Torsion Artillery

arms & armour, Vol. 12 No.1, Spring 2015, 67–89 Performance of Greek–Roman Artillery Cesare Rossi Sergio Savino Dept. of Industrial Engineering, University of – “Federico II” Arcangelo Messina Giulio Reina Dept. of Engineering for Innovation, University of Salento, Lecce The main throwing machines invented and used by the Greeks and adopted, more widely, by Roman armies are examined. The kinematics and dynamics of both light and heavy Greek–Roman artillery are used in order to accu- rately assess its performance. Thus, a better understanding is obtained of the tactics and strategies of the legions of the Roman Empire as well as the reasons for some brilliant campaigns. Reconstructions of a repeating catapult, considered to be the ancestor of the modern machine gun, are also presented. The development of the mechanical design of such machines is discussed and pictorial reconstructions proposed. keywords ancient throwing machines, history of warfare, catapults, Roman weaponry. Introduction It is well-known that the Roman legions took advantage of a skilled corps of e ngineers during their campaigns. Perhaps the best example is represented by the most famous Roman engineer: Vitruvius (Marcus Vitruvius Pollio 70–80 BC to after 15 AD). He authored the very famous engineering treatise De architectura, whose 10th book was dedicated to the war machines. Moreover, Vitruvius probably was a high officer (praefectus fabrum) of the corps of military engineers during the campaigns of Julius Cesar in Gallia and in Britain. His considerable knowledge of the field of military engineering, allowed the legions to have a considerable advantage as far as both tactics and strategy were concerned. In fact, the possibility of rapidly built roads allowed legions to be quickly moved, while the wide number of different war machines including rams, siege towers and other siege engines, throwing machines etc., gave the legions a big advantage over © The Trustees of the Armouries 2015 DOI 10.1179/1741612415Z.00000000050 68 CESARE ROSSI et al. less technologically developed peoples that represented the largest part of the world of those times. Among these engines, the throwing machines are particularly interesting. They represented the ancient artillery, both light and heavy, and included pieces to be used in the sieges for static warfare and pieces to be used in open field battles as heavy artillery and as infantry support gun or battalion gun. This is why so many authors have studied ancient throwing machines.1–22 Therefore, it is interesting to study both the kinematics and the dynamics of these machines in depth in order to assess their performance, and, thus, to better under- stand the tactics and strategies of the legions and of the Roman Empire and, conse- quently, the development of some brilliant campaigns and battles. These engines are described as Greek–Roman since, generally, they were invented by the Greeks but standardized for mass production and widely used by the Romans. In addition, this study reveals that the knowledge of mechanics was surprisingly advanced, although this field is probably less well than others because archaeological finds are less evident, smaller and sometimes unrecognized. The motors First of all, it is necessary to describe the motors of these throwing machines. It is well-known that one of the first throwing devices was the bow, which works on the principle of flexion. Essentially, an elastic rod is flexed to store elastic energy and, when released, the rod s this elastic energy to a projectile as kinetic energy. The early throwing machines, capable of throwing stones and big arrows or javelins, were built on the same principle. In Figure 1 some pictorial reconstructions of these flexion- based throwing machines are represented1,2. In Figure 1A and 1B the pictorial reconstruction of static flexion motor catapults are shown; in Figure 1C a gastraphetes, a type of big crossbow, is depicted. Throwing machines, whose motor is based on the elastic energy generated by the flexion of a rod, cannot generally reach a high level of performance because such a motor does not allow heavy projectiles to be thrown with a relatively high velocity. Therefore, in the third century BC, a different kind of motor became common in practically all the artillery pieces: the torsion motor, which was small and powerful and provide a superior performance. The Greeks from Syracuse developed the first catapults, as the result of engineering research funded by the tyrant Dionysius the Elder in the fourth century BC.2,3 Special mathematical and technical skills were necessary to build and main- tain a catapult. All the surviving catapult specifications imply that an optimum configuration was indeed reached. Archimedes, either invented or improved a device that would remain one of the most important forms of warfare technology for almost two millennia: the catapult. Later, during Alexander the Great's times, catapults were the big advantage for conquering central Asia. The last major improvement in catapult design came in later Roman times, when the basic material of the frame was changed from wood to iron. This innovation made In Figure 2. The new open frame also simplified aiming. in the middle a pictorial exploded view1. are considered in more depth. Design rules and concepts were practised extensively by the engineers of ancient times leading to machine design from single machine elements to the design of a machine as a whole system. Therefore such artillery pieces. an increase in stress levels and a greater freedom of stroke for the bow arms. a rope was affixed. is reported. on the left a specimen found in Xantem. horsehair or women’s hair23. Germany.1–3 Inside the coils. particularly for close moving targets. and a bundle of fibres on the right. arms were fitted. powered by torsion motors. possible a reduction in size. These coils were made by a bundle of elastic fibres: bovine sinews. a motor of a Roman catapult is shown. like the ends of an archery bow. The torsion motor This motor consisted of a strong wooden square frame. The central section was used to insert the shaft of the weapons. reinforced by iron straps. whereas the sides were for the two coils of twisted rope. the latter natural fibres had the best mechanical properties and were the most widely used. One of the main steps was represented by the estab- lishment of the optimum ratio between the diameter and the length of the coil. at the other end of each of the arms. divided into three separate sections. The last major improvement in catapult design was achieved during the Roman Empire when the most stressed components . which with the wood construction of the earlier machines had been limited. PERFORMANCE OF GREEK–ROMAN ARTILLERY 69 figure 1 Flexion throwing machines.2. 3 The design of Greek–Roman throwing machines was based on a module. the first ancient scien- tist who stated the relationship between the weight of the projectile and the modulus diameter was Archimedes of Syracuse. (e. an increase in the maximum stress levels and greater freedom of travel for the bow arms. of these machines were made by metal (iron and bronze) allowing a reduction in size. Probably. That is to say.e. even if only a part of an ancient machine is found. i. Philon of Byzantium and Vitruvius). figure 2 Propulsor of a Roman catapult: remains found at Xantem. the design of the machines was modular: all the main components and parts were sized as a multiple or a sub-multiple of a modiolus. From Philon of Byzantium24 to Vitruvius. According to ancient engineers. the diameter of the modiolus marked in Figures 2 and 3. Figure 3 shows a scheme of a ballista and a particular of the frame with the modioli.5 mm) m is the mass of the projectile in minae (1 mina ≈ 431 g).25 all the throwing machines designers and theoreticians say that this relationship is: D = 1. Thus.g.70 CESARE ROSSI et al. it is still possible to evaluate the weight of the projectile and its energy. once the diameter of the modiolus was stated as described.1 ⋅ 3 100 ⋅ m (1) where D is the diameter of the modiolus (hence of the hair bundle) in digits (1 digit ≈19. all the other main dimensions of the machine were referred to this dimension. Germany (left) and reconstruction (right). . In Figure 4.5 In the upper part of Figure 4 the maximum bundle torsion (beyond the tensile stress limit) as a function of L/D ratio is reported. bundles in which it was possible to store the same energy.5. C ~ 0. diameter of the arm near the bundle.e. PERFORMANCE OF GREEK–ROMAN ARTILLERY 71 figure 3 Schematic drawing of a ballista. we deduce that the bundle length L was 7 times its diameter D. If operating arm rotation angles and bundle L/D ratios are considered for ballistae and catapults. F = 4D. All the graphs were obtained considering the same bundle volume.5D (this datum is deduced by some relicts). and d2 = 7/16D. From the results. the horizontal line marked with ‘Emax’ represents the elastic energy that corresponds.1. B = 3+ ¼D. the energy that is possible to store in a bundle is reported as a function of the bundle rotation for a few L/D ratios and for a given value of the Young’s modulus. for each bundle. that is to say. diameter of the arm near the rope. d1 = 9/16D. If we consider that about ¼D of the hair bundles are reasonably blocked in the modioli. the maximum elastic energy which corresponds to a given stress limit is also reported. from Figure 4 it is possible to conclude that those machines were designed with ancient engineers having a thorough understanding of the mechanics . As for the design of this machine. In the lower part of Figure 4. Figure 4 summarizes some of the results on a model of the fibres bundle. The L/D ratio between the length of the bundle and its diameter was decisive for obtaining the maximum energy from the bundle itself. i. E = 1D. to a rotation over which the external hair stress exceeds the proportionality limit. we can consider that the coil of fibres that really were twisted by the arm A had a ratio L/D = 0. Vitruvius24 is meticulous in giving the ratios between the diameter of the modiolus and all the other main dimensions of the machine: A = 7D. it must be said that ballistae and catapults. Another throwing machine was part of the Greek–Roman armies: the onager. This last aspect is similar to what happens for firearms where. Moreover. the wider the arm rotation must be in order to store the maximum possible elastic energy in the bundle. of those devices. First of all. while the word ballista (from the Greek βαλλω = to throw) was used for a machine that throws balls. figure 4 Effect of varying the bundle L/D ratio. it is evident that the higher the L/D ratio. The word catapult comes from the Greek (κατα = through and πελτη = shield). the greater the slope of the curve. perhaps. the onager (in Latin onagrum) had a high-arcing ballistic trajectory. quick burning powders are used. Finally. From Figure 4.72 CESARE ROSSI et al. with heavy projectiles. from the figure it is noted that the lower the L/D ratio. . During the Roman Empire the word catapulta was used for a machine that throws darts. slow burning powders are used whereas with light projectiles. we can observe that steeper slopes correspond to a faster release of energy when throwing the projectile. with higher efficiency. The torsion artillery The term ‘torsion artillery’ is used to refer to those throwing machines whose motor was the torsion elastic bundle described in the previous paragraph. In contrast to the previous machines that gave to the projectile a rather smooth trajectory. As far as this aspect is concerned. a few words must be said about terminology. During the Middle Ages the words were used with the opposite meaning: ballista for a dart throwing machine and catapult for a ball throwing one. This suggests that high L/D ratios for the bundle could have been used for machines throwing heavier projectiles and. 8.20.25 Around the second century BC. allowed larger rotations of the arms with the probable advantages reported above. The palintone design. In Figure 7. Biton of Byzantium tells about an important improvement in throwing machine design. from the ancient Greek root πάλιν (palin) that means newly. were quite similar. PERFORMANCE OF GREEK–ROMAN ARTILLERY 73 from a mechanical and architectural point of view. Moreover. according to what was computed in Figure 4. The onager. Figure 6 shows schemes of the euthytone and of the palintone design. In these ‘new’ machines.2 according with the data by Vitruvius. was rather different. from the relics. its arms had a wider rotation. the arms are mounted inside the mainframe.1. having the same mechanical architecture represented in Figure 3.8.8 The latter was a gigan- tic machine designed to throw very heavy projectiles (up to 33 kg for some relics) and. a pictorial reconstruction of the great ballista. obviously. whereas in traditional machines (called euthytone) the arms were outside the mainframe. 20 figure 5 Pictorial reconstruction of the ballista of Vitruvius. The ballista Figure 5 shows a pictorial reconstruction of the ballista. it was found that the bundle casings were designed for bundles having an approximate L/D ratio of 9. the remains of which were found in Hatra (actually al-Hadr in Iraq) is represented. however.21 many machines begin to be built having a new design often called ‘palintone’. . According to several authors. The projectile trajectories from this type of machine were computed by using a simple model for the air drag force R: 1 R=− Cv ρ V2A v (2) 2 where Cv is the drag coefficient for a rough sphere ≈ 0. and A is the area of the projectile’s cross section. figure 7 Pictorial reconstruction of the great ballista of Hatra. Using the information that Vitruvius gives about its dimensional design. ρ is the mass density of the air = 1225 kg m–3. thence. kinematic and dynamic models of such machines were obtained1.5 showed that these machines threw stones having a muzzle velocity of about 104 m s–1 for the euthytone and about 124 m s–1 for the palintone. figure 6 Schemes of A the euthytone and B the palintone machines. . the elastic energy stored in the bundle was calculated. V is the speed (module with its unit vector v) of the projectile.5 and. giving a measurement of the performance of these machines. The results1.74 CESARE ROSSI et al.5. a 40 minae = 21.55 kg projectile consisting of an almost spherical stone having about 254 mm diameter was considered. PERFORMANCE OF GREEK–ROMAN ARTILLERY 75 The differential equations governing the motion can be obtained by projecting along the classical horizontal rightward. One such hole is shown in Figure 10. the velocity at the impact Vf. Equations 1–3 were applied in the following examples. 10°. Equation (3) was numerically solved. it is interesting to observe the holes produced by stone balls thrown against the walls of the city of Pompeii8 during Lucius Cornelius Silla’s siege in 89 AC. . y(t). for a machine used in battle. and vertical upward direction. Table 2 and Figure 9 give the corresponding range figures and trajectories. As for the terminal effect of those projectiles. including the angle of elevation θ. Because the computed initial velocity of 100 m s–1 was almost the maximum value for such a machine in very good condition. it seemed more realistic. Table 1 gives examples of range figures. the following vector equation: 1 m a (P) + Cv ρ VA V(P) − m g = 0 (3) 2 where P is the vector configuring the position of the projectile for any instant of time. so the holes have a diameter of almost 150 mm.31 kg in the form of an almost spherical stone of about 149 mm diameter. a 10% decrease in the maximum energy was also considered. Palintone ballista For the palintone. 20° and 30°. figure 8 Trajectories for the euthytone (axes expressed in metres). the range. and the time of flight Tf for elevation angles θ of 5°. Euthytone ballista A medium-sized ballista consisted of a throwing projectile having a mass of 10 Roman minae = 4. to consider an initial velocity of 95 m s–1 giving an initial energy of about 10% lower than the maximum energy that the machine could achieve. Figure 8 shows the trajectories for the same conditions. x(t). thus the projectile initial velocity was assumed to be 118 m s–1. each ruler mark is 10 cm. the same as the projectile considered for the example given in Table 1 and Figure 8. the angle at the impact β. the maximum height reached by the projectile. Because this machine architecture was often conceived for large machines. i.e. 6 73 40.5 10.5 19. probably because its arrows acted like the stinger of that animal. being a truly automatic weapon.5 2 10 396.7 5. Small catapults.3 56. two were particularly interesting: the repeating catapult and the carroballista.5 137.3 8. Among these relatively small machines. there were no significant differences between the mechanical architecture of the ballistae and the catapults.76 CESARE ROSSI et al.7 76. The repeating catapult The repeating catapult was among the ancestors of modern machine guns.55 KG AND INITIAL VELOCITY 118 M S–1 θ (deg) Range (m) hmax (m) Vf (m/s) β(deg) Tf 5 221 5.2 43.31 KG.1 110.3 3 20 406.1 12 4 20 645.5 30 785. used around the first century BC.6 figure 9 Trajectories for the large Palintone. substantially. the term catapult refers to a machine that throws big darts or javelins but.6 10 252 12.6 3. INITIAL VELOCITY 95 M/S θ (deg) Range (m) hmax (m) Vf (m s–1) β(deg) Tf (s) 5 141.7 59. it was part of the arsenal of Rhodes that may be considered as a concentration of the most advanced mechanical kinematic and automatic systems . The Catapult. apparently. TABLE 1 EUTHYTONE BALLISTA RANGE FIGURES FOR A PROJECTILE MASS = 4.2 89.4 TABLE 2 PALINTONE BALLISTA RANGE FIGURES FOR A PROJECTILE OF MASS = 21. were called by the Romans scorpio.6 1.1 6 30 491 87.9 41. literally scorpion.3 79. the Scorpio and the Carrobalista As previously reported. The machine was attributed to Dionysius of Alexandria and was.6 26.8 5. used as light field artillery pieces. It was described by Philon of Byzantium6–10 and can be considered as a futuristic automatic weapon that throws 481 mm long darts.1 68.3 70 12.5 7.7 27. The operators then turned the windlass in the opposite direction in order to carry the mechanism back to the starting configuration. was not written to eliminate all doubt because it lacks a technical glossary and an analytic style. Finally. and the teeth of the chainmails are called περονατς. The machine was described ‘in modern times’ by Bernardino Baldi. increasing both the rate of fire and the working safety. it was difficult to operate during a battle and it was dangerous for the operators. ‘fin’.7 It should be pointed out that ancient Greek has no technical terms: for instance in Ta Filonos Belopoika 75. among other things. a mechanism that was operated by turning the windlass always in the same direction of rotation and the presence of a non-return mechanism could have greatly simplified all the operating sequence by the operators. it would have been possible to stop the working sequence at any stage. Erwin Schramm. the torsion motor was charged and no non-return device could be used because the windlass had to be free to rotate in both directions.30 who built a model of it at the beginning of the XX century giving unquestionable demonstration of its potential during the testing performed before the Kaiser.7. we proposed a rather different reconstruction and working cycle. the operators had to turn the windlass in a direction to charge the weapon and at the end of this phase the missile was thrown. ‘little brick’.31 All the reconstructions proposed have almost the same working principle. although readily understood. 33–34 the chainmail is called πλτνθτα.6. many of which show working principles and concepts that are still considered modern. of the time. Thus.29 but the first studies on it were carried out by a German officer. the description left to us by Philon. once one cycle was started. Such a working principle had some disadvantages: it was not efficient. it was difficult to stop or to pause it because. Therefore. the whole mechanism would have been automatic from a wider point of view.2. In the first phase of the working cycle. . Hence.6. in the first half of the cycle.10 based on the translation of the original description by Philon of Byzantium. PERFORMANCE OF GREEK–ROMAN ARTILLERY 77 figure 10 Holes caused by the impact of ballistae projectiles. With this way of operating. Conversely. There were some later proposed studies on this device. The details that permit operation of the whole cycle by rotating the windlass always in the same sense of rotation are shown. a simple rotation of the crank was sufficient to move the cylinder.78 CESARE ROSSI et al. the latter is considered as the first (1862 U. figure 11 Pictorial reconstruction of the automatic catapult. the slide. the slide S and the pentagonal wheels P are also represented. According to Philon and to other authors’ reconstructions. Figure 12 shows another pictorial reconstruction with some details of the mechanism. The cycle repeated automatically without interruption or inverting the rotation of the sprocket until the magazine was empty. the slide hooking mechanism and the trigger mechanism. the arrows A were located in a vertical feeder M (Figures 13 and 14) and were transferred one at a time into the firing groove by means of a rotating cylinder C activated alternatively by a guided cam. a cylinder feeding device and movement chain.S. This seems more realistic because. the ratchet could have worked correctly and the rate of fire could have been maintained quasi constant. Figure 13 also shows the feed mechanism compared with the one of the Gatling machine gun. The repeating device consisted of a container holding within it a number of arrows. Hence. whereas we have assumed the direction of rotation was always the same. in this way. patent) machine gun and . a magazine that could be reloaded without suspending firing. The guided cam is represented by a helical groove in the rotating cylinder in which a pin connected to the slide is located. In Figure 12. in turn activated by a slide. The difference between our reconstruction of this device and the previous ones is mainly in the reload sequence: it was previously supposed that the crank handles had to reverse the rotation for each strike. A pictorial reconstruction of the repeating catapult is shown in Figure 11. . PERFORMANCE OF GREEK–ROMAN ARTILLERY 79 figure 12 Details of the mechanism. Gatling gun mechanism (right). figure 13 Details of the mechanism (left and centre). . Figure 15 shows the projectile velocity plotted versus the arm position for arrow weights of 100. 150 and 200 g with a cross section of a circle of 32 mm diameter1. the performance was computed by using equation 3. The results are summarized in Table 3. the speed of firing must have been an average of five strokes per minute.35.80 CESARE ROSSI et al.10 From a ballistic perspective. figure 14 Technical drawing of the repeating catapult. its working principle is still used for modern aircraft automatic weapons.25 calculations were made starting from the length of the arrow S. very little compared with modern automatic weapons. In order to compute the performance of such a machine.24. Figure 14 shows a technical drawing of the device. The diameter D of the modiolus is: D = S/9(4) The ratios between the diameter of the modiolus and all the other main dimensions of the machine are the same as those already considered. For the arrow weight. according to ancient engineers. but certainly impressive for that time. The ballistic trajectories of such a small scorpio are reported in Figure 16. The air drag coefficient in equation 2 was assumed to be Cv =0. reasonable values are between 100 and 150 g. This explains why. highly movable war machine was probably developed after four Roman Legions were surprised in an ambush in the . INITIAL VELOCITY 65 M/S θ (deg) Range (m) hmax (m) Vf (m/s) β(deg) Tf (s) 5 70. PERFORMANCE OF GREEK–ROMAN ARTILLERY 81 figure 15 Projectile velocity as a function of the arm position.2 1.6 1. Figure 17 shows some pictures of this machine from the Trajan and Marcus Aurelius columns and from De Rebus Bellicis (an anonymous treatise of the IV–V century AD).32.9 48. Moreover.3 30 289. figure 16 Trajectories for a repeating catapult (small scorpio). in particular.1 56 11 2.14 but was mounted on a cart in order to provide a quick deployment of the artillery piece to give close support to infantrymen.8 50.8. powerful and.5 4. TABLE 3 REPEATING CATAPULT RANGE FIGURES.6 60 5. the Roman imperial carroballista was developed in the first century AD and represents the earliest example of mobile artillery.2 20 229.5 6.8. PROJECTILE MASS = 150 G.2 The carroballista The carroballista was the first example of an infantry support gun (or battalion gun) that was much later developed in modern (eighteenth–twentieth century) warfare. From a historical point of view.33 each of the Imperial Roman Legions was equipped with about 24 of these machines.1 10 132. such a lightweight.1 22. according to several reports.8 46. It was very similar to the cheirobalistra or manubalista.8 23.8 36 6. 32 we assume that this ballista (Figure 18) was based on a palintone design shown in Figure 6B. XVI Sec.33 such highly movable and powerful machines would have been decisive in such conditions.15. Thus. .82 CESARE ROSSI et al. B Aurelian column. figure 17 A and C: Trajan’s column. forest of Teutoburgo.14. Based on some of our previous studies1.8.5 and on those of others. It is also surprising to consider the modernity of the concept that consisted of providing the legions with a battalion gun for close support about 1900 years ago.) figure 18 Bas relief and scheme of the carroballista. D: De Rebus Bellicis (Trans. the carroballista was an effective example of an infantry support gun in the open field.2. 6 g bullet fired by a NATO 5. it is reasonable to assume such a design for a machine that had to develop sufficient power in small dimensions. it is described as a throwing machine having only a big arm instead of two little arms.24 No further mention is found until the fourth century AD when Ammianus Marcellinus (325/330–after 391) describes it in detail and names it onagrum. Some detail about a monoanchon can be found in the 5th book.22 as shown in Figure 19.33 are given in Figure 19. Because those modern bul- lets are much lighter than the ballista projectile. there is a high probability of hitting the target even when there are some errors in estimating the real distance of the target itself. the most probable torsion motor of these machines was made by a helical torsion spring. 220 BC). for instance. As it shown in a previous study. It is interesting to recall that inside the city of Pompeii. is much lower than the projectiles thrown by the carroballista. about which there is very little information available in the ancient literature. Trajectories for the bolt for an initial velocity of 104 m s–1 are given in Figure 21. Tables 4 and 5 give the range figures for a lead sphere and a bolt.32. is more efficient because the rotation angle of the arms is wider than that of a euthytone.34 from the latin onagrus meaning donkey. PERFORMANCE OF GREEK–ROMAN ARTILLERY 83 figure 19 Schematic diagram of the machine.5 this design. of the treatise on the mechanics Mechanike syntaxis (Compendium of Mechanics) by Philo of Byzantium (ca. For comparison. hence the shock at impact. ordnance rifle at 300 m from the muzzle.14.34 In order to evaluate the projectile range. probably because its working principle was similar to the kick of a donkey. The main dimensions of the machine suggested previously8. NATO ordnance pistol. named Belopoeica. their translational momentum.56 × 45 cal. having the arms inside the main frame of the machine. The onager The onager was a rather mysterious ancient war machine. Thus. and a bolt having about the same mass and cross section. Even Vitruvius25 does not mention it. an initial velocity of 104 m s–1 was computed for a projectile of 200 g.18. 280 BC – ca. several stone balls were found that were larger than the holes on the walls that were made by the impact of the projectiles thrown by the ballistae. which shows that the trajectories are rather flat. Therefore. whereas 500 J is the energy of a 8 g bullet at the muzzle fired by 9 × 19 cal. similar to those reported in Figure 20. moreover. we considered two possible projectiles: a 200 g lead ball 32 mm in diameter. This type of motor was compatible with the technology at that time and was small and powerful enough. For such a machine. 650 J is the energy of a 3. Those big balls had been thrown . respectively. by the onagers of Silla and had jumped over the walls of Pompeii during the siege in 89 BC.uk/ham-hill-p2. Yale University Art Gallery. co.org/ballista. http://alexisphoenix. B. The only intact specimen of a Roman ballista bolt ever discov- ered was excavated in Dura Europos.84 CESARE ROSSI et al. Great Britain by Dr Chris Evans. The onager comprised a single arm (A in Figure 22) that is inserted into a bundle of yarns made from woman hairs.1–11.php.466ad.com/roman-ballista-bolts. from Greek and Roman Artillery 399 BC–AD 363. A modern reconstruction weighting about 195 g. figure 20 Roman bolts: A.html and http://imgbuddy. Syria. figure 21 Trajectory of the bolt.asp.23 This bundle is the torsion motor of the machine. A bolt head found at Ham Hill. from the Cambridge Archaeological Unit. Photo by. http://hillforts. C.25 A pictorial reconstruction of the onager is shown in Figure 22 and the working principle of the machine is given in Figure 23. by Duncan Campbell. . 4 630 15 421 72.) Range (m) Vf (m s–1) Impact energy (J) 5 165 84.6 79.4 712 10 290 72.3 426 TABLE 5 RANGE FIGURES FOR THE BOLT Elevation angle (deg. figure 23 Working principle of the onager.5 526 15 385 65. . PERFORMANCE OF GREEK–ROMAN ARTILLERY 85 TABLE 4 RANGE FIGURES FOR THE LEAD BALL Elevation angle (deg.) Range (m) Vf (m s–1) Impact energy (J) 5 172 89.3 797 10 310.7 529 figure 22 Pictorial reconstruction of the onager and detail of the linkage of the sling. weight of the projectile. In order to evaluate the performance of an onager. by solving the differential equations. by changing the angle γ. When the trigger is pushed. varying the releasing angle γ and the bundle torsion are reported: Ranges by varying the releasing angle γ The results in Table 6 and Figure 24 refer to the same bundle torsion (θund = 110°). the dynamical behaviour of the machine itself was computed. A mathematical model of tise machine was developed and.86 CESARE ROSSI et al. and different θr (i. To illustrate this. the initial throwing angle of the projectile and its initial velocity can both be set. and β the angle of the projectile at the impact. Finally. The projectile is released by the sling when its ropes are approximately aligned with the pin axis because in this condition the ring of the sling climbs over the pin. hmax maximum height reached by the projectile. the following data are reported: θr arm angular position when the projectile is released.2 m. a sling holds the projectile. 2. the machine. the range figures were computed by means of equations 2 and 3. V0 projectile initial velocity. Thus. this allowed the projectile initial velocity to be calculated under several different working conditions. in addition to the range. a capstan rotates the arm to charge the torsion spring and. On the other end of the arm. figure 24 Onager trajectories. . length of the sling. In the range figure tables.e. θund =110°. by assuming a different releasing angle γ between the finger and the arm). that is to say by releasing the arm from a different starting position. two examples. The range of this throwing machine could be adjusted both by changing the angle γ and by changing the bundle torque. 17. Ranges by varying the bundle torsion The results in Table 7 and Figure 25 refer to almost the same angle γ between the finger and the arm but the range is varied by changing the bundle torsion (θund).44 kg (=40 Roman minae). Vf projectile velocity at the impact. One of the sling ropes is fixed to the arm and the other rope is linked by means of a ring that is put on a pin (F in the detail of Figure 22). comprising a stone sphere of approximately 237 mm diameter. 1 m. In turn. the axis of this pin can be set with a desired angle γ with respect to the axis of the arm. Finally. which gives an elastic couple (C in Figure 23) to the arm. α projectile initial direction. a machine having the following dimensions was considered: length of the arm. the arm is released and it rotates because of the couple given by the torsion motor. hence. 64 118.2 67 85 52.7 80.3 33.5 28. Moreover.5 50.4 10.6 .7 TABLE 7 ONAGER RANGE FIGURES.1 29.41 32.72 73.3 53.6 85 37.5 179.78 31.8 57. the range could be adjusted by changing the angle γ.5 50.1 132.9 74 75 43. it is possible to observe that this war machine was capable of effective performance allowing a considerable projectile to be thrown with sufficient energy to clear the walls. we could conclude that the methods of adjusting the range essentially corresponds to both a variation of the gun barrel elevation and of the weight of the firing charge.5 34 105 56.6 36.4 37.67 30. θR =95° –1 θr (°) V 0 (m s ) α (°) Range (m) hmax (m) V f (m s–1) β(°) 75 29.69 71.4 32.1 45. θr = 95°.8 115 66. PERFORMANCE OF GREEK–ROMAN ARTILLERY 87 From the previous tables and figures.99 63. on the other side.6 40.8 32.5 229. the range can be also adjusted by changing the bundle torque obtaining ‘flatter’ trajectories than previously.66 65.3 52. If a comparison with modern howitzers can be made.4 27.18 252.9 41. generally. it is interesting to note that.1 34.3 95 46.46 293.7 30.2 74.71 337.3 47.7 18.7 55. θUND =110° θr (°) V 0 (m s–1) α(°) Range (m) hmax (m) V f (m s–1) β(°) 65 35.2 59.57 32. Conclusions An overview of all the artillery of the Greek and Roman armies is presented.7 35.8 42.5 95 61. TABLE 6 ONAGER RANGE FIGURES. these war machines were used from the third century BC until the fall of the Roman Empire figure 25 Onager trajectories. in Italian). Lewis. T. tary equipment from the Punic Wars to the fall of (Dordrecht: Springer. Coulston. and some of them survived until the Middle Ages. International 19 V. L’artiglieria navale liber VIII. 67 (2009). T. Artillery of the Roman Legions. Available at: <www. Edited by Rome (Second Series). Foley. ‘Ancient Greek Artillery Technology 6 E. Die antiken Geshützen der Saalburg. Iriarte. reconstruction: I. Hart and M.. Theoretics’. G. Russo. Shramm. W. 18: La grande Balista di are described. Transactions of the ASME. Minneapolis MN 55344. 45 (1) (2010). 1971). 8. 1–13 (2012). Examples of the performance of these ancient artillery pieces are based on the functional reconstruction of these machines that allowed their kinematics and dynamics to be obtained. Machine Theory. 21 M. 25 Vitruvius.php?query=creator%3A%22App 10 C. 106–84. Gladius. Proceedings of HMM 2008. ‘The Development of Machine Journal of the Society of Archer-Antiquaries. Marsden. Canzler and P. 41 (1994). Ancient Engineers’ Britannia. Russo. and by Matthew Figures in Mechanism and Machine Science. 240 (1979). able in English at <http://penelope. Roman Military Equipment Greece and Contributions and Legacies. Wars against Carthage. Yang. J. Jeff Schirer. J. 160 A. ‘Pseudo-Heron’s cheiroballistra a(nother) Road. 5 C. Design. ‘Ancient Throwing Machines: a Method 15 A. W. 2008). Journal of Engineering Mathematics.de/Greeks/war/ Press.D. Their Bennett. 7 E. Rossi and F. 79–81. 8 F. Iriarte. Notes 1 C.html>. DOI 10. Harpham and D. Russo. 1969). Part 1.org/search. 40 Design as a Science from Classical Times to Modern (1997). p. Ist ed.mlahanas. Batsford. Hatra. Mechanism and (2003). 20(4) Mechanisms (Dordrecht: Springer. Molari. 40.uchicago. avail- 12 E. G. 2012. ‘Ancient Catapults’. Fiber. 16 D. De Architectura. 2007). University of Cassino. Lahanas. in particular 11 F. Torre del Greco (2009). Sannipoli Technical Treatises (Oxford: Oxford University P. 9 (1978). Rossi. Rossi and S. 137–38. Russo. ‘Heron’s (Dordrecht Springer. Archimedes (287–212 BC) History this book by Boris Rankov in The Classical Review of Mechanism and Machine Science 1. Hysitron Incorporated 10025 Valley View 14 A. 1–17. 261–73. Ed. . Italy 18 R. See reviews of 3 T.pdf>. 4 T. Reprint (Bad Homburg: Saalburg Museum. Rome (London: B. Inventions – Precursors of the Present. The authors hope that this study provides a useful contribution to the understanding of ancient warfare. G.edu/ 1918. Bishop and J. Greek and Roman Artillery: 22 P. Tormenta Navalia. CatapultTypes. Roman mili- History of Mechanism and Machine Science. C. ‘The Inswinging Theory’. storia.com/Portals/0/App%20Notes/BIO13ANr1. A. c. liber X. Distinguished (New Series). archive. Series: 17 M. 13–17. 150–60.htm>. 2012. Hart and M. 1980). Greek and Roman Artillery from Catapults to the Architronio Cannon’. Romana – un piacevole viaggio fra fantasia. Fred Tsuchiya and Dehua 13 W. 15 B. (Rome: Poligrafico e Zecca dello Stato. N. Vol.. that part called Belopoeica where torsion artilleries tavole ricostruttive. ‘Mechanics of the Symposium on History of Machines and Onager’. Stevenson. f. Journal of Mechanical Mathematics. Vol. ‘Improvement in Ballistae 20 V. Chondros. ‘Ricostruzione della balista imperiale Press. pp. G. ESA (Naples: ESA. The performance of these machines showed their reliability and sometimes their surprising efficiency. available in English at <https:// romana (Rome: USSM Italian Navy. 345–65. 44 1994). taxis (Compendium of Mechanics). 135 (8) (2013). Mechanism and 24 Philo of Byzantium (III Century BC) Mechanike syn- Machine Theory. Cheiroballistra (A Roman Torsion Crossbow)’. 26 Qiang Xiao. G. Nanotensile Study of Single Human Hair Scientific American. 11 (2000). Chondros. ‘Recent Finds of Ancient Artillery’. Soedel and V. T. 1993). Le baliste dell’Impero. 23 to Compute Their Performances’. F. 36–45.88 CESARE ROSSI et al. 111–40. 2004).6092/unibo/amsacta/3306. 2007). Cenni storici.C. Angelini. L’artiglieria delle legioni romane (The tecnologia e progettazione’. ‘A reconstruction of the ianus%2C%20of%20Alexandria%22>. Marco Ceccarelli. and F. Lewis. 2009). Russo. reperti. Thayer/E/Roman/Texts/Vitruvius/home. avail- Historical Development (Oxford: Oxford University able at <http://www. 2 C. Rossi. Baatz. G. Journal of Roman hysitron. ‘The Hatra Ballista: Design from Eutitonon to Palintonon: A Study on A Secret Weapon of the Past?’ Journal of Engineering the Mechanical Advantages’. 23 Appianus Alexandrinus. Pagano. C. Russo. W. 47–75. Military Equipment Studies. 51. W Marsden. University of Bologna. 1–7. (1986). 9 F. Era’. Greek–Roman repeating catapult’. He became Professor of Mechanics for Machines and Mechanical Systems at the Università del Salento. Email: cesare. vehicle dynamics. Savino. Die antiken Geschütze der Saalburg C. Traiana argomenti per ricostruire la balista imperiale romana’. and a PhD in Mechanical Engineering. His main research activities are on the topics of mechanical vibrations.imss. hoc est. Correspondence to Cesare Rossi. C. Manna. his main areas of research are video applications for robotics. His main research activities are on the topics of tribology.rossi@unina. composite materials. Russo. behavior of the imperial carroballista’. 150–60.“Federico II”. 1 (Milan: Hoepli.it . chaotic motions in mechanical systems. Italy in 2006. and a PhD in Mechanical Engineering. (2011). Guest editorial.D. 1950). Rossi.fi. Shramm. 1966). 28 34 F. typis Davidu Ammianus Marcellinus (IV Century A. Italy. Vol. G. Rossi. Engineers’. 30 37 E. and vision systems in robotics. His research focuses on the topics of field robotics. Tonelli. Italy and a member of its Permanent Commission for the History of Mechanism and Machine Science. ura. and S. F. In press Notes on contributors Cesare Rossi graduated in 1973. focusing on humanities. Russo F. Giulio Reina received the Mechanical Engineer Degree cum Laude at Politecnico di Bari in 2000. 295 (2009). 1–2. ‘On Designs by Ancient 31 Soedel and Foley. 135(6) (2013). Heronis Ctesibii Belopoeka. 2011. 90–95.“Federico II” in 2001. Augusta Vindelicorum. 32 Molari P. robot mechanics. damage detection and modal analysis. 2013. Baldi. and Machine Theory.php?id=oai%3Awww. ‘La lezione di Teutoburgo’. Currently Research Assistant of Mechanics for Machines and Mechanical Systems at the University of Napoli . rotor dynamics. 142–50. 36 internetCulturale. Archeo. 54–61. 1616. Sergio Savino received his Mechanical Engineer Degree at the University of Napoli . Penta. and became Professor of Mechanics for Machines and Mechanical Systems there in 2000. He became Assistant Professor of Mechanics for Machines and Mechanical Systems at the Università del Salento. 311 A17%3AFI0029%3A324104&teca=Museo+Galileo>.caspur. ‘Mechanical Unviersity of Naples. Attenti all’asino. Archeo. Note sulle funi Metalliche (Naples: F. filat. signal processing in mechanical systems. and video applications for robotics. and a PhD in Mechanical Engineering. In 1979. 80 (2014). mechatronic systems. For several years he has researched the history of engineering and cooperates with other researchers in the field mainly involv- ing Technology in the Classic Age (in which he has taught PhD courses at other Italian universities. Mechanism 29 B. Tecnologia Tessile – Fibre tessili. PERFORMANCE OF GREEK–ROMAN ARTILLERY 89 27 33 L.it/ms/ gestae. 2013. in 2005. He is currently Chair of the IFToMM. Available at <http://iccu01e. Arcangelo Messina received the Mechanical Engineer Degree cum Laude at Politecnico di Bari in 1991. ‘Dal fregio della Colonna Transactions of the ASME. mechanical vibrations. Proceedings of Colonna Traiana All web addresses have been rechecked by accessing MCM – Accademia di Romania in Roma 7–8 June on 26 March 2015.it%3 F. and the history of mechanism and machine science.) Res Frany. Russo and F. 35 Telifactiva. he received the Mechanical Engineer Degree cum Laude at the University of Napoli – “Federico II”. Journal of Mechanical Design. 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