Forces in Flight

 

The flight of an airplane, a bird, or any other object involves four forces that may be measured and compared: lift, drag, thrust, and weight. As can be seen in the figure below for straight and level flight, these four forces are distributed with the 1) lift force pointing upward; 2) weight pushing downward; 3) thrust pointing forward in the direction of flight; 4) and the drag force opposing the thrust. In order for the plane to fly, the lift force must be greater than or equal to the weight. The thrust force must be greater than or equal to the drag force

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Direction of Forces in Straight and Level Flight

 

 Weight

 

The weight of the aircraft, as discussed earlier in the chapter, is a measure of a natural force that pulls the plane down towards the earth (gravity). Therefore, the direction assigned to the weight is downward.

 

 Lift

 

The force that pushes an object up against the weight is lift. On an airplane or a bird, the lift is created by the movement of the air around the wings (the lift created by the body or tail is small). The figure below shows two streamlines about a typical airfoil (or wing); one travels over the top of the airfoil, the other moves underneath it.

 

 

If two particles were released from the same point at the same time, one on each streamline, they would start out moving together. As they approach the front of the airfoil, however, their velocity will start to change. Due to the shape of the airfoil, the air moves faster over the top of the airfoil than it does on the lower surface. The faster air leads to a lower pressure (from Bernoulli's Law) on the upper surface.

 

 A smaller force, on top, will be pointed downward, and a larger force (underneath) will be pointing upwards. When the two forces are combined, the net force is lift, which is directed upwards.

 

 The shape of the airfoil (wing) is a very important part of lift, and airplane designers design these shapes very carefully. Most airfoils today have camber, meaning they have curved upper surfaces and flatter lower surfaces. These airfoils generate lift even when the flow is horizontal (flat). The Wright brothers used symmetric airfoils to build the wings on their airplane. Since the upper and lower surfaces were the same, the particles on the streamlines above and below the symmetric airfoil move at the exact same velocity. The pressures on either surface (top or bottom) are exactly the same, so the net combined force on the airfoil is zero! No lift is generated by a symmetric airfoil in horizontal flow (flat wings moving straight ahead cannot fly). How, then, did the Wright brothers get their airplane off the ground?

 

 In order to generate lift with a symmetric airfoil, the airfoil must be turned (tilted) with respect to the flow, so that the upper surface is "lengthened" and the lower surface is "shortened".

 

 This "tilting against the airflow" is called angle of attack. It can be used for either cambered or symmetric wings. This is why an airplane rotates slightly at takeoff; the pilot is increasing the angle of attack to generate more lift. If the angle of attack is doubled, the lift doubles. There is a limit to how much lift can be generated, however. The angle of attack can be increased to a point where the net lift force drops drastically.

Airflow deflection is another way to explain lift. To understand the deflection of air by an airfoil let's apply Newton's Third Law of Motion. The airfoil deflects the air going over the upper surface downward as it leaves the trailing edge of the wing. According to Newton's Third Law, for every action there is an equal, but opposite reaction. Therefore, if the airfoil deflects the air down, the resulting opposite reaction is an upward push. Deflection is an important source of lift. Planes with flat wings, rather than cambered, or curved wings must tilt their wings to get deflection.

 

 Another way to increase lift on a wing is to extend the flaps downward. This again lengthens the upper surface and shortens the lower surface to generate more lift.

 

 The velocity of the freestream air (actually of the airplane) is the most important element in producing lift. If the velocity of the ariplane is increased, the lift will increase dramatically. If the velocity is doubled, the lift will be four times as large.

 

 The generation of lift can be found elsewhere. Race car designers use airfoil-like surfaces to generate negative lift, or downward-directed force. This force, combined with the weight of the race car, helps the driver maintain stability in the high-speed turns on the race track.

 

 Thrust

 

Any force pushing an airplane (or bird) forward is called thrust. Thrust is generated by the engines of the airplane (or by the flapping of a bird's wings). The engines push fast moving air out behind the plane, by either propeller or jet. The fast moving air causes the plane to move forward.

 

 Drag

 

The drag is the fourth of the major forces for flight. It is a resistance force. This force works to slow the forward motion of an object, including planes. There are four types of drag: friction drag, form drag, induced drag and wave drag. These drag types develop around the shape of the body, the smoothness of the surfaces, and the velocity of the plane. All four sum together for the total drag force. The drag forces are the opposite of thrust. If the thrust force is greater than the drag force, the plane goes forward, but if the drag force exceeds the thrust, the plane will slow down and stop.

 

 The friction drag is sometimes also called the skin friction drag. It is the friction force at the surfaces of the plane caused by the movement of air over the whole plane. If a person were to look at the furface of a wing, for example, he or she would see that all the sheets of metal join smoothly, and even the rivets are rounded over and are as flush with the surface as possible. This helps keep the friction drag at a minimum.

 

 The form drag, or pressure drag as it is sometimes called, is directly related to the shape of the body of the airplane. A smooth, streamlined shape will generate less form drag than a blunted or flat body.

 

 Any object that moves through a fluid (water/air) can get a decrease in form drag by streamlining. Automobiles are streamlined, which translates (allows) better gas mileage; there is less drag so less fuel is required to "push" the car forward. Buses, vans, and large trucks are less streamline, and this one reason why they use more fuel than smaller, streamlined cars (weight is another reason).

 

 Form drag is easy to demonstrate using a hand out the window of a moving car. If the hand is held flat, like a wing, it is a streamlined object. The person only feels a small tug or drag. If he or she turns the hand so that the palm is facing forward, the drag force is greatly increased, and the hand is pulled backwards! It is no longer streamlined. There are two additional drag forces, the induced drag and wave drag.

 

 Induced drag is sometimes called the drag due to lift. As the lift force is generated along a wing, a small amount of excess (lift) force can be generated in the opposite direction. This force acts like drag and slows the forward motion of the airplane. Aircraft designers try to design wings that lower induced drag.

 

 The last of the four types of drag is the wave drag. This generally only happens when the airplane is flying faster than the speed of sound. Wave drag is caused by the interactions of the shock waves over the surfaces and the pressure losses due to the shocks. Wave drag can also occur at transonic speeds, where the velocity of the air is already supersonic, locally. Since most commercial jets today fly at transonic speeds, wave drag is an important part of the total drag.

 

 Summary

 

Every pilot knows and uses these four basic forces of flight. Aerobatic pilots are constantly balancing these forces to design amazing stunts to delight the crowds watching them. They will deliberately stall the wings of the airplane to cause the plane to lose lift and drop suddenly. They very carefully fly upside down, balancing the new lift force with the weight of the plane. They will point the airplane straught up into the air and fly staight up as far as they can, let the plane hang there for a second, then let it fall back down its original path. After a few heartbreaking seconds, the pilot will turn the airplane back so the nose points downward into the direction of the air flow to again regain level flight. These stunts are possible because the pilots carefully balance the forces of weight, lift, drag and thrust.


How Airplanes Fly: A Physical Description of Lift

 

Level 3

 

 

 

 

Almost everyone today has flown in an airplane. Many ask the simple question "what  makes an airplane fly"? The answer one frequently gets is misleading and often just  plain wrong. We hope that the answers provided here will clarify many misconceptions about  lift and that you will adopt our explanation when explaining lift to others. We are going  to show you that lift is easier to understand if one starts with Newton rather than  Bernoulli. We will also show you that the popular explanation that most of us were taught  is misleading at best and that lift is due to the wing diverting air down.

 

 Let us start by defining three descriptions of lift commonly used in textbooks and  training manuals. The first we will call the Mathematical Aerodynamics Description  which is used by aeronautical engineers. This description uses complex mathematics and/or  computer simulations to calculate the lift of a wing. These are design tools which are  powerful for computing lift but do not lend themselves to an intuitive understanding of  flight.

 

 The second description we will call the Popular Explanation which is based on  the Bernoulli principle. The primary advantage of this description is that it is easy to  understand and has been taught for many years. Because of it’s simplicity, it is used  to describe lift in most flight training manuals. The major disadvantage is that it relies  on the "principle of equal transit times" which is wrong. This description  focuses on the shape of the wing and prevents one from understanding such important  phenomena as inverted flight, power, ground effect, and the dependence of lift on the  angle of attack of the wing.

 

 The third description, which we are advocating here, we will call the Physical  Description of lift. This description is based primarily on Newton’s laws. The  physical description is useful for understanding flight, and is accessible to all that are  curious. Little math is needed to yield an estimate of many phenomena associated with  flight. This description gives a clear, intuitive understanding of such phenomena as the  power curve, ground effect, and high-speed stalls. However, unlike the mathematical  aerodynamics description, the physical description has no design or simulation  capabilities.

 

The popular explanation of lift

 

 Students of physics and aerodynamics are taught that airplanes fly as a result of  Bernoulli’s principle, which says that if air speeds up the pressure is lowered. Thus  a wing generates lift because the air goes faster over the top creating a region of low  pressure, and thus lift. This explanation usually satisfies the curious and few challenge  the conclusions. Some may wonder why the air goes faster over the top of the wing and this  is where the popular explanation of lift falls apart.

 

 In order to explain why the air goes faster over the top of the wing, many have  resorted to the geometric argument that the distance the air must travel is directly  related to its speed. The usual claim is that when the air separates at the leading edge,  the part that goes over the top must converge at the trailing edge with the part that goes  under the bottom. This is the so-called "principle of equal transit times".

 

 As discussed by Gale Craig (Stop Abusing Bernoulli! How Airplanes Really Fly.,  Regenerative Press, Anderson, Indiana, 1997), let us assume that this argument were true.  The average speeds of the air over and under the wing are easily determined because we can  measure the distances and thus the speeds can be calculated. From Bernoulli’s  principle, we can then determine the pressure forces and thus lift. If we do a simple  calculation we would find that in order to generate the required lift for a typical small  airplane, the distance over the top of the wing must be about 50% longer than under the bottom. Figure 1 shows what such an airfoil would look like. Now, imagine what a Boeing  747 wing would have to look like!

 Fig 1 Shape of wing predicted by principle of equal  transit time.

 

If we look at the wing of a typical small plane, which has a top surface that is 1.5 -  2.5% longer than the bottom, we discover that a Cessna 172 would have to fly at over 400  mph to generate enough lift. Clearly, something in this description of lift is flawed.

 

 But, who says the separated air must meet at the trailing edge at the same time? Figure  2 shows the airflow over a wing in a simulated wind tunnel. In the simulation, colored  smoke is introduced periodically. One can see that the air that goes over the top of the  wing gets to the trailing edge considerably before the air that goes under the wing. In  fact, close inspection shows that the air going under the wing is slowed down from the  "free-stream" velocity of the air. So much for the principle of equal transit  times.

 Fig 2 Simulation of the airflow over a wing in a wind  tunnel, with colored "smoke" to show the acceleration and deceleration of the  air.

 

The popular explanation also implies that inverted flight is impossible. It certainly  does not address acrobatic airplanes, with symmetric wings (the top and bottom surfaces  are the same shape), or how a wing adjusts for the great changes in load such as when  pulling out of a dive or in a steep turn?

 

 So, why has the popular explanation prevailed for so long? One answer is that the Bernoulli principle is easy to understand. There is nothing wrong  with the Bernoulli principle, or with the statement that the air goes faster over the top  of the wing. But, as the above discussion suggests, our understanding is not complete with  this explanation. The problem is that we are missing a vital piece when we apply  Bernoulli’s principle. We can calculate the pressures around the wing if we know the  speed of the air over and under the wing, but how do we determine the speed?

 

 Another fundamental shortcoming of the popular explanation is that it ignores the work  that is done. Lift requires power (which is work per time). As will be seen later, an  understanding of power is key to the understanding of many of the interesting phenomena of  lift.

 

Newton’s laws and lift

 

So, how does a wing generate lift? To begin to understand lift we must return to high  school physics and review Newton’s first and third laws. (We will introduce  Newton’s second law a little later.) Newton’s first law states a body at rest  will remain at rest, or a body in motion will continue in straight-line motion unless  subjected to an external applied force. That means, if one sees a bend in the flow of  air, or if air originally at rest is accelerated into motion, there is a force acting on  it. Newton’s third law states that for every action there is an equal and opposite  reaction. As an example, an object sitting on a table exerts a force on the table (its  weight) and the table puts an equal and opposite force on the object to hold it up. In  order to generate lift a wing must do something to the air. What the wing does to the air  is the action while lift is the reaction.

 

 Let’s compare two figures used to show streams of air (streamlines) over a wing.  In figure 3 the air comes straight at the wing, bends around it, and then leaves straight  behind the wing. We have all seen similar pictures, even in flight manuals. But, the air  leaves the wing exactly as it appeared ahead of the wing. There is no net action on the  air so there can be no lift! Figure 4 shows the streamlines, as they should be drawn. The  air passes over the wing and is bent down. The bending of the air is the action. The  reaction is the lift on the wing.

 Fig 3 Common depiction of airflow over a wing. This  wing has no lift.

Fig 4 True airflow over a wing with lift, showing  upwash and downwash.

 

The wing as a pump

 

As Newton’s laws suggests, the wing must change something of the air to get lift.  Changes in the air’s momentum will result in forces on the wing. To generate lift a  wing must divert air down; lots of air.

 

 The lift of a wing is equal to the change in momentum of the air it is diverting down.  Momentum is the product of mass and velocity. The lift of a wing is proportional to the  amount of air diverted down times the downward velocity of that air. Its that simple.  (Here we have used an alternate form of Newton’s second law that relates the  acceleration of an object to its mass and to the force on it; F=ma) For more lift the wing  can either divert more air (mass) or increase its downward velocity. This downward  velocity behind the wing is called "downwash". Figure 5 shows how the downwash  appears to the pilot (or in a wind tunnel). The figure also shows how the downwash appears  to an observer on the ground watching the wing go by. To the pilot the air is coming off  the wing at roughly the angle of attack. To the observer on the ground, if he or she could  see the air, it would be coming off the wing almost vertically. The greater the angle of  attack, the greater the vertical velocity. Likewise, for the same angle of attack, the  greater the speed of the wing the greater the vertical velocity. Both the increase in the  speed and the increase of the angle of attack increase the length of the vertical arrow.  It is this vertical velocity that gives the wing lift.

 Fig 5 How downwash appears to a pilot and to an  observer on the ground.

 

As stated, an observer on the ground would see the air going almost straight down  behind the plane. This can be demonstrated by observing the tight column of air behind a  propeller, a household fan, or under the rotors of a helicopter; all of which are rotating  wings. If the air were coming off the blades at an angle the air would produce a cone  rather than a tight column. If a plane were to fly over a very large scale, the scale  would register the weight of the plane.

 

 If we estimate that the average vertical component of the downwash of a Cessna 172  traveling at 110 knots to be about 9 knots, then to generate the needed 2,300 lbs of lift  the wing pumps a whopping 2.5 ton/sec of air! In fact, as will be discussed later, this  estimate may be as much as a factor of two too low. The amount of air pumped down for a  Boeing 747 to create lift for its roughly 800,000 pounds takeoff weight is incredible  indeed.

 

 Pumping, or diverting, so much air down is a strong argument against lift being just a  surface effect as implied by the popular explanation. In fact, in order to pump 2.5  ton/sec the wing of the Cessna 172 must accelerate all of the air within 9 feet above the  wing. (Air weighs about 2 pounds per cubic yard at sea level.) Figure 6 illustrates the  effect of the air being diverted down from a wing. A huge hole is punched through the fog  by the downwash from the airplane that has just flown over it.

 Fig 6 Downwash and wing vortices in the fog.

 (Photographer Paul Bowen, courtesy of Cessna Aircraft, Co.)

 

 So how does a thin wing divert so much air? When the air is bent around the top of the  wing, it pulls on the air above it accelerating that air down, otherwise there would be  voids in the air left above the wing. Air is pulled from above to prevent voids. This  pulling causes the pressure to become lower above the wing. It is the acceleration of the  air above the wing in the downward direction that gives lift. (Why the wing bends the air  with enough force to generate lift will be discussed in the next section.)

 

 As seen in figure 4, a complication in the picture of a wing is the effect of  "upwash" at the leading edge of the wing. As the wing moves along, air is not only diverted down at the rear of the wing, but air is pulled up at the leading edge. This  upwash actually contributes to negative lift and more air must be diverted down to  compensate for it. This will be discussed later when we consider ground effect.

 

 Normally, one looks at the air flowing over the wing in the frame of reference of the  wing. In other words, to the pilot the air is moving and the wing is standing still. We  have already stated that an observer on the ground would see the air coming off the wing  almost vertically. But what is the air doing above and below the wing? Figure 7 shows an  instantaneous snapshot of how air molecules are moving as a wing passes by. Remember in  this figure the air is initially at rest and it is the wing moving. Ahead of the leading  edge, air is moving up (upwash). At the trailing edge, air is diverted down (downwash).  Over the top the air is accelerated towards the trailing edge. Underneath, the air is  accelerated forward slightly, if at all.

 Fig 7 Direction of air movement around a wing as seen  by an observer on the ground.

 

 In the mathematical aerodynamics description of lift this rotation of the air around  the wing gives rise to the "bound vortex" or "circulation" model. The advent of this model, and the complicated mathematical manipulations associated with it,  leads to the direct understanding of forces on a wing. But, the mathematics required  typically takes students in aerodynamics some time to master.

 

 One observation that can be made from figure 7 is that the top surface of the wing does  much more to move the air than the bottom. So the top is the more critical surface. Thus,  airplanes can carry external stores, such as drop tanks, under the wings but not on top  where they would interfere with lift. That is also why wing struts under the wing are  common but struts on the top of the wing have been historically rare. A strut, or any  obstruction, on the top of the wing would interfere with the lift.

 

Air has viscosity

 

The natural question is "how does the wing divert the air down?" When a  moving fluid, such as air or water, comes into contact with a curved surface it will try  to follow that surface. To demonstrate this effect, hold a water glass horizontally under  a faucet such that a small stream of water just touches the side of the glass. Instead of  flowing straight down, the presence of the glass causes the water to wrap around the glass  as is shown in figure 8. This tendency of fluids to follow a curved surface is known as  the Coanda effect. From Newton’s first law we know that for  the fluid to bend there must be a force acting on it. From Newton’s third law we know  that the fluid must put an equal and opposite force on the object which caused the fluid  to bend.

 

 Fig 8 Coanda effect.

 

Why should a fluid follow a curved surface? The answer is viscosity; the resistance to  flow which also gives the air a kind of "stickiness". Viscosity in air is very  small but it is enough for the air molecules to want to stick to the surface. At the  surface the relative velocity between the surface and the nearest air molecules is exactly  zero. (That is why one cannot hose the dust off of a car and why there is dust on the  backside of the fans in a wind tunnel.) Just above the surface the fluid has some small  velocity. The farther one goes from the surface the faster the fluid is moving until the  external velocity is reached (note that this occurs in less than an inch). Because the  fluid near the surface has a change in velocity, the fluid flow is bent towards the  surface. Unless the bend is too tight, the fluid will follow the surface. This volume of  air around the wing that appears to be partially stuck to the wing is called the "boundary layer".

 

 Lift as a function of angle of attack

 

There are many types of wing: conventional, symmetric, conventional in inverted flight,  the early biplane wings that looked like warped boards, and even the proverbial "barn  door". In all cases, the wing is forcing the air down, or more accurately pulling air  down from above. What each of these wings have in common is an angle of attack with  respect to the oncoming air. It is this angle of attack that is the primary parameter in  determining lift. The inverted wing can be explained by its angle of attack, despite the  apparent contradiction with the popular explanation involving the Bernoulli principle. A  pilot adjusts the angle of attack to adjust the lift for the speed and load. The popular  explanation of lift which focuses on the shape of the wing gives the pilot only the speed  to adjust.

 

 To better understand the role of the angle of attack it is useful to introduce an  "effective" angle of attack, defined such that the angle of the wing to the oncoming air that gives zero lift is defined to be zero degrees. If one then changes the  angle of attack both up and down one finds that the lift is proportional to the angle.  Figure 9 shows the coefficient of lift (lift normalized for the size of the wing) for a  typical wing as a function of the effective angle of attack. A similar lift versus angle  of attack relationship is found for all wings, independent of their design. This is true  for the wing of a 747 or a barn door. The role of the angle of attack is more important  than the details of the airfoil’s shape in understanding lift.

 Fig 9 Coefficient of lift versus the effective angle  of attack.

 

Typically, the lift begins to decrease at an angle of attack of about 15 degrees. The  forces necessary to bend the air to such a steep angle are greater than the viscosity of  the air will support, and the air begins to separate from the wing. This separation of the  airflow from the top of the wing is a stall.

 

The wing as air "scoop"

 

We now would like to introduce a new mental image of a wing. One is used to thinking of  a wing as a thin blade that slices though the air and develops lift somewhat by magic. The  new image that we would like you to adopt is that of the wing as a scoop diverting a  certain amount of air from the horizontal to roughly the angle of attack, as depicted in  figure 10. The scoop can be pictured as an invisible structure put on the wing at the  factory. The length of the scoop is equal to the length of the wing and the height is  somewhat related to the chord length (distance from the leading edge of the wing to the  trailing edge). The amount of air intercepted by this scoop is proportional to the speed  of the plane and the density of the air, and nothing else.

 Fig 10 The wing as a scoop.

 

As stated before, the lift of a wing is proportional to the amount of air diverted down  times the vertical velocity of that air. As a plane increases speed, the scoop diverted  more air. Since the load on the wing, which is the weight of the plane, does not increase  the vertical speed of the diverted air must be decreased proportionately. Thus, the angle  of attack is reduced to maintain a constant lift. When the plane goes higher, the air  becomes less dense so the scoop diverts less air for the same speed. Thus, to compensate  the angle of attack must be increased. The concepts of this section will be used to understand lift in a way not possible with the popular explanation.

 

Lift requires power

 

When a plane passes overhead the formally still air ends up with a downward velocity.  Thus, the air is left in motion after the plane leaves. The air has been given energy.  Power is energy, or work, per time. So, lift must require power. This power is supplied by  the airplane’s engine (or by gravity and thermals for a sailplane).

 

 How much power will we need to fly? The power needed for lift is the work (energy) per  unit time and so is proportional to the amount of air diverted down times the velocity  squared of that diverted air. We have already stated that the lift of a wing is  proportional to the amount of air diverted down times the downward velocity of that air.  Thus, the power needed to lift the airplane is proportional to the load (or weight)  times the vertical velocity of the air. If the speed of the plane is doubled the  amount of air diverted down doubles. Thus the angle of attack must be reduced to give a  vertical velocity that is half the original to give the same lift. The power required for  lift has been cut in half. This shows that the power required for lift becomes less as the airplane's speed increases. In fact, we have shown that this power to create lift is  proportional to one over the speed of the plane.

 

 But, we all know that to go faster (in cruise) we must apply more power. So there must  be more to power than the power required for lift. The power associated with lift,  described above, is often called the "induced" power. Power is also needed to  overcome what is called "parasitic" drag, which is the drag associated with  moving the wheels, struts, antenna, etc. through the air. The energy the airplane imparts  to an air molecule on impact is proportional to the speed squared. The number of molecules  struck per time is proportional to the speed. Thus the parasitic power required to  overcome parasitic drag increases as the speed cubed.

 

 Figure 11 shows the power curves for induced power, parasitic power, and total power  which is the sum of induced power and parasitic power. Again, the induced power goes as  one over the speed and the parasitic power goes as the speed cubed. At low speed the power  requirements of flight are dominated by the induced power. The slower one flies the less  air is diverted and thus the angle of attack must be increased to maintain lift. Pilots  practice flying on the "backside of the power curve" so that they recognizes  that the angle of attack and the power required to stay in the air at very low speeds are considerable.

 Fig 11 Power requirements versus speed.

 

At cruise, the power requirement is dominated by parasitic power. Since this goes as  the speed cubed an increase in engine size gives one a faster rate of climb but does  little to improve the cruise speed of the plane.

 

 Since we now know how the power requirements vary with speed, we can understand drag,  which is a force. Drag is simply power divided by speed. Figure 12 shows the induced,  parasitic, and total drag as a function of speed. Here the induced drag varies as one over  speed squared and parasitic drag varies as the speed squared. Taking a look at these  curves one can deduce a few things about how airplanes are designed. Slower airplanes,  such as gliders, are designed to minimize induced drag (or induced power), which dominates  at lower speeds. Faster airplanes are more concerned with parasite drag (or parasitic  power).

 Fig 12 Drag versus speed.

 

Wing efficiency

 

At cruise, a non-negligible amount of the drag of a modern wing is induced drag.  Parasitic drag, which dominates at cruise, of a Boeing 747 wing is only equivalent to that  of a 1/2-inch cable of the same length. One might ask what effects the efficiency of a  wing. We saw that the induced power of a wing is proportional to the vertical velocity of  the air. If the length of a wing were to be doubled, the size of our scoop would also  double, diverting twice as much air. So, for the same lift the vertical velocity (and thus  the angle of attack) would have to be halved. Since the induced power is proportional to  the vertical velocity of the air, it too is reduced by half. Thus, the lifting efficiency  of a wing is proportional to one over the length of the wing. The longer the wing the less  induced power required to produce the same lift, though this is achieved with and increase  in parasitic drag. Low speed airplanes are effected more by induced drag than fast  airplanes and so have longer wings. That is why sailplanes, which fly at low speeds, have  such long wings. High-speed fighters, on the other hand, feel the effects of parasite drag  more than our low speed trainers. Therefore, fast airplanes have shorter wings to lower  parasite drag.

 

 There is a misconception by some that lift does not require power. This comes from  aeronautics in the study of the idealized theory of wing sections (airfoils). When dealing  with an airfoil, the picture is actually that of a wing with infinite span. Since we have  seen that the power necessary for lift is proportional to one over the length of the wing,  a wing of infinite span does not require power for lift. If lift did not require power  airplanes would have the same range full as they do empty, and helicopters could hover at  any altitude and load. Best of all, propellers (which are rotating wings) would not require power to produce thrust. Unfortunately, we live in the real world where both lift  and propulsion require power.

 

 Power and wing loading

 

Let us now consider the relationship between wing loading and power. Does it take more  power to fly more passengers and cargo? And, does loading affect stall speed? At a  constant speed, if the wing loading is increased the vertical velocity must be increased  to compensate. This is done by increasing the angle of attack. If the total weight of the  airplane were doubled (say, in a 2g turn) the vertical velocity of the air is doubled to  compensate for the increased wing loading. The induced power is proportional to the load  times the vertical velocity of the diverted air, which have both doubled. Thus the induced  power requirement has increased by a factor of four! The same thing would be true if the  airplane’s weight were doubled by adding more fuel, etc.

 

 One way to measure the total power is to look at the rate of fuel consumption. Figure  13 shows the fuel consumption versus gross weight for a large transport airplane traveling  at a constant speed (obtained from actual data). Since the speed is constant the change in  fuel consumption is due to the change in induced power. The data are fitted by a constant  (parasitic power) and a term that goes as the load squared. This second term is just what  was predicted in our Newtonian discussion of the effect of load on induced power.

Fig 13 Fuel consumption versus load for a large  transport airplane

 traveling at a constant speed.

 

The increase in the angle of attack with increased load has a downside other than just  the need for more power. As shown in figure 9 a wing will eventually stall when the air  can no longer follow the upper surface. That is, when the critical angle is reached.  Figure 14 shows the angle of attack as a function of airspeed for a fixed load and for a  2-g turn. The angle of attack at which the plane stalls is constant and is not a function  of wing loading. The stall speed increases as the square root of the load. Thus,  increasing the load in a 2-g turn increases the speed at which the wing will stall by 40%.  An increase in altitude will further increase the angle of attack in a 2-g turn. This is  why pilots practice "accelerated stalls" which illustrates that an airplane can  stall at any speed. For any speed there is a load that will induce a stall.

Fig 14 Angle of attack versus speed

 for straight and level flight and for a 2-g turn.

 

 Wing vortices

 

One might ask what the downwash from a wing looks like. The downwash comes off the wing  as a sheet and is related to the details on the load distribution on the wing. Figure 15  shows, through condensation, the distribution of lift on an airplane during a high-g  maneuver. From the figure one can see that the distribution of load changes from the root  of the wing to the tip. Thus, the amount of air in the downwash must also change along the  wing. The wing near the root is "scooping" up much more air than the tip. Since  the root is diverting so much air the net effect is that the downwash sheet will begin to  curl outward around itself, just as the air bends around the top of the wing because of  the change in the velocity of the air. This is the wing vortex. The tightness of the  curling of the wing vortex is proportional to the rate of change in lift along the wing.  At the wing tip the lift must rapidly become zero causing the tightest curl. This is the  wing tip vortex and is just a small (though often most visible) part of the wing vortex.  Returning to figure 6 one can clearly see the development of the wing vortices in the  downwash as well as the wing tip vortices.

 Fig 15 Condensation showing the distribution of lift  along a wing.

 The wingtip vortices are also seen.

 (from Patterns in the Sky, J.F. Campbell and J.R. Chambers, NASA SP-514.)

 

 Winglets (those small vertical extensions on the tips of some wings) are used to  improve the efficiency of the wing by increasing the effective length of the wing. The  lift of a normal wing must go to zero at the tip because the bottom and the top  communicate around the end. The winglets blocks this communication so the lift can extend  farther out on the wing. Since the efficiency of a wing increases with length, this gives  increased efficiency. One caveat is that winglet design is tricky and winglets can  actually be detrimental if not properly designed.

 

Ground effect

 

Another common phenomenon that is misunderstood is that of ground effect. That is the  increased efficiency of a wing when flying within a wing length of the ground. A low-wing  airplane will experience a reduction in drag by 50% just before it touches down. There is  a great deal of confusion about ground effect. Many pilots (and the FAA VFR Exam-O-Gram  No. 47) mistakenly believe that ground effect is the result of air being compressed  between the wing and the ground.

 

 To understand ground effect it is necessary to have an understanding of upwash. For the  pressures involved in low speed flight, air is considered to be non-compressible. When the  air is accelerated over the top of the wing and down, it must be replaced. So some air  must shift around the wing (below and forward, and then up) to compensate, similar to the  flow of water around a canoe paddle when rowing. This is the cause of upwash.

 

 As stated earlier, upwash is accelerating air in the wrong direction for lift. Thus a  greater amount of downwash is necessary to compensate for the upwash as well as to provide  the necessary lift. Thus more work is done and more power required. Near the ground the  upwash is reduced because the ground inhibits the circulation of the air under the wing.  So less downwash is necessary to provide the lift. The angle of attack is reduced and so  is the induced power, making the wing more efficient.

 

 Earlier, we estimated that a Cessna 172 flying at 110 knots must divert about 2.5  ton/sec to provide lift. In our calculations we neglected the upwash. From the magnitude  of ground effect, it is clear that the amount of air diverted is probably more like 5  ton/sec.

 

Conclusions

 

Let us review what we have learned and get some idea of how the physical description  has given us a greater ability to understand flight. First what have we learned:

   The amount of air diverted by the wing is proportional to the speed of the wing  and the air density.

    The vertical velocity of the diverted air is proportional to the speed of the  wing and the angle of attack.

    The lift is proportional to the amount of air diverted times the vertical  velocity of the air.

    The power needed for lift is proportional to the lift times the vertical velocity  of the air.

 

 Now let us look at some situations from the physical point of view and from the  perspective of the popular explanation.

    The plane’s speed is reduced. The physical view says that the amount of air  diverted is reduced so the angle of attack is increased to compensate. The power needed  for lift is also increased. The popular explanation cannot address this.

    The load of the plane is increased. The physical view says that the amount of air  diverted is the same but the angle of attack must be increased to give additional lift.  The power needed for lift has also increased. Again, the popular explanation cannot  address this.

    A plane flies upside down. The physical view has no problem with this. The plane  adjusts the angle of attack of the inverted wing to give the desired lift. The popular  explanation implies that inverted flight is impossible.

 

As one can see, the popular explanation, which fixates on the shape of the wing, may  satisfy many but it does not give one the tools to really understand flight. The physical  description of lift is easy to understand and much more powerful.

 

 

 

The preceding is an article by David Anderson, Fermi National Accelerator Laboratory, and Scott Eberhardt, Department of Aeronautics and Astronautics, University of Washington.