Hacker News new | ask | show | jobs
by mbell 5033 days ago
> Imagine one of these payloads landing on someone's head. Wolfram Alpha offers up "2.4x impulse force acting on a baseball being hit by a bat" as a comparison when you plug in "5 lbs * 30 mph".

I'm not sure what value this comparison has. Impulse force doesn't tell you much of anything about how much damage would be done to a persons head.
1 comments
elteto 5032 days ago
You are working with the wrong concept, m * v is momentum, not impulse. Impulse would be equivalent to the change in momentum over time [1]. Actually 5 lbs falling at 30 mph would probably crush a human skull or at least crack it open. It is easy to see why from the equations:

F * delta t = m * delta V, therefore F = m * delta V / delta t

This means that the force generated in the impact is inversely proportional to the time of the impact. Since the skull is pretty hard, we can say that the impact time will be very short, probably in the order of 1e-2 seconds. Such a sudden change in velocity, from 30mph to 0mph in 1e-2 seconds, generates a big force, and therefore a big impulse.

[1] http://en.wikipedia.org/wiki/Impulse_%28physics%29

link
mbell 5032 days ago
Indeed, however to say anything about damage you need to know the area where the force is applied and more about the materials. If the bottom of the copter is padded the duration of the impact coud be much longer and spread over a larger area.

Also, F = m * delta V / delta t is only valid if force is constant in this context. I would expect acceleration to vary during the course of the impact so this relation would likely not hold [EDIT] in terms of determining damage I mean.

link
elteto 5032 days ago
Yes, in this case the equation refers to the average force over an interval of time: if at time instant A we had a speed v1 and at a later instant B we have some speed v2 then a force with a magnitude of at least m * (v2 - v1) / (tB - tA) must have acted, therefore the analysis should hold.

As you point out the area is very important in the analysis, since Pressure = F / A. For large areas the force "spreads out" and the damage is less.

The fatality of the accident can vary due to many circumstances however I think we can safely assume that for the purposes of our initial analysis, 5 lbs traveling at 30mph and crashing into my head is not something I am looking forward to ;)

link