Library / Driveline and transmission / DRV-05
Driveline and transmission
Top-gear ratio for a target top speed
Overall ratio at which the engine reaches its top useful speed just as the vehicle reaches its target top speed.
- Ref
- DRV-05
- Rev
- v1
- Field
- Driveline and transmission
- Result
- itop
If the engine turns at ntop rpm (angular speed 2πn/60 rad/s) when the vehicle reaches vmax, the overall ratio itop = ωe r/vmax with ωe = 2πntop/60. This is the ratio for the highest gear, including the final drive. It sets the kinematic speed only, with no tyre or converter slip: the engine must also deliver the power needed at that speed, or the vehicle will not reach it.
Overall ratio at which the engine reaches its top useful speed just as the vehicle reaches its target top speed. A real top speed also needs enough power at that speed, not only the right ratio.
Calculator
- Target top speed in km/h90 km/h
- Engine angular speed at top speed230.4 rad/s
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.
- To reach 25 m/s (90 km/h) with the engine at 2,200 rpm on a 0.55 m rolling radius needs an overall ratio of 5.068.
- A ratio lower than this lets the vehicle go faster at the same engine speed, but only if the engine has the power to overcome the extra air drag. Reaching 25 m/s needs about 46.9 kW against drag alone for a 5 m² drag area.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| vmax Target top speed | 5 to 80 m/s | 1.584 | 25.34 | 23.76 | +10% | −9.09 % |
| ntop Engine speed at top speed | 1,000 to 6,000 rpm | 2.304 | 13.82 | 11.52 | +10% | +10 % |
| r Rolling radius | 0.25 to 0.9 m | 2.304 | 8.294 | 5.99 | +10% | +10 % |
Sweep of Target top speed
| Target top speed (m/s) | Overall top-gear ratio |
|---|---|
| 5 | 25.34 |
| 14.38 | 8.815 |
| 23.75 | 5.335 |
| 33.13 | 3.825 |
| 42.5 | 2.981 |
| 51.88 | 2.443 |
| 61.25 | 2.069 |
| 70.63 | 1.794 |
| 80 | 1.584 |
Sweep one variable
Variables and how each one contributes
Overall top-gear ratio
What the equation gives you. Everything else feeds it.
Engine speed at top speed
The engine speed at the target top speed, in rpm: usually near the speed of maximum power. Raises the ratio in proportion: a higher engine speed at the same road speed needs more reduction. Raising it by 10 % (to 2,420) moves the result by +10 %, from 5.068 to 5.575.
Rolling radius
The rolling radius of the tyre, in m. Raises the ratio in proportion. Raising it by 10 % (to 0.605) moves the result by +10 %, from 5.068 to 5.575.
Target top speed
The target top speed, in m/s. 25 m/s is 90 km/h. Lowers the ratio in inverse proportion: a higher speed needs less reduction. Raising it by 10 % (to 27.5) moves the result by −9.09 %, from 5.068 to 4.608.
Worked example with the values above
- Engine angular speed: ωe = 2π × 2,200/60 = 230.4 rad/s.
- Multiply by the radius and divide by the speed: 230.4 × 0.55 / 25.
- itop = 5.068.
Assumptions and limits
- No tyre slip and no converter slip; rolling radius constant.
- The overall ratio is expressed engine over wheel.
Common mistakes
- Assuming a nominal top-gear ratio gives the top speed without checking power.
- Using the tyre’s nominal outer radius rather than its rolling radius.
Statistics and uncertainty
Tyre rolling radius changes with load and pressure by a few per cent, which changes the actual speed at a given engine speed by the same amount. A governor setting or speed limiter then matters more than the ratio.
Where it is used
- Setting the highest gear and the final drive for a target top speed.
- Checking where the engine speed will be at cruise.
Maths you need
- Angular speed: 2π times revolutions per second
- Rolling radius: distance travelled per revolution divided by 2π