# Skipping a Stone across Water

1. Sep 3, 2009

### mistercrowley

Hi all!

I'm new to this thread, but I had a question about the Physics of skipping a stone across water.

I am going to school for Game and Simulation Programming and for my Portfolio assignment to graduate, I have taken on a fairly advantageous assignment. I plan on making an Adobe Flash simulation of skipping a rock across water. The user will be able to control the radius, height, and texture of the stone as well as the angle of attack, velocity, wind speed and direction, wave size and spin related to throwing the stone.

My physics is a bit dodgy, I understand some of the idea of the process, but what I do know is Actionscript in Flash so if I can somehow research/locate formulas related to these physicis and real life data about skipping a stone I would be able to program those as variables in Flash. Does anyone know of a good place where I can acquire this data?

2. Sep 3, 2009

### mistercrowley

What I have found so far in my research is several different formulas that may add up to one formula but it seems as though there are still factors which are absent.

What I have already is inertia of the stone = MR/t^2

And collision time(t) = (MR/pS)^-1/2 / U Where (pU^2)S is lift force. Not sure how (pU^2)S is calculated though.

I also found this equation for the action of the water on the stone as: FL = ClPwU^2*Swettedf(a,B)n

I got that Cl is the lift coefficient and Swetted is the area of the stone affected by the water

and that Swetted = R^2(cos^-1(1-s/R)-(1-s/R)sqrt(1-(1-s/R))

From that I see tell that R is radius and that s=|z|/sin(a)

z being the lowest height point of the stone

The remaining parts of this equation can be found here: http://large.stanford.edu/courses/ph210/serpry1/ [Broken]

It seems like this is pretty complicated. I'm not sure if I can break this down into components or not.

Basically without adding friction of the surface of the stone, wind resistance or waves, this could still be quite a challenge.

As far as real world data about skipping a stone I found that the optimum angle for attack is 20 degrees and the world record number of skips is 51

Basically in terms of motions in Actionscript in Flash. I would need to create some type of looping arc or bounce where the angle of attack, velocity, collision time, min height, max height, length of time between skips, distance between skips and total number of skips are stored as variables or in an array which I can use as the rock velocity degrades to the point in which the rock sinks.

Maybe then regards to other factors like wind, inconsistencies, etc I could add in some randomness to the numbers + or - a tad.

Last edited by a moderator: May 4, 2017
3. Sep 8, 2009

### mistercrowley

Does anyone have any idea on where I go from here? I have the whole process broken down into different parts.

The thrower will first have to throw the stone. The user can set the Initial Velocity, Spin, Height off of the water, angle of attack and angle and direction at which the stone is released as well as the radius, height and mass of the stone itself.

This will translate into gravity and drag as the stone heads towards the water surface.

I then need to know the factors that keep the stone above the surface of the water and by how much the velocity and height of the arc the stone is degraded each time. Ultimately I probably need to know the number of skips of the stone before it is even animated.

Any help on this would be greatly appreciated.