Forces of 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, in straight and level flight these four forces are distributed with the lift force pointing upward, opposite to the weight, the thrust pointing forward in the direction of flight, 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, and the thrust force must be greater than or equal to the drag force. The terms and concepts that were defined earlier in this chapter can now be used to compute each of these forces.

Direction of Forces in Straight and Level Flight

Weight

The weight of the aircraft is equal to its mass times the acceleration of gravity, as discussed earlier in the chapter. It is a natural force, and it is a measure of the force that pulls the plane down towards the earth. 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 figure below shows two streamlines about a typical airfoil; 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 approached the front of the airfoil, however, their velocity will start to change. Initially, each will start to move faster; their velocities will increase. As they turn back downward along the back half of the airfoil, they will slow back down to their initial freestream velocity. 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 and hence a net force is produced.

When the total force on each surface is computed, the difference in the pressures between the upper and lower surfaces will create a smaller force on the upper surface, and a larger force on the lower surface. The smaller force will be pointed downward, and the larger force will be pointing upwards. When the two forces are combined, the net force (lower force minus the upper force because the directions are opposing) is the lift force, and it will be directed upwards.

The shape of the airfoil (wing) is important for lift, and is designed carefully. Most airfoils today have camber, or curved upper surfaces and flatter lower surfaces. These airfoils generate lift even when the flow is horizontal (flat). The Wright brothers used symmetric airfoils in their airplane design. Since the upper and lower surfaces were the same the pressures on either surface (top or bottom) are the same, so the net combined force on the airfoil is zero and there is no lift! 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 turning with respect to the flow is called the angle of attack. A pilot can increase the lift for both cambered and symmetric wings by increasing the angle of attack of the wing with respect to the freestream flow. 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 flow on the upper surface separates (see diagram below). The streamline above the upper surface now travels over the separation bubble. The pressures on the upper surface suddenly increase, and the net lift force drops drastically.

Airflow deflection is another way to explain. 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 the lift on a wing is to extend the flaps. 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 airplane is increased, the lift will increase dramatically. If the velocity is doubled, the lift will be four times as large.

The generation of lift is also used in other applications. Race car designers use airfoil-like surfaces to generate negative lift, or a 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. In other words, the additional downward facing force helps offset the opposing forces in the turns.

Lift on an airplane or a bird is primarily generated by the wings. The amount of lift generated by the body, or fuselage, of the plane or bird and the tail is very small. So, the lift force generated by the wings is the basic lift force on the airplane. Its direction is upward, opposite the weight. If the lift is greater than the weight, the plane will fly. After the plane has climbed to the cruising altitude, it will level off (decrease the angle of attack to zero), and the lift force will be equal to or very slightly larger than the weight. If the lift force is smaller than the weight, the plane will lose altitude and return to earth.

Thrust

A forward direction force called the thrust is generated by the engines of the airplane (or by the flapping of a bird's wings). The engines push high velocity air out behind the plane, and the difference between the high velocity exhaust gases and the original velocity of the airplane creates the forward directed thrust. Because its direction is perpendicular to the forces of weight and lift, the thrust force is unaffected by either.

Drag

The drag is the fourth of the major forces for flight. It is a resistance force to the forward motion of any object, including planes. There are four types of drag: friction drag, form drag, induced drag, and wave drag, and they are functions of the shape of the body, the smoothness of the surfaces, and the velocity of the plane. All four sum together for the overall drag force. Since the drag force resists the motion of the plane, its direction is opposite the thrust force. 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. In the boundary layer along each surface, a skin friction coefficient can be computed as a function of the velocity of the air and the surface roughness. The summation of all the local skin friction coefficients is used to compute the friction drag. Aerodynamicists design the outside of the airplanes to be smooth surfaces so that the friction coefficients and therefore the friction drag will be small. If a person were to look at the surface 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. Sometimes the aerodynamicist will design small tabs to be placed along a wing surface to trip the boundary layer for transition to turbulence. While this increases the friction drag slightly, the increase in lift and control of the airplane are judged worth the cost.

The form drag, or pressure drag, as it is sometimes called, is directly related to the shape of the body or airplane. A smooth, streamlined shape will generate less form drag than a blunted or flat body. The term streamlined comes from the idea that a shape is designed so that streamlines above and below the body barely change and rejoin smoothly right behind the body. A thin, relatively sharp-nosed airfoil is a perfect example of streamlining.

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

Form drag is easy to demonstrate using a hand out the window of a moving car. If the hand is held flat and horizontal to the ground, it is basically a streamlined object, and the observer feels only 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! If the observer could see what was happening in the invisible air, he or she would see many little swirls of air, or eddies, behind the hand. The streamlines around the hand would have to travel around these eddies, the pressures would be higher along the streamlines, and the drag is increased dramatically.

An interesting offshoot of the discussion of form drag is in the design of large banners like those used to advertise school fairs, church picnics, or museum openings. If a large cloth or plastic banner is strung between two buildings across a street, and the wind blows against it, it has a high form drag. This form drag can be so large that the banner rips and tears, and it may be destroyed. Banner designers now know that they must include slits in the fabric to allow the air to move through the banner, so that the drag on the banner is decreased.

These first two types of drag are often added together and called the profile drag by aerodynamicists. Pilots call the sum of these two drags the parasite drag. In either case, these drags are primarily a function of the shape of the body and the smoothness of the surfaces. All objects moving through a fluid will have these drag forces. Airplanes, because of the amount of lift generated and the velocities at which they travel, are also subject to two additional drag forces, the induced drag and the 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 force can be generated in the direction opposing the motion, or in the direction of drag. This excess is called the induced drag, and because of its direction, it causes a decrease in the plane's motion. Therefore, it is considered a type of drag force. It is one of the odder concepts that an aerodynamicist must consider during the design of an airplane. Any change that he or she can make to increase the lift is a positive change. In the design of a better wing a designer will optimize the generation of the lift so as to minimize the generation of induced drag; a well designed wind will generate the needed lift, while minimizing the induceddrag. However, other factors such as structural strength, overall weight, cost and complexity will also control the design of the "optimal" wing.

The last of the four types of drag is the wave drag. This generally only occurs when the airplane is flying faster than the speed of sound in supersonic flight. It 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 supersonic locally. Since most commercial jets today fly at transonic speeds, wave drag is an important part of the total drag.

Summary

Every pilot has a working knowledge of these four basic forces of flight, and he or she uses this knowledge to fly the plane. Aerobatic pilots, in particular, are constantly balancing these forces, and using the concepts in this chapter to design amazing stunts to delight the crowds. 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 straight up into the air and fly straight up as far as they can, let the plane hang there for a second, then let it fall back down its original path. In this configuration, the lift force now points to the right, the thrust force points straight up, and the weight and drag forces point downward towards the earth. The drag and weight forces together exceed the thrust, and the higher the plane flies, the less thrust is generated. Eventually, they are even, and the plane seems to hang there for a second or two. Then the weight and drag forces dominate, and the plane drops backwards. After a few heartbreaking seconds, the pilot will turn the airplane back so the nose points downward into the direction of the flow, increase the thrust, and re-establish the original force balances for level flight.

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Last modified: Sat Jun 20 13:33:53 PDT 1998

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