A Sizing Bound for Human-Powered Machines: The Sustained Mechanical Power Available from Pedals or a Treadle over a Working Day

Human-powered machines are often sold or described with power figures taken from short efforts: a strong rider can produce several hundred watts for a minute, but a machine that must run for a working day lives on a much smaller number. This paper derives a sizing bound from three stated assumptions: a basal metabolic rate of 82 W, a sustainable total metabolic rate of five times basal for heavy labour, and a gross pedalling efficiency of 0.22. While pedalling, the worker delivers 72.2 W of mechanical power. Under a realistic duty pattern of 50 minutes of work and 10 minutes of rest per hour, and after a drivetrain efficiency of 0.90, the average power delivered to a machine is 54.1 W, with a sensitivity range of 33.2 W to 80.0 W across the tested assumptions. A four-hour shift delivers 0.216 kWh and an eight-hour shift 0.433 kWh. A treadle, worked by one leg intermittently, delivers about 29.8 W on the same duty pattern. The sizing rule follows directly: a human-powered machine intended for all-day use must have a continuous load of no more than about 54 W, and any device whose average draw exceeds that figure will run down any buffer and stop. Commonly advertised pedal-generator outputs of 200 W to 750 W as continuous outputs exceed the while-pedalling bound by factors of 2.77 to 10.39 and do not survive the arithmetic as sustained claims.