The Steepest Gradient for All-Day Loaded Work: A Bound for Porters, Handcarts, and Draught Carts

Paths that are too steep waste the working day: the carrier slows, rests multiply, and loads that should arrive do not. This paper derives the steepest gradient that loaded traffic can climb for a full working day, from stated energetics. A porter of 70 kg carrying 25 kg, modelled with the Pandolf load-carriage equation at 0.9 m/s and a sustainable metabolic power of 400 W, is limited to a gradient of 5.1%. Slowing to 0.7 m/s raises the bound to 8.6%, and a heavier load of 35 kg lowers it to 3.4%. A handcart of 180 kg total mass pushed by one person on firm dirt is limited to 4.6%, and a 600 kg cart drawn by a 450 kg ox is limited to 3.4%, in the ox case by sustained tractive force (436 N at the bound) rather than by power. Short efforts are different: at a one-hour power of 550 W the porter bound rises to 10.2%, which is the gradient above which switchbacks or steps become unavoidable for a route intended for repeated all-day use. Descent does not bind harder on routes built to the climbing bound: the modelled knee-load factor at 5.1% is only 1.46 against an all-day limit of 3.0 reached at 22.2%, and one person can hold the handcart on descents up to 13.8%. Descent becomes the controlling problem only on short, steep pitches that climbing traffic would never use all day.