# Car crumple zone deformation physics

1. Feb 19, 2012

### skazis

Hi,

I got confused thinking about cause and effect. If force is applied to a car due to collision, it deforms car. The longer is the time of a collision, the smaller is average force applied. Longer time is achieved by crumple zone deformation, which is affected by force. I find here circular argumentation. Could someone clarify for me this?

Thanks.

2. Feb 19, 2012

### jambaugh

The key is its is a zone, i.e extensive in space. The impactor hitting the car is not accelerating the whole of the car at the same rate so it is imparting less force on the driver.

• You take a running start.
• "Mr. Headlight being very light and quick is able to get up to the same speed as you almost the instant you cross the starting line He experiences an intense bit of acceleration at that point. It's as if you hit him as you cross the start line and carry him with you.
• I being old and heavy and fragile and weak need a longer time to accelerate to your speed and so to make it fair you give me enough of a head start so that by the time you and Mr. Headlight catch up with me I'm up to speed and we're all running even.
Can you visualize such a race start?

Now imagine if your car (made of concrete so it won't crumple, but very massive) hits the front my stationary car with a front crumple zone, the headlights and bumper of my car almost instantaneously accelerate to your speed. I in the driver's seat accelerate up to your speed but over a longer period of time. Eventually you I and my headlights are moving at the same speed. The headlights of my car are closer to me and the space in between them and me has to have crumpled.

Imagine you're designing a new special forces landing device to replace the parachute. It consists of a very long telescoping pogo stick (pneumatically driven). Some aerodynamic fins keeps the faller oriented so the stick lands upright. The pogo stick compresses but locks before the rider can bounce and the hot compressed air inside is released via vents.
He steps off and begin his intended combat mayhem.

3. Feb 19, 2012

### skazis

It gets better. Thanks.

Energy absorbed by car equals its kinetic energy (assuming head-on collision and that both cars stop after), so work done by average force on the car is

$F_{aver}d = -\frac{1}{2}mv^2$

where d is the deformation of the car.
From 2nd Newton's law the average force is equal to

$F_{aver} = m\frac{\Delta v}{\Delta t}$

Are these 2 average forces the same?

Last edited: Feb 19, 2012
4. Feb 19, 2012

### afreiden

Yes, the deformation depends on the force and the force depends on the deformation. Many problems are like this in structural engineering - even static problems can usually only be solved if one knows the properties of the materials involved. It would be particularly difficult to find a closed-form solution to your crumple zone problem since it has the additional complexities of being 1) dynamic and 2) inelastic. That's why such problems are not solved analytically. Rather, they are solved using methods that march forward in time in incremental steps, numerically satisfying the equation of motion along with the applicable force-deformation relationships (dependent on material properties) at each increment in time. Such methods can be terminated once a steady-state is reached (i.e. the collision is complete), for example.

As mentioned by jambaugh, the acceleration of the driver would be the key parameter. One would seek to design the crumple zone so as to minimize the acceleration that the driver experiences, at the expense of the "headlights" and hood, etc.

Looks fine to me