A Safe-Load Bound for Cargo Behind the Rear Axle of a Small Motorcycle on Unpaved Roads

Small motorcycles of the 125 cc class carry much of the light freight on unpaved roads in many regions, frequently with cargo stacked on a rack behind the rear axle at loads of 100 kg or more. This paper computes the safe-load bound for such cargo from three limits evaluated together: the front-wheel load fraction, braking distance, and the rear tyre load rating. The reference machine weighs 110 kg with a 75 kg rider (185 kg combined, wheelbase 1.30 m, front wheel carrying 41.5% unladen), and the cargo centre is 0.60 m behind the rear axle. Requiring the front wheel to retain at least 25% of the total weight for steering gives a maximum cargo load of 42.8 kg. The rear tyre rating (load index 54, 212 kg) permits 71.0 kg, so steering, not the tyre, sets the bound; with a 10% tyre margin the tyre limit falls to 56.5 kg, still above the steering bound. Braking from 40 km/h on dirt takes 12.6–21.0 m of braking distance at friction coefficients of 0.50–0.30, plus 11.1 m of reaction distance. Loads of the size commonly observed are outside every limit at once: at 100 kg of cargo the front wheel carries 10.7% of the weight and the rear tyre is at 120.0% of its rating; at 150 kg the front wheel carries 2.2% — 7.5 kg in total — and the rear tyre is at 154.5% of its rating. The bound is 42.8 kg at 0.60 m behind the axle, rising to 54.7 kg if the load is moved forward to 0.40 m behind the axle and falling to 35.2 kg at 0.80 m.