### Kinetic energy and arrow weight.

Hokay, so KE (J) = 0,5 x mass (kg) x velocity2 (m/s). Increase either the mass or the velocity, and kinetic energy increases.

Say we have 2 arrows, and 2 bows. One arrow weighs 300gr, and one weighs 500g. And the bows are rated at 300fps and 350fps (let's assume that the bows shoot both arrows at their rated speed, although this is unlikely to be the case)

We need the mass of the arrow in kg, and the velocity it's travelling at in m/s, so quick maths gives us 0,01944kg, 0,0342kg, and 91,44m/s and 106,68m/s.

Plugging those in gives us the following for the 300fps bow..

KE = 0,5 x 0,01944 x 91,442 and KE = 0,5 x 0,0342 x 91,442.

Which gives us 81,27J, and 135,45J

For the 350fps bow, we get these KE = 0,5 x 0,01944 x 106,682 and KE = 0,5 x 0,0342 x 106,682.

Which gives us 110,61J and 184,36J

So what about the full results? I've included 350gr arrows, as a direct comparison, as you're more likely to see a 350fps bow, than a 500fps one ;)

V\M 300gr 350gr 500gr
300fps 81,27J 94,81J 135,45J
350fps 110,61J 129,05J 184,36J
500fps 225,75J 263,38J 376,25J

So we know that increasing the arrow mass from 300gr to 500gr while keeping the speed the same increases KE by about 50J, whereas increasing just the velocity by 50fps gives us an increase of about 30J. If you can go that silly fast, increasing velocity from 300fps to 500fps gives you a 140J increase in energy, instead of just a 50J one by increasing the mass.

Because velocity is always squared, if you can increase velocity by the same amount that you can increase mass, then that will give you more kinetic energy than just an increase in mass will. It's why the compound market for speed has really been driven forward by the hunting crowd. They're after those higher speeds that keep their heavy arrows going fast. More KE in the same place, and you're more likely for a clean kill in a lot of cases, especially for very large game with dense bones. 225J will smash that out of the way, whereas 81J might be deflected or even reflected.

So that's the maths done, the second part is about the arrow itself. Now the only thing I hunt is layered foam, and you can't exactly eat that (I've tried, sort of), but the point itself can make up a large amount of mass, which moves the FOC balance forwards, giving you a slightly more stable arrow flight, keeping those sharp bits going forwards.