A Wheelchair That Survives Unpaved Ground: Step-Climbing and Soil Rolling Resistance Computed from Wheel Geometry, and a Long-Wheelbase Design Priced from Bicycle Parts

Standard hospital wheelchairs are designed for smooth floors, and they fail on unpaved ground in two distinct ways: their small front casters cannot climb ordinary steps and thresholds, and their narrow wheels sink into soil and demand more push force than the user can sustain. This paper computes both failure modes from first principles. For a rigid wheel, the horizontal axle force needed to mount a step of height h is F = W sqrt(2Rh - h^2)/(R - h), where W is the load on the wheel and R its radius. For a standard 200 mm diameter caster carrying 110.4 N, a 50 mm step requires 191.2 N per caster - 1.732 times the load on the wheel - and the largest step two casters can mount together within a stated 200 N peak push is 25.9 mm. A simplified Bekker soil model (pressure-sinkage p = K z^n, with compaction resistance from the work of compacting the soil) gives a total push force for the standard chair of 76.6 N on packed dirt and 133.9 N on gravel, against a stated sustainable push of 80 N. A proposed long-wheelbase chair replaces the casters with 660 mm (26 in) bicycle wheels 57 mm wide at all four corners, on a 1.10 m wheelbase that places 30% of the load on the front pair. It requires 49.5 N on packed dirt, 86.5 N on gravel and 10.9 N on pavement, and mounts a 63.6 mm step head-on (143.6 mm approaching one wheel at a time). Its parts, priced from bicycle components, total 837 USD. An optional lever-drive kit with a stated mechanical advantage of 1.6 raises the head-on climbable step to 115.5 mm for a total parts cost of 932 USD. The design still fails, at full size, on loose sand and on wet clay: rear-wheel sinkage reaches 57.5 mm and 54.9 mm respectively, above the stated 50 mm failure bound, and the required push forces of 124.7 N and 134.0 N exceed what can be sustained. All results are computed, not measured. SIMULATED, NOT MEASURED.