Earth-moving machine and the arithmetic of excavation
Notes comparing an earth-lifting engine with rival methods, and costing a ditch in ducats and denari.
This crowded sheet works out an earth-moving machine and its economics. Leonardo sketches a large graduated wheel or rota worked by men and argues that his device raises excavated earth far faster and more cheaply than rival methods, doing in three months what another does in five and spending 9,000 ducats where the other spends 15,000. Further notes cost a ditch thirty braccia wide and sixteen deep at so many denari per braccio, converting the price to soldi per mile, alongside columns of arithmetic.
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An earth-lifting engine measured against rival methods
Leonardo compares his machine with another for raising excavated earth: in the time the rival raises the load one foot, his raises it thirty-two feet, and where the rival needs five months and 15,000 ducats his needs three months and 9,000. He remarks that the usual methods lose great time filling the earth-crates and far more in lifting the spoil to its appointed place.
Graduated wheel (rota) worked by men
The lower half of the sheet is dominated by a large circle drawn as a stepped or graduated wheel, with the note that if one man pulls, four are pulled here; a quadrant of the circle is drawn separately. The device is reckoned to place earth three times its own weight, thirty high, in ten turns of the wheel.
Costing a ditch in denari per braccio
A section of ground sixteen braccia deep is scaled against the cost of digging: two denari to cut the ditch in the first braccio and one to throw the spoil out, the cutting holding steady at two denari the braccio. Leonardo tallies ten denari over sixteen braccia, a soldo and a half, and scales it to 3,500 soldi the mile; a ditch thirty wide and sixteen deep is reckoned at 4,500 for the mile.
Columns of calculation
Several blocks of figures are worked down the sheet, multiplying and adding the quantities behind the machine and the cost estimates. They accompany the running-braccio costing set out beside the ditch section.