# Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the coefficient of friction between any pairing of surfaces, but that's not practical for the amount of objects and terrains this game (will) have.

So my questions are,

• How do I find the force of friction between two objects, when I have their surface area and any other constants I need to add?
• How can I somewhat accurately simplify that to something on the order of $z=x*y+a*b$ ?
• I'd like to account for static vs kinetic friction, is there an easy way to do that?

Edit: failing any established approximations, if I make up some abitrary "grippiness" constant for all of the surfaces, what's the best way to combine them into a coefficient of friction?

• Related: physics.stackexchange.com/q/16213/2451 and links therein. – Qmechanic Mar 23 '14 at 1:04
• I'm more looking for a way to combine the coefficients of friction of two different materials into one usable coefficient of friction. Sorry if that wasn't clear. – Isaac Roberts Mar 24 '14 at 3:42
• You can start with just the minimum of the two. – John Alexiou Mar 25 '14 at 21:20
• Does that reflect the phenomena? That doesn't seem right, just based on sliding rubber over wood – Isaac Roberts Mar 27 '14 at 20:32

## 2 Answers

Sorry, but there's no obvious way to figure out this stuff a priori. It depends critically on things like how smooth the surfaces are. And it does not, to a first approximation, depend on surface area.

About all you can tell about sliding vs static friction is that sliding friction is less than static.

For the simple answer, if you are treating every object as hard and smooth and every motion as sliding, then you really are better just creating a database of material combinations and copy pasting values from readily available sources. Data is easy to get, and doesn't take up much space. I would be shocked if it was more than a few kB. Cheating and using the lesser of the 2 material coefficients of friction isn't all that bad of an option either as was suggested by @ja72.

You can use the formula f=μN

• f=friction force
• μ=coefficient of friction
• N=normal force (Pressure*ContactArea)

For the complex answer, you need to look into various things like traction, rolling resistance, elastic modulus, etc if you have anything other than perfectly hard and smooth non-elastic non-plastic objects sliding against each other.

https://en.wikipedia.org/wiki/Frictional_contact_mechanics