eMotor Calculator
Physics explained ⚙️
Forces
- Rolling: \(F_r = m g \cos\theta\, C_{rr}\)
- Aerodynamic: \(F_a = \tfrac{1}{2}\,ρ\,C_d\,A\,v^2\)
- Grade: \(F_g = m g \sin\theta\)
- Total: \(F_{tot}=F_r+F_a+F_g\)
Motor regions
- Below base speed: constant wheel torque \(=T_{max}\,η_d\,i_{gear}\)
- Above base speed: constant wheel power \(=P_{motor}\,η_d\) (until rpm limit)
- Base speed ≈ \(ω_{base} = P_{motor}/T_{max}\)
Range
- \(P_{wheel}=F_{tot}(v_c)\,v_c\)
- \(P_{batt}=P_{wheel}/(η_d \, ζ)\)
- Wh/km \(=P_{batt}/v_{km/h}\), Range \(=E_{usable}/(Wh/km)\)
Acceleration
- \(F_{drive}=\min(F_{motor},\, μ m g \cos\theta \cdot f_{drive})\)
- \(a=(F_{drive}-F_{tot})/m\), integrate \(dv=a\,dt\)
Simplifications: constant efficiencies, no regen, ρ=1.225 kg/m³.
KVO Engineering — Required Power & Torque Calculator
Input: speed & acceleration → Output: power, torque, rpm
Inputs
Approx. DC→wheel efficiency
May be negative (downhill)
Please enter valid numbers. All fields must be > 0 except Grade, which may be negative (−100 to +100). Efficiency must be > 0 and ≤ 100. Acceleration must be ≥ 0.
Results (at target speed)
Required wheel force
–N
Required wheel power
–kW
Required DC power
–kW
Motor torque
–Nm
Motor RPM
–rpm
Estimated DC current
–A
Breakdown @ target speed
Acceleration force (m·a)– N
Rolling resistance (m·g·Crr)– N
Grade force (m·g·sinθ ≈ m·g·grade%)– N
Aero drag (½ρCdAv²)– N