Catapults of yore.

Abstract

In her Essay “The sinews of war: ancient catapults” (6 Feb., p. 771), S. Cuomo examines the associations set up in antiquity between researchers and the leaders of warlike states to improve weaponry. The catapults she uses as an example can also provide insight into the methods used by ancient engineers, which are recognizable in engineering practices of today ([1][1]). Torsion catapults ([2][2]–[5][3]) were modular. All the dimensions of a family of catapults were proportional to one parameter, the diameter of the hole for the torsion spring. We can express the rules of the Greeks in our more compact notation, D = 1.1 W 1/3, in which D is the diameter of the spring hole, in dactyls, and W is the weight of the shot, in drachmae. The invention of this scaling law was a major accomplishment. It predicts that the stress in each component is invariant no matter how large the catapult. One can therefore use the same materials—sinew, wood, iron—for any size machine, and all catapults in the same family would have had the same range. Although they may look primitive, catapults are similar to three-stage rockets, in that the stages must be precisely timed to contribute their energy most effectively to the acceleration of the missile, leaving no residual kinetic energy in the arms, which would cause the projectile to crash into the stanchions. Modern simulations show that the ancient engineers achieved optimal designs, with any deviation from the canon resulting in degraded performance. Achieving these optimal solutions would have required that the Greeks have a significant engineering test program ([1][1]). The Greeks chose the multiplier within the scaling law to be 1.1. At this value, a trade-off between the range of the catapult and the destructive energy at impact is set to favor high-impact energy rather than maximum range. Hence, the ancient engineers made explicit choices in the design of their machines to meet the demands of their sponsors. Their catapults were optimized to wage aggressive war by battering down defensive fortifications from a relatively short distance, rather than to attack unprotected besieging troops from a great range. 1. 1.[↵][4]1. W. G. Vincenti , What Engineers Know and How They Know It (Johns Hopkins Univ. Press, Baltimore, MD, 1990). 2. 2.[↵][5]1. E. W. Marsden , Ed. Heron, Belopoeica (Artillery), in Greek and Roman Artillery: Technical Treatises (Oxford Univ. Press, Oxford, 1971), pp. 17-60 translated. 3. 3.1. E. W. Marsden , Greek and Roman Artillery: Technical Treatises (Oxford Univ. Press, Oxford, 1971). 4. 4.1. E. W. Marsden , Greek and Roman Artillery: Historical Development (Oxford Univ. Press, Oxford, 1971). 5. 5.[↵][6]1. E. W. Marsden , Ed. Philon, Belopoeica (Artillery), in Greek and Roman Artillery: Technical Treatises (Oxford Univ. Press, Oxford, 1971), pp. 105-184 translated. [1]: #ref-1 [2]: #ref-2 [3]: #ref-5 [4]: #xref-ref-1-1 View reference 1. in text [5]: #xref-ref-2-1 View reference 2. in text [6]: #xref-ref-5-1 View reference 5. in text