Galileo was Wrong: The Geometrical Design of Masonry Arches

Abstract

Since antiquity master builders have always used simple geometrical rules for designing arches. Typically, for a certain form, the thickness is a fraction of the span. This is a proportional design independent of the scale: the same ratio thickness/span applies for spans of 10 m or 100 m. Rules of the same kind were also used for more complex problems, such as the design of a buttress for a cross-vault. Galileo attacked this kind of proportional design in his Dialogues. He stated the socalled square-cube law: internal stresses grow linearly with scale and therefore the elements of the structures must become thicker in proportion. This law has been accepted many times uncritically by historians of engineering, who have considered the traditional geometrical design as unscientific and incorrect. In fact, Galileo’s law applies only to strength problems. Stability problems, such as the masonry arch problem, are governed by geometry. Therefore, Galileo was wrong in applying his reasoning to masonry buildings