Electric Vehicle Motor Power, Torque and Battery Sizing – A Practical Guide

Electric Vehicle Motor Power, Torque and Battery Sizing

Author: Dr. Vipinkumar Rajendra Pawar

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1. Introduction

To design or evaluate an electric vehicle (EV), three quantities are critically important: motor power, motor torque, and battery capacity. These parameters decide how fast the vehicle can go, how well it can climb hills, and how far it can travel on a single charge.

This chapter explains the formulas behind these calculations in very simple language, with clear meaning of every term used.

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2. Total Vehicle Mass

Before calculating any force or power, we must know the total mass of the vehicle.

Total Vehicle Mass (m) = Kerb Weight + Load Capacity

This total mass is used in almost every formula because a heavier vehicle needs more force to move and climb.

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3. Forces Acting on an Electric Vehicle

When an EV moves forward, the motor must overcome three resisting forces. The sum of these forces is called tractive force.

3.1 Rolling Resistance Force

F_rr = m × g × C_rr

Explanation:
Rolling resistance comes from tyre deformation on the road.

• m = total vehicle mass (kg)
• g = gravity (9.81 m/s²)
• C_rr = rolling resistance coefficient

Heavier vehicles or poor road conditions increase rolling resistance.

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3.2 Aerodynamic Drag Force

F_d = ½ × ρ × A × C_d × v²

Explanation:
Aerodynamic drag is the resistance caused by air.

• ρ = air density (1.225 kg/m³)
• A = frontal area of vehicle (m²)
• C_d = drag coefficient
• v = vehicle speed (m/s)

Since speed is squared, air resistance increases very rapidly at higher speeds.

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3.3 Gradient Resistance Force

F_g = m × g × sin(θ)

Explanation:
This force appears when the vehicle climbs a slope.

• θ = road gradient angle

On flat roads (θ = 0), this force becomes zero.

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3.4 Total Tractive Force

F_total = F_rr + F_d + F_g

This is the total force that the motor must generate at the wheels to move the vehicle.

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4. Motor Power Requirement

Motor Power (P) = F_total × v

Explanation:
Power tells us how fast the motor can do work.

• Higher force → more power
• Higher speed → more power

Power is expressed in kilowatts (kW).

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5. Motor Torque Requirement

5.1 Understanding Torque

Torque is the twisting force produced by the motor. It is very important for:

• Starting from rest
• Climbing slopes
• Carrying heavy loads

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5.2 Torque Formula

Wheel Torque (T) = F_total × r

Explanation:

• r = wheel radius (m)

Larger wheels need more torque to generate the same driving force.

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6. Battery Capacity and Driving Range

6.1 Battery Energy

Battery capacity is measured in kilowatt-hours (kWh). It indicates how much energy the battery can store.

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6.2 Energy Consumption

Energy consumption tells how much energy the vehicle uses per kilometer.

It is usually expressed in watt-hours per kilometer (Wh/km).

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6.3 Driving Range Formula

Driving Range (km) = Battery Capacity (Wh) ÷ Energy Consumption (Wh/km)

Explanation:
Larger batteries or lower consumption result in longer range.

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7. Integrated EV Calculator

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8. Final Conclusion

Motor power determines sustained speed, torque determines acceleration and climbing ability, and battery capacity determines how far the EV can travel.

A well-designed EV balances all three parameters efficiently.

9. References

1. Larminie & Lowry – Electric Vehicle Technology Explained
2. Gillespie – Fundamentals of Vehicle Dynamics
3. NREL – Electric Vehicle Energy Consumption Studies