A Sizing Rule for Switchback Paths: Leg Length, Turn Spacing, Extra Distance, and Drainage on a Hillside

When a hillside is steeper than loaded traffic can climb all day, a path must gain height indirectly, traversing back and forth across the slope. This paper gives a complete sizing rule for such a switchback path, from its own stated numbers. The design gradient for loaded traffic is taken as 6.0%, the path width as 1.8 m, and the vertical interval between successive legs as 3.6 m. Those three choices fix the leg length at 60.0 m. On a hillside of 30% slope, the rule gives 27.8 legs and 26.8 turns for each 100 m of height gained, a path length of 1667 m against 333 m for the direct fall line, an extra-distance factor of 5.0, and a spacing between legs of 12.0 m measured down the hillside. The bench cut into the hillside is 0.54 m deep at the uphill edge on a 30% slope and the turn cut is 0.90 m. Unwalled turn cuts reach a stated stable limit of 1.2 m at a hillside slope of 40.0%, and by a slope of 50% the turn cut is 1.5 m and leg spacing has fallen to 7.2 m, below the space a turn platform needs; above 50% switchbacks stop working in this design and terracing or steps take over. Drainage is not an afterthought: cross-drains every 30 m, 33.3 per km, carry a design storm flow of 1.25 litres per second each, cost 8.3 labour-days per km to install, and reduce the flow length that drives erosion enough that the modelled erosion ratio between an undrained and a drained path is 2.58 in favour of the drained path.