F24 Drivetrain Calculations

Design calculations for a mechanical transmission module built for the Formula 24 (F24) Kit Car, an electric single-seat vehicle. Written for the ME2-DMF autumn group project at Imperial College London, 2025-2026, group P-36.

The transmission steps down the output of a 24 V DC brushed motor to keep the car below the 25 km/h competition limit, while fitting inside the rear compartment of the chassis and being removable with standard tools.

The project

The design poster for the module, produced by the group:

Group P-36: Arnav Popley, Ali Al-Shahristani, William Bolton, Sayuri Shukawa, Simon Mebrahtu.

This repository contains the calculation side of the project. The CAD, engineering drawings and fabrication were the work of the wider group.

The design

A three stage drivetrain giving an overall reduction of 10.1:1:

Stage	Type	Teeth	Ratio
1	Chain	16T to 30T	1.875
2	Spur gear	18T to 80T	4.444
3	Chain	14T to 17T	1.214

Chain first, because it handles the high initial motor torque and lets the motor sit on top of the frame without the gear colliding with the motor body. Spur gears in the middle, for efficiency and a large reduction in one step. Chain last, to deliver power to the wheel and allow tension adjustment.

What is calculated

Gear ratios. Works backwards from the 20 km/h target speed to the drive shaft speed, then to the power required at the motor after stage losses, then reads the motor characteristic to find the operating point and the ratio needed.

Spur gear face width. Lewis form factor method. Uses the motor start-up torque, its maximum output, so the result is a conservative worst case. Both gears need under 10 mm, and 20 mm parts were used.

Shaft stresses. Two checks. A load based check treats the shaft as a simple beam with the mounted components as point loads and the shaft mass distributed, giving peak bending stress. A torque based check takes the smallest diameter section and gives a shear stress and a safety factor against the Tresca criterion.

Bearing life. A design life of 100 hours was assumed, since the car is not intended for continuous use. Converts to revolutions and gives the minimum dynamic load rating for selection.

Car speed. Newton's second law in differential form, one dimensional, with motor torque from the characteristic line, drivetrain efficiency, and drag modelled as 2% of the weight of the car. The resulting ODE solves to v(t) = 19.8(1 - e^-0.337t), so the car reaches 19.8 km/h, 1% off the 20 km/h target and safely under the 25 km/h limit.

Results

Running scripts/run_analysis.py reproduces the report values:

Gear ratio selection
  drive shaft speed     21.9 rad/s, 209 rpm
  power required        237.97 W
  ratio achieved        10.12:1

Minimum face width
  gear 18T           9.72 mm required, 20 mm actual
  gear 80T           6.87 mm required, 20 mm actual

Shaft torsion, Tresca
  permissible shear     160 MPa
  shaft 1        32.5 MPa   SF 4.92
  shaft 2       144.6 MPa   SF 1.11

Velocity model
  terminal speed        19.8 km/h

The safety factor of 1.11 on shaft 2 looks low, but the calculation assumes the maximum motor torque, which occurs only briefly at start-up. Operational torque is lower at every stage.

Layout

src/drivetrain/
  parameters.py       design values from the report and project brief
  ratios.py           gear ratio derivation, stage speeds and torques
  gears.py            Lewis form factor minimum face width
  shafts.py           bending, torsion, Tresca safety factor, keyways
  bearings.py         life in revolutions, minimum dynamic load rating
  velocity_model.py   solved equation of motion for car speed
scripts/
  run_analysis.py     reproduces the report calculations, saves figures
tests/
  test_drivetrain.py  checks the code against the reported values
figures/              generated output

Usage

pip install -r requirements.txt
python scripts/run_analysis.py
pytest tests/ -v

Or directly:

from drivetrain import total_ratio, velocity, safety_factor, shear_stress

print(total_ratio())              # 10.12
print(velocity(15))               # km/h at t = 15 s
print(safety_factor(shear_stress(21.56, 0.015)))

Notes on the model

The velocity model makes several simplifications. Driver mass is taken as 80 kg, the modal average of the group, and will vary in testing. Drivetrain efficiency is the product of nominal stage efficiencies and will fall under load depending on alignment and lubrication. Drag is a flat 2% of weight as given in the brief, which does not capture the velocity dependence of real aerodynamic drag.

Component selection was also constrained by availability. RS Components was the obligatory supplier and many sprocket and gear combinations were out of stock, so the first stage ratio had to be more conservative than the 2.16:1 per stage originally planned.

References

Evolvent Design (2018) Gear Strength Calculator: Lewis Form Factor.

Ihracska, A. B., Gosling, G., Jeffers, J. and Kutlay, A. (2023) ME1 DMF Notes: Design and Manufacture. Imperial College London.

Mohammed, I. K. (2025) ME2-DMF: Autumn Group Project 2025-2026 Project Brief. Imperial College London.

TSM Steel (2025) 230M07 (EN1A) Mild Steel, Specification and Data Sheet.

Licence

MIT, see LICENSE.