Moving Earth and Heavy Loads: Levers, Carts, Oblique Motion
Stepped wheels, hauling drums, and the mechanics of shovels, carts and inclined planes for earthworks
This crowded sheet joins mechanical theory with the practical problem of moving earth and heavy loads. The notes work through how a 'middling obliquity' halves a body's natural weight and a mover's power, how a stepped wheel of diameter 12 loses true leverage, and how carts drawn by animals compare with shovel-work; Leonardo cites the fourth book of his 'Elementi machinali'. Large drum-and-rope mechanisms on triangular inclined planes are drawn across the top, with stepped wheels, lever schemes and small pulling figures below. He closes by counting the time lost loosening and loading earth, and praises his own instrument that lets the loosened earth leap by itself onto the carrier.
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Oblique haulage halves a body's weight and a mover's power
Leonardo states that carts cannot climb to a given height by a shorter route than a 'middling obliquity', which renders to every body half of its natural weight. In the same oblique pull every mover loses half of its power. He cites this as proved in the fifteenth conclusion of the fourth book of his 'Elementi machinali'.
Stepped wheel: diameter 12, axle 1, and lost leverage
For the stepped wheel the diameter is 12 and the axle (subbio) is 1, tagged by the labels 12 - r b - l - b. The place where the mover stands diminishes the true lever of the wheel and 2/3 of the mover. Leonardo notes that something arises which spoils this invention, taken at 37 when the weight rises 3 braccia.
Loss in throwing dry, sandy or gravelly earth with a shovel
Whoever throws earth upward with a shovel loses a quarter of the shovel's hold when the ground is dry, sandy, or gravelly. In that case a quarter of the time and of the cost is lost as well.
Cart and mover in double proportion on level ground
On level ground, if the mover's power stands in double proportion to the cart's resistance, it moves the load easily; Leonardo sets the cart's resisting power as 2 and the mover's as 4, so the mover exceeds by 2. He warns that on oblique ground the mover must many times exceed its own power, since as resistance grows the mover's power fails.
Time lost loosening and loading earth; a self-loading instrument
Much more time goes into filling the carts than into driving them to be emptied. Leonardo breaks the labour into pressing the shovel with the foot, prying it loose with its load, and readying the limbs to lift and unload, so that long days become very short. He proposes instead that loosened earth should leap of itself onto the carrier, as appears in his own instrument.
Hauling drums on triangular inclined planes
The top of the sheet carries a mirrored pair of large drum-like mechanisms set against triangular inclined planes, with cords running along them. Below appear smaller stepped wheels, small figures shown pulling, and the lever schemes labelled c 25 - b 50 - a 25 - e d.
