Calculating the Labour of Digging a Ditch
Time, weights and volumes for a worker moving earth, and the fill of a mile of ditch
The page reduces the work of excavation to numbers: a good worker shifts 500 shovelfuls of earth per hour, each throw of about six braccia costing six "harmonic times" (loading, twisting, swinging down, and returning the shovel). Leonardo tallies the weights — a shovelful is 10 lb, a cubic braccio 1,800 lb, a cubic canna 115,200 lb — and concludes a man moves a cubic canna in about 25 3/5 hours, two summer days. He then sizes a ditch 40 braccia wide at the mouth, 32 at the bottom and 16 deep and computes the earth in a mile of it: 1,728,000 cubic braccia, 27,000 cubic canne, weighing 3,110,400,000 lb. A cross-section of the ditch and columns of working arithmetic fill the lower sheet.
On this page
A worker's rate of excavation
A good labourer durably moves 500 shovelfuls of earth per hour, standing midway between where he lifts and where he sets it, a span of six braccia. Each throw takes six harmonic times: two to load the shovel with two or three thrusts, one to lift and twist, one for the swing that throws the earth, and one to return the shovel. Some manage it in four times, Leonardo adds, but they do not last.
Weights and volumes of earth
The reckoning fixes the units: a shovelful weighs 10 lb, a cubic braccio 1,800 lb, a cubic canna 115,200 lb. From these, 180 shovelfuls make a cubic braccio and 64 cubic braccia make a cubic canna, so 500 shovelfuls an hour equal 2 1/2 cubic canne.
The earth in a mile of ditch
The ditch measures 40 braccia across the mouth, 32 across the bottom and 16 deep, giving a cross-section of 576 braccia (36 superficial canne). Over a mile such a ditch contains 1,728,000 cubic braccia, or 27,000 cubic canne, weighing 3,110,400,000 lb. A drawn section labels the 40, 32 and 16.