centre of mass made it more stable. Though i cannot get it to be stable anyway.

Each green sphere is a buoyancy force calculation which has this code, and it applies the force upwards at the spheres position:

         _volumeUnderPlane = VolumeBelowPlane();
        if (_volumeUnderPlane > 0)
        {
            // P = 1027 (approx density of water at sea level)
            var force = -_volumeUnderPlane * Physics.gravity * P; 
            _parentRB.AddForceAtPosition(force, transform.position,ForceMode.Force);
        }

Where Volume below the plane is calculated as:

    private float VolumeBelowPlane()
    {
        //water level is always 0 for now
        //math based on https://en.m.wikipedia.org/wiki/Spherical_cap
        var dist = -transform.position.y + _radius;
        dist = Mathf.Clamp(dist, 0, 2 * _radius);
        var dist2 = dist * dist;
        var frac = Mathf.PI * dist2 / 3f;
        var volume = 3 * _radius * frac - frac * dist;
        return volume;
    }

But the result is totally unstable, this is how it looks with a lowish mass:

https://i.imgur.com/LLoVzP5.gif

With a high mass it looks like this:

https://i.imgur.com/WNrO33z.gif

I am trying to replicate how assassins creed does it, they used spheres to approximate the buoyancy without it being too computationally heavy, yet they didn't go into any details on how they did the math for it but they did post this image of it:

https://www.fxguide.com/wp-content/uploads/2012/12/immerse_spheres.jpg

Am i doing any thing wrong with my math here? I don't know why its so unstable for me.
 

Why do you need the green spheres? Can you not calculate the buoyant force precisely, computing the water pressure at each face?

They are a simplifications. A real ship gets overwhelmingly complicated quickly. To precisely calculate the forces in such a dynamic system one would at least need:

- the shape of the hull and the construction waterline.

- center of mass and center of lift to calculate righting moments from the static forces. Weight distribution and heel angle play a role here.

- pressure point of the wind force, to calculate righting and turning moments induced from the sails. Easier for a for- and aft rigg (the typical sloop), but a tall ship like in the op is something much more complicated (basic Wikipedia article on wind forces).

- other dynamic forces, resulting from movement of the whole thing in water and wind. These can be decisively strong when underway. Example: rudder and keel, drag and differences in displacement.

My naive idea would be, if one wants it somewhat more realistic, to pre-calculate or -define polar curves for the moments and look up values for certain situations, interpolating between them. Don't ask me for detail, pls ?

For a more simplistic model, how about (suggestion) just looking at the two centres of lift and mass. Assume the centre of mass is stable (or calculated when in harbour and after being loaded) and the centre of lift wanders around it depending on whatever dynamic aspects one needs. That way you only have a lever between the two centres and a resulting vector. You only have to take into account the righting force from the angle and the distance between the two centres.

But you don't need the balls any more. Don't forget to model a dampening effect.

Edit: btw. modelling flight is easier ?

I used the wrong terms. Pls. replace lift with displacement. I didn't mean aerodynamic lift on the sails, but the force that counters the weight of the boat immersed in water. Sorry for being incorrect. Still, the suggestion might be worth thinking over ... ?

On 7/9/2019 at 4:35 AM, alvaro said:

Why do you need the green spheres? Can you not calculate the buoyant force precisely, computing the water pressure at each face?

You sure can