# Braking Basics

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NEW YORK – Prof. John Fieldhouse presented what he refers to as “A pragmatic approach to braking a road vehicle” in a post by the Brake Academy. This is the first of two excerpts from that post.

### A pragmatic approach to braking a road vehicle: Part 1 of 2

During acceleration, the power unit must provide all the torque necessary to move the vehicle as a rigid body. In addition to accelerating the rigid body, the power unit must provide additional torque to accelerate the rotational parts of both the driveline (including the driven wheels) and the non-driven wheels. As such there needs to be sufficient adhesion at the tire/road interface of the non-driven wheels to cause them to rotate. The rotational inertia of a vehicle may be reduced to a “mass equivalent”, so acceleration may be determined using the vehicle mass plus the mass equivalent.

That is not the case for braking. The tires do not need to be in contact with the ground for the rotational parts to be decelerated.

Consider the vehicle being raised off the ground with all wheels and driveline rotating at the same speed. When the brakes are applied all the rotational parts will decelerate dependent on the braking torque at each axle. As such the wheels do not need to be in contact with the ground. If this is accepted, the brakes will need to be designed to account for the different rotational inertias at each axle plus the braking force at each axle, due to linear deceleration on the rigid body, taking account of the load transfer. It must be noted that the mass equivalent has no influence on the load transfer effect. The driven axle brake needs to take account of all the driveline inertia, plus the driven wheel rotational inertias, plus the linear braking force (at the driven axle). Whereas the non-driven axle brake has only the wheels to decelerate and the linear braking force. In essence, the brakes need to decelerate the vehicle as a rigid body, which is dependent on the tyre/road adhesion, in addition to the rotational inertia at each axle. It is not correct to simply treat braking as the inverse of acceleration, the braking analysis should be related to each axle.

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The front braking force (torque) would include the total braking force (torque) proportioned to the front axle plus the force (torque) necessary to decelerate the non-driven wheels. The rear braking force (torque) would include the total braking force (torque) proportioned to the rear axle plus the force (torque) needed to decelerate the rotational parts of the driveline including the driven wheels.