Heat Transfer Porn!
dwhitlat's analysis above is pretty good. I'm actually a bit jealous, since I used to know how to figure that kind of thing out. Alas, much of Heat & Mass Transfer has left me.
The link below is to a PDF of the IR imaging article that might have been referenced above. A couple differences from dwhitlat's calcs:
- The bullet is a .30 cal boat-tail (assume FMJ)
- The images are taken soon after the bullet leaves the muzzle
What's interesting is that the IR image has been processed to account for differences in emissivity, or (I think) how easily a given region radiates heat. Their analysis indicates frictional heating where the bullet contacts the rifling lands, and aerodynamic heating at the bullet tip (as well as reflection from the heat of the muzzle flash at the bullet's base).
So, what do we need to solve this problem conclusively? (I'm just guessing, but it's kind of neat to pretend I still remember this stuff):
- Heat transfer coefficient of the air (fairly easy to get)
- Heat transfer coefficient and thickness of the copper jacket (again, easy)
- Heat transfer coefficient and thickness of lead core to center (easy)
- Coefficient of friction between bullet and rifling (not so easy?)
- Initial bullet temp (assume this from the IR analysis?)
- Travel time (say on a 100 m range?)
- Effects of aerodynamic heating (maybe where dwhitla's calcs come in?)
Figure all that, and you could probably get a good approximation of the temp (both surface and core) at the instant before impact.
I agree, though, that it would take less time, and be a lot more fun, just to shoot it and see.
Any other ideas?
http://www.indigosystems.com/PDF/articles/AdvImg3-04.pdf