On Towers and Catapult Sizes Author(s): T. E. Rihll Source: The Annual of the British School at , Vol. 101 (2006), pp. 379-383 Published by: British School at Athens Stable URL: http://www.jstor.org/stable/30073263 . Accessed: 08/12/2014 16:01

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JOSIAHOBER'S paper on 'Early Artillery Towers: Messenia, Boiotia, Attica and Megarid', published in the AmericanJournal of Archaeology,91. 4 (1987), 569-604, is informative and interesting on the topic of its title: towers. However,in his 'Conclusions' he speculated on the sizes of catapults that these towers might have housed. The connections between fortification design and the artillery that such buildings supported or were built to withstand is an important and intriguing issue. However,Ober's ideas on catapult sizes need reconsideration, especially since they are beginning to be repeated elsewhere.2My concerns are several. Since this is a technical area, however, I shall begin with a basic guide to ancient catapults, so that those who are not familiarwith key terms and concepts may follow the argument should they wish to do so. Ancient catapults are classified in a number of ways.3The three principal distinctions concern (i) the power source (bow or spring), (ii) the missile (sharp or heavy), and (iii) the design (euthytone or palintone). I use the term 'sharp-caster'for the Greek oxybeles,which was any catapult that shot broadly arrow-shapemissiles, from darts to ; stone-throweris the usual term for catapults that shot stone balls, lithobolosor petrobolosin Greek. A catapult will be a bow or torsion, sharp-casteror stone-thrower, euthytone orpalintone, catapult. A euthytone, which has a single frame through which both springs pass, is usually a sharp-caster;a palintone, which has each spring mounted in separate frames and the frames are bolted together, is normally a stone-thrower but may be sharp-caster (see FIG.1). Both are torsion catapults. The earliest catapultsdid not have springs but were mechanised bows. These are sometimes called gastraphetai,belly-bows, though it is a very rare word in surviving ancient literature. Torsion catapults, by contrast, were powered by 'springs' made of skeins of hair or sinew rather than by a bow. They became the standard catapults of the Graeco-Roman world. During the Hellenistic period, formulae were discovered for the manufacture of effective designs of torsion catapults. These formulae utilized the size of the missile that the catapult was designed to shoot, and all the key components of the catapult were measured in terms of a single basic unit. The unit in dactylswas ideally /9th of the length of the sharp, in the case of the euthytone, and l 'loth times the cube root of the weight of the stone in drachmas, in the case of the palintone. The spring-hole, through which the spring power source of the had to pass, was made one unit in diameter (henceforth D), and all other parts of the machine were expressed in terms of a number of such diameters or a fraction of that

' Abbreviations F. E. Winter 'The use of artillery in fourth-century and Marsden 1969 = E. W. Marsden, Greek and Roman Hellenistic towers', Echosdu mondeclassique/Classical Views Artillery,i: HistoricalDevelopment (Oxford, 1969). 16 (1997): 247-92. Marsden 1971 = E. W. Marsden, Greek and Roman 3 The principal ancient sources for the classifications Artillery,ii: TechnicalTreatises (Oxford, 1971). are Heron Ktesibios'Belopoiika 74.5-75.9 and 104-4-106.5 2 himself in 'Towards a of Greek Philon, and e.g. by typology (Wescher), Belopoiika51.8-55. 1 (Th venot), artillery towers: the first and second generations (c. , o. to. 1-10o. 11. 7. English 375-275 BC)' in S. van de Maele and J. M. Fossey (eds), translations are available in Marsden 1971. FortificationesAntiquae (Amsterdam, 1992), 147-169, and

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D Loj Palintone,after Marsden, shown spanned

Frame Arms Slider Trigger Stock Windlass

Euthytone,after Marsden,shown braced

D

FIG. 1. The two principal designs of Greek and Roman torsion catapults.

diameter. Thus, for example, the recommended formula for the arms might be 6D long and 2 D thick.4The springhole therefore served as a stable substitute for the spring, which was a consumable whose characteristicscould and would have varied with time, use, and even the weather (see FIG. 1). My first concern with Ober's paper is that he invents a 'calibrationformula' for a euthytone sharp-caster.He says that the total length of such a catapult is 3oD, that is, 30 times its spring diameter (table 3 on p. 6oo and n. 65). In the text below the table, he says that this formula is 'derived from comparison with the formula for the length of the stoneshooter' given by

4 The formulae and key dimensions are given in the same sections of the treatises cited in n. 3.

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Marsden.5 But palintone stone-throwers and euthytone sharp-casters are quite different and one cannot simply transferdimensional formulae from one to the other, at least without discussion.6Their calibration formulae are completely different, sharp-casters'being linear, while stone-throwers'are non-linear and involve a cube root. Consider some worked examples of these formulae in action, which will demonstrate the point. According to Philon (Belopoiika55.10), the case, which is the 'stock' in a sharp-caster euthytone catapult, has a length of 16D (spring diameters). The spring diameter is o th the length of the sharp. Therefore, the stock of a sharp-casteris alwaysa bit less than twice the length of the sharp it is built to shoot, since twice 9 (the sharp length) is 18, and the stock is 16D. The length of the stock of a sharp-castershooting 3-span bolts (missiles c.27 inches or 69 cm long) is about 4 feet or 1.2 m and the length of stock of a sharp-castershooting 6-span sharps (3 cubits, c.55 inches long or 1.4 m) is about 8 feet or 2.4 m. With linear ratios, if the length of the sharp doubles, then the length of the stock doubles. But doubling the weight of the stone thrown by a palintone does not result in a stock twice as long as on the lighter machine. The ladder, which is the 'stock' in palintone catapult (stone-thrower or sharp- caster), ideally has a length of 19D (Philon 54.8; Vitruvius,De Arch.10. 11. 7 has the same). A half-talent (or 3o-mna) catapult will have a 19-foot or 5.8 m stock, but a one-talent catapult will have a stock just five feet longer, at 24 feet or 7.3 m not twice as long, at 38 feet or 1 1.6 m.7 Therefore one cannot simply take ratios for stock length from one type of catapult and use them for the other type. Further,in the Poliorketika,in an undamaged section of text (A7 = 85. 1-4), Philon says explicitly that a 1-talent stone-throwerhas a case just 12 cubits8 long-six feet or 1.2 m shorter than the figure he gives in his Belopoiika--whichwith 4 cubit9 handspikes togetheradd up to about 19D. The inconsistency between passages is irreconcilable, but it is arbitrary to ignore the Poliorketika'sevidence in favour of the Belopoiika's. The second point concerns what Ober calls the 'formula for the length of the stonethrower', for which he cites Marsden as his authority.Marsden said that 'the complete length of a stone-thrower,including the maximum projection of the handspikes behind the stock and small allowances for clearance at the front and rear, comes to 30 diameters of the spring-hole' (1969: 34). Now, (i) no ancient source gives a figure for the 'complete' length like this, (ii) Marsden does not demonstrate how he arrivesat the 'length = 3oD' figure, and (iii) it is absent from his tabulated lists of dimensions for either euthytone or palintone . It transpires that this 'complete length of a stone-thrower ... comes to 30 spring diameters' is the sum of the length of the stock plus the handspikes-for which Marsden apparently took Vitruvius'figure of ioD for the handspikes of a euthytone sharp-caster (de

5 The reference to 'p. 34 and fig. 34' in Marsden 1969 modern measures, taking 1 dactyl as 19-3 mm with is wrong; it should be 'p. 34 and fig. 18 on p. 36'. Marsden Marsden. Multiplying by 19 to find the length of the stock does not present this figure as a formula. gives c.5,810o mm or 19 feet in modern measures (so 6 It is not relevant here that stone-throwers could be Marsden 1969: 145). Let us now consider a larger adapted also to shoot sharps. machine to throw stones twice as heavy as those above. 7 A half-talent = 3,ooo drachmai. Applying the formula One talent = 6ooo drachmai; the cube root of 6,ooo = for = palintones (1.1 3Cx) and rounding figures to the 18; multiplied by 1.1 20, so that is the spring diameter nearest quarter for simplicity of presentation (but not in dactyls of a one-talent palintone, which is 385 mm in rounding them in the calculations), the cube root of modern measures. Multiplying this by 19 to obtain the is c. = 3,000 141/2;multiplied by 1.1 15/4, which is therefore length of the stock gives c.7,315 mm or 24 feet long. the recommended width in dactyls of the spring diameter 8 = 288 dactyls. D for a half-talent palintone. This is about 300 mm in 9 = 96 dactyls.

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Architecturao0. 10. 5)-plus trivial 'small allowances' front and rear (to wit, ID, added to round 29 to 30?). It is now clear that this would represent the maximum extent of such a catapult, laid horizontally and, more importantly,with handspikes that were almost half the length of the stock, protruding horizontally out of the back. This sum does not, therefore, represent the stock length. As we saw above, Philon and Vitruviusgive stock lengths of 16D and 19D. Marsden's 3oD for the 'complete length of the catapult plus clearance space' was therefore an exaggerated figure, to the extent that 30 is nearly twice 16, and half as much again on top of 19. The problem was exacerbated when Ober transformedthat exaggeration into a 'formula' and gave '3oD' as the 'stock length' (tables 3 and 4). Taking this 3oD as his key formula, instead of Philon's or Vitruvius' 16D or 19D, Ober then calculated the stock length of a 30o-mnastone-thrower as over 27 feet (8.4 m, Table 4, p. 6o01). Marsden actually gave the stock length of a 30o-mnastone-thrower as eight feet less than this, to wit, 19 feet (5.8 m) (1969: 145), and his figure equates to 19D for a stone-thrower of this size, which is what Philon and Vitruvius say it should be (and McNicoll arrived at a similar figure too; see below). Ober's figure is in fact the length of the stock plus a (very long) projecting handspike, rather than the stock length. Marsden'sdesire to give a total length for the catapult was misleading, and has misled. He should not have included handspikes 1oD long, laid horizontally. For comparison, the length of the arm of the catapult is only 6D (euthytone) or 7D (palintone), so he would have us imagine a catapult with handspikes that are considerably longer than the arms. In addition, there are all sorts of problems with Vitruvius'text, especially the numbers therein, and all editors consider the text corrupt on the length of the handspikes (De Arch. 10. 10o. 3 and 5). In any case, one would expect fast operation for catapult loading, and therefore sensibly sized windlasses;handspikes exceeding about 5' (1.5 m) in length would be impractical, since the operator has to be able to reach and exert some force on the end of the spike in order to reap the mechanical advantage that it offers. According to the ancient sources, the stock length of torsion catapults was 16-i9D, not 3oD. If, when playing the game of fitting catapults to fortifications, one wishes (quite reasonably) to add to this some space for windlass handspikes, so be it, but they should be sensibly sized and accounted for separately. Otherwise, the false idea that a catapult stock length equals 3oD could turn into a factoid. The late A. W. McNicoll observed that a 30 mna stone-thrower 'measured some 5-70 m. in length', presumably having calculated it himself, but his editor has added in brackets, and with a note referring to Marsden's misleading comment, 'and would need a working space of c. 9.20o m.'" It seems not to have occurred to said editor that his 9.2 metres is a lot bigger than McNicoll's 5.7 metres, and that something might have gone adrift here." The difference is, in effect, the handspike. Third, Ober's assertion that 'torsion stone-throwershad to be built with very long stocks, since the power of the weapon was directly related to the length of the stock' (p. 6oo00)perhaps hints at his own discomfort with his results, but anyway seems to misunderstand the

,o HellenisticFortifications from the Aegean to the Euphrates catapult (table 4, p. 601), and this, together with the last with revisions and a new chapter by N. P. Milner (Oxford, note, highlights another point. We are not all using the 1997), io. I calculate it to be 5.8 m, approximately 19 same conversion scales for dactyls to feet or metres, and feet. most scholars do not give the conversion ratios that they = " Ober gives 8.4 m as the 'stock length' for such a are using. I use 1 dactyl 19.3 mm as Marsden.

This content downloaded from 137.22.1.233 on Mon, 8 Dec 2014 16:01:42 PM All use subject to JSTOR Terms and Conditions ON ARTILLERYTOWERS AND CATAPULTSIZES 383 mechanical and aerodynamic principles underlying these machines. In fact, stocks could be shorter even than arms were wide. For example, Charon's stone-thrower (as reconstructed by Marsden 1971: 78-82, with diagram 1), which was a bow catapult of the type that 'first generation' towers were built for, has a stock that is actually shorter than the arms are wide. The 'power' of the weapon depends not just on the drawlength but also on the drawweight." For example, a recurved bow increases the draw weight (and thus the 'power') without changing the draw length. Now, the length of the stock relative to the height of the stand set a limit on the maximum range. According to Philon (Belopoiika 76. 23-4; see also 51. 8-io), increased range was what most people desired of these machines, and that was achieved by laying the stock at a 450 angle or thereabouts. A stock twice as long as the stand was high simply could not, for that very reason, be set at a 45o trajectoryto maximize its range; indeed, such a ratio would limit the maximum possible trajectoryto about 20o, and thereby shorten the potential range very significantly. Fourth and finally, Ober's towers were, as he himself states when considering the thinness of their walls, almost certainly built for a world that knew only non-torsionmachines, that is, bow catapults, gastraphetai,which have no springs, and therefore no calibration in terms of spring diameters. Consequently, dimensions in terms of spring diameters are anachronistic and irrelevant to the first generation artillerytowers, such as (PLATE39), the whole concept of which he has done so much to help define.

Universityof WalesSwansea T. E. RIHLL

2 Ober is referring to draw length though he does not catapult internal dynamics', EuropeanJournal of Physics,24 use the term; the mechanics are explained by B. Cotterell (200oo3),367-78, though the latter does not understand and J. Kamminga, TheMechanics ofPre-Industrial Technology how a torsion catapult is spanned or 'drawn'. (Cambridge, gg99o):180-92, and M. Denny, 'Bow and

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PLATE40 a. View of the summit of Mount Kephalos from the south-west (A. Vionis).

VIONIS THE THIRTEENTH - SIXTEENTH-CENTURYKASTRO OF KEPHALOS PLATE40 b. View of the arched arcosol next to church I in Kephalos (A. Vionis).

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