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

Chapter 4. Short-Range Trajectories: Elementary Aerodynamics

4 Short-Range Trajectories Internal ballistics takes place in the gun barrel; transitional ballistics happens at the muzzle; and external ballistics covers the trajectory from near the gun barrel to the target. So far in this book we have covered the path of a projectile only for a few inches or feet—while it is in physical contact with the launcher, be it a human hand, a catapult sling, or a gun barrel. Most of the remainder of the book will cover the much greater distance of a projectile's airborne trajectory as it describes a graceful arc across the sky. During this phase, a projectile is acted on by the force of gravity and by the force of flowing air—producing aerodynamic drag and sometimes aerodynamic lift. The physics gets increasingly complex as range increases; I will carefully unpack the science of external ballistics over the next three chapters. TRANSITIONAL BALLISTICS First, though, there is a gap that must be covered, an awkward transition region in the trajectory of a gunpowder weapon projectile: the physical space that exists between the two regions covered by internal and external ballistics. For muscle-powered weapons such as the longbow or sling, there is no intermediate region; internal ballistics becomes external ballistics . Not so for gunpowder weapons. Transitional or intermediate ballistics seeks to explain the physics of this transition, as the projectile leaves the muzzle and enters the atmosphere. It is clear where, physically, internal ballistics ends: at the muzzle of our pistol or howitzer, at the instant that the projectile separates from the barrel. It is less clear where external ballistics takes over. For a millisecond or so after it leaves the gun barrel, propellant gas rushes past the projectile, freed from the barrel like gas from a popped champagne bottle. Propellant gas is usually traveling at supersonic speed; shock waves both precede and follow the projectile. eLEMENTARY aERODYNAMICS 78 WHIZZ! External Ballistics Figure 4.1. Ka-BOOM! A full broadside from the USS Iowa's nine 16-inch guns (and six 5-inch guns) displays the power of the blast on the water surface. Impressive—but to a ballistician this represents wasted energy. U.S. Navy photo. These shock waves can be very damaging to nearby objects—such as gun crews. Aerodynamic drag is not yet a factor that influences the projectile. In technical note 14,1provide a rough estimate of the physical extent of this awkward and very complicated transitional region by making the reasonable assumption that external ballistics takes over when the propellant gas pressure is reduced to ambient atmospheric pressure. When the projectile emerges from the muzzle, gas pressure is several hundred or thousand atmospheres; the energy of this gas is then dissipated through the air, as is shown dramatically in figure 4.1. Before dissipating, the gas adds a final boost to the projectile, which is now free of muzzle friction. It is important that the rear end of the bullet or shell be symmetric, and that the barrel end be symmetric, so that the blast does not cause the projectile to tumble or to deviate from its trajectory, as this would cause loss of range and accuracy. Along with gas, unburned propellant is ejected from the barrel, and this propellant ignites in the presence of atmospheric oxygen to produce a flash. Such flashes are undesirable in a military context, particularly for Short-Range Trajectories 79 ordnance, because they give away a gun battery's position. Flash sup pressors at the end of the gun barrel subdue the flash by causing the propellant gas flow to become turbulent. This turbulence reduces combustion efficiency and so reduces the size and brightness of the flash. UNDERSTANDING TRAJECTORY PHYSICS: A SLOW LEARNING PROCESS Since the invention of firearms, people have tried to learn about the shape of the projectile trajectory and understand the forces that define it. For 300 years after gunpowder weapons first appeared, it was thought that the trajectory of the projectile consisted of straight lines connected by circular arcs. In the middle of the sixteenth century the Italian mathematician Tartaglia proved that this could not be the case—that all trajectories must be curved—and that flatter trajectories resulted from projectileswith higher speeds. In the seventeenth century Galileo showed us that if we could ignore the effects of the air, trajectories were parabolic; and Newton showed us why this was the case (gravitational force). Newton...