The Physics of Fire by Friction

[PEZenfuego]

I wasn't sure where to post this, so hopefully I didn't post it in the wrong place and hopefully I won't get flamed.

Anyway, I am a boyscout and last weekend I was doing a demonstration on fire by friction. I use a bow drill. For those of you who do not know, this is how it works: A spindle (stick-like piece of wood) is spun by use of a bow on a surface that has a depression. That sounded confusing, here's a picture.

http://www.google.com/imgres?imgurl=http://www.raymears.com/blog/wp-content/uploads/2010/06/FMBC_bow_1.jpg&imgrefurl=http://www.raymears.com/blog/fire-by-friction-the-bow-drill-method/362/&usg=__XwvfWjBPuDJq3ejXBkHs5W0bEWQ=&h=276&w=400&sz=41&hl=en&start=0&sig2=-HBP3uAHLmhqMb_-bIrjgg&zoom=1&tbnid=ZAZzxtu8aKGl3M:&tbnh=144&tbnw=197&ei=pcrITIfIJs2XnAfY_aibDA&prev=/images%3Fq%3Dfire%2Bby%2Bfriction%2Bbow%26um%3D1%26hl%3Den%26safe%3Doff%26sa%3DN%26biw%3D1024%26bih%3D613%26tbs%3Disch:1&um=1&itbs=1&iact=rc&dur=428&oei=U8rITNC-I9LtngfDtuwT&esq=13&page=1&ndsp=12&ved=1t:429,r:1,s:0&tx=144&ty=49

My question is what kind of friction is this and how can I go about calculating it?

 

[Jasongreat]

Do you know the suface areas of the parts in contact? Do you know the friction values of the wood you are using? Do you know the pressure you are exerting on the stick? Do you know the speed in which you are spinning the stick with the bow? Are you able to keep all these forces the same from one time to the next?

Did you get a fire started? Then you had enough friction, if not you didnt.

It doesn't seem to me it would be possible to get an exact figure, repeatable from one time to the next, but if you just want to find an approximate figure to quell your curiosity, this may help: http://en.wikipedia.org/wiki/Friction"

It looks to me like it is dry kinetic friction.

 

[PEZenfuego]

I can find the coefficient of kinetic friction for cottonwood on cottonwood (maybe...but wood on wood wouldn't be too far off). Calculating speed would be easy too because I can just figure out how many times I move the bow back and forth and how many times the spindle spins per stroke. I can find the force exerted by pushing on a scale in the correct position with my thunderhead in hand (close enough). Can I just multiply the coefficient of kinetic friction by the normal force (force of gravity plus force applied) to get the force of friction? Do I then multiply the force of friction by the distance to find heat energy? How do I find the distance? Am I going about this the right way at all? I'm having trouble wrapping my mind around it. This isn't actually going to help me in any way as far as fire by friction goes, but I'm curious as to how this would work.

I also have no idea how the surface area would factor into this, but I know it has to. I could find it pretty easily though.

 

[Archosaur]

This is kinetic friction, aka "sliding" friction. The force of friction is equal to the force of contact between the stick and the surface multiplied by a constant that represents the "stickiness" between the two materials. (i.e. rubber on asphalt is very "sticky", while metal on asphalt is not.)

Friction is a force, and a force isn't what starts a fire. It's energy. Specifically in, the case of fire, a minimum "activation energy" is required, at which point, the fire takes off on its own. (as you've no doubt noticed, you don't have to keep spinning the spindle to keep the fire going)

One way energy can be expressed is "force across a distance". It takes energy to push a crate across a room, because you are opposing friction for a certain distance. The law of conservation of energy says that the energy has to go somewhere, and in the case of the crate (and the spindle) it's heat.

To calculate the energy converted from friction-across-distance to heat at the tip of the spindle is complicated, but, we can invoke conservation of energy again and ask "Where did the friction-across-distance energy come from?"

It came from your arm, pushing a bow back and forth. Again, the energy supplied by your arm in one oscillation is equal to the (average) force of your arm on the bow, multiplied by the distance your arm moves in one oscillation. A much simpler calculation.

"But wait," you might ask "why do I have have to move it so darn fast then?"
Because the heat dissipates. In order for a net gain of heat, you have to add heat faster than it dissipates.