Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics

Chapter 1. Before Gunpowder

1 Before Gunpowder Projectile weapons are as old as our species. Before gunpowder, weapons began and ended with the rock; Stone Age man would throw a small one by hand, whereas medieval man would launch a large one from a sophisticated counterpoise siege engine such as a trebuchet. Between these two extremes, other projectiles appeared: sling stones, arrows, throwing spears, and crossbow bolts. Ballistics enters into the trajectories of all these projectiles—and of musket balls, bullets, and shells—even before they leave the weapon that launched them. A projectile weapon, be it a bow, a trebuchet, or a Winchester rifle, is a machine designed to supply energy to its projectile. More specifically, it is designed to send the projectile at high speed in a very particular direction. Internal ballistics describes the process of generating the desired velocity;1 external ballistics describes how a projectile flies through the air. In these first three chapters I will be describing internal ballistics and will begin here with the internal ballistics of pre-gunpowder weapons. ONE HAND Throwing a Rock About as simple as it gets, you might suppose, and yet the biomechanics of rock throwing is far from trivial. The throwing arm is not a simple stiff lever that rotates to generate hand speed—though we will model it as such here. Ifwe observe the throwing arm with more care, we see that it moves more like a whiplash, generating great speed at the thin end. Also, when you throw a rock (carefully chosen for shape and weight), you add speed 1. Speed describes how fast; velocity describes how fast and in what direction. People often refer to muzzle velocity when they mean muzzle speed. S BANG! Internal Ballistics by arching your body forward at just the right moment, and add force by pushing with your trailing leg.2 All this action (generated with barely a thought) serves to launch a rock perhaps 50 or 60 yards. Wewill learn later how maximum range relates to launch velocity: that is the subject of external ballistics. For now I will simply state that, to be thrown 50 or 60 yards, the rock must leave your hand with a speed around 75 feet per second (ft/s), angled upwards at about 45°. Suppose we were to approximate the action of a throwing arm by the rotation of a rigid rod about one end. We know that this is only a rough model (the more sophisticated model of Cross 2003 models the arm as a hinged rod), but it will suffice for my purposes. A stiff arm that is 2 feet long needs to rotate at a rate of five cycles per second (5 Hertz, or 5 Hz) to achieve such a range. In technical note 1, I show that a real arm (hinged at the elbow) can do better than this stiff arm. A hinged arm creates a whiplash effect that increases launch speed by about a third for the simple model of technical note 1—and probably by more for a real arm. This is why we throw rocks or baseballs with elbow initially bent. In cricket, the pitcher (called a "bowler") is obliged to keep his throwing arm straight, reducing the ball speed. However, he gets some of this speed back because, unlike a baseball pitcher, he is allowed to run up to where he throws the ball, instead of standing still. Throwing a Javelin Olympic javelin throwers also run up to the launch point, to increase their distance. In this action, modern javelin throwers are imitating historical antecedents (fig.1.1) who threw javelins or other throwing spears (such as the Zulus' assegai). A javelin is heavier than a sling stone, and so the point can cause damage to an enemy even if he is armored. Javelin throwers of classical history were often skirmishers who peppered the ranks of enemy heavy infantry, softening them up just before their own heavy infantry attacked . The Roman javelin (the pilum) had a characteristically long tip made of soft metal, with a barbed end. The metal would bend when it struck an enemy shield, so that the pilum could not be thrown back. If it penetrated the shield, it could not be easily removed, so the enemy soldier 2. The physiology of throwing is described by Chowdhary and Challis (2001); a physical model is provided by Cross (2003). Before Gunpowder 9 Figure 1.1...