# “Magic” Speed to Drive Over a Speed Bump: Myth or Reality?

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?

• Mythbusters tested this some time ago, they do find that going faster negates the bumpiness. – Kyle Kanos Sep 18 '14 at 14:51
• This is not true: the hit will always cause higher momentum transfer to the car the higher its speed. – rmhleo Sep 18 '14 at 14:53
• @KyleKanos They tested "bumpy" or corrugated roads, but only speculated about the effect of a large obstruction like a speed bump on vehicle dynamics. – Bryson S. Sep 18 '14 at 14:54
• Or maybe if you had a soft enough suspension? – Bryson S. Sep 18 '14 at 14:58
• @BrysonS: Hmm, I thought they covered an actual singular speed bump (and didn't really read the link I provided because of this). It's been some time since I've watched Mythbusters, let alone TV in general, so my apologies! – Kyle Kanos Sep 18 '14 at 15:05

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.

• "Driving faster will cause a bigger jolt." I'm reasonably certain going too slow (in my non-fancy car) over a speed bump does jolt me more. There seems to be a minimum, not at say 60 mph but more like 10-15 mph. Maybe it's my imagination, but I could believe the transfer function from my tires to me fails to dampen particularly low frequencies. Perhaps this all hinges on the definition of "jolt." – user10851 Sep 18 '14 at 16:12
• @ChrisWhite I was using impulse as a surrogate for "jolt," whether that is a justifiable choice or not. So a higher force over a proportionately shorter time would result in the same "jolt" by that metric. – Bryson S. Sep 18 '14 at 16:23
• @ChrisWhite - there definitely is a speed where the car "waddles" over a speed bump - where the natural frequency of the suspension matches the "up" and "down" parts of driving over the bump, you will get a double whammy (mini resonance). We are talking about going considerably faster than that... – Floris Sep 18 '14 at 16:35
• @Floris I think you revealed that there are more aspects than just speed, but the insight you provided is enough to nab the selected answer. Top posts as always Floris. – Bryson S. Sep 18 '14 at 19:12
• @Floris This video adds more contect to the project and is in english. It's awesome!!! – Bryson S. Sep 19 '14 at 19:43

The answer depends on lots of factors:

• The nature of the speed bump,
• The nature of your vehicle's suspension,
• The weather (your suspension is a bit stiffer in winter than summer),
• Whether there's stuff such as a rather low oil pan under your vehicle that you would rather not lose to your vehicle bottoming out, and
• Which you care more about: The impact on you versus the impact on your suspension.

I'm sure I'm missing a factor or two in the above.

There several different types of speed bumps. Your behavior needs to vary depending on the type of speed bump over which you are driving.

Hand-built speed bumps in a city park.
The civil servants who build these bumps using a load of asphalt and shovels know absolutely nothing about vehicular suspension systems, and they don't care. They're civil servants. Treat these bumps with extreme care! The shape and height of the bump varies across width of the street. What's optimal at one spot will leave your oil pan in your rear view mirror at another spot.

Extremely aggressive commercially-made speed bumps in parking lots.
These are typically narrow (less than a foot wide) and a few inches high. The height of the bump dictates the design speed. Tall ones are designed to slow vehicles to one or two MPH. The only way to go over these aggressive bumps comfortably is to convince the managers of the stores to remove them. Let the owners of the stores know that you will not be shopping there any more until those bumps are removed or replaced with less aggressive speed bumps. If you drive faster than the design speed over these bumps, you might reduce how the bump feels to you but you also dramatically increase the chance your car will bottom out and leave your oil pan behind you, and you also dramatically increase the damage to your suspension.

Not-quite so aggressive commercially-made speed bumps in parking lots.
These speed bumps are similar to the above, but are not quite so tall as the aggressive ones. The reduced height lets you drive over these at a speed considerably faster than the design speed. When you drive over these bumps at the design speed you feel a pair of jolts that damp out slowly as your front wheels and then rear wheels pass over the bump. This is an overdamped response. If you drive over the bump at excessive speeds, you feel a series of sharp jolts that send your car into oscillatory behavior. This is an underdamped response. There is some intermediate speed where your vehicle's behavior is critically damped. The speed that results in a critically damped response is the optimal speed for driving over these bumps, at least with regard to passenger comfort.

On the other hand, if the store owners kindly replaced their overly aggressive bumps with these nicer bumps, and did so at your request, you might want to think of being nice in return and driving over these bumps at the design speed.

Broader speed bumps on a residential street.
These bumps are typically three feet wide and are designed to slow vehicles to a bit below the speed limit. The extra breadth means the forcing function is less impulsive than the foot wide (or less) speed bumps used in parking lots. Done right, the design speed is exactly that that yields a critical damping response in a typical vehicle. If you have such a typical vehicle, you want to drive over the bump at a bit under the speed limit. There is no better speed. The optimal speed will of course differ from the design speed if your vehicle is atypical.

Very broad speed humps on a non-residential street.
These speed humps are typically very wide, as wide as the wheel base of a typical vehicle. These speed humps temporarily launch offending vehicles off the ground. The design speed is once again exactly the speed you want to use to drive over these speed humps.

Yes it's true. I had a 1990 Toyota Camry and my friend had a 1987 Honda Accord. If we drove 30mph over 15mph speed bumps it glide right over and when hit 50mph over our many 25mph speed bumps on Ramblewood Drive Columbus Ohio 43235 lived on Maleka Ct 43235 from 1986/87 to 1998/parents moved 2002. I'm not sure if we had to exactly double the speed or if we could go higher to glide over. If we went 35mph over the 50mph it was really bumpy.

## protected by Qmechanic♦Sep 26 '17 at 5:53

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