Car Crash Scenario Math: Is 114285 Pa Too High?

[Frank_Horrigan]

Hi I am trying to simulate a car crash scenario mathematically and come up with reasonable numbers for a project. The problem is I do the calculations and everything seems mathematically correct but the numbers seem weird.

I simulated an 80 kg passanger in a car crash that was going 20 m/s and the car has crumple zones of .5 m, the seatbelts streatch 20 cm, and the airbag+seatbelt area on the driver is .2 m^2

After doing the calculations I got numbers which seem high but I don't know, considering this is a pretty fast crash here.

I got pressure on the driver of 114285 pascals, with an acceleration of about 300 m/s.

Area these numbers ridiculously high and I did something wrong, or do they seem about right considering the scenario?

 

[andrevdh]

Well, if one takes the area of the ball of your foot to be four centimeters by four centimeters you get a pressure of about 500 kPa if you stand on one foot (it is probably even smaller than this estimate). Your pressure is about 100 kPa, which is one fith of the pressure when a person stands one one foot. So this pressure you are stating is quite low by comparison.

 

[vtmemo]

Hidden factor

You may also not be considering the natural elasticity of the human body.
http://www.gm.com/company/gmability/safety/images/chest-impact.jpg
Take, for example, the ability of the limbs to extend outward (forward) in a collision. Because the torso of a human body makes up for only about 40-50% of someone's weight (that's a generous estimate), that allows for a considerable amount of mass to continue moving even after the chest is stopped.

The head rolls forward, the arms extend out, the legs push forward and outward, and even the hips slide forward... allowing the entire body to compensate for the force of the impulse. It's like being tackled - you don't want to tighten your muscles up because the impact will just hurt more - relax, and your body has more time to absorb the force.

I know those factors are almost impossible to account for when performing calculations (since you don't have a crash test dummy of your very own... if you do, you are a very lucky guy). But hopefully that may shine some light on your too-high acceleration problem.

 

[vtmemo]

supplemental

I got pressure on the driver of 114285 pascals, with an acceleration of about 300 m/s.

FYI, 300 m/s is a measure of velocity (you meant m/s^2?)
Also, your numbers don't quite match up - did you drop an exponent somewhere in your calculations?

Atmospheric pressure: $$1 atm = 101325 pascals = 101.325 kPa$$
Acceleration: $$300 m/s^2 = 30.6 G's$$
...just to give your numbers some context.