Motor and Battery Sizing for an Electric Scooter from Performance Targets

The problem

Two-wheeler startups and student teams often pick a motor and pack by copying a competitor, then find the scooter cannot climb a flyover or falls short on range. Sizing from targets with the road-load equation, then checking in simulation, gives a defensible choice and shows which target drives which component.

Objectives

• Translate top speed, 0–40 km/h time, gradeability and range targets into torque, power and energy requirements.
• Select a motor rating (continuous and peak) and a reduction ratio, or a direct hub motor.
• Select a pack voltage and capacity, and check C-rate and usable energy.
• Verify the sizing in a Simulink model on IDC and on a gradient test.
• Show which target drives each rating through a sensitivity study.

What you need

Key concepts

Gradeability

The steepest slope the vehicle can climb at a given speed. It sets the peak wheel torque: T = r·(m·g·sinθ + m·g·Crr·cosθ + drag).

Continuous versus peak rating

A motor can deliver peak torque for seconds to a minute before overheating, while continuous rating must cover cruising at top speed and long climbs.

Usable energy

The part of nominal pack energy available in service after excluding reserves at the top and bottom of SOC, often 80–90 per cent.

C-rate

Pack current divided by capacity in Ah. Peak power demand divided by pack voltage and capacity must stay within the cell's rated discharge C-rate.

Step-by-step guide

1. 1

   Write the performance targets

   Set example targets for a city scooter: laden mass 150 kg (vehicle plus rider), top speed 70 km/h, 0–40 km/h in 5 s, a 10 per cent (about 5.7°) slope climbed at 20 km/h, and 100 km range on IDC. Use example road-load values Crr 0.015, CdA 0.6 m², wheel radius 0.22 m. Put targets and parameters in a MATLAB struct and print them as a table.

   Checkpoint: A requirements table with each target, its source and a numerical value.

2. 2

   Compute the top-speed power

   At 19.4 m/s, rolling resistance is about 22 N and aerodynamic drag about 136 N for the example values, so wheel power is roughly 3.1 kW. Divide by a drivetrain and motor efficiency of about 0.85 to get electrical power. Write a function roadLoad(v, theta, a, p) that returns force and reuse it for every target so the calculation is consistent.

   Checkpoint: Top-speed power computed by the function agrees with your hand calculation to within a few watts.

3. 3

   Compute acceleration and gradeability demands

   Simulate the 0–40 km/h target with a constant-torque-then-constant-power motor model using ode45, and find the minimum peak torque and power that meet 5 s. For the gradient, compute the wheel torque needed at 20 km/h on 10 per cent with a little acceleration margin. Plot all demand points (top speed, launch, grade) on a wheel torque–speed plane. Keep each demand point in a table with its source target so later steps can trace every rating back.

   Checkpoint: A torque–speed plot with each demand point marked and labelled, and the peak torque and peak power needed identified.

4. 4

   Choose the motor and ratio

   For a hub motor, wheel torque equals motor torque, so check whether the peak torque is reasonable for a hub motor. For a mid-drive motor, choose a reduction ratio from motor maximum speed and top speed, G = ω_max·r / v_max, and check launch torque at the motor shaft. Pick continuous power to cover top-speed cruise and a long climb, and peak power to cover acceleration.

   Checkpoint: A motor envelope curve on the torque–speed plot that sits above every demand point with a stated margin.

5. 5

   Size the battery

   Build a quick Simulink model of the scooter (vehicle body, motor envelope, PI driver) and run IDC repeatedly to get Wh/km, typically a few tens of Wh/km for this example. Multiply by the 100 km target and divide by the usable fraction (say 0.85) to get nominal energy. Choose a pack voltage (for example 60 V or 72 V nominal) and compute Ah and the peak C-rate from peak electrical power.

   Checkpoint: Pack energy, voltage, Ah and peak C-rate listed, with the C-rate inside a typical cell rating such as 2–3C.

6. 6

   Verify on the drive cycle

   Set the Simulink model to the chosen motor and pack and run enough IDC repetitions to cover 100 km, or scale from one repetition if the model has no SOC-dependent behaviour. Use a fixed-step solver (ode4, 0.01 s). Log speed, torque, power and battery energy to the Simulation Data Inspector. Check that the scooter follows IDC without hitting the torque limit for long periods.

   Checkpoint: IDC speed tracking within ±2 km/h and final usable energy remaining greater than or equal to zero at 100 km.

7. 7

   Verify the hill climb and top speed

   Create a test with a constant 10 per cent grade and a 20 km/h reference, and a flat-road full-throttle test. Measure the steady speed reached on the slope and the top speed on the flat. Also run a launch from standstill to 40 km/h and record the time. Use a Stateflow chart or MATLAB script to switch test cases automatically if you like.

   Checkpoint: Simulated top speed, 0–40 km/h time and slope speed each meet their target.

8. 8

   Sensitivity and trade-off

   Sweep laden mass from 120 to 200 kg and the range target from 60 to 120 km, rerunning sizing for each point with a script. Plot required pack energy and peak motor power against each variable. Identify which target drives the motor rating (usually acceleration or grade) and which drives pack size (range). Discuss what happens with two riders. Save the sweep results so the report plots can be regenerated without rerunning the models.

   Checkpoint: Two trade-off plots and a short paragraph naming the dominant target for each component.

9. 9

   Report the sizing

   Present the targets, equations, demand-point plot, chosen ratings with margins, battery configuration, verification results and sensitivity plots. Make clear that the parameters are example values and that real sizing would use measured road-load coefficients and a supplier's motor map. Include a short checklist that another team could follow for a different two-wheeler. Add a one-page summary sheet listing each component rating, the target that set it and the margin achieved in simulation.

   Checkpoint: A report where every chosen rating is traceable to a target and confirmed by a simulation test.

Testing & validation

• Hand calculation and MATLAB function agree for top-speed power.
• Simulated top speed, acceleration time and slope speed meet the targets.
• Range on repeated IDC reaches the target with usable energy left.
• Peak battery C-rate stays within the assumed cell rating.

Expected results

A documented, target-driven motor and battery specification for an example electric scooter, with a torque–speed demand plot, verification in Simulink against every target, and trade-off plots for mass and range.

Take it further

• Add a motor efficiency map and repeat the range check.
• Compare hub-motor and mid-drive solutions on mass and efficiency.
• Include an ECM battery so voltage sag reduces available power at low SOC.
• Add a thermal check on continuous motor rating during a long climb.

Viva and review questions

Learn it at DIYguru

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