Why loads roll easily: axle friction and the lever
With a question on a crossbow bolt stopped at the middle of its flight
Leonardo states that a long, slow 'primitive' motion produces the same effect through its derivative as a swift, short one, and poses a thought-experiment: if a crossbow bolt were arrested halfway along its flight, would it still complete its due course? The lower half of the page explains why loads move easily on wheels, treating the axle as a lever: with the centre of the axle 40 parts from the ground against one part above, forty pounds of friction cost only one pound of effort. He contrasts this with dragging the whole cart on the ground (about 13 1/3 pounds of drag) and notes that carters chain their wheels on steep descents. A cart axle running between two wheels is drawn, with the number 40 beneath it.
On this page
A crossbow bolt stopped at mid-flight
Leonardo finds that long, slow primitive motion yields the same effect through its derivative as swift, short primitive motion. He asks whether, if the bolt shot by the crossbow were suddenly held back at the middle of its course, it would still finish the run assigned to it, and whether that run would be greater or less.
The loaded axle as a 40-to-1 lever
The ease of weights carried on wheels comes from the great difference between lever and counter-lever acting through friction on the axle. Taking the centre-to-ground distance as 40 parts and the axle radius as one, forty pounds of friction reduce to a single pound of effort for the mover.
Chaining cart wheels on steep descents
Dragging the whole cart on the ground would cost about a third of its weight, some 13 1/3 pounds against 40. Carters hauling loads through mountainous places therefore lock one or two wheels, or chain all four, so the load does not run down with impetus, and use windlasses to hold or raise great weights uphill.