Physics of Braking Systems
The Physics of Braking Systems
By James Walker, Jr. of scR motorsports
Copyright © 2005 StopTech LLC
Author’s disclaimer: mechanical systems operating in the physical world are neither
100% efficient nor are they capable of instantaneous changes in state. Consequently, the equations and relationships presented herein are approximations of these braking system components as best as we understand their mechanizations and physical attributes.
Where appropriate, several examples of limiting conditions and primary inefficiencies have been identified, but please do not assume these partial lists to be all-encompassing or definitive in their qualifications.
The Conservation of Energy
The braking system exists to convert the energy of a vehicle in motion into thermal energy, more commonly referred to as heat. From basic physics, the kinetic energy of a body in motion is defined as:
Kinetic Energy =
•
•
1
2
× mv × vv
2
where mv = the mass (commonly thought of as weight) of the vehicle in motion where vv = the velocity (commonly known as speed) of the vehicle in motion
Ideally, this energy is completely absorbed by the braking system. While this is not entirely the case, for a stopping event at maximum deceleration most of the vehicle’s kinetic energy is converted into thermal energy as defined by:
1
2
× m v × v v ⇒ mb × C p × ∆Tb
2
•
•
•
where mb = the mass of the braking system components which absorb energy where Cp = the specific heat of the braking system components which absorb energy (a constant based on material properties) where ∆Tb = the temperature rise experienced by the braking system components which absorb energy
Note that for most single-stop events, the rotors serve as the primary energy absorbing components. It follows then that the temperature rise of the braking system is directly proportional to the mass of the vehicle in motion. More importantly perhaps, the temperature rise of the braking system
By James Walker, Jr. of scR motorsports
Copyright © 2005 StopTech LLC
Author’s disclaimer: mechanical systems operating in the physical world are neither
100% efficient nor are they capable of instantaneous changes in state. Consequently, the equations and relationships presented herein are approximations of these braking system components as best as we understand their mechanizations and physical attributes.
Where appropriate, several examples of limiting conditions and primary inefficiencies have been identified, but please do not assume these partial lists to be all-encompassing or definitive in their qualifications.
The Conservation of Energy
The braking system exists to convert the energy of a vehicle in motion into thermal energy, more commonly referred to as heat. From basic physics, the kinetic energy of a body in motion is defined as:
Kinetic Energy =
•
•
1
2
× mv × vv
2
where mv = the mass (commonly thought of as weight) of the vehicle in motion where vv = the velocity (commonly known as speed) of the vehicle in motion
Ideally, this energy is completely absorbed by the braking system. While this is not entirely the case, for a stopping event at maximum deceleration most of the vehicle’s kinetic energy is converted into thermal energy as defined by:
1
2
× m v × v v ⇒ mb × C p × ∆Tb
2
•
•
•
where mb = the mass of the braking system components which absorb energy where Cp = the specific heat of the braking system components which absorb energy (a constant based on material properties) where ∆Tb = the temperature rise experienced by the braking system components which absorb energy
Note that for most single-stop events, the rotors serve as the primary energy absorbing components. It follows then that the temperature rise of the braking system is directly proportional to the mass of the vehicle in motion. More importantly perhaps, the temperature rise of the braking system