Library / Automotive and vehicle dynamics / VEH-02
Automotive and vehicle dynamics
Vehicle speed from engine speed
Road speed of a vehicle for a given engine speed in a given gear, assuming no wheel slip.
- Ref
- VEH-02
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- U [m/s]
Ne is the engine (or motor) speed in rpm, G the total reduction ratio from engine to wheels and Re the effective rolling radius in m. The result is the road speed in m/s, assuming the driven wheels roll without longitudinal slip. On soft ground or under heavy driving the real speed is lower by the slip fraction.
Road speed of a vehicle for a given engine speed in a given gear, assuming no wheel slip. It is the kinematic partner of the drive-force equation.
Calculator
- Speed in km/h28.27 km/h
- Speed in mph17.57 mph
- Road distance per engine revolution, 2πRe/G0.1571 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 the car moves 7.854 m/s (28.27 km/h) at 3000 rpm in a gear with a total ratio of 12. The same engine speed in top gear gives a much higher road speed because G is smaller.
- Speed times drive force equals ηd times engine power, because F ∝ G and U ∝ 1/G. Gearing moves the car along the force–speed trade-off but cannot create power.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| G Total reduction ratio (gearbox × final drive) | 2 to 20 | 4.712 | 47.12 | 42.41 | +10% | −9.09 % |
| Ne Engine speed | 800 to 7,000 rpm | 2.094 | 18.33 | 16.23 | +10% | +10 % |
| Re Effective rolling radius | 0.2 to 0.5 m | 5.236 | 13.09 | 7.854 | +10% | +10 % |
Sweep of Engine speed
| Engine speed (rpm) | Vehicle speed (m/s) |
|---|---|
| 800 | 2.094 |
| 1,575 | 4.123 |
| 2,350 | 6.152 |
| 3,125 | 8.181 |
| 3,900 | 10.21 |
| 4,675 | 12.24 |
| 5,450 | 14.27 |
| 6,225 | 16.3 |
| 7,000 | 18.33 |
Sweep one variable
Variables and how each one contributes
Vehicle speed
What the equation gives you. Everything else feeds it.
Effective rolling radius
The effective rolling radius of the driven tyres, in m. Directly proportional: bigger tyres cover more road per turn, so the speed at a given rpm rises with the same percentage. Raising it by 10 % (to 0.33) moves the result by +10 %, from 7.854 to 8.639 m/s.
Engine speed
Engine or motor speed, in rpm (revolutions per minute, not rad/s). Directly proportional: the speed follows the rpm exactly in a fixed gear. Raising it by 10 % (to 3,300) moves the result by +10 %, from 7.854 to 8.639 m/s.
Total reduction ratio (gearbox × final drive)
The overall reduction from engine shaft to driven wheels: gearbox ratio times final-drive ratio. Inversely proportional: a lower gear (bigger G) gives a lower speed at the same rpm. Raising it by 10 % (to 13.2) moves the result by −9.09 %, from 7.854 to 7.14 m/s.
Worked example with the values above
- Engine speed in rad/s: ωe = 2π Ne / 60 = 2π × 3,000 / 60 = 314.2 rad/s.
- Wheel rolling speed: U = ωe Re / G = 314.2 × 0.3 / 12 = 7.854 m/s.
- That is 7.854 m/s, or 28.27 km/h.
Assumptions and limits
- Free rolling with no longitudinal slip, and a constant effective rolling radius.
- A fixed total reduction ratio, with the clutch fully engaged and no torque-converter slip.
Common mistakes
- Entering the engine speed in rad/s: this formula expects rpm.
- Forgetting the final drive. The gear ratio shown for the gearbox alone is not the total ratio G.
Statistics and uncertainty
U is directly proportional to Re and Ne and inversely proportional to G, so independent errors add in quadrature: 1 % in each of the three gives about 1.7 %. The rolling radius is the least certain, because it changes with tyre pressure, load, wear and speed. A speedometer that over-reads by a few per cent is often a tyre-radius effect.
Where it is used
- Choosing gear ratios so that the engine reaches its power peak at the target top speed.
- Converting between engine speed and road speed for cruising, tachograph and fuel-use work.
Maths you need
- Rotational speed: rpm to rad/s
- Gear ratios: speed falls as torque rises