L]Z Lgzwjx]Zi

Recent reconstructions and computer simulations reveal the operating principles of the most powerful weapon of its time by Paul E. Chevedden, Les Eigenbrod, Vernard Foley and Werner Soedel

enturies before the development of eÝective cannons, huge artillery pieces were demolishing castle walls with projectiles the weight of an Cupright piano. The trebuchet, invented in China between the Þfth and third centuries B.C.E., reached the Mediterranean by the sixth century C.E. It displaced other forms of artillery and held its own until well after the coming of gunpowder. The trebuchet was instrumental in the rapid expansion of both the Islamic and the Mongol empires. It also played a part in the transmis- sion of the Black Death, the epidemic of plague that swept Eurasia and North Africa during the 14th century. Along the way it seems to have inßuenced both the development of clockwork and theoretical analyses of motion. The trebuchet succeeded the catapult, which in turn was a mechanization of the bow [see ÒAncient Catapults,Ó by Werner Soedel and Vernard Foley; SCIENTIFIC AMERICAN, March 1979]. Catapults drew their energy from the elastic deformation of twisted ropes or sinews, whereas trebuchets relied on gravity or direct human power, which proved vastly more eÝective. The average catapult launched a missile weighing between 13 and 18 kilo-

66 SCIENTIFIC AMERICAN July 1995 Copyright 1995 Scientific American, Inc. manajaniq (An Elegant Book on Treb- uchets), written in 1462 C.E. by Yusuf ibn Urunbugha al-Zaradkash. One of the most profusely illustrated Arabic manuscripts ever produced, it provides detailed construction and operating in- formation. These writings are particu- larly signiÞcant because they oÝer a unique insight into the applied mechanics of premodern societies. We have made scale models and computer simulations that have taught us a great deal about the trebuchetÕs opera- tion. As a result, we believe we have un- powerful trebuchets, in contrast, could covered design principles essentially launch missiles weighing a ton or more. lost since the Middle Ages. In addition, Furthermore, their maximum range we have found historical materials that could exceed that of ancient artillery. push back the date of the trebuchetÕs spread and reveal its crucial role in me- grams, and the most commonly used Recovering Lost Knowledge dieval warfare. heavy catapults had a capacity of 27 Historians had previously assumed kilograms. According to Philo of Byzan- e have only recently begun to re- that the diÝusion of trebuchets west- tium, however, even these machines Wconstruct the history and operat- ward from China occurred too late to could not inßict much damage on walls ing principles of the trebuchet. Schol- aÝect the initial phase of the Islamic at a distance of 160 meters. The most ars as yet have made no comprehen- conquests, from 624 to 656. Recent sive eÝort to examine all the available work by one of us (Chevedden), howev- evidence. In particular, Islamic technical er, shows that trebuchets reached the literature has been neglected. The most eastern Mediterranean by the late 500s, 1 important surviving technical treatise were known in Arabia and were used on these machines is Kitab aniq Þ al- with great eÝect by Islamic armies. The

MODERN RECONSTRUCTION of a medieval siege engine hurls a piano across the English countryside. This trebuchet, patterned after ones used in Europe and the Middle East, has lofted objects weighing as much as 500 kilograms. Its largest forebears could toss more than a ton. (The 60-foot-high reconstruction was built in Shropshire by Hew Kennedy and Richard Barr.)

2 7

4 6 VIN GUGLIELMO GAL

Copyright 1995 Scientific American, Inc. technological sophistication for which logical warfare had perhaps its most neers thickened walls to withstand the Islam later became known was already devastating impact. As Mongol forces new artillery and redesigned fortiÞca- manifest. besieged this Genoese outpost on the tions to employ trebuchets against at- The Mongol conquests, the largest in Crimean peninsula, the Black Death tackers. Architects working under al- human history, also owed something swept through their ranks. Diseased Adil (1196Ð1218), SaladinÕs brother and to this weapon. As a cavalry nation, the corpses were then hurled into the city, successor, introduced a defensive sys- Mongols employed Chinese and Mus- and from KaÝa the Black Death spread tem that used gravity-powered trebu- lim engineers to build and operate treb- to the Mediterranean ports of Europe chets mounted on the platforms of tow- uchets for their sieges. At the invest- via Genoese merchants. ers to prevent enemy artillery from com- ment of KaÝa in the Crimea in 1345Ð The trebuchet came to shape defen- ing within eÝective range. These towers, 46, the trebuchetÕs contribution to bio- sive as well as oÝensive tactics. Engi- designed primarily as artillery emplace-

Sling was attached firmly to the beam at one end The Physics and looped over a metal prong at the other. When it of the Trebuchet reached the proper angle in its arc, the loop would fly free, releasing the projectile. Proper adjustment of the prong and the overall length of the sling were he motion of the trebuchet is crucial to achieving maximum range. T simple enough in its essentials to have inspired medieval studies of motion, but its details are subtle and require computer simulations to interpret accurately. Only recently have we come to understand how the rotation of the counterweight plays a crucial role in transferring energy to the beam and thence to the sling and projectile.

FIXED COUNTERWEIGHT

TRACTION

Earliest trebuchets were powered by crews Addition of counterweights increased the power of the treb- pulling on ropes rather than by counterweights. uchet. The elimination of the pulling ropes made possible anoth- Crews of as many as 250 men pulled to send er innovation: by placing a trough under the trebuchet beam to projectiles 100 meters or more. In this example of hold the projectile, engineers could lengthen the sling and in- a small traction machine, the sling-holder’s weight crease the range even further. The sling rotates faster after the flexed the beam and increased the range. shot is airborne, so its length controls the launch angle.

68 SCIENTIFIC AMERICAN July 1995 Copyright 1995 Scientific American, Inc. ments, took on enormous proportions long end swung upward, hurling the projectile on the other end of the arm to accommodate the larger trebuchets, missile from the sling. might weigh between 200 and 300 kilo- and castles were transformed from Three major forms developed: trac- grams, and a few trebuchets reportedly walled enclosures with a few small tow- tion machines, powered by crews pull- threw stones weighing between 900 and ers into clusters of large towers joined ing on ropes; counterweight machines, 1,360 kilograms. With such increased by short stretches of curtain walls. The activated by the fall of large masses; capability, even dead horses or bundled towers on the citadels of Damascus, and hybrid forms that employed both humans could be ßung. A modern re- Cairo and Bosra are massive structures, gravity and human power. When trac- construction made in England has as large as 30 meters square. tion machines Þrst appeared in the tossed a compact car (476 kilograms Mediterranean world at the end of the without its engine) 80 meters using a Simple but Devastating sixth century, their capabilities were so 30-ton counterweight. far superior to those of earlier artillery During their heyday, trebuchets re- he principle of the trebuchet was that they were said to hurl Òmountains ceived much attention from engineersÑ T straightforward. The weapon con- and hills.Ó The most powerful hybrid indeed, the very word ÒengineeringÓ is sisted of a beam that pivoted around machines could launch shot about three intimately related to them. In Latin and an axle that divided the beam into a to six times as heavy as that of the most the European vernaculars, a common long and short arm. The longer arm ter- commonly used large catapults. In ad- term for trebuchet was ÒengineÓ (from minated in a cup or sling for hurling the dition, they could discharge signiÞcant- ingenium, Òan ingenious contrivanceÓ), missile, and the shorter one in an at- ly more missiles in a given time. and those who designed, made and tachment for pulling ropes or a coun- Counterweight machines went much used them were called ingeniators. terweight. When the device was posi- further. The box for the weight might Engineers modiÞed the early designs tioned for launch, the short arm was be the size of a peasantÕs hut and con- to increase range by extracting the most aloft; when the beam was released, the tain tens of thousands of kilograms. The possible energy from the falling counterweight and to increase accuracy by minimizing recoil. The Þrst diÝerence between counterweight machines and their traction forebears is that the sling Hinged counterweight HINGED on the end of the arm is much longer. COUNTERWEIGHT machines added yet another This change aÝects performance dra- increment to the range by im- matically by increasing the eÝective proving the efficiency with length of the throwing arm. It also which the trebuchet converted opens the way for a series of additional gravitational energy to projec- improvements by making the angle at tile motion. The center of grav- which the missile is released largely in- ity of the weight fell straight dependent of the angle of the arm. By down during the first phase of varying the length of the sling ropes, acceleration; as the hinge engineers could ensure that shot left straightened, the rotation of the machine at an angle of about 45 the weight around its center of degrees to the vertical, which produces gravity added to the energy the longest trajectory. transferred. Continued rota- At the same time, so that more of the tion helped to slow the beam weightÕs potential energy converts to as the projectile was released, motion, the sling should open only reducing strain on the mecha- when the arm has reached an approxi- nism. The smoothness of the mately vertical position (with the coun- trebuchet’s action meant it did terweight near the bottom of its travel). not have to be repositioned af- Observations of the trebuchet may ter each shot and so could dis- have aided the emergence of important charge more missiles in a giv- medieval insights into the forces asso- en time. HINGED AND PROPPED ciated with moving bodies. COUNTERWEIGHT Swinging Free

he next crucial innovation was the Propped counterweights development of the hinged coun- allowed engineers to squeeze T terweight. During the cocking process, even more energy out of the the boxes of hinged counterweight ma- counterweight. By propping chines hang directly below the hinge, at up the counterweight at an an- an angle to the arm; when the arm of gle before firing, they gave it the trebuchet is released, the hinge slightly farther to fall. This in- straightens out. As a result of this mo- novation also increased the tion, the counterweightÕs distance from distance between the center of the pivot point, and thus its mechanical gravity of the counterweight advantage, varies throughout the cycle. and the pivot around which The hinge signiÞcantly increases the the trebuchet beam rotated. amount of energy that can be delivered —Vernard Foley through the beam to the projectile. Me-

JARED SCHNEIDMAN DESIGN dieval engineers observed that hinged

Copyright 1995 Scientific American, Inc. SCIENTIFIC AMERICAN July 1995 69 CAIRO CITADEL (top) was remodeled at the turn of the 13th century to accommodate the most powerful trebuchets then in use, the counterweight machines. The earlier wall, with its small, half-round towers ( foreground of picture, blue circles on plan), was augmented by a series of much more massive towers (red ) that supported counterweight machines used to prevent enemy ar- ) H

G tillery from getting within I range. An illustration from H S An Elegant Book on Treb- R E AUL E. CHEVEDDEN uchets (bottom left ) shows T E both a counterweight treb- M 5 uchet and a traction ma- . 8 TESY OF P chine mounted on the top ( S

COUR of a tower. F I L

OLD TOWERS K NEWER TOWERS C

100 METERS IAN WORPOLE. SOURCE: K.A.C. CRESWELL

counterweight machines, all else being The much gentler release of the treb- equal, would throw their projectiles far- uchet meant that engineers did not ther than would Þxed-weight ones. Our have to reposition the frame between computer simulations indicate that shots and so could shoot more rapidly hinged counterweight machines deliv- and accurately. A machine of medium ered about 70 percent of their energy to size built by the Museum of Falsters the projectile. They lose some energy Minder in Denmark has proved capable after the hinge has opened fully, when of grouping its shots, at a range of 180 the beam begins to pull the counter- meters, within a six-meter square. weight sideways. Although it exacts a small cost, this Capturing the TrebuchetÕs Lessons swinging of the counterweight has a signiÞcant braking eÝect on the rotat- ater engineers attempted to capture ing beam. Together with the transfer of L the great power that trebuchets rep- energy to the sling as it lifts oÝ and resented. Some of these eÝorts are turns about the beam, the braking can made visible in historical records by the bring the beam nearly to a stop as it proliferation of counterweight boxes in comes upright. The deceleration eases the form of the mathematical curve Istanbul the strain on the machineÕs framework called the saltcellar, or salinon. The just as the missile departs. As a result, counterweight boxes of the more elab- the frame is less likely to slide or orate trebuchets took this shape be- bounce. Some pieces of classical-era ar- cause it concentrated the mass at the ALACE MUSEUM tillery, such as the onager, were notori- farthest distance from the hinge and ous for bucking and had to be mount- also reduced the clearance necessary OPKAPI P

T ed on special compressible platforms. between the counterweight and the

70 SCIENTIFIC AMERICAN July 1995 Copyright 1995 Scientific American, Inc. frame. The same form reap- leverage of its arm, may have peared on later machines that spurred JordanusÕs related at- incorporated pendulums, such tempts to analyze the equilibri- as pendulum-driven saws and um of bent levers and to em- other tools. phasize that it was the horizon- Most attempts to extend the Göttingen tal distance between the mass Y trebuchetÕs principles failed be- on a lever arm and its fulcrum cause the counterweightÕs pow- that determined the work it er could not be harnessed eÛ- could do. Observations of the ciently. Success came only in diÝering distances to which timekeeping, where it was not Þxed and hinged counterweight the trebuchetÕs great force but machines could throw their

rather its regular motion that TE AND UNIVERSITY LIBRAR stones may have helped Jor- A engineers sought. Pendulums danus in his pioneering efforts were a dramatic step forward in to define the concept of work, accuracy from earlier controller or force times distance. mechanisms. JordanusÕs observations are

Although the pendulum is LOWER SAXONY ST usually studied as an example usually associated with the COUNTERWEIGHT TREBUCHET was a mainstay of me- of pure physics, based on the time of Galileo and Christiaan dieval artillery. This illustration from Conrad KyeserÕs teachings of earlier natural phi- Huygens, evidence for pendu- Bellifortis shows the dimensions of the main beam (46 losophers, such as Archimedes. lum controllers can be traced feet for the long arm, eight for the short) and some of The closeness of his mechanics back to a family of Italian its other parts. The text, left incomplete at KyeserÕs to trebuchet function, however, clockmakers to whom Leonar- death in 1405, does not describe the machine in detail. suggests that engineering prac- do da Vinci was close. Indeed, tice may have stimulated theory. da Vinci explicitly says some of his de- force. Jordanus held that for equal dis- Closing the circle, Galileo later incorpo- signs can be used for telling time. His tances traveled, a weight was Òheavier,Ó rated such Jordanian ideas as virtual drawings include a hinge between the or more capable of doing work, when its displacement, virtual work and the anal- pendulum shaft and bob, just as ad- line of descent was vertical rather than ysis of inclined planes to support such vanced trebuchets hinged their coun- oblique. In particular, he compared cas- newer mechanics as his famous analy- terweights, and show notable formal es in which the descents were linear sis of the trajectory of cannon shot. resemblances to Þxed counterweight with those that followed arcs. Eventual- GalileoÕs theoretical innovations came machines as well. In the case of earlier ly this understanding led to the notion only after the replacement of trebuchets clockwork, there is a marked similarity that work is proportional to weight and by cannon, a process that took nearly both in form and in motion between vertical distance of descent, no matter two centuries and was not fully accom- the saltcellar counterweight and a what path is taken. plished until metallic shot replaced speed controller called the strob. The The connection is clear. Engineers stones. The last instance of trebuchet strob oscillates about its shaft just as knew that machines with hinged coun- use comes from the New World, at the the counterweight does before quieting terweights, in which the weight de- siege of Tenochtitl‡n (Mexico City) in down at the end of a launch. scends essentially straight down dur- 1521. As ammunition was running crit- Trebuchets also appear to have ing the Þrst, crucial part of the launch ically low, CortŽs eagerly accepted a played a role in the greatest single me- cycle, would throw stones farther than proposal to build a trebuchet. The ma- dieval advance in physical science, the would their Þxed counterweight equiv- chine took several days to build, and at innovations in theoretical mechanics alents, in which the mass travels in a the Þrst launch the stone went straight associated with Jordanus of Nemore. curve. up, only to return and smash it. In view The key to JordanusÕs contribution is Other aspects of JordanusÕs work of the tremendous power of these de- his concept of positional gravity, a re- may show military connections as well. vices, and the Þnesse required to make vival in the Middle Ages of the idea of a The suspension of the hinged counter- them function properly, would-be repli- motion vector, or the directedness of a weight, with the constantly changing cators should take careful note.

The Authors Further Reading

PAUL E. CHEVEDDEN, LES EIGENBROD, VERNARD FOLEY and TREBUCHETS. Donald R. Hill in Viator, Vol. 4, pages 99Ð115; 1973. WERNER SOEDEL combine engineering and history in their CHINAÕS TREBUCHETS, MANNED AND COUNTERWEIGHTED. Joseph Need- studies of the trebuchet. Chevedden, a historian specializing in ham in On Pre-Modern Technology and Science: Studies in Honor of Lynn premodern siege tactics and fortiÞcations, teaches at Salem White, Jr. Edited by Bert S. Hall and Delno C. West. Undena Publications, State College in Massachusetts. He received his Ph.D. from the 1976. University of California, Los Angeles, in 1986. Eigenbrod, an as- BESSON, DA VINCI, AND THE EVOLUTION OF THE PENDULUM: SOME FIND- sociate professor of mechanical engineering technology at Pur- INGS AND OBSERVATIONS. Vernard Foley, Darlene Sedlock, Carole Widule due University, teaches statics, dynamics and Þnite-element and David Ellis in History and Technology, Vol. 6, No. 1, pages 1Ð43; analysis. He spent 24 years in industry before going to Purdue. 1988. Foley, an associate professor at Purdue, specializes in the his- ARTILLERY IN LATE ANTIQUITY: PRELUDE TO THE MIDDLE AGES. Paul E. tory of technology and science. This is his Þfth article for Sci- Chevedden in The Medieval City under Siege. Edited by Ivy Corfis and entiÞc American. Soedel is a professor of mechanical engineer- Michael Wolfe. Boydell & Brewer, 1995. ing at Purdue, with a strong interest in mathematical models SCIENCE AND CIVILIZATION IN CHINA, Vol. 5: CHEMISTRY AND CHEMICAL and simulations of machinery. He reports that his idea of a TECHNOLOGY, Part 6: MILITARY TECHNOLOGY: MISSILES AND SIEGES. Jo- good time is to sit in the garden and read history books. seph Needham and Robin D. S. Yates. Cambridge University Press, 1995.