The armature of arches, and the weight of turbid water
Statics of arches, vaults and a leaning beam, with a note on muddy rivers
A statics sheet dominated by studies of arches, vaults and the wedge-shaped voussoirs that compose them, worked out alongside notes on how supports carry weight. Leonardo lays down rules for the 'armature of arches', that every support receives the ultimate weight between equal angles and that all the parts of a masonry arch press against the middle of its chord, and analyses a leaning beam to locate its line of maximum resistance (ab, not ac). In the upper margin and beside a vessel hung from a balance he weighs a different question: whether turbid, silt-laden water is heavier than clear, and whether great muddy rivers could shift the 'centre of the world'. He at once records the objection that turbid water is in fact lighter than earth and hard mud.
On this page
The armature of arches
Leonardo sets down principles for the abutments and centring of arches: every support receives the ultimate load between equal angles, and the true supports align their strength along the direction in which the loaded mass tends to descend with its greatest weight. All the parts of a masonry arch, he adds, bear down against the middle of its chord, so the support's utmost power must be directed against the utmost heaviness of the sustained thing.
Line of maximum resistance in a leaning beam
For a beam supported obliquely, Leonardo marks the front edge a b as the seat of its greatest power in descending. The line a b, he concludes, is the line of maximum resistance, and not the line a c.
Do turbid rivers move the centre of the world?
A vase hung from a balance can hold air, clear water, or water muddied with soil of varying heaviness; the more earth mixed in, the more weight the mixture bears, so that great turbid rivers might move the centre of the world. Leonardo immediately contradicts himself, noting that turbid water is actually lighter than earth and hard mud, and the lighter can never weigh upon the heavier.
Voussoirs and vault profiles
Rows of trapezoidal wedge-blocks and small vaulted and domed profiles are drawn across the sheet, illustrating how individual voussoirs and rib segments combine into arches and vaults. These worked sketches accompany the written rules on arch support.