## What’s the best way to go over a speed bump?

I’ve noticed that a lot of people try to avoid using the four wheels of the car when they go over a speed bump. Out of curiosity, I asked some of those drivers and all of them gave me the exact same answer: “Because if you only hit the obstacle  with the wheels of one side of the car, you will cause less damage to the vehicle and, besides, it is less uncomfortable for occupants”. Is that true? Let’s find out.

Let´s start from the beginning. The first thing we need to know is that cars have two axles (i.e.front and rear) and each of them has two wheels (i.e. right and left). On the other hand, speed bumpers are road obstacles which are designed to make drivers reduce the speed in certain areas and they are usually as wide as the lane. Why is that? Well, basically bumps are thought to be encountered by the two wheels of each axle simultaneously, creating a scenario known as “vertical symmetric load case”. This situation causes results in a bending moment which is applied to the structure of the car.

However, sometimes we can find some bumps which present a smaller width or even gaps. These are the situations where some drivers decide to vary the direction of the car so that the wheels of one of the sides avoid the contact with the obstacle. Therefore, only one wheel goes over the bump. Hence, the vehicle will suffer an “asymmetric vertical load case”. In other words, the automotive structure will be subjected to a torsional load, which is a worse scenario than the one introduced above since it can cause one of the wheels to lift off. I will show you how a relatively simple approach can be used to prove this statement.

Source: Payton Chung

Let´s consider an asymmetric case. In this case, the torque which will  be created depends on the stiffness of the structure (K). In the schematic, one of the axles is illustrated. H is the height of the bump; B s the width; Pl and Pr are the reaction forces on the left and right wheels respectively; T is the torque; theta is the twist of the structure; and P is the total load  in the axle.

From the schematic and considering small displacements and rotations, the torque can be expressed as follows:

Now, simply applying equilibrium, another expression for the torque is found:

From that last equation, it is easy to see that the torque will be maximum when the reaction force in the left wheel is equal to zero. In other words, when the left wheel lifts off. You can argue that if an ideal torsion case was considered, then the reaction would be negative, making the calculations a bit different. Well, the answer is that in reality, the reaction force will never be negative: a zero value means than the wheel is no longer in contact with the road, making the car to roll over.

Based on that information, we can determine the maximum height of the bump which would cause the left wheel to lift off. We can see that it depends on the stiffness and the width of the car (as well as the load to which the car is subjected).

Well, I really hope that from now on you will always try to go over these obstacles using two wheels at a time instead of one. Sorry if this is not comfortable for the occupants, but trust me, you’ll be safer this way! And one more thing: if someone asks you what an asymmetric vertical load case is, please do not say “A case which is not symmetric”!