LIFT AND DRAG

Flying is all about balancing forces: thrust and drag in the horizontal direction, and lift and gravity in the vertical direction. The engines generate the thrust required to pull or push a plane through the air. For a steady speed, this thrust must be equal to the aerodynamic drag on the airplane. If the thrust is lower than the drag, the plane will slow down. If it is higher, the plane will accelerate. However, with increasing speed the drag will also increase, so at a certain moment the drag on the plane will again be equal the thrust. When that happens, the vehicle will continue to fly at a constant speed that is higher than it was at the lower thrust level.

In the vertical direction, the aerodynamic lift generated by the wings must be in balance with the force of gravity pulling the plane down. If the lift is too small, the airplane will descend; if the lift exceeds the plane’s weight, it will gain altitude. To maintain a constant altitude, the lift must precisely balance the weight of the plane. When thrust equals drag, and lift equals weight constant velocity, straight and level flight is possible; but if any of the forces changes, the balance will be lost and the airplane will go up or down, accelerate or decelerate. These changes often occur in combination: for example in a dive, a plane will lose altitude and at the same time speed up.

Aerodynamic drag is a familiar thing: you feel it when you walk against the wind or when you stick you hand out of a car window. The amount of drag depends on the speed of the air (wind) or the speed of the car in the second example. Whether the air moves to you, or you move through the air doesn’t matter: what is important is your relative velocity with respect to the air. Aerodynamic drag increases as a function of the square of the speed, so if you go twice as fast, the drag will increase by a factor of four. If you double your speed again, the drag will become sixteen times what it was originally. You can see where this goes: the drag increases at a much higher rate than your speed, so the higher your velocity, the harder it will be to go even faster.

Drag also depends on the size and shape of an object moving through the air. For similar shapes, an object with a large frontal surface will experience more drag than one with a smaller surface: a small hand out of a car window will feel less drag than a big hand, and a truck will suffer more drag than a small car. Aerodynamic drag on a vehicle can be decreased by using a good shape: the easier the air can flow around an object, the lower the drag will be. This is why sleek aircraft and racing cars have pointy noses. Lower drag means it takes less thrust to attain a certain speed, or that you can reach a higher velocity with the same thrust. Minimizing aerodynamic drag has therefore always been one of the driving issues in airplane design, and has led to continuous improvements in the shape of fuselages, the use of undercarriages which retract and the elimination of high-drag beams and cables.

The aerodynamic force that holds an airplane up is the lift is created by its wings.

Lift principle 1.

The physics behind lift are complicated. I have a book written in 1909 called Flying, The Why & Wherefore, in which several theories on lift generation are presented; six years after the invention of the airplane, at a time when many types of planes were flying around, it was still not really understood what made those machines stay in the air! Even more surprising is that those same theories are all still employed to explain how lift is generated, even today, after over a century of flying experience. First there is the ‘Longer Path’ theory, which is also known as the ‘Bernoulli’ or ‘Equal Transit Time’ explanation. This theory is based on the assumption that air molecules that reach the leading edge of a wing at the same time, then flow either over or under it but all reach the trailing edge at the same moment. As the top surface of a typical asymmetrical wing is more curved than the underside, air molecules going above the wing have to travel a longer distance than those that pass under the wing, doing so in the same amount of time. Air flowing over the wing must therefore travel faster than that under the wing. Bernoulli’s equation, a fundamental of fluid dynamics, states that as the speed of the air increases, its pressure decreases (the air molecules have less time to exert pressure on the surface). Hence the faster moving air on the top surface of the wing develops a low pressure area, while the slower moving air maintains a higher pressure on the underside. The low pressure essentially ‘sucks’ the wing upward (or the high pressure pushes it up, depending on your point of view). The weakness of this theory lies in its assumption that two molecules that become separated by the leading edge of the wing rejoin at the trailing edge at exactly the same moment. Even though you can measure that the air on top of a curved wing does indeed travel faster than under the wing, there is no fundamental reason why the molecules ought to meet again at the trailing edge and reach it at exactly the same time.

Another way to explain why wings generate lift is the ‘Newtonian’ explanation, based on the ‘action equals reaction’ idea which is also the working principle of the rocket engine. Air molecules hitting the bottom surface of an inclined wing bounce off and are deflected downward. In reaction, the wing is not only pushed up (lift) but also backwards (drag). You can ascertain that this is true by sticking your hand horizontally out of the window of a moving car, and slowly rotating it vertically. The

greater the angle with respect to the airflow, the stronger will your hand be pushed up and in the direction of the airflow. This idea explains why airplanes with symmetrical airfoils (symmetrical wing cross sections) or even flat wings (such as those of paper airplanes) can fly, but it does not explain why an asymmetric airfoil with a strongly curved upper surface provides more lift. In fact, the Newtonian explanation leaves the top of the wing completely out of the picture. We also now know that molecules in the dense lower atmosphere, in which aircraft normally fly, do not act as individual particles, they actually interact and influence each other in complex ways. Nevertheless, air is indeed deflected downwards by an angled plate. The Newtonian explanation also correctly predicts that if you increase the inclination of the wing with respect to the airflow (its ‘angle of attack’) it will provide more lift but also experience more drag.

What happens in reahty is a combination of these explanations, plus some more complex fluid dynamics. Air approaching the top surface of a wing is compressed into the air above it as it moves upward near the leading edge. The top surface then curves downward and away from the airflow, creating a low-pressure area that pulls the air above down toward the back of the wing. Simultaneously air approaching the bottom surface of the wing at the leading edge is slowed, compressed and directed downward. When this air nears the rear of the wing, its speed and pressure gradually match that of the air coming over the top. When you sum up all the pressures acting on the top and bottom of the wing, you end up with a net force that pushes the wing upward. However this force is not aimed straight up, it has a component in the backward direction. This is the aerodynamic drag described before. If the angle of attack is increased, the pressure differences between the bottom and top of the wing become larger, resulting in more lift as well as increased drag. There is of course a limit to how steep the angle of attack can be made, because beyond a certain angle the airflow over the wing is no longer able to nicely follow its curved contour; it no longer ‘sticks’ to the upper surface. This detached airflow creates a large turbulent wake that dramatically decreases the lift while increasing the drag. This is called a stall, and if the plane does not have enough engine thrust to compensate for the loss of lift it will fall out of the sky like a leaf falhng from a tree. Normally it will accelerate going down, building sufficient speed to regain lift and control. However, if the plane is turning while falling it can enter what is called a spin. If the aircraft is forgiving and/or the pilot is lucky, this spin will be a normal one in which the nose points somewhat downwards and the corkscrewing descent provides sufficient control to achieve a recovery. The aircraft may be upside down, which is called an inverted spin. Much more serious is a flat spin, where the plane is falling straight down in a horizontal orientation and rotating on an axis perpendicular to its wings. In that case the airflow around the wings and tail is completely useless, and recovery often impossible.

The fact that the upper surface of an asymmetrical airfoil is curved means the pressure effects on the upper wing surface are more pronounced than those on the bottom of the wing. The upper part of the wing therefore contributes most to the generation of lift, which is one reason why most airplanes that use wing-mounted engines have them hanging under the wings rather than attached on the top of the wings: disturbing the air beneath a wing is less detrimental to flight than disturbing the air above a wing. This is also why the aforementioned ‘liquid-air’ rocket plane designed by Augustus Post in 1928 had air being expanded over the wing to create additional lift at high altitudes.

The wings of an airplane are optimized for a certain use in terms of speed and altitude. Airplanes that need a lot of lift at relatively low speeds have wings with strongly curved upper surfaces. This makes it possible to take off and land at low speeds and with heavy loads; very useful for military cargo carriers that have to be able to use short, improvised runways. The downside of such wings is that along with the powerful lift they also generate a lot of drag, which makes it difficult and uneconomical to fly at high speeds. If you want to fly really fast, you require small, thin wings designed to minimize drag while still generating sufficient lift to remain airborne at high speed. But such wings do not provide much lift at low speeds, and consequently planes that have such wings have higher take off and landing speeds and require long, smooth runways. If speed is of paramount importance, as it is for military fighter planes, you will go for the benefits of small, thin wings and accept the disadvantages that go with their use.

Lift not only depends on speed, but also on the density of the air. High up in the atmosphere the density of the air is much lower than at sea level, so that the lift that any given wing creates will diminish with increasing altitude (which is why aircraft have maximum operating altitudes). To be able to fly high, you must either employ larger wings or you must go very fast so that your wings generate more lift (as lift, just like drag, is a function of the square of the velocity of the air). But flying very fast increases aerodynamic drag and so requires large, powerful engines. Using big, slender wings is more economical in terms of engine power and fuel consumption. An example of the long-wing solution to reach extreme altitudes is the famous U2 spy plane, the modem version of which can reach an altitude of almost 26 km (16 miles) but has a maximum speed of only 800 km per hour (500 miles per hour). The SR-71 Blackbird spy plane can reach a similar altitude, but its short delta wings give it a top speed of no less than 3,530 km per hour (2,200 miles per hour). The penalty, of course, is that the SR-71 has a much more voracious fuel consumption.

AEROPLANE ANATOMY

An airplane consists primarily of a fuselage, wings, stabilizers and engines. The fuselage is the body that connects all the other parts and holds the passengers, cargo and the pilots who control the vehicle from the cockpit. The required lift is provided by the wings. Besides these basic elements, much more is however needed to safely control an airplane.

Normal wings are designed to work optimally at the normal, cruise speed of the airplane. At take-off and landing, airplanes necessarily fly much slower, so ideally at those times you would rather have wings that give more lift at low speed. Airplanes are therefore often equipped with mechanical ‘flaps’ and ‘slats’ that can effectively change the shape of the wings. Flaps can be extended rearward and downward from the trailing edge to give the plane more lift at low speeds. Slats do a similar job, but on the front of the wing. In normal flight, when they are not needed, flaps and slats are retracted in order to minimize the aerodynamic drag of the wings. ‘Spoilers’ are door-Uke flaps on top of the wing. When moved up, they disturb (spoil) the airflow over the wing and thereby quickly diminish lift and increase drag. They are used to slow down and reduce altitude in landing, and also to assist with braking as well as to keep the plane firmly on the runway as it rolls after touchdown.

Like any object, an airplane tends to rotate around its center of mass. To steer an airplane, a pilot must control its movements around three axes that can be imagined

to radiate orthogonally from the center of mass, also known as the center of gravity. Rotation around the horizontal axis that runs from one wingtip to the other, making the nose go up or down, is called ‘pitch’. The left-right movement of the nose, in other words the rotation around the vertical axis, is called ‘yaw’. The third axis runs from the nose to the tail and is the line around which an airplane can ‘roll’ to make one wing rise and the other one drop. When driving your car you can only steer it to go left or right, but a pilot has two more rotation axes to take care of. In addition, your car can only go forward or backward, but a plane can also go up and down (although normally not backward). All this makes flying a plane much more complex than driving a ground vehicle.

Conventional airplanes have horizontal tail stabilizers, also called the tailplane. When normal wings are generating lift, they have the tendency to push the airplane’s nose downwards, i. e. make the plane pitch down. To avoid this, the small horizontal stabilizers act as wings that provide a negative lift, pushing the tail down (and hence the nose up) and thereby counterbalance the pitching-down effect of the main wings. They are equipped with moveable flaps called ‘elevators’, which can increase or decrease the lift of the horizontal stabilizers and thereby make a plane pitch up or down. If a pilot pulls on his control stick, the elevators point up, pushing the tail down and therefore the airplane’s nose up. This increases the angle of attack of the wings, increasing the lift and making the airplane gain altitude. Pushing the control stick forward has the opposite effect. By use of the elevators a pilot can control the altitude of the plane.

The vertical stabilizer on the tail gives stability in the horizontal direction, much like the keel of a boat. A moveable flap on its trailing edge, called the ‘rudder’, lets the pilot move the nose of the airplane left and right and thus provides yaw control. The rudder is operated with the pedals at the feet of the pilot: pushing the left foot forward moves the airplane’s nose to the left and vice versa. Roll is controlled by ‘ailerons’ on the main wings. If the pilot pushes the stick to the right, the aileron on the left wing moves down and increases the lift of that wing. On the right wing the opposite happens. The result is the left wing goes up and the right wing goes down. From the pilot’s point of view the airplane rolls clockwise. The spoilers can also be used to roll an airplane. Extending the spoilers on one of the wings will reduce the lift on that wing and make it drop, so that the plane will roll in the direction of the ‘spoiled’ wing.

Many planes also exhibit a so-called dihedral angle in their wings, which means the wings are canted slightly upward to form a weak Y-shape. This helps to prevent unwanted roll, making the plane more stable. When a plane with wing dihedral rolls away from level flight, the lift force on its wings will no longer point straight up but somewhat to the side. As a result, the plane will sideslip, which means it is not only flying forward but also slightly sideways. Because of the wing dihedral the situation of the wings with respect to the airflow, which now comes shghtly from the side, is asymmetrical. The upward tilted wing presents a less favorable angle to the airflow than the wing that is angled downwards, and hence produces less lift than the other wing. This unbalance in lift will automatically roll the plane back until both wings are again at the same angle to the horizon; in essence, the sideslip airflow ‘pushes’ the wings back to the horizontal level.

The undercarriage, normally fitted with wheels, enables a plane to move over the runway during take-off and landing, and to taxi around on the airport. At very low speeds the rudder on the tail of a jet or rocket plane cannot work, because of the low velocity of the air flowing over it. A rotating nose wheel can then be used to steer the airplane. The undercarriage creates a lot of aerodynamic drag during flight, so in most modern airplanes it is retracted when not needed. Although there still are airplanes that have fixed undercarriages with wheels, floats or skids, high-speed

Dihedral wings.

airplanes must always get their undercarriage out of the way, either by retracting it into the wings and/or fuselage, or by dropping it altogether; the last option has the benefit that the plane does not have to drag the heavy undercarriage around in flight, but of course it still needs something to land on. The landing undercarriage can however be less robust and often smaller, because the weight of the plane at landing will be lower than at take-off by the amount of fuel consumed. This may be a good idea for experimental planes and spaceplanes with severe weight limitations, but it reduces the operational flexibility by requiring the airplane to be re-mated to the jettisonable undercarriage prior to each flight.

An important issue in the design of an airplane is whether it should be able to fly faster than the speed of sound. Sound has a speed limit that is easily noticeable: when you observe a flash of lightning in the distance the light reaches your eyes virtually instantaneously, but you may hear the thunder only several seconds later. Clearly, sound travels through the air at a speed that is much lower than that of light. In fact, every three seconds that elapse between lightning and thunder means that the event occurred about 1 km further away from you (or 1 mile every five seconds); if the flash and boom arrive at about the same time, you are in real danger. The speed of sound is defined as Mach 1, after the Czech/Austrian physicist Ernst Mach. The velocity of airplanes able to fly faster than the speed of sound is usually expressed in terms of Mach numbers, with Mach 2 meaning twice that speed. Flying significantly faster than the speed of sound is called supersonic. In contrast, subsonic flight means a speed of less than Mach 1. For example Mach 0.5 means half the speed of sound. Flying at precisely the speed of sound is called sonic flight. The Mach number not only depends on the actual speed of an airplane, but also on its altitude. The higher you go in the atmosphere, the lower the speed of sound because of the diminishing temperature of the air. At sea level and 20 degrees Celsius (68 degrees Fahrenheit), Mach 1 corresponds to a velocity of 340 meters per second (1,130 feet per second), or 1,240 km per hour (770 miles per hour). However, at 11 km (7 miles) altitude it means 1,060 km per hour (660 miles per hour). At altitudes from about 11 to 20 km (7 to 12 miles) the air temperature is constant, and so too is the speed of sound. But above this region up to about 50 km (30 miles) the air temperature and the speed of sound increase again. If it is mentioned somewhere that a plane is capable of flying at Mach 2, you will need to know at which altitude it can achieve this in order to be able to derive its real velocity.

The engines generate the thrust necessary to pull or push the plane through the air. For relatively slow aircraft like commercial airliners that do not exceed the speed of sound, the engines are often attached to the outside of the wings or the fuselage with struts. This makes it easier to maintain and replace the engines, and allows the use of different types of engines without the need to modify the rest of the aircraft. Aircraft that need to be more streamlined, for instance for supersonic flight or high speed at low altitudes, require their engines to be inside the fuselage or attached very closely to the wings, without struts. Typical examples are military fighter jets and the Concorde. Conventional airplanes which fly at relatively low speeds and low altitudes often use propellers, which, in simple terms, are spinning wings. The rotation provides the propeller blades with the necessary speed to generate lift in the

horizontal direction. Helicopter blades operate on the same basic principle. Propellers work best in dense air, so are not suitable for high altitude flight. Another major disadvantage is that a propeller’s performance drops quickly when the blade speed exceeds the speed of sound, because shock waves will form that dramatically increase the aerodynamic drag on the propeller whilst decreasing the thrust that it develops. As the speed of a propeller blade depends on both its rotational speed and the velocity of the aircraft, the blades will reach sonic speed long before the rest of the aircraft. Consequently, aircraft equipped with conventional propellers are only good for flight speeds up to about Mach 0.6. Propellers can be driven by combustion engines similar to those in cars, or by gas turbine engines.

Gas turbine engines (often simply called jet engines) all consist of the same basic components: an inlet for the air, a compressor, combustion chamber(s), a turbine and an exhaust. The compressor consists of rotating rows of fan blades that suck in air through the inlet and compresses it to increase the amount of oxygen available per liter of air. The high-pressure air then enters the combustion chamber(s), where it is mixed with fuel (typically kerosene) and burned. The resulting powerful stream of high-pressure exhaust gas then expands through (and therefore turns) another set of fans called the turbine. The turbine is connected to the compressor via a shaft, so the exhaust turns the turbines which turn the compressors to suck in and compress more air and thereby keep the engine running. In addition to the compressor, the shaft can be connected to a propeller, making the engine a so-called turboprop engine. Since the propeller needs to spin at a much lower speed than the compressor, it is linked to the shaft via a gearbox. Using the same principle a gas turbine engine, now referred to as a turboshaft engine, can drive the propellers of a ship, the wheels of a tank or the blades of a helicopter.

The momentum of the exhaust from a gas turbine engine can also be used more directly to provide thrust by Newton’s ‘action equals reaction’, just like in a rocket engine. In such an engine, called a turbojet engine, it is the flow of gas that pushes

J L

A turbojet engine [Federal Aviation Administration].

the aircraft through the air. This enables very high speeds and is therefore primarily used in military fighters. The principal difference between a turbojet engine and a rocket is that a turbojet uses atmospheric oxygen to burn with the fuel, rather than oxidizer drawn from a tank. The working principle is otherwise basically the same. The powerful thrust of a turbojet can be further increased by using an afterburner, a long tube that is installed behind the jet engine’s exhaust, and into which additional fuel is injected and burned with the unused oxygen remaining in the hot gas coming out of the engine. As per the ‘action equals reaction’ principle, this provides a large boost in thrust. It is however a pretty inefficient means of propulsion and it greatly increases fuel consumption. Afterburners are typically used on fighter aircraft, and even then only for rapid acceleration during brief periods of time. Afterburners are however a great way to attract attention at air shows, because they provide lots of noise and long, dazzling exhaust plumes.

In the gas turbine engines that most modern jet aircraft employ, only part of the exhaust gas is used directly to provide thrust through a fast and hot exhaust jet. An important part of its energy is used to drive a large fan in front of the compressor. Instead of compressing air into the engine for combustion, this fan moves ‘bypass air’ around the actual engine, forming a cold jet that flows out at a lower velocity than the hot gas from the core. Rather than giving a small amount of air a very high velocity as occurs in the hot part of the engine, the fan gives a lot of air a relatively low velocity. Turbofan engines that have relatively large fans are typically used by commercial airliners, because they are ideal for the high but still subsonic speeds at which they fly. In addition, the low-speed air helps to cushion the noise of the hot and fast core exhaust, making the engine quieter than a pure turbojet. Modern

A Trent 1000 turbofan engine [Rolls Royce],

fighter planes also employ turbofan engines, but use smaller fans that are more optimal for supersonic flight.

Gas turbines configured as turboprop, turboshaft, turbofan or turbojet engines, deliver a lot of power compared to the weight of the engine. Their power-to-weight ratio is in fact much higher than for reciprocating engines such as those used in cars. In addition, gas turbine engines are relatively small for the power they provide. One disadvantage is that, because of the high rotation speeds of the compressors and the turbines, and the high temperatures employed, they are relatively compUcated and expensive. Another limitation is that at flight speeds exceeding about Mach 3, the temperatures inside the engine can become so hot that the turbine blades melt and break apart.

How about removing the fragile turbine blades and fans? This is indeed feasible. At speeds over Mach 1, air is rammed into the engine at such high velocity that the shape of the inlet duct will satisfactorily compress the air. Such a ‘ramjet’ typically resembles a tube with a pointy core in the middle of the air intake; rather Uke a gas turbine engine without turbines and compressors. The shape of the tube and the core ensure that the incoming high-velocity air is squeezed into a small area and thereby compressed to a high enough density that it can be burned with the fuel (ramjets are therefore also known as ‘stovepipe’ jets). The good thing is that at around Mach 3, where gas turbine engines start to run into trouble, ramjets not only work well but actually perform more fuel-efficiently than turbojets. In addition, a ramjet is much less complex than a turbine engine, and therefore cheaper and more robust. These advantages make them ideal for use in long-range cruise missiles. A disadvantage is that a ramjet only produces thrust when it moves at high speeds, and only becomes reasonably efficient near supersonic speed; at low velocities the air does not rush into engine fast enough for proper compression and hence combustion. Cruise missiles are therefore usually accelerated up to high-subsonic or low-supersonic speeds using expendable rocket stages, whereupon the ramjet is engaged. But a manned high­speed plane used for reconnaissance or the interception of enemy planes needs to be able to switch from subsonic to high-supersonic velocities at any time. Expendable rocket engines that can only be used once are not very useful for that purpose. A reusable rocket engine or a gas turbine engine could be employed but at the penalty of extra weight. For the aforementioned SR-71 Blackbird, a solution was found by combining a gas turbine and a ramjet engine into a turboramjet. This hybrid engine essentially consists of a turbojet mounted inside a ramjet. For take-off and while climbing to altitude, flaps inside the SR-71 engines force the incoming air into the compressor of the turbojet part of the engine. Just short of Mach 1 the afterburners of both engines are ignited to accelerate the plane to supersonic speed. Then the bypass flaps are moved to block the flow into the turbojet and instead direct the air around the turbojet core and bum it with the fuel only in the afterburner part of the engine. At that moment the engine has been turned into a ramjet, with the air being compressed by the shock cones at the air inlets, without the need for fan compressors. This unique engine enabled the SR-71 to operate from zero speed to Mach 3 +, and to fly at speeds between Mach 3 and 3.5 for long durations. As we will see later, the combination of different types of airbreathing engines with rocket

engines may be the solution for future spaceplanes, something which Max Valier gave some thought to in the 1920s when he proposed designs for planes that would employ propellers in the lower atmosphere and rocket engines at extreme altitudes.