# Homework Help: Maximum impulse a human can withstand?

1. May 29, 2012

### bduffany

1. The problem statement, all variables and given/known data

For a project I am doing I have to disprove something I see in a video. In the video, a person falls into a cart full of hay from a height that is irrelevant. What I know is that the person's speed at the top of the leaves is given by v (I have the actual number for v but I would rather see it done theoretically). The person's speed changes from v to 0 in time t. Given that the person's mass is m, I need to determine whether this collision would be lethal. In the video the person survives but I need to mathematically and statistically prove that he wouldn't survive this collision.

Is there a standard way to determine whether a certain impulse, etc. will kill an average person?

2. Relevant equations

ΔP=FavgΔt = mΔv

3. The attempt at a solution

I wound up calculating that the average acceleration (or "g-force") was about 75 g, and this acceleration occurred over roughly 0.033 seconds. The impulse would be m*a*t which would be 85 kg * (75 * 9.8) * 0.033 = 2061.68 N*s.

I know I need to use this impulse, the force, or the acceleration, and I have done so, but my concern is, I have no real standard for figuring out whether the collision will be lethal. I have seen plenty of documents online but they only refer to things like "humans can withstand sustained g-forces of yada-yada-yada" or "humans can take instantaneous g-forces of yada-yada-yada". The trouble is, instantaneous is too vague, and sustained is not what I am looking for.

2. May 29, 2012

### Nessdude14

The impulse isn't what is potentially dangerous; you can experience a very high impulse and be perfectly unharmed. For example, you can accelerate with 1/10 g for an hour, or a day, or a year and be perfectly unharmed, all the while the impulse you experience over that time is increasing. The real cause of death is high acceleration. The highest recorded survivable acceleration I've been able to find is about 100g (g-forces) of shock. Shock just means a sudden acceleration, over just a fraction of a second. If it's a constant acceleration over more than just a fraction of a second, the highest recorded survivable acceleration is about 46g in that circumstance. If you're just looking to calculate for a collision of some kind though, then about 100g is survivable.

Last edited: May 29, 2012
3. May 29, 2012

### bduffany

Re: Maximum [instantaneous] impulse a human can withstand?

Thank you for the reply. Again you use the term "fraction of a second" which is basically as vague as "instantaneous" and doesn't give me much physical evidence. In any case though, I should be able to 'science' something together, such as "several experts say that in an average, instantaneous collision ... 100g is the max," or something along those lines.

The other question I have, though, is whether the person could easily get out of the cart after being subjected to 75g for a "fraction of a second." A person can survive 100g, as you said, but could they easily walk away? My guess is no. But for 75g? Ehh, I'm starting to feel a bit unsure here. Is it statistically likely within 90% confidence or so that a person couldn't simply walk away from an instantaneous 75g acceleration? Again, my guess is no, it's not likely they can just walk away, but it's just a guess.

Is there anyone here with first-hand experience? :rofl:

4. May 29, 2012

### Staff: Mentor

It is possible to mathematically model a system like this using finite element structural modeling (dynamics). You would need to approximate the mechanical properties of the bodily flesh and the bones (Elastic modulus, Poisson ratio, density), and would need to input the geometry of the body parts. You would also need to input the detailed force, velocity, and displacement boundary conditions. The boundary conditions, of course, would depend on the geometry with which the body landed. The outputs of the calculation would be the stress distribution within the flesh and bones as a function of time. You would also need to provide failure criteria (strength) for the flesh and bones to ascertain the extent of the local structural damage (if any).

Chet