How the time is calculated
Tempowatt estimates the speed at every point of the route with a physical model, then adds up the travel time of each segment.
Principle
The route is split into segments a few metres to a few tens of metres long. For each segment, the calculation finds the speed at which the power supplied by the rider and the motor balances the forces that resist forward motion. The segment time is its length divided by that speed.
The travel time is the sum of all segment times, plus an estimate of the stops at junctions.
The equation
= v·(Crr·m·g·cos θ + m·g·sin θ) + ½·ρ·CdA·(v + wind)²·v
The left-hand side is the power available at the wheel: the rider's and the motor's, multiplied by the drivetrain efficiency η. The right-hand side is the power needed to ride at speed v. It has three terms: tyre rolling resistance, gravity on climbs, and air resistance.
The speed that balances both sides is found by bisection.
Motor power
The power delivered by the motor is the smallest of the following three values.
Assistance ratio
The selected mode multiplies the rider's power. For a motor with a maximum assistance of 400 %, Tour mode applies about 164 %: with 120 W from the rider, the motor adds about 197 W.
Peak power
The motor's maximum mechanical power, between 250 and 600 W for most models in the catalogue.
Maximum torque
At low speed, the power that can be transmitted depends on torque and pedalling cadence. On a steep climb, an 85 Nm motor therefore delivers more power than a 50 Nm motor.
Which limit applies depends on the mode and on the rider's effort. In Tour mode with a rider at 120 W, it is the assistance ratio: raising the motor's peak power then does not change the result.
Assistance tapers off as the speed approaches 25 or 45 km/h, in line with the EN 15194 standard.
Route data
The route is calculated by BRouter. It provides the position and elevation of every point, and the OpenStreetMap attributes of every section. These data are used as follows:
- elevation gives the gradient of each segment and the air density;
- surface gives the rolling resistance coefficient, about three times higher on grass than on asphalt;
- road type is used to estimate stops at junctions and the energy needed to pull away again.
Elevations come from a digital terrain model with a vertical accuracy of about one metre. To avoid wrong gradients on short segments, they are smoothed over a 35-metre window.
Wind
The wind can be entered by hand or fetched from Open-Meteo for the starting point. Its component along each segment is added to the air speed.
Wind is measured ten metres above the ground, where it is stronger than at rider height. A factor of 0.65 is applied, a usual value in open country; in towns or forests the actual effect is smaller.
For example, between Morges and Lausanne on a speed pedelec, a 30 km/h wind changes the time from 25 to 34 minutes as a headwind, and to 21 minutes as a tailwind.
Results shown
| Figure | How it is calculated |
|---|---|
| Travel time | Sum of segment times, stops included |
| Energy use | Energy supplied by the motor, divided by its electrical efficiency |
| Range | Battery capacity relative to the energy used on the trip |
| Calories | Energy supplied by the rider, corrected for muscular efficiency |
| Coloured profile | Speed calculated at each point, from fastest to slowest |
Limitations
- Assistance ratios are calibrated on the modes of Bosch motors; other brands may differ slightly.
- Stops are estimated from the road type, not from actual traffic lights and junctions.
- Rider fitness, tyre pressure, battery temperature and traffic are not taken into account.
- Elevation smoothing softens very abrupt changes in gradient.
The time shown is an estimate. It is most useful for comparing settings on the same route: assistance modes, bike models, or the 25 and 45 km/h categories.