Startability of a Loaded Bicycle: A Gearing Sizing Rule from Pedal Force at the Worst Crank Angle

A cargo bicycle is useful only if its rider can start it — from rest, on the grades of an ordinary town, at full load. This paper derives a gearing sizing rule from the force balance. The tractive force needed to hold and start a total mass of 100–200 kg (rider, bicycle, and cargo) on grades of 0–10% ranges from 7.8 N on the flat at 100 kg to 210.8 N on a 10% grade at 200 kg. That force is related to pedal force through the gear development and the crank: at the worst starting crank angle (30 degrees past top dead centre, where only half of a vertical pedal force acts tangentially), the rider force required is twice the mean tangential force. Requiring the worst-angle rider force to stay within 50% of the 75 kg rider's body weight (367.9 N) gives the lowest usable gear directly: at a total mass of 150 kg the gear must be no higher than 55.0 gear-inches on a 2% grade, 32.1 on 4%, 22.7 on 6%, 17.5 on 8%, and 14.3 on 10%; at 200 kg the 10% figure falls to 10.7 gear-inches. A common single-speed gear of about 66 gear-inches fails the criterion cleanly: at 150 kg it cannot start the load on any grade above 1.53%, and at 200 kg above 0.95%, even though it starts the same loads easily on the flat. Standard gearing is therefore not a viable choice for a loaded cargo bicycle wherever grades exceed about 2%, and this paper states that as a result, not a caveat.