How Fast Is Too Fast for Tomatoes: A Vibration Damage Bound for Crates on Unpaved Roads

Soft produce carried to market by motorcycle or bicycle over unpaved roads arrives bruised, and the bruising is usually blamed on the road. This paper shows it is better blamed on the speed, and derives the speed at which the damage becomes unacceptable for each class of road. Road roughness is stated as a vibration dose at the crate — root-mean-square acceleration at a reference speed of 20 km/h of 0.20 g on paved road, 0.55 g on packed gravel, and 0.95 g on corrugated dirt, scaling linearly with speed, with a crest factor of 3.2 converting root-mean-square to peak acceleration. Fruit damage accumulates as the cube of peak acceleration relative to a stated bruise reference of 2.5 g, over the trip time for a stated 8 km farm-to-market distance, with a stacking multiplier of 1.35 for a three-layer crate; a damage index of 1.0 is defined as the dose corresponding to 10 % bruised fruit on arrival. On corrugated dirt the uncushioned crate reaches that ceiling at 20.3 km/h: its damage index is 0.971 at 20 km/h, 1.517 at 25 km/h, and 2.185 at 30 km/h, where the peak acceleration is 4.56 g. Packed gravel reaches the ceiling only at 46.1 km/h, and paved road does not reach it at any realistic speed. The bottom layer of the crate, carrying a stacking multiplier of 1.75, reaches the corrugated ceiling earlier, at 17.8 km/h. A foam liner attenuates peak acceleration; under a stated attenuation of 2.2 % per millimetre, a 10 mm liner still leaves the crate over the ceiling at 30 km/h on corrugated dirt (damage index 1.037), while a 15 mm liner brings it to 0.657 and raises the corrugated speed limit to 37.0 km/h, and a 20 mm liner raises it to 48.4 km/h. The practical rule is short: on corrugated dirt, ride at 20 km/h or fit at least 15 mm of foam.