Physics of The Crumple Zone

I was curious to see how effective the crumple zone of my car (Honda Accord Coupe) was and how it compared to a car that I've always considered to be relatively unsafe (Smart Car).

----------------------------------------------------------------------------------------------------------------------------------

BACKGROUND

First thing first, the crumple zone of a car was introduced by Mercedes Benz as a safety feature in the 1950s.  Over the years, more research has produce a more effective crumple zone.  The Crumple Zone of a car is usually located in the front and the back of a car.  Focusing primarily on the front end, the crumple zone is created by purposely making the front end weaker in some areas so that the car "crumples" (kind of like an accordion).  The physics behind the crumple zone entails the use of the equation for Impulse.

Impulse = change in momentum = All forces * change in time

The idea behind crumple zones is to increase the time it takes for a car to decelerate, thereby making the force acting on the passengers at any point during the collision to be less.  In other words, the longer the collision (or longer it takes to decelerate, the lower the magnitude of the force of the collision on the passenger).

----------------------------------------------------------------------------------------------------------------------------------

So now looking at the two cars I am interested, Honda Accord Coupe and the Smart Car, I needed to collect some information.  Going on to Youtube to find timed crash tests of both the cars, I found that the crumple zone makes the length of the collision 0.092 seconds (for the Honda Accord Coupe) and 0.061 seconds (for the Smart Car).  These times were collected from the moment of contact with the crash wall to the moment just before rebound. I will assume that without the crumple zone, the car would stop in 0.01 seconds.

Now to see how much force my body (65 kg) would feel hitting a stationary wall at 100 km/hr (27.8 m/s), I calculated the following:


Me in a car with NO CRUMPLE ZONE

Impulse = change in momentum = All forces * change in time

                                       mv-mv = F * t

                      (65 kg)(0 m/s)-(65 kg)(27.8 m/s) = F * (0.01 sec)

                                                F = -181,000 N

Me in the HONDA ACCORD COUPE with Crumple Zone

Impulse = change in momentum = All forces * change in time
                                       mv-mv = F * t
                      (65 kg)(0 m/s)-(65 kg)(27.8 m/s) = F * (0.092 sec)

                                                F = -19,600 N



Me in the SMART CAR with Crumple Zone

Impulse = change in momentum = All forces * change in time

                                       mv-mv = F * t

                      (65 kg)(0 m/s)-(65 kg)(27.8 m/s) = F * (0.061 sec)

                                                F = -29,600 N

Thus, in looking at the values, my car is much safer than the Smart Car, but the Smart Car's crumple zone (as small as it may be), is still incredibly effective at decreasing the magnitude of the force.

While 19,600 N of force is still a lot, one must not forget the other safety features (seat belt, air bags, etc) that follow the same principle of trying to elongate the time of force.


RESOURCES

http://www.youtube.com/watch?v=aGf57UUhO7w
http://www.youtube.com/watch?v=1z0EhZ0-EWo