Encyclopedia of Renaissance Philosophy

Living Edition
| Editors: Marco Sgarbi

Ballistics in Renaissance Science

  • Patrick BrughEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02848-4_902-1


This entry discusses the historical legacy in innovations of ballistics as they relate to warfare in Europe between 1300 and 1700. It primarily deals with the problems of smoothbore gunpowder weapons (both artillery and small arms) and the ways in which commanders and artillerists adjusted their strategies and tactics to account for the limitations of accuracy and unreliability of these weapons. Also discussed are modern comparative studies of early modern gunpowder small arms and early modern scientific and mathematical studies of the trajectory of gunpowder weapons.


Gunpowder Weapons Early Modern Modern Comparative Studies Vegetius Militari 
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Definition of Ballistics and Importance for Early Modern Warfare

Ballistics is the study of the flight of projectiles, most frequently associated with the flight of missile weapons, artillery ordinance, and bullets. The bulk of our knowledge about the ballistic properties of early modern arms comes from historical resources such as battlefield reports and military treatises of the early modern period, eighteenth- and nineteen-century tests of artillery, and some contemporary recreations using both manufactured reproductions and original artifacts. In particular, thanks to debate surrounding the impact of gunpowder warfare on European society, modern scholars have looked closely at the physics of smoothbore weaponry. Among the challenges to study accurately the ballistics of early modern weapons are the unreliability and lack of technical detail in early modern and late medieval sources, the impossibility of reproducing battlefield conditions, and the chemical and metallurgical differences between weapons and combustibles with different geographical and historical origins. Strictly speaking, the majority of scientific knowledge about ballistics was created centuries after the more practical considerations of warfare brought weapons such as guns, catapults, and crossbows to the battlefield.

Heritage and Rupture with Tradition: Vegetius’s Legacy in the Age of Gunpowder Weapons

The bulk of the written record of ballistic studies in the middle ages stems from interactions with the military treatise De re militari by Flavius Vegetius Renatus (fl. fourth century C.E.), more commonly known as Vegetius. Vegetius’s work was heavily translated and summarized by early modern military theorists, among others by Christine de Pizan in her Fais d’armes et de chevalerie (ca. 1410), Conrad Kyeser’s Bellifortis (ca. 1405), and even later Leonhard Fronsperger in his Kriegsbuch (1573). Vegetius’s mark on medieval and early modern siegecraft and preparations for war should not be understated, since even today some 150 manuscripts of his De re militari dating from the tenth to fifteenth centuries survive in various languages. Although his text was written centuries before the advent of gunpowder warfare, its recommendations are passed along almost unchallenged save the addition of cannons and gunpowder to the list of materials needed for war next to trebuchets, mantelets, and other siege machines. Gunpowder weapons, therefore, became another – increasingly important – tool in the military commander’s kit of ballistic weaponry. Due to the early ineffectiveness, burden, and unreliability of gunpowder weapons to make decisive victories in all but a handful of military conflicts, versions of Roman missile weapons, of which many were passed down by Vegetius, remained an operative part of the manuals of war written well into the sixteenth and early seventeenth centuries.

Innovative and Original Aspects: Smoothbore Ballistics and Early Modern Theories of Ballistic Flight

The Magnus effect (1852) and Bernoulli’s principle (1738) have helped to explain the inaccuracy of smoothbore ballistics in retrospect, but the operators of early modern firearms were more interested in developing battlefield tactics for overcoming these shortfalls than explaining them. Since smoothbore weapons fired rounded shot from unrifled gun barrels, slight imperfections in the shot or the barrel could send the shot spinning on an axis, giving it unpredictable angular momentum. The effect of this spin, as explained by Gustav Magnus and discovered in experiments recorded by Benjamin Robins in his New Principles of Gunnery (1742), resulted in deviations from several inches to several feet from the original target depending on its distance. Since musketballs (and cannonballs) could miss a target by a wide margin when mounted on a fixed position and fired under ideal conditions, it is not hard to imagine how far flung a bullet could fly in the havoc of battle.

Some early modern mathematicians and scientists, in particular Niccolò Fontana Tartaglia (d. 1557) in his work Nova scientia (1537), did try to deal with the mechanics of trajectory and distance, by applying different forms of reasoning such as geometrical, Archimedean, and algebraic approaches to the trajectory of ballistical objects. Tartaglia’s goal, as he states in the opening of his work, was to solve the “bombardier’s challenge” and determine the proper angle of a shot to create the maximum range of a cannon. Despite the fact that he claimed to pull from both observed and theoretical physics and geometry, Tartaglia’s work does not account for the parabolic motion of a fired object, a mechanical fact that he would have encountered in Archimedes’ Quadrature of the Parabola (third century B.C.), which he seems to have read and whose writer he cites as central to his own work (Ekholm 2010: 196). Based on his ideal cannon angle of 45 degrees, his diagrams depict an object flying upward at a 45-degree angle in a straight line, then making a slightly circular descent, and finally falling again to earth in a perfectly straight line perpendicular to the ground. Tartaglia’s patchwork method of calculating the maximum distance of a shot had little grounding in the actual mechanics or practical application of ballistics, but it did arrive at a moment in which the debate over the relationship between natural science and theoretical mathematical proofs was beginning to shape the development of renaissance scientific method in the Aristotelian traditions.

It would be another century before Galileo published his dialogues on Two New Sciences (1638), which would address the motion of projectiles, in particular those launched from firearms. In contrast to his scientific worldview, Galileo depicted the force behind firearms as “supernatural” and thus deserving of a differentiated approach from other projectiles. One consequence of “the enormous momentum of these violent shots” from firearms helps to explain the straight trajectory that Tartaglia had assumed a century earlier, because, as Galileo points out in “The Motion of Projectiles, Theorem I, Proposition I,” the “beginning of the parabola” may be flatter and less curved than at the end, but “this is a matter of small consequence in practical operations, the main one of which is the preparation of a table of ranges for shots of high elevation, giving the distance attained by the ball as a function of the angle of elevation” (Galileo 1638). Perhaps notably above, and found also in his many other caveats placed throughout the dialogue in which he considers the flight of projectiles, Galileo points out that the number of factors that could affect the accuracy and speed of a cannon shot in real life are beyond his ability to calculate abstractly. More useful to the bombardier, it seemed, are tables that carefully lay out charge weights, shot weights, firing angles, and distances for consideration in practical matters of war.

Galileo was not alone in believing that practice with firearms seemed to be an important element in gunpowder warfare. Even though Tartaglia and Galileo had tried to reason the theoretical trajectories of cannonballs, and others such as Ufano, Pizan, and Fronsperger had compiled and recorded tables and practical lessons for consideration, the operator of small arms and artillery alike had to be aware that technical limitations and a lack of standardization made practice with the actual equipment a necessary part of military training. The weapons manufacturer, meanwhile, should strive to increase standardization in order to render firing outcomes more predictable. From England to Sweden to the Hapsburg and Ottoman Empires, firearms manufacturers did indeed begin standardizing their weaponry in the sixteenth and seventeenth centuries. Nations also slowly began to standardize their militaries to account for gunpowder ballistics. At the end of the sixteenth century, in fact, around the same time that Galileo was teaching the concepts of physics that he would later commit to writing in the Two New Sciences, the idea of drilling soldiers with their weapons in very careful and exact ways was innovated by Maurice of Orange and illustrated in a bound series of images by Jacob de Gheyn. Whether firing a pistol or a gigantic bombard, the soldier on the battlefield needed to marry technical knowledge and disciplined movements to Galileo’s scientific theory to overcome the number of complicating physical, psychological, strategic, and technical factors that could impact the ballistical function of his guns.

SMALL ARMS: Modern efforts to understand the ballistics of smoothbore small arms on the battlefields of Europe from the 1400s to 1700s turn to three questions with an eye to gunpowder weaponry – “How fast did the bullets travel? How accurate was smoothbore gunfire? And how much damage did such bullets inflict on their target?” (Hall 1997: 135). In terms of speed, historical comparisons of modern shoulder and side arms show that bullets fired from early modern weapons have supersonic muzzle velocities about half that of modern assault rifles but faster than most standard modern handguns. As discussed above, the accuracy of these weapons was typically poor, despite the fact that gun makers as early as the fifteenth century were familiar with the idea of rifling, a trick of physics that they had learned from the fletchers of arrows. Although it (sometimes) led to greater accuracy, rifling was not typically added to battlefield firearms because it reduced the rate of fire and became easily clogged with gunpowder residue. Thus, a shot fired from typical musket or handgun could easily miss its target by several feet. Modern tests of smoothbore weapons have shown that there was a 50–50 chance of hitting a man-sized target at 100 m under ideal conditions. Finally, tests conducted in Austria in the late 1980s using period weapons and armor showed that smoothbore small arms created wound cavities at a short range that were two to three times larger than wound cavities made by modern assault weapons. When used against 3 mm plate armor at a distance of 8.5–9 m, the bullets would fragment, badly wounding or at least seriously bruising the target, but not inflicting immediately mortal damage. Taken together, these results showed that typical early modern European guns were tremendously dangerous at a short range, but quickly lost their effectiveness both in accuracy and inflicted damage at greater distances.

ARTILLERY: Cannons were first used as siege weapons, another kind of catapult to besiege towns and knock down walls. In fifteenth-century military treatises and fictional war literature, which drew heavily on Vegetius, such as Heinrich Wittenwiler’s Der Ring (ca. 1410), cannons and trebuchets were given similar importance in terms of their means of delivering blows to a target. The earliest bombard cannons of the fourteenth century were little more than massive metal tubes stuffed with gunpowder and huge stones to be flung in the general direction of a defensive walls, fortifications, and towers. Accuracy was of less importance than force. Through the 1300s, these weapons were also incredibly difficult to transport, and thus to place, and therefore were of little use to field tactics. Only under the leadership of Jan Zizka, the Hussite Rebels of the 1420s demonstrated the potential value of gunpowder weapons in field warfare by using medium to large caliber Wagenburg-mounted artillery to fire on charging knights and infantry. Even when artillery grew more mobile and accurate in the fifteenth and sixteenth centuries, the value of cannons for siege warfare was the ability to constantly barrage a large target area with the general idea of inflicting damage. As with small arms, field artillery’s inaccuracy required high rates of fire and oblique angles to the targets, which had to be slow and large, such as massed formations of marching men. There is significant evidence in European war treatises of the fifteenth, sixteenth, and seventeenth centuries that artillerists were constantly experimenting with angles of attack and defense, the weight and composition of gunpowder charges, design of the ordinance, and the tools used to determine distance of targets in order to add some degree of accuracy to a relatively inaccurate ballistic tool.

Impact and Legacy

Thanks to the inaccuracy and unreliability of early modern firearms, tacticians and commanders of the sixteenth and seventeenth (even eighteenth) centuries took a stochastic approach to gunpowder weapons for both the infantry and artillery. Infantry and heavy cavalry units, especially in the late 1500s, developed tactics and drills like the countermarch, the caraçol, and weapons drill that sought to sustain high rates of fire on the battlefield in order to increase the chances of hitting targets. Thus, soldiers were grouped carefully together in rows that could fire past each other, were trained to mechanize their movements to improve efficiency, and were deployed to maximize the surface area of the target. Gunpowder artillery was also used widely from the late fourteenth century on but required continuous technical and tactical tinkering to make it more effective both in siege, field, and sea warfare. By the mid-sixteenth century, artillery established itself as a necessary division of all large-scale armies, and the challenges of smoothbore gunpowder ballistics had become mandatory considerations in the training and deployment of both infantry and cavalry units.



Primary Literature

  1. Anonymous. Feuerwerkbuch. Munich. Bayerische Staatsbibiliothek. Cod. germ. 600. Ca. 1400–1420Google Scholar
  2. Fronsperger, Leonhard. 1573. Kriegsbuch. Vol. 3. Frankfurt: Feyerabend.Google Scholar
  3. Galilei, Galileo. 1638. Discorsi E Dimonstrazioni Matematiche: intorno à due nuoue scineze Attenenti alla Mecanica & i Movimenti Locali. Leiden: Elsevirius.Google Scholar

Secondary Literature

  1. Ekholm, Karin. 2010. Tartaglia’s ragioni: A maestro d’abaco’s mixed approach to the bombardier’s problem. The British Journal for the History of Science 43 (2): 181–207.CrossRefGoogle Scholar
  2. Hall, Bert. 1997. Weapons and warfare in renaissance Europe. Baltimore: Johns Hopkins UP.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Loyola University MarylandBaltimoreUSA

Section editors and affiliations

  • Matteo Valleriani
    • 1
  1. 1.Max Planck Institute for the History of ScienceBerlinGermany