Size an EV's Motor and Battery in a Spreadsheet

Why this happens

Motor and battery sizing rests on a few road-load equations: the power needed to hold top speed, the torque needed to climb a slope and the energy needed per kilometre. A spreadsheet makes every assumption visible and lets you see quickly how mass, tyres or gear ratio change the answer.

What you need

Step by step

1. 1

   Set up an inputs block

   In one block at the top, list every input with its unit: total mass including rider, gravitational acceleration, rolling resistance coefficient, drag coefficient, frontal area, air density, wheel radius, gear ratio, drivetrain efficiency, motor efficiency, target top speed, maximum gradient in per cent, target range and usable battery fraction. Colour input cells differently from calculated cells so nobody overwrites a formula by mistake.

2. 2

   Calculate power at top speed on the flat

   Convert top speed to metres per second. Rolling force is mass times g times the rolling coefficient; drag force is half times air density times drag coefficient times frontal area times speed squared. Multiply the total by speed to get wheel power, then divide by drivetrain and motor efficiency for electrical input power. This sets a lower bound on the motor's continuous rating.

3. 3

   Calculate gradeability torque

   Convert the gradient to an angle with the arctangent of per cent divided by 100. Grade force is mass times g times the sine of that angle, plus rolling force at low speed. Multiply by wheel radius for wheel torque, then divide by gear ratio and drivetrain efficiency for motor torque. This usually sets the peak torque requirement for a two- or three-wheeler.

   Tip: Check a loaded vehicle on the steepest ramp it will meet, such as a basement car park.

4. 4

   Add acceleration if specified

   If you have a target such as 0 to 40 km/h in a given time, compute average acceleration, multiply by mass and an allowance for rotating inertia, and add rolling and drag at mid-speed. Multiply by speed for peak power near the end of the run. Compare this with the top-speed power; the larger figure guides peak motor power.

5. 5

   Estimate energy per kilometre and battery size

   For a simple estimate, calculate electrical power at a typical cruising speed and divide by that speed to get Wh/km, then add a margin for stops, starts and auxiliaries. Multiply by target range to get energy needed, and divide by your usable battery fraction to get nominal pack energy. Divide by the chosen system voltage to get the amp-hour rating.

6. 6

   Check current and C-rate

   Divide peak electrical power by the minimum pack voltage under load to get peak battery current. Divide that by pack amp-hours to get the peak C-rate and compare it with a typical cell's allowed discharge rate from its datasheet. If the C-rate is too high, you need a larger pack, a higher voltage or a less demanding specification.

7. 7

   Run what-if scenarios

   Duplicate the sheet or add a scenario table to compare options: lighter frame, different tyre, higher voltage, lower top speed. Use a simple chart showing battery energy and peak torque for each scenario. Note which input changes the result most; this often shows that mass and top speed dominate, which is a strong talking point in a review.

8. 8

   Sanity-check against real vehicles

   Compare your results with the published motor power, battery energy and claimed range of similar vehicles in the same class. If your numbers are far off, revisit coefficients and efficiencies rather than forcing the result. Write a short assumptions list beside the sheet so reviewers can see exactly where each figure came from.

How to tell it worked

Changing any input instantly updates motor power, torque, Wh/km and battery size, and your figures land in the same range as comparable production vehicles with a clear list of assumptions.

Questions