Calculating Putt Break Over Distance w/ Friction

[DylanB]

How would you go about calculating how much a putt would break over a given distance without neglecting friction?

EDIT: I've realized this would be more appropriate in the coursework section, unforunately it's too late now.

 

[AlphaNumeric]

You'd need the equation of the surface $$f(x,y)$$ along with the equation for friction in terms of velocity, like $$F = -kv^{2}$$. You'd compute $$\nabla f$$ which would give you the slope behaviour (so you can work out the force on the ball) and then it's just solving differential equations, including your initial conditions (where the ball starts and it's initial velocity).

For a real life green this isn't practical since you don't know f(x,y).