Library / Driveline and transmission / DRV-01
Driveline and transmission
Overall driveline reduction ratio
Overall reduction between the engine and the wheels: the gearbox ratio multiplied by the final-drive ratio.
- Ref
- DRV-01
- Rev
- v1
- Field
- Driveline and transmission
- Result
- i
The engine speed divided by the wheel speed is the overall ratio i. Each reduction stage multiplies it, so i = ig if, and a transfer case or hub reduction would add another factor. With i greater than 1, the engine turns faster than the wheels and the torque at the wheels is larger than the engine torque by about the same factor, less losses. A ratio below 1 is an overdrive. A published gearbox ratio of 1.19, for example, is still a reduction, not an overdrive.
Overall reduction between the engine and the wheels: the gearbox ratio multiplied by the final-drive ratio. A ratio above one is a reduction, so the engine turns faster than the wheels.
Calculator
- Wheel speed when the engine turns at 2000 rpm142.9 rpm
- Vehicle speed at 2000 rpm with a rolling radius of 0.55 m29.62 km/h
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.
- A 3.5 gearbox ratio and a 4 final drive give an overall ratio of 14. At 2000 rpm that is 29.6 km/h on tyres of 0.55 m radius.
- Because ratios multiply, a 10 % change in either stage changes the overall ratio by 10 %. A ratio above 1 multiplies torque and divides speed by the same factor, less the losses in the driveline.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| ig Gearbox ratio | 0.7 to 7 | 2.8 | 28 | 25.2 | +10% | +10 % |
| if Final-drive ratio | 1 to 8 | 3.5 | 28 | 24.5 | +10% | +10 % |
Sweep of Gearbox ratio
| Gearbox ratio | Overall ratio |
|---|---|
| 0.7 | 2.8 |
| 1.487 | 5.95 |
| 2.275 | 9.1 |
| 3.063 | 12.25 |
| 3.85 | 15.4 |
| 4.638 | 18.55 |
| 5.425 | 21.7 |
| 6.213 | 24.85 |
| 7 | 28 |
Sweep one variable
Variables and how each one contributes
Overall ratio
What the equation gives you. Everything else feeds it.
Gearbox ratio
The ratio of the gearbox in the gear being used, engine speed divided by output-shaft speed. A first gear is around 3 to 7 and a top gear near or below 1. Raises the overall ratio in proportion. Raising it by 10 % (to 3.85) moves the result by +10 %, from 14 to 15.4.
Final-drive ratio
The ratio of the final drive (the axle), input divided by output. Heavy vehicles often use 3 to 8. Raises the overall ratio in proportion. Raising it by 10 % (to 4.4) moves the result by +10 %, from 14 to 15.4.
Worked example with the values above
- Multiply the stage ratios: i = ig × if = 3.5 × 4.
- i = 14.
- So the engine turns 14 times for each wheel revolution; at 2000 rpm the wheels turn at 142.9 rpm.
Assumptions and limits
- Ideal gear stages with no slip, using the engine-to-wheel convention for the ratio.
- Ratios of all stages are expressed the same way (input speed over output speed).
Common mistakes
- Mixing the engine-to-wheel convention with its inverse in one stage.
- Calling a ratio above 1 an overdrive.
Statistics and uncertainty
Tooth-count ratios are exact, so the overall ratio is known precisely. The uncertainty in road speed comes from the rolling radius, which changes with tyre pressure, load and wear by a few per cent, and from slip.
Where it is used
- Combining gearbox, transfer-case and axle ratios before working out wheel force and road speed.
- Checking that a published ratio table gives the right overall ratio.
Maths you need
- Ratios: multiplying stage by stage
- Gear ratio: input speed divided by output speed