# How much force/torque act on a wheel of a vehicle when vehicle moves a constant speed and suddenly got a bump or jerk?

I am working on disturbance rejection technique in a vehicle of a wheel. Suppose our vehicle moves with a constant speed 15 km/h. Since roads are uneven in nature, suddenly vehicle got a bump or jerk. Is there any method or relationship to find out the force or torque applied by the jerk or bump?

Assume mass of a vehicle is M (kg) and radius of wheel is r (cm).

• It may be en electric machine but it is a physics problem. I suggest you ask at the physics stack exchange.
– oldfart
Apr 24 '18 at 6:20
• Torque will probably be the force at the centre of mass x height of centre of mass above ground. The pivot points will be the points of contact between tyre and ground. Best to consider a quarter-car model first. This question is not appropriate for this website, however.
– Chu
Apr 24 '18 at 6:56
• Bump or jerk is just the sum of all the derivatives higher than the second derivative of position (or acceleration) with respect to time. The 3rd is usually sufficient. You'll need to estimate it somehow.
– jonk
Apr 24 '18 at 6:56
• @jonk So that's why there is no term for rate of change of a jerk. . the question needs much better specs! Also it needs to define which destructable parts will absorb the energy and it's compliance, range etc.and about a dozen other variables. I once had an Audi CD5000 Turbo that went perfectly smooth over a washboard road at 80 kph until the strut seized , separated and put a golf ball size dimple in my hood. Since all such vehicles have a complex transfer function, start with that after specs then desired functions and design the difference Apr 24 '18 at 12:17
• I hit an 12” deep channel that was 12” wide at 60mph in a Landrover - no damage, but definitely there! Apr 24 '18 at 13:39

Not at all trivial problem! A vehicle is not rigid. More or less elastic wheels are the the first defence line against hits.

More complexities:

1. The vehicle does not fall down vertically, it flies horizontally at the same time. This makes difficult to calculate how the wheels meet the next obstacle

2. Different wheels receive different hits. The vehicle does not fall and rise, it also rotates. It's in 3D.

3. You need a realistic model of the road

4. Rolling wheel (assuming it does not fly nor modify the road) meet the road profile. Solving the route of the wheel axis is a numerical equation solving problem. In practice the road can be smooth and the vehicle sometimes flies.

As a coarse approximation assume at first some road profile. Assume the wheel rises as high as is needed to prevent the wheel to sink into the road (=solve the route of the axis at first). If your wheel moves horizontally (= to X) 15km/h, present Y as function of the time. The second derivative is the acceleration input to your wheel.

Wheel elasticity, vehicle mass and frictional losses make a low pass filter. They make the effective hit input smoother. The second derivative should be calculated from the filtered signal.

Calculations like this are coarse. Make some measurements or use proper physics simulation software. Building the simulation model is a major task and the needed software can cost \$10k. Making acceleration measurements give to you realistic info much easier.

Horizontal forces $$\sigma F_1= F_2+F_r$$

$$F_2 \sin \theta × R$$ etc where r is radius of wheel and $$\Theta$$ is angle between vertical impact and perpendicular to direction of travel

The image explains some forces for consideration. Is basic to point out the obvious issues...