Friday, 4 November 2011

Mass Velocity and Energy

I've had a bit of a cold all week, so I thought I'd make do with some gentle experimentation.
The title says it all, how exactly does projectle mass effect speed and energy?
I made a crossbow bolt which I could add weights into by glueing some thinwall steel tube onto a short bolt. A rubber blunt head was then put over the end. I wanted to test for even higher weights and ended up sticking a long M8 coach bolt with several M10 nuts on it into my test bolt. For lower weights I cut down a bolt until it was just about 5" long with no point added. The very low weight bolt actually broke the 200 fps barrier (best shot 202.9 feet per second) .
Pretty obviously the lighter the bolt the faster it goes, what is less obvious is that the maximum energy isn't when the bolt is at it's fastest.
In fact the energy levels off despite the ever increasing weight of the bolt. The real point is that if you want to get maximum range and maximum energy then there is an optimum weight.
For this particular bow you can see it's about 12-15 grams. As the mass increases beyond that the energy doesnt get much higher and the velocity (and thus range) drops off rather a lot.
The text on the graph isn't too clear, so here's a description.
Vertical scale and blue line:- Velocity in m/s
Red line is Bolt Energy (multiplied by 4 to get it to sit nicely on the graph for comparison).
Horizontal scale Bolt mass in grams.
A bit more explanation: (I noticed the 'explain more' box is ticked).
You can only get out of the bow the energy you put into it, or a little less. That accounts for the energy of the bolt not getting any higher once it has levelled off on the graph.
I was slightly surprised that it didn't drop off a bit as bolt mass increased, but there is no real reasn why it should until you make the bolt so heavy that the bow can't push it or friction becomes significant, but presumably that would be at a silly weight, say a couple of pounds.
The energy put in to cock the bow is used up accelerating the bow limbs, the bolt and the string. With the very light bolt more of the energy is staying in the bow limbs and string and less in the bolt. As the bolt gets heavier most of the energy stays with the bolt.
The tips of the bow move faster than the rest of the bow limbs, but even they don't move as fast as the bolt! That's because the string pulls back about 120mm but the bow tips only move back 40mm! That's one of the remarkable things about the simplicity of a bow, a simple piece of string effectively gives you 3:1 leverage.
Anyhow the string and bow tips both return to rest at the same time so the bolt must go 3 times faster than the actual bow tips.
The modern compound bow takes this to extremes by adding extra wheels (like a block and tackle) and cams to make the centre of the string where the arrow is nocked travel much faster than the bow tips. This allows short, stiff, fast limbs to propell an arrow very fast... but at the cost of complexity.


  1. LOL... yes. I make everything on here!

  2. Great graph! Love the pistol stock. Do you have pics of the trigger mechanism and did you make your own design of trigger? Great to see a craftsman working in both wood and metal.

  3. Hi, the trigger is pretty much a standard rolling nut type but the "nut" is more rectangular than round, it's fabricated from 3 plates of steel riveted together, with the sear case hardened.