The Physics of War

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The Physics of War Page 19

by Barry Parker


  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.4

  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.”5 The tests also showed that longer, narrower wings were better than what they had been using.

  With their new knowledge the Wright brothers eagerly began building a new glider. It had longer, narrower wings with a reduced camber. They also now realized that wing warping caused an additional drag at the wing tips, and they would have to take it into consideration. Finally, they also attached to their new model a tail with a rudder for steering. They soon discovered during the early tests, however, that the vertical rudder on the tail was important not just in turning, but also during banking turns and when leveling off after turns. They now had “three-axis control”: wing warping for rollover, forward elevator flaps for pitch (up-and-down motion), and a rear rudder for yaw (side to side motion). And between September and October 1902 they made about one thousand tests. They were now ready to add an engine to the glider to power it.

  What type of engine was best? It obviously had to be as light as possible, and because of this, they decided that it should be made of aluminum. They checked with several engine manufacturers, but none could produce the engine they wanted, so they decided to build it themselves. Fortunately, the shop mechanic in their bicycle shop was an expert on engines. They told him what they wanted, and within six weeks he had it completed. It was cast from aluminum, and as was common at the time, it had a very primitive fuel-injection system; the gasoline was gravity fed.

  The Flyer I, as they called it, had a wingspan of just over forty feet and weighed 605 pounds, and it had a twelve-horsepower engine. It was built of spruce, with muslin covers over the wings. The propeller was eight feet long and had been designed for maximum lift. After some thought they decided to use a “pusher” design with the propellers mounted behind the pilot so that they pushed the craft rather than pulled it.

  Top: 1901 model of Wright brothers’ glider.

  Bottom: 1903 model in which they made their first powered flight of twelve seconds.

  When they were finally ready, they took the craft to Kitty Hawk, or more exactly, a part of Kitty Hawk called Kill Devil Hills, which consisted of sand dunes up to one hundred feet high. They arrived at their camp in early December 1903. After a delay created by a broken propeller, they began their tests on December 14. Again there were problems, but they were quickly overcome; then came the historic day: December 17. The first attempt was made by Orville; it consisted of a flight of 120 feet in a time of twelve seconds. The next two flights covered a distance of 175 and 200 feet respectively. Wilbur and Orville alternated as pilots. For the first time in the history of the world, man had flown a power-driven plane over a respectable distance. The Wright brothers were ecstatic; they telegraphed their father telling him to inform the press. Surprisingly, the Dayton Journal refused to publish the story, stating that the flights were too short to be important. But news of the event was leaked to other newspapers, which quickly published a highly inaccurate story to the dismay of the Wright brothers. The problems were soon ironed out, but strangely, the story created very little public interest at first.

  The Wright brothers went on to build their Flyer II in 1904, and it was tested closer to home at an airfield about eight miles from Dayton. Without the “sea breezes” the takeoff was more difficult, so they built a weight-powered catapult to make takeoffs easier. The new airplane was more powerful, however, and they were soon flying it in circles. On September 20, 1904, they flew the first complete circle, but by December 1 they were covering almost three miles in four circles above the camp.

  In 1905 they built Flyer III. It had a major improvement: all three of the axes—pitch, roll, and yaw—now had their own independent controls. A flight of almost twenty-five miles was made during these trials.

  WHAT MAKES AN AIRPLANE FLY?

  Most people have some sort of idea of how and why an airplane flies, but few really understand it in detail. There is, in fact, a lot of misinformation in books about this question. Lift can come from a propeller, a jet, or a rocket, but for now we will talk only about propellers. There are three approaches to answering this question. The first is what is called the simple explanation, and it is ba
sed on Bernoulli's principle, which we discussed earlier. And of course there's the highly mathematical approach based on various aeronautical principles—the approach aeronautical engineers use to design aircrafts—which is well beyond the scope of this book. The third approach is what we'll call the physical explanation, which is based on physics. It can get slightly complicated, but we'll try to keep it as simple as possible. In any case, it is the most accurate explanation at this level. It is based on the Bernoulli principle, but it shows that there's much more to it than just this principle.6

  In this section I'll begin with the simplest approach because it's the easiest to understand. First of all, during the takeoff and landing of an airplane, and also when it is in flight, there are four forces acting on it: lift, weight, thrust, and drag. As the name implies, lift is a force that lifts the plane off the ground. It is created by the interaction between the wings and the air they pass through. According to Bernoulli's principle, the air pressure on the top of the wing decreases as the plane begins to move because the air traveling over the wing moves faster in comparison to the background air. The faster the plane moves, the greater the decrease in pressure upon the top of the wing. This creates a pressure difference between the top and bottom of the wing, which creates a net upward force.7

  The four forces on an airplane.

  Opposing lift is a force due to the weight of the airplane, namely gravity. During takeoff lift continues to build up as the upward force on the wing increases, and when it is finally greater than the weight of the airplane, liftoff occurs. In short, the plane leaves the ground.

  The third force, namely thrust, is the force that moves the plane forward. It can be generated by a propeller, a jet engine, or a rocket, but for now we will confine our analysis to propeller-generated thrust. The propeller is curved in such a way that when it spins it pushes air backward. It is very much like the wing in that an air-pressure differential is created, with lower air pressure on the front of the blade and higher air pressure behind it. This creates a thrust that moves the plane forward. But, again, there is a force opposing it. As the plane begins to move through the air there is friction between it and the air, and this friction is called drag. Again, thrust has to be greater than drag for the plane to move forward, as the two forces oppose one another. As most people know, drag can be minimized by streamlining the shape of the moving object. A “teardrop” shape is among the best for minimizing drag.

  If lift is greater than the weight of the airplane, and thrust is greater than drag, the airplane leaves the ground. So, basically an airplane flies because of the Bernoulli principle, which is the explanation given in most popular articles and books. But if you look carefully at this explanation, it's easy to see that it is not complete. Wings that have no camber (curve) also create lift, and if you calculate how much camber is needed for a small plane to lift off, you find that the distance over the top of the wing has to be 50 percent longer than the distance across the bottom. This looks like the wing shown in the diagram below, and we know that in most planes the distance across the top of the wing is only about 2 percent greater than the distance across the bottom.

  The simple explanation of lift using the Bernoulli principle.

  THE PHYSICAL, MORE EXACT EXPLANATION OF LIFT

  The simple explanation above has many problems. First, it relies on what is called the principle of equal transit times. This states that the section or volume of air that goes over the top wing converges and joins at the trailing edge with the section or volume that goes under the bottom. Wind tunnel experiments show that this is not the case. The volume of air that goes over the wing reaches the end of the wing before the bottom volume reaches it.

  Furthermore, the Bernoulli explanation ignores the fact that work is done by the lift. Lift obviously requires power and a force. And this relates to Newton's first law. As we saw earlier, Newton's first law states that a body at rest will remain at rest, and a body in motion will continue in a straight-line motion unless subjected to an external applied force. In the Bernoulli explanation there is no evidence of an external applied force. The streamlines above and below the wing are the same in this explanation. But in reality it's easy to see that there is a bend in the flow of the air; this means there is an acceleration, and therefore there must be a force acting on the wing (Newton's second law: F = ma).

  Let's look at this force. Newton's third law tells us that for every action there is an equal opposite reaction. It's easy to show that the action in this case is what the wing does to the air. The reaction is the lift generated as a result of this action. We can understand this better if we go back to Newton's second law. The variables in our problem include the force on the wing, which equals the mass of the air moving downward times the change in air velocity. This is the lift on the wing, and it is effectively the amount of air moved downward per second times the downward velocity of the air. So, to a large degree, it's the downward velocity of the air that gives the lift. I should also point out that the downward velocity behind the wing is called the downwash (it creates an increased pressure), and there is an upwash at the front of the wing that also creates increased pressure.

  The physical, more exact explanation of lift, showing positions of increased and reduced pressure.

  Something else the Bernoulli explanation ignores is the angle of attack. This is the angle between the wing (or a line through the center of the wing) and the oncoming air. It has a large effect on lift. As the angle of attack increases, the air is deflected through a larger angle and the vertical component of the velocity is increased. This causes a large increase in lift. Eventually, however, at an angle of about 15 degrees it maxes out, and beyond this it decreases.

  Diagram of wing showing angle of attack.

  DETAILS OF DRAG

  Drag is a mechanical force, and to be generated, the body must be in contact with the air. This is, of course, true in the case of the wing passing through air. Simply, it is friction between the air and the wing, and it is generated because of the difference in velocity between the wing and the air. Furthermore, it acts in a direction exactly opposite to the motion of the airplane. And finally, it is classified as an aerodynamic friction.8

  Three types of drag friction exist: skin friction, form friction, and induced friction. Skin friction is the friction between the moving molecules of air and the molecules of the solid surface of the wing, so it depends on the interaction between these molecules. This means that a very smooth surface will have less skin friction than a rough one. It also depends on the viscosity of the air, where viscosity is a measure of the internal resistance of a fluid to deformation. For example, molasses has greater viscosity than water. When air is in contact with a moving surface, the air will try to follow the surface. In other words, it has a sort of “stickiness”; as a result, the relative velocity between the wing and the air at the surface of the wing is zero. As you move away from the wing, however, it gradually increases.

  Form friction is an aerodynamic resistance to the motion of an object through air that depends on the shape of the object. The more streamlined the shape, the less the form friction. A teardrop shape has one of the lowest form frictions. This type of friction is particularly important in the case of cars; we stream them to decrease this type of drag as much as possible, which increases their fuel efficiency.

  Induced friction occurs near the tip of wings that are curved or distorted. The “effective curving” causes a pressure difference between the top and the bottom of the region near the tip of the wing. It's called induced friction because it is induced by the action of vortices near the tip of the wings. Its magnitude depends on the shape of the wings and the amount of lift they produce. Longer, thinner wings produce less induced drag.

  STEERING AND MANEUVERING THE AIRPLANE

  As we saw earlier, after considerable experimentation the Wright brothers finally developed an effective three-axis control that allowed them to control and properly maneuver their airplanes
. Wing warping was used for roll, or lateral motion, and a forward elevator on the wings was used to control up-and-down motion, or pitch, while a rear rudder was used to control side-to-side motion, or yaw. Within a few years, however, Glenn Curtiss of New York developed what are now called ailerons to replace the wing warping of the Wright brothers. Ailerons are small control surfaces that are attached to the trailing edge of the wing.

  So how do we maintain control over an aircraft? As it turns out, takeoff, landing, and cruising each have to be stabilized and maneuvered differently. Wings are generally designed for an appropriate amount of lift, along with a minimum of drag, during cruising. But it's fairly obvious that things have to be quite different during takeoff and landing. The plane's speed is much less at this time, and the plane must be adjusted accordingly. And this is where flaps and slats come in. Without them the pilot would not be able to take off or land.

  Flaps are hinged surfaces on the trailing edge of the wings that are used to reduce the speed of the airplane so that it can safely take off and land. They decrease the distance needed for both landing and takeoff. When they are extended downward from the trailing edge of the wing they effectively alter the shape of the wing so that it creates more lift on takeoff and more drag on landing.

  Slats perform a similar function, but they are mounted on the front edge of the wing. Again, they are used to temporarily alter the shape of the wing to increase lift. In effect, they temporarily change the angle of attack of the wings. Using them, a pilot can fly at slower speeds during takeoff and can land in shorter distances.

 

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