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To move a vehicle, the motor must overcome three steady forces plus any acceleration. Rolling resistance (tyres) is m·g·Cr·cosθ; aerodynamic drag is ½·ρ·Cd·A·v² and grows with the square of speed; gradient force for climbing is m·g·sinθ; and acceleration adds m·a. Multiplying the total tractive force by speed gives the wheel power, and dividing by the drivetrain efficiency gives the electrical motor power.
| Force | Formula |
|---|---|
| Rolling resistance | Fr = m·g·Cr·cosθ |
| Aerodynamic drag | Fd = ½·ρ·Cd·A·v² |
| Gradient (climb) | Fg = m·g·sinθ |
| Acceleration | Fa = m·a |
| Wheel power | P = (Fr+Fd+Fg+Fa) · v |
Grade is entered as a percentage (rise/run × 100); the angle is θ = arctan(grade/100). At low speed rolling resistance and grade dominate; at highway speed aerodynamic drag dominates because of the v² term. Uses g = 9.81 m/s² and air density ρ = 1.225 kg/m³.
Add the rolling, aerodynamic, gradient and acceleration forces to get the total tractive force, multiply by speed for wheel power, then divide by drivetrain efficiency: P = (Fr+Fd+Fg+Fa)·v/η.
Cr is the ratio of rolling drag force to vehicle weight, typically 0.010–0.015 for car tyres on tarmac. Lower values mean less tyre drag and better efficiency.
Modern cars have drag coefficients of about 0.24–0.32 and frontal areas of roughly 2.1–2.8 m². SUVs are higher on both counts, which raises their highway energy use.
Drag force grows with the square of speed and drag power with the cube, so at highway speeds aerodynamics dominates the energy budget, while at low speeds rolling resistance and gradient matter more.
Climbing adds a force m·g·sinθ. Even a modest 8% grade can add over a kilonewton of force for a typical car, often exceeding the combined rolling and drag forces at moderate speed.
Grade percent is rise over run times 100, so the angle is θ = arctan(grade/100). A 10% grade is about 5.7°. For small grades, sinθ is close to grade/100.
Cruising on the flat needs only 10–20 kW, but the motor is rated for acceleration, hill climbing and overtaking, which need brief bursts of 100 kW or more. Peak power is sized for performance, not cruising.
Divide the electrical power (in watts) by the speed (in km/h): Wh/km = P(W)/v(km/h). For example, 15 kW at 100 km/h is 150 Wh/km.
Standard sea-level air density is about 1.225 kg/m³ at 15 °C. It falls at altitude and in hot weather, slightly reducing aerodynamic drag.
EV drivetrains (inverter, motor, gearbox) are typically 85–95% efficient. Use around 90% for a first estimate; the motor draws a little more electrical power than the wheels receive.
Add the acceleration force m·a to the road load, then multiply by speed. Because this term is m·a, heavy vehicles need proportionally more force and power to accelerate hard.
The tractive power here is for propulsion. During braking the same forces act in reverse, and regeneration can recover part of the kinetic and gradient energy — see a regenerative braking calculator for that.
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