# How to model collisions with a irregular surface?

I'm trying to find an angle probability distribution for a particle (sand grain) bouncing on an irregular surface.

I'm wondering if you could approach this irregular surface like a Lattice of triangles or spheres and see how the particle could bounce depending where it hit's. The problem with this approach is that it doesn't seem to provide the random nature of the collision with a real irregular surface. Making a random lattice seems like the obvious solution but without real knowledge of the material, it seems really hard to find the right distribution of lattices.

As a side note, i'm looking for the case of a surface like glass or maybe paper.

• At the scale of a sand grain can glass and paper be considered irregular/rough surfaces? – Deep Jul 8 '17 at 3:34
• physicsforums.com/threads/… – sammy gerbil Jul 8 '17 at 11:04

## 1 Answer

For reflection we use the law $$\textrm{incoming angle} = \textrm{outgoing angle}$$ Therefore, the initial distributions of angles on the surface (with respect to the velocity of the sand grain) will completely determine the reflected angle -- unless (1) you account for elasticity, so that the sand can be scattered from two or more points, or (2) you allow "cavities", so that you get multiple reflections.

If it's you need the angle distribution for an experiment, I would suggest you try different distributions and check whether or not they agree with your data. My best guess (!) would be, that the angles are uniformly distributed.

• If they aren't uniformly distributed, their probability distribution is probably well approximated by some combination of low-order spherical harmonics. – probably_someone Jul 8 '17 at 7:39
• Is there a way to approximate this distribution using an analytical or geometrical approach? Is the shape of the projectile more important than the irregularity of the surface? – Jhon Jack Jul 8 '17 at 17:14