Library / Automotive and vehicle dynamics / VEH-16
Automotive and vehicle dynamics
Brake torque from clamp force
Braking torque produced by a disc brake: pad friction coefficient times the total clamp force on both pad faces times the effective friction radius.
- Ref
- VEH-16
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Tb [N·m]
μp is the friction coefficient between pad and disc, Fclamp the total normal force of the pads on the disc (the sum over both faces, so the hydraulic force on one piston when it acts on both sides), and Reff the effective radius at which the friction force acts, close to the mid-radius of the pad. The friction force on the two faces is μp Fclamp, and multiplying by the radius gives the torque on the disc, in N·m. The result is the torque on one disc, which the wheel converts to a force at the tyre.
Braking torque produced by a disc brake: pad friction coefficient times the total clamp force on both pad faces times the effective friction radius.
Calculator
- Friction force on the disc, μp Fclamp8 kN
- Torque per kN of clamp force48 N·m/kN
- Heat dissipated per disc revolution, 2π Tb6.032 kJ
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With μp = 0.4, 20 kN of clamp force and a 120 mm effective radius, one disc gives 960 N·m. At the tyre with Re = 0.3 m this is a braking force of 3,200 N from that wheel.
- Pad fade is the reason for large margins. If hot pads lose 25 % of their friction coefficient, the torque falls by exactly 25 %, with the same pedal force.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N·m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Fclamp Total clamp force (sum of both pad faces) | 1 to 80 kN | 48 | 3,840 | 3,792 | +10% | +10 % |
| Reff Effective pad friction radius | 50 to 250 mm | 400 | 2,000 | 1,600 | +10% | +10 % |
| μp Pad friction coefficient | 0.2 to 0.7 | 480 | 1,680 | 1,200 | +10% | +10 % |
Sweep of Total clamp force (sum of both pad faces)
| Total clamp force (sum of both pad faces) (kN) | Brake torque (N·m) |
|---|---|
| 1 | 48 |
| 10.88 | 522 |
| 20.75 | 996 |
| 30.63 | 1,470 |
| 40.5 | 1,944 |
| 50.38 | 2,418 |
| 60.25 | 2,892 |
| 70.13 | 3,366 |
| 80 | 3,840 |
Sweep one variable
Variables and how each one contributes
Brake torque
What the equation gives you. Everything else feeds it.
Pad friction coefficient
The friction coefficient between the pad and the disc: about 0.35 to 0.45 for road pads, 0.5 or more for race pads when hot. Directly proportional, which is why pad fade (a fall in μp when hot) directly reduces braking torque. Raising it by 10 % (to 0.44) moves the result by +10 %, from 960 to 1,056 N·m.
Total clamp force (sum of both pad faces)
The total clamp force of the pads on the disc (the sum of the normal forces on both faces), in kN. Directly proportional to the brake line pressure and the piston area, so doubling the pressure doubles the torque. Raising it by 10 % (to 22) moves the result by +10 %, from 960 to 1,056 N·m.
Effective pad friction radius
The effective friction radius of the pad on the disc, in mm: roughly the mid-radius of the pad. Directly proportional: a larger disc diameter gives more torque for the same force. Raising it by 10 % (to 132) moves the result by +10 %, from 960 to 1,056 N·m.
Worked example with the values above
- Friction force: μp Fclamp = 0.4 × 20 kN = 8 kN.
- Effective radius: Reff = 120 mm = 0.12 m.
- Tb = 8,000 N × 0.12 m = 960 N·m.
Assumptions and limits
- A constant friction coefficient and a clamp force spread evenly over the pad faces, with the force acting at the effective radius.
- Fclamp is the sum on both pad faces. For a floating calliper it equals twice the piston force.
Common mistakes
- Using the force on one pad face alone for Fclamp, which gives half the torque if the disc has two pad faces.
- Entering the outer disc radius in place of the effective pad radius, which overstates the torque.
Statistics and uncertainty
The torque is a product of three terms. The clamp force is known from the pressure and piston area to about 3 to 5 %, the effective radius to better than 2 %, but the pad friction coefficient varies by ±10 to 20 % with temperature, speed, wear and moisture, so it dominates. A quoted brake torque is only valid for the stated pad temperature.
Where it is used
- Sizing callipers, pads and discs to a braking requirement.
- Converting hydraulic pressure and piston area into braking torque at the wheel.
Maths you need
- Friction: F = μ N
- Torque: T = F r