A Hand-Crank Drivetrain for Rural Roads: Gearing Computed from an Arm-Power Budget and Unpaved-Surface Resistance

A hand-crank tricycle is the independent road vehicle available to a person whose legs cannot pedal, but standard bicycle gearing is chosen for leg power on pavement. This paper specifies a drivetrain from the other end: from a stated arm-power budget. Taking a sustainable arm-crank power of 30-60 W for untrained users (45 W nominal), a sustainable tangential hand force of 70 N on a 0.19 m crank, a total rider-vehicle-cargo mass of 95 kg, and rolling-resistance coefficients of 0.008 (pavement), 0.020 (packed dirt), 0.040 (gravel) and 0.120 (sand), the required wheel torque, crank power and hand force are computed for cruising and for grades of 0-10%. A commodity drivetrain - 24T/40T double chainring, 11-51T cassette, parts cost US$280 - satisfies both ends of the reachable envelope: a 40T/28T cruise gear holds 3.0 m/s (10.8 km/h) on pavement at 34.2 W and 61 rpm, and the 24T/51T lowest gear delivers up to 26.0 N m at the wheel and 78.8 N of tractive force. At 45 W the maximum speeds on the flat are 12.8 km/h on pavement, 7.4 km/h on packed dirt, 4.0 km/h on gravel and 1.3 km/h on sand. The limits are printed at the same size as the results: sand cannot be traversed even on the flat within the hand-force bound (99.4 N required in the lowest gear against a 70 N bound), grades above 6.5% on packed dirt, 4.5% on gravel and 7.7% on pavement exceed the force bound at any speed, and gravel at 10% and every sand grade from 2% upward also exceed the 60 W power ceiling at the minimum practical climbing speed. Gearing trades force against cadence; it does not create power. A shoulder-overuse usage bound is stated as a design limit: sessions of at most 30 minutes, at most four per day, at a cadence of 50-70 rpm. All results are computed, not measured; no vehicle was built and no rider was tested. SIMULATED, NOT MEASURED.