# Q & A: heating via friction

Q:
I am interested in calculating the amount of friction (and ultimately heat) generated in primitive friction fires. In it most basic form, the fire-making method I am considering involves the rotation of a wooden dowel (with a rounded, half-spherical end) in a corresponding wooden, half-spherical socket. I am aware of the formula for calculating the coefficient of dynamic friction, but am wondering if there is a formula that is more applicable. Ideally, I would like to determine the relative amounts of friction and heat generated by various combinations of wood species with a set dowel diameter. Any help would be greatly appreciated. Thank you!
- Henry
Wilton, NH, USA
A:
Here I don't think that details like the friction coefficient are very important. After all, you can adjust the friction force by pressing the dowel more or less into the socket.

Probably what is more important for your purposes is the amount of heat (thermal energy) generated. That's not too hard to calculate. You will be doing some work on the system as you rotate the dowel. Although the dowel briefly acquires some rotational kinetic energy, that energy never gets very large. Nearly all the energy you put in via work ends up converted to thermal energy near the dowel-socket contact. So you can use ordinary work-energy equations to figure out how much energy ends up there.
If you're turning the dowel with a string:
How much force do you exert on the string?
How far does the point you're pulling on move?
The product of force times displacement is the work done.

Mike W
Lee H

(published on 10/22/2007)