A Bound on Head Portage: The Maximum Sustainable Daily Load–Distance Product for Head-Supported Loads

Head-supported carrying moves a substantial share of the world's goods where vehicles cannot go, yet there is no simple statement of how much transport one person can sustainably deliver in a day by this method. This paper derives such a bound. Walking energy cost is modelled with the Pandolf load-carriage equation, corrected for the empirical finding of Maloiy and co-workers that experienced head-load carriers transport up to 20% of body mass with no measurable extra energy cost: only load above that free fraction is charged to the walker. At each load, the speed that minimises the cost of transport is chosen, and the daily distance is the smaller of an energy-limited distance (a stated locomotion budget of 10 MJ per day) and a time-limited distance (8 hours of walking). For a reference porter of 60 kg body mass, the daily load–distance product is maximised at a load of 51.6 kg (86% of body mass), giving 1.59 tonne-km per day over 30.77 km. The maximum is broad and shallow: loads from 48 to 60 kg all deliver within 9% of it. Common practice does much less. A 30 kg load delivers 0.81 tonne-km per day, 51.1% of the bound; a 40 kg load delivers 1.14 tonne-km per day, 71.8% of the bound. Without the free-carry correction the bound falls to 1.25 tonne-km per day at 48.6 kg, so the measured economy of head carrying accounts for about a quarter of the bound. The maximising load is an energetic result only: at 86% of body mass it is far above loads that cervical and musculoskeletal limits would permit day after day, and this paper does not recommend it. The bound states what the energy budget allows, not what the body tolerates.