# B How to measure the impact force of a moving object

1. Jan 26, 2017

### Darkest_Fallen

So I have been researching, I'm no genius, on how to measure the force of a moving object.

Now I have seen some of the equations and newtons law and all but what I am specifically trying to do is figure out the impact force of an arrow. eventually this will be calculated into how much force of an arrow is being created per pound of draw on different bows.

Measuring the poundage of the draw is easy with a spring weight scale. That is not in question. Though I am having a hard time knowing if I am about to go at this at the right angle.

So I am thinking about making a rudimentary accelerameter on a large enough scale that I can hit the weighted end with an arrow. and I am thinking about making a way so that the swing arm the "weight" is attached to pushes a magnet along a compass style scale. much like making the paper version with a string and a nut. So that I can know the peak amount of acceleration force on impact.

Now I know how to build all these items an what not, but I need to know what all I use for measuring it into foot pounds of force on impact, or if this design would even work. Any and all suggestions are more then welcome.

Last edited by a moderator: Jan 26, 2017
2. Jan 26, 2017

### Darkest_Fallen

Well I would like to apologize for not reading that before I entered it. My typing skills in that question are horrible.

3. Jan 26, 2017

### ZapperZ

Staff Emeritus
What you need to learn about is the concept of Impulse.

The force exerted is defined at the rate of change of momentum of the object, i.e.

F = dp/dt, or Δp/Δt

where p is the momentum of the object, and t is time. Here Δp is the change in momentum that the object undergoes over a period of time Δt. It means that if the object changes momentum from some value to zero, it will exert a greater force the smaller Δt is. If this change in momentum is spread out over a larger distance, it will change in a longer time, and the force exerted will be smaller.

So now that we have this down, let's look at your arrow. The question can only be answered if you can make an estimate on (i) how fast the arrow is moving right before it hits the object, and (ii) how far it went into the object. Let me explain by using this picture below:

Let's say in the top part is the arrow being shot into a piece of wood, while the bottom part the arrow is shot into a piece of jello.

It will travel very little when it enters the wood, and so, it travels a short distance Δx1. On the other hand, it travels a longer distance Δx2 before it is stopped. If it enters with the same speed, and it travels until it is stopped, then it travels for a LONGER period of time Δt when it enters the jello, i.e. Δt1<Δt2

If you apply this to the force equation that I wrote at the beginning of this, it means that the force that is applied by the arrow is larger when it hits the wood than when it enters the jello.

What I'm trying to illustrate here is that there is no one single value. The impact force here depends on how much the arrow moves while it is being stopped by the material.

Zz.

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4. Jan 26, 2017

### Darkest_Fallen

Thank you for the reply, that explains a lot on an arrows force with piercing. I guess I should have gone into a little more detail. The subject is specifically on LARP arrows. Arrows designed safely in a matter that they can be fired at people without causing injury. Currently the way they measure safety on this is the pull weight of the bow. I believe that the pull weight of the bow is not the only factor in the matter of safety though. The pull weight determines how much force is being applied to the arrow. but when you look at different lengths of bows the amount of force to pull a bow to a certain length is not the only definitive answer of how much impact there is by the arrow. A longer bow could be pulled further back because the string is longer. the amount of force being applied to the arrow could be larger one way or the other. So to determine safety I want to measure a flat headed/padded arrow on impact without penetration. Would this still apply to the equation you stated?

5. Jan 26, 2017

### Staff: Mentor

A simple method would be to make a pendulum, have the arrow hit the weight at the bottom, and measure how far the pendulum swings. A little bit of freshmen physics can let you calculate how much energy was imparted to the pendulum to swing that far. Energy relates to the impulse that @ZapperZ talked about.

You may not need a numerical measurement of energy or force. If by experiment, you can find out how much the pendulum swings for an arrow just gentle enough to cause injury, then you can test new arrows to see if they do or do not exceed that limit.

6. Jan 26, 2017

### Darkest_Fallen

Right, that's why I was figuring on using a accelerometer style setup. But I wanted to give it some facts not just this hurts and this does not. I was wondering like, say I set up markers to tell how far the pendulum swung, how to equate that into say foot pounds of pressure.

7. Jan 26, 2017

### Staff: Mentor

That's even more difficult to apply the concept of "force" to than an arrow that pierces the target, since at least an arrow that pierces a target is going to have some sort of consistent and continuous deceleration function. An arrow that doesn't pierce the target is going to have a very chaotic and short deceleration profile.
Your concern is correct. @ZapperZ said you should learn about impulse, but I think a simpler way is to use work. If we assume the force varies linearly as you draw, then the work done on the arrow (and therefore its kinetic energy) is half the draw weight times the draw length.

Caveat here being that I'm thinking that how much the arrow hurts is proportional to its kinetic energy, not momentum.

8. Jan 26, 2017

### Staff: Mentor

Suppose you did measure for pounds of work (not pressure). Let's say the answer is 11 (just to pick a number). So what does that mean? Is 11 good or bad? Numbers without context are meaningless.

9. Jan 28, 2017

### OldYat47

There's still the problem of deflection of the target. An arrow that doesn't penetrate will generate a much higher impulse on my lean tummy than it will on someone with, shall we say, more inactive girth? I think you're left with a range of possible outcomes depending on the target. I suppose you could select some standard and go with that (chubby?).

10. Jan 29, 2017

### Nidum

Make an intelligent arrow . One fitted with instrumentation .