# Why are 3 different road tests enough to say the suspension system of a car can handle any random road?

In an assignment I am given a random car with a random suspension system, and told that it is sufficient to test the safety of the car with regards to the suspension on three different sinusoidal roads.

The first road has an amplitude of 5 centimeters and a period of 20 meters, the second road has an amplitude of 2.5 centimeters and a period of 2 meters and the third road has an amplitude of 1 centimeter and a period of 20 centimeters.

I can't figure out why a test on these three roads would be sufficient to conclude that the car can handle any random other road, and I am given no other information.

Could anyone please tell me why it is sufficient to test the suspension on only these three roads?

• It's sufficient because the person told you it is. That's the parameter which defines your problem. Sure, in the real world it may not be, but consider your analysis in light of this given constraint. So: what is the actual question you were asked to solve? Something about the car's resonant frequency or damping, e.g. ? Mar 26, 2014 at 11:39
• I guess that you have to check whether the suspension has an eigenfrequency (a resonance frequency) that is in the range of those roads. And you have to check that it is not under-damped. Mar 26, 2014 at 11:40
• The question is part of an assignment in which I have calculate values for the suspension system, like the spring rate of the tires among other things, and make sure that it makes the car as 'safe' as can be. (safe meaning here that the suspension system keeps all the tires on the road at all times for speeds of up to 200 km/h). The testing is done on those three roads and I can't figure out why it is sufficient. Mar 26, 2014 at 11:49
• Maybe it is, maybe it's not. It doesn't matter because the validity of that claim is not within the scope of the question. Move on, accept it as truth and solve the actual question. Mar 26, 2014 at 12:16

I think this test conditions are more about comparability than completely testing any possible road condition. When you test products, such as car suspensions, you design your test to be standardized. A standardized test gives you the possibility to compare results over various models and over time.

If every suspension manufacturer would test its suspensions on the worst road in a 50 mile radius around the factory, each manufacturer would end up with its own representation of "worst road conditions". Furthermore, these test conditions would also change over time, as a bad road might deteriorate or even be shut down.

Another comment, you might have noticed that the amplitude gets smaller for smaller periods. When testing a suspension there is a certain parameter range for the period of the road profile. A very large period would not excite the suspension are the car would follow the road profile like one solid body. If the period gets too small, then the great inertia of the car would damp the excitation away.