Library / Automotive and vehicle dynamics / VEH-01
Automotive and vehicle dynamics
Wheel drive force from engine torque
Force at the tyre contact that the driven wheels can deliver, from engine or motor torque multiplied through the gearbox and final drive.
- Ref
- VEH-01
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- Fdrive [kN]
Te is the torque at the engine or motor shaft, G is the product of the gearbox ratio ig and the final-drive ratio i0 (a ratio above 1 multiplies torque), ηd is the efficiency of the whole driveline and Re is the effective rolling radius of the driven tyre. The result is the force at the contact patch, in kN, before it is compared with the grip limit, the road load or the vehicle mass. It assumes steady torque and no clutch or torque-converter slip.
Force at the tyre contact that the driven wheels can deliver, from engine or motor torque multiplied through the gearbox and final drive. It ignores wheel slip and grip limits.
Calculator
- Wheel torque, Tw = ηd G Te3,240 N·m
- Drive force in newtons10,800 N
- Force per N·m of engine torque, ηd G / Re36 N per N·m
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.
- At the defaults 300 N·m of engine torque becomes 10.8 kN at the tyres, about 1.1 tonnes of force. Gearing is a torque multiplier: it trades speed for force.
- Force and speed trade off exactly. Multiplying F by the road speed U = 2πReNe/(60 G) gives ηd times the engine power, so gearing changes the balance between force and speed but never the power.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Te Engine or motor torque | 50 to 600 N·m | 1.8 | 21.6 | 19.8 | +10% | +10 % |
| G Total reduction ratio (gearbox × final drive) | 2 to 20 | 1.8 | 18 | 16.2 | +10% | +10 % |
| Re Effective rolling radius | 0.2 to 0.5 m | 6.48 | 16.2 | 9.72 | +10% | −9.09 % |
| ηd Drivetrain efficiency | 0.7 to 1 | 8.4 | 12 | 3.6 | +10% | +10 % |
Sweep of Total reduction ratio (gearbox × final drive)
| Total reduction ratio (gearbox × final drive) | Wheel drive force (kN) |
|---|---|
| 2 | 1.8 |
| 4.25 | 3.825 |
| 6.5 | 5.85 |
| 8.75 | 7.875 |
| 11 | 9.9 |
| 13.25 | 11.93 |
| 15.5 | 13.95 |
| 17.75 | 15.97 |
| 20 | 18 |
Sweep one variable
Variables and how each one contributes
Wheel drive force
What the equation gives you. Everything else feeds it.
Engine or motor torque
The torque at the engine or motor shaft, in N·m. Directly proportional: every other input only scales it. Raising it by 10 % (to 330) moves the result by +10 %, from 10.8 to 11.88 kN.
Total reduction ratio (gearbox × final drive)
The overall reduction from engine shaft to driven wheels: gearbox ratio times final-drive ratio. Lower gears have a larger G. Directly proportional: first gear gives far more force than top gear, but at the cost of speed. Raising it by 10 % (to 13.2) moves the result by +10 %, from 10.8 to 11.88 kN.
Drivetrain efficiency
The fraction of shaft torque that survives gear, bearing and joint losses, typically 0.85 to 0.95. Enter a number between 0 and 1. Directly proportional, but a small lever compared with the gear ratio, because efficiency only varies by a few per cent. Raising it by 10 % (to 0.99) moves the result by +10 %, from 10.8 to 11.88 kN.
Effective rolling radius
The effective rolling radius of the driven tyres, in m. It is a little smaller than the unloaded radius because the tyre is squashed under load. Inversely proportional: larger tyres give less force at the ground, the same effect as a taller final-drive ratio. Raising it by 10 % (to 0.33) moves the result by −9.09 %, from 10.8 to 9.818 kN.
Worked example with the values above
- Wheel torque: Tw = ηd G Te = 0.9 × 12 × 300 = 3,240 N·m.
- Divide by the rolling radius: F = Tw / Re = 3,240 / 0.3 = 10,800 N.
- Fdrive = 10.8 kN.
Assumptions and limits
- Steady engine torque, with no clutch or torque-converter slip, and one driveline efficiency for every gear.
- A free-rolling tyre at a fixed effective radius. Grip is not checked here: use the available-force formula for that.
Common mistakes
- Using the unloaded tyre radius instead of the effective rolling radius, which is a few per cent smaller.
- Entering the gearbox ratio alone. The final-drive ratio must be included in G.
Statistics and uncertainty
F is a product and quotient of its inputs, so their relative errors combine in quadrature: a 2 % error in torque, 3 % in the overall ratio, 3 % in efficiency and 2 % in rolling radius give about 5 % in F (√(2² + 3² + 3² + 2²) ≈ 5.1 %). Efficiency and rolling radius are rarely measured on the actual vehicle, and efficiency changes with load, temperature and gear, so they are the usual weak points.
Where it is used
- Checking whether an engine and gearbox can accelerate a vehicle or climb a given slope.
- Choosing gear ratios so that force and speed in each gear meet a performance target.
Maths you need
- Torque and force: T = F r for a force at a radius
- Gear ratios: how a reduction multiplies torque