# Inelastic collisions, impulse, energy, and swordfighting.

1. Sep 26, 2014

### jgalak

I have an interesting problem. I am involved in a historical fencing group which uses blunted swords to thrust with (think fencing foils and épées, but heavier and stiffer, with a rubber blunt on the end). We've been discussing various new weapons and needed to address safety. I decided to gather some actual data.

I mounted a Force Sensitive Resistor on the tip and am polling the resistance with an Arduino. At about 25kHz, I am getting really nice curves showing force over time (a sample can be seen here: http://lh4.googleusercontent.com/-N.../AAAAAAAAIms/bVAbGUvkxlM/s2048-no/IMAGE_1.jpg ). The problem is how to interpret the data.

I was hoping to figure out total energy transfer, but I now realize that the area under the curve is impulse, not energy. The collision is highly Inelastic - the sword bends, the target is squishy, etc. I really have no way to measure displacemen, and the energy transfer is far more than just the distance things move - there's mechanical deformation, possibly chemical changes in the target's body, etc.

Is there any way to get the energy of the impact? If not, what does the impulse actually mean in this case? I'm used to thinking of it as change in momentum in a classic elastic collision setting, less sure of what it means here.

The ultimate goal is to figure out how "hard" an impact is. The concern is a) injury and b) penetration of the (cloth) armor worn. Any thoughts on the best way to quantify this from the data? Should I just look at peak force and ignore the "width" of the peak?

2. Sep 26, 2014

### A.T.

Not without displacement.

A transfer of
momentum. But it's not the net change in momentum, because there are other forces acting on the body.

Peak force and peak contact pressure (force / contact area) should be relevant here.

3. Sep 26, 2014

### jgalak

Peak contact pressure is easy - the sensor is really measuring pressure in the first place, but since it's area is constant (ignoring things like side loads and uneven impact) the conversion is easy.

4. Sep 26, 2014

### sophiecentaur

This is a very common question on PF - but in a slightly different guise. It's usually stated in terms of vehicle collisions ("What was the force of impact on my car when an idiot ran into me?") and we normally conclude that there isn't a proper answer available.
You want to find the energy transferred but I wonder if this is actually indicative of the damage. If you sat the fighter in a motor car and accelerated him to 100mph, there would be a lot of energy transfer but no damage at all. There's more to it and I don't think you have enough information yet.
It strikes me that one important quantity involved in this is how much penetration there is of the blade against the surface. I can't think of a direct method to infer motion in detail from force and you would need some other information - like the speed on impact - to support your existing measurements. Could you make supplementary measurements with video or still photography? (You seem to have done the difficult part already - which is encouraging.)

5. Sep 28, 2014

### jgalak

Video, yes, but doing actual calculation for it? No clue how to do it. And I really don't have the gear or knowledge for high speed photography, which is probably what would be needed to do it right.