For example, engineers had to use the correct ratio between the diameter and length of the elastic bundles in the torsion springs (10). Also, formulas were invented, one even using the cube root, which was not fully understood by Greek mathematicians when invented. Even more remarkable, to create these equations, understanding of types of energy must be had, and these were not completely known until the 1700s (12). What makes these formulas even more amazing were their use. Duncan B. Campbell wrote a paper called Ancient Catapults Some Hypotheses Reexamined. In it, he examines different aspects of the catapult that have been misunderstood. In a section where Campbell talks about the torsion principal, he explains how a specific sized arrow was used in a catapult corresponding to that size. This meant that each catapult had to be built with the final size projectile in mind. This also meant that the size of any catapult could be so a different size arrow could be used. Campbell writes, “By the mid-3rd century, ancient artificers had decided upon an optimum set of proportions for the arrow-shooting catapult, so that any given design could be scaled up to produce weapons of different calibers. The basic module was the thickness of the torsion spring, most easily expressed as the inner diameter of the washer through which the spring was fed (Campbell 684). This meant that the ancient engineers understood the required relationship between the thickness of the torsion bundles and the result that would have on the catapult. This is amazing because their understanding of this relationship must have been so great that we're able to predict accurately what sized catapult was needed for a specific sized
For example, engineers had to use the correct ratio between the diameter and length of the elastic bundles in the torsion springs (10). Also, formulas were invented, one even using the cube root, which was not fully understood by Greek mathematicians when invented. Even more remarkable, to create these equations, understanding of types of energy must be had, and these were not completely known until the 1700s (12). What makes these formulas even more amazing were their use. Duncan B. Campbell wrote a paper called Ancient Catapults Some Hypotheses Reexamined. In it, he examines different aspects of the catapult that have been misunderstood. In a section where Campbell talks about the torsion principal, he explains how a specific sized arrow was used in a catapult corresponding to that size. This meant that each catapult had to be built with the final size projectile in mind. This also meant that the size of any catapult could be so a different size arrow could be used. Campbell writes, “By the mid-3rd century, ancient artificers had decided upon an optimum set of proportions for the arrow-shooting catapult, so that any given design could be scaled up to produce weapons of different calibers. The basic module was the thickness of the torsion spring, most easily expressed as the inner diameter of the washer through which the spring was fed (Campbell 684). This meant that the ancient engineers understood the required relationship between the thickness of the torsion bundles and the result that would have on the catapult. This is amazing because their understanding of this relationship must have been so great that we're able to predict accurately what sized catapult was needed for a specific sized