A somewhat controversial aspect of speed bumps (sleeping policemen for those in the UK) is that they arguably cause more loss of life than they prevent by acting as a hindrance to emergency response vehicles. In thinking of ways to minimize this adverse impact, I vaguely remembered hearing the claim that if a car travels fast enough, there is a critical velocity beyond which the vehicle would just glide over the bump as if there were no obstruction at all. This sounds too outlandish to be true, but then again Mother Nature has surprised me before. I'm obviously not promoting (or condoning) unsafe driving practices, but is there any experimental or theoretical merit to the claim that the impulse of a speed bump can be negated by merely driving fast enough across it?
Answer
Normally, suspension consists of a damping component and a spring component. For such a suspension, higher speed means higher acceleration and greater force. Driving faster will cause a bigger jolt.
However, high end cars these days use active suspension - and that changes everything. With active suspension, you can either respond quickly to bumps in the road, or even anticipate them. See for example this crazy example:
There is actually a youtube movie with the various tricks that this suspension can do - including the above "jump", but also including various bumps including speed bumps. It shows that active suspension on emergency vehicles would make this a non-issue... See in particular the "rolling bumps" (start at 0:43), the speedbump bit (starts at 1:02), and the "hold your breath" at the end, which demonstrates the jump shown above.
UPDATE after writing the initial answer, I found [an XKCD what-if}(http://what-if.xkcd.com/61/) that "analyzes" the same issue. A couple of interesting points it makes:
- the tires and suspension absorb much of the shock
- if you go fast enough, the wheels don't have time to move and the tire takes it all.
That's an interesting perspective. You can model a car driving over a speed bump as a pair of connected masses with springs:
Where the force $F$ is due to the bump, mass $M_1$ is the wheel, $k_1$ represents the elasticity of the tire, $k_2$ is the main suspension and $M_2$ is the car.
Now something interesting happens with the equations of motion. Using $x$ as the displacement from equilibrium, the acceleration of the wheel "absorbs" the impact of the bump so that less force is transmitted to the car! Let's use subscript 0 (ground), 1 (wheel) and 2(car), then
$$F_{01} = k_1 (x_1 - x_0) \text{ force from ground on tire}\\ F_{12} = k_2 (x_2 - x_1) \text{ force on suspension}\\ F_{12} - F_{01} = M_1 \ddot x_1 $$
(You may want to check I got the signs right...)
The point here is that there is no force felt by the car until the wheel has moved - so if the spring constant $k_1$ is low (soft tire) and the wheel is heavy, then driving fast across the bump prevents the shock from being transmitted to the body of the car.
As Randall pointed out in the what-if, at the limit of driving very fast over a bump, the wheel doesn't have time to get out of the way and the tire is deformed so much that it explodes.
The cleverness of active suspension is that it changes the above equations - it can "undo" some of the force of the weight of the car on the wheel, so that the wheel can bounce up more easily. If you wanted to be able to really drive fast over the bump, you would want the ability to pull on the wheel so it is lifted over the bump - this would prevent the tire from exploding.
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