The Physics of War (24 page)

In most cases the spiral rifling is encountered by the shell almost immediately after it leaves the chamber; in some cases, however, the spin is increased gradually. This is referred to as gain-twist. In this case there is no rifling from the chamber to the “throat” of the gun. When the bullet first leaves its cartridge, therefore, it is not spinning. However, it encounters rifling after it has traveled a short distance, and in most cases the rifling increases its twist rate gradually. This allows the projectile to spread out its increase in torque over a larger distance.

The number of grooves in the barrel can vary, as can their shape and depth. Furthermore, the twist direction can be either clockwise or counterclockwise, and the twist rate can vary depending on the bullet shape, weight, and length. In breach-loaded guns the projectile is placed in the chamber. When it is fired, “seating” occurs in the throat. The throat is usually slightly larger than the bullet, so when the bullet is fired it expands under the pressure of the gas behind it until its diameter matches that of the interior of the barrel. The enlarged bullet then travels down the throat to the rifling, where it is “ingrained”; in other words, grooves are cut into it. As a result of these grooves, the bullet begins to spin.

The twist rate given to a particular bullet is critical. First of all, it has to be sufficient to stabilize the bullet, but it should be no greater than this, and the ideal twist rate depends on the bullet's weight, length, and overall shape. Twist rates can vary considerably; older guns, for example, frequently had twist rates as low as one in seventy inches. More modern guns have much higher twist rates, such as one in twelve inches, or even one in ten inches. In general, rifles have much greater twist rates than pistols. The twist rate (T) is frequently expressed as T = L/D, where L is the length for one revolution, and D is the barrel diameter.

If the twist rate is too small, the bullet will yaw (move back and forth along the direction of flight), and if this happens, it will eventually begin to tumble and
lose its accuracy. A twist rate that is too low can also cause a bullet to precess around its center of gravity. As we saw earlier, this is a motion you can easily see in a gyroscope.

On the other hand, the twist rate can also be too high. In many spinning objects there is an outside force usually called the centrifugal force (this is actually an erroneous term), and the faster the spin, the greater this force. Countering it is a cohesive force that is holding the bullet together. When the centrifugal force becomes greater than the cohesive force, the shell disintegrates and flies apart. In theory, a bullet can have a spin rate up to about three hundred thousand revolutions per minute. Most bullets, however, have spin rates much smaller than this, typically in the range twenty to thirty thousand revolutions per minute.

TERMINAL BALLISTICS

Terminal ballistics is a study of what happens to the bullet or projectile after it hits the target. It's obvious that its velocity will change rapidly. It may be stopped by the target, or it may pass through it. There are two ways in physics to deal with this case; they are referred to as the force or momentum picture, and the energy picture. In the force picture we deal with forces (or momenta), so we use Newton's third law, which says that for every action force there is an equal and opposite reaction force. In this case we are concerned with the force applied to the target, or the momentum delivered to it. In the other view, the energy picture, we are concerned with the kinetic, potential, and any other types of energy that might be involved. In most cases the energy picture is the easier of the two to use, and the major reason for this is that conservation of energy states that energy cannot be created nor destroyed; it can only be changed from one type into another. So for a given problem all you have to do is look at each type of energy involved to make sure that everything adds up. In the case of a bullet fired from a gun the chemical energy of the bullet is transformed immediately to gas pressure and heat energy in the barrel. This energy is then transferred to the kinetic energy of the bullet's motion plus sound energy. And some energy is lost to air resistance. It's the kinetic energy that the bullet finally has just before it hits a target that is important.
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Several things can happen when a bullet hits a target. If the bullet stops within the target, it transfers all its kinetic energy to the target, and at the same time it transfers its momentum to the target. It may also pass through the target and emerge at the other side. In this case the bullet transfers some of its kinetic energy and some of its momentum to the target. Finally, it is possible that in
the case of a well-armored target, the bullet could bounce back. In this case it delivers all its kinetic energy to the target, but the target actually receives more momentum than the bullet initially had. Because of this, terms such as “knockdown power” and “stopping power,” which are frequently used in terminal ballistics, are actually meaningless. Knockdown power refers to the momentum transfer only, but in reality it is kinetic energy transfer that does the real damage. What happens to a target depends on the details of the collision and which of the above three cases applies, so you can't say a certain type of ammunition (or gun) has a certain knockdown power.

One of the major issues related to terminal ballistics is the penetration of the bullet. A measure of it is given by the impact depth of the bullet, which is the depth the bullet reaches before it is stopped. In some cases bullets are designed to achieve maximum penetration, in others they are designed to do maximum damage. Bullet design is quite different in the two cases. Bullets designed for maximum penetration are made so that they do not deform on impact (or at least, deform as little as possible). They are usually made of lead that is covered with a layer of copper, brass, or steel. The jacket usually covers only the front region of the bullet. In particular, armor-piercing bullets for small arms are usually made of copper jacketed with steel. For larger artillery such as tank guns, tungsten, aluminum, and magnesium are usually used in the shells.

Although some bullets are made to expand when they hit the target, this type of ammunition is now prohibited in warfare according to the Hague Convention of 1899, Declaration III.

Soon after the first airplanes were invented they became important weapons of war. Early on they were used mostly for observation and reconnaissance, but it soon became obvious that they could play a much more important role. They could be used to release bombs on the enemy. It was a mere ten years after the Wright brothers flew their first airplane that the First World War began, but by then airplanes had already been used in warfare. In 1911 the Italians used an airplane to drop grenades on the Turks in Libya. And as it became obvious that airplanes would be useful in war, the technology associated with them advanced rapidly, and soon after World War I started they began to be used extensively by both sides.

DISCOVERIES THAT LED TO THE AIRPLANE

Although the most eventful day in airplane history was December 17, 1903, when the Wright brothers made their first flight in a power-driven, heavier-than-air machine, it was not the first attempt that humans had made to fly. Many important developments led up to that day, and I will begin with them.

We saw earlier the Leonardo da Vinci was obsessed with flight. Not only did he observe birds in flight for hundreds of hours, but he also studied the flow of both air and water around objects of many different shapes under various conditions. He noticed that water sped up as it moved around a rock in a stream, and he assumed that air did the same thing. Much of his effort went into trying to develop a pair of wings, like those of a bird, which a man could use to fly. He wasn't successful, but he did design a helicopter and a parachute, and both of these designs would have worked. Furthermore, he stated that the fluid dynamics are the same for an object moving through a fluid as they are for a fluid moving past the object in the same way. And finally, he also made an extensive study of drag, the frictional force an object experiences when moving through a fluid.

It was Galileo, however, who showed that the drag exerted on a body moving through a fluid is directly proportional to the density of the fluid, where density is mass per unit volume. The French scientist Edme Mariotte took this a step further in 1673 when he showed that drag is also proportional to the velocity of the object squared (v
²
).

One of the most significant discoveries in relation to aeronautics, however, came in 1738 when Daniel Bernoulli of Holland showed that in a flowing fluid the pressure decreases as the velocity of the fluid increases. And of course this applies to all fluids, including air. It eventually became known as Bernoulli's principle. About the same time, the French chemist Henri Pitot demonstrated a device he called the pitot tube in which the change of velocity could easily be measured as the diameter of the tube changed.
¹

A further advance in the understanding of drag came in 1759 when the English engineer John Smeaton invented a device for measuring the drag produced on a paddlewheel moving through air. He showed that D = ksv
²
, where D is drag, s is surface area, v is the velocity of the paddle, and k is a constant that became known as Smeaton's coefficient.

One of the most important people in the history of aeronautics, however, was the engineer George Cayley of England. He is usually considered to be the first person to understand most of the basic underlying principles and forces involved in flight, and because of this he has frequently been referred to as the father of aerodynamics. In particular, he discovered and identified the four major forces associated with flight: lift, weight, thrust, and drag. We will look at each of them in detail later. He also showed that “cambered” or curved wings produced the best lift. His three-part treatise titled “On Aerial Navigation,” which was published in 1809 and 1810, was the most important early work on airplane flight. Most of the basic ideas associated with lift, drag, and thrust are discussed in it.

Although Cayley designed, made, and flew many gliders, it is
Otto Lilienthal of Germany who is usually referred to as the “glider king.” He made several important advances in hang gliders, and over his lifetime he made over two thousand flights in gliders of his own design. In August 1896, however, while making a flight, his glider stalled. He tried to regain control by adjusting the position of his body, but he failed. The glider fell to the earth from a height of fifty feet. He was conscious when help reached him, but he died soon thereafter.

The first American to make important contributions to aviation was Octave Chanute, a civil engineer from Chicago, Illinois. He published the book
Progress in Flying Machines
in 1894, which was the most complete survey of the research on heavier-than-air aviation up to that time. And although he
designed many gliders and invented the “strut-wire” braced wing, he never flew any of his gliders himself. He is perhaps best remembered for the interest and encouragement he gave to the Wright brothers. Indeed, he visited their camp near Kitty Hawk, North Carolina, in 1901, 1902, and 1903—the critical years in the development of their first airplane.

THE WRIGHT BROTHERS

Although many men made important contributions, the Wright brothers of Dayton, Ohio, are credited with designing and building the first engine-powered heavier-than-air craft to successfully carry a man on an airborne flight. This occurred on December 17, 1903. Their major contribution to aeronautics is usually considered to be their invention of the three-axis control, which enabled the pilot to maintain equilibrium and to steer the aircraft effectively.
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Orville and Wilbur Wright spent their early years in Dayton, Ohio. They were the two youngest of eight children, and according to most biographers their interest in flying was sparked at a young age when their father bought them a toy helicopter that was powered by a rubber band. Wilbur was four years older than Orville. Neither man completed high school, but they became interested in newspaper publishing after they built a printing press. They started with the
West Side News
and later published other newspapers.
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Orville Wright.

In 1892 they opened a bicycle shop for the sale and repair of bicycles. A few years later, in 1896, they began selling bicycles that they had built. It was during this time that the work of Otto Lilienthal of Germany came to their attention. Lilienthal had built and tested several gliders. His work inspired them, and they began to read about Cayley's and Canute's exciting exploits in the field, and by 1899 and they had begun their own experimentation. As the older brother, Wilbur was the leader of the team.

Wilbur Wright.

Over the preceding decades several different approaches had been used in various attempts to fly, but the Wright brothers decided the best approach was to leave power-driven flight until they had solved all the problems associated with gliding. In particular, they believed that the pilot should have complete control of the plane at all times, using a system for banking, turning, and changing altitude. They decided to design such a system before adding an engine to the craft. Early on they discovered “wing warping,” in which control lines were used to twist or warp the outer section of the wings so the plane could bank properly. Wing warping was controlled by four lines, set up so that the two wings work together. When the lift on one wing increased, the lift on the other wing would decrease.

When their glider was finally ready, they wrote to Canute, asking him where the best place was to test it. He suggested several places, but the one that interested them the most was Kitty Hawk, North Carolina. It had excellent breezes from the Atlantic that would be helpful, and it had soft sand to land on. They decided that it
would be ideal, and in the autumn of 1900 they traveled to Kitty Hawk with their glider. It was a “double-decker” with two wings, and the top of each wing had a camber (curvature). It had no tail, since they saw little need for a tail at that time.

Both manned and unmanned tests were made, but when the glider was unmanned extra weight was added to account for a pilot. Wilbur was the pilot in the manned flights; he stretched out on his stomach across the lower wing. In all cases the glider was only about ten feet above the ground, and it had tether lines attached to it. They were particularly interested in testing the wing-warping apparatus that they had attached to the glider. As it turned out, they were extremely pleased at how well it worked. Having used Smeaton's equation for calculating lift, however, they were disappointed that the lift appeared to be much less than that predicted by the equation. Nevertheless, they were generally happy with their results but knew that improvements were needed.
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First glider of the Wright brothers.

Over the following months they worked feverishly to build a new glider. It had a much larger wingspan, and improvements had been made to the wing-warping apparatus. This time they arrived at Kitty Hawk in July, and during July and August they made about one hundred flights varying in distance from twenty to four hundred feet. Everything appeared to go well, but again they were disappointed with the lift the glider gave. It was well below—only about one-third—the
value predicted by Smeaton's equation, and they began to wonder about the equation's accuracy.

One of the factors in the equation was a constant called Smeaton's constant. Its value had been worked out years earlier and had become the accepted value, but the Wright brothers were sure it was wrong, and there was only one way to prove it. They had to build a wind tunnel; and indeed, over the next year they built a wind tunnel in their bicycle shop. It was six feet long, and between October and December 1901 they tested two hundred different wing shapes, comparing their experimental results to the predictions of Smeaton's equation. And indeed they were right; Smeaton's constant was incorrect. Not only did they correct the equation, but they also learned a tremendous amount about wings. As Fred Howard, one of their biographers, said, “They were the most critical and fruitful aerodynamics experiments ever performed in so short a time with so few materials and at so little expense.”
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The tests also showed that longer, narrower wings were better than what they had been using.