Forces of flight Summary

Humans’ first attempts to fly, inspired by birds, were limited until humans realized they could not fly like birds. Birds, with their very light weight, great strength, and complex biological design, can use their wings to create both lift and thrust to overcome the natural forces of weight and drag, and to maintain control. Humans, in contrast, had to invent a different approach to meet any success in aviation. The functions of lift and thrust had to be separated. For that, wings and engines were introduced. While wings produce lift, engines produce thrust.

Following the first flights made by Orville and Wilbur Wright in December, 1903, the pace of aeronautical development accelerated, and the progress made in overcoming the natural forces in the aviation industry in following decades was dramatic. The understanding of natural forces is thus as important for an airplane’s aerodynamics as the creation of artificial forces to counterbalance these natural forces. The engine and propeller combination is designed to produce thrust to overcome drag. The wing is designed to produce lift to overcome weight, or gravity. In unaccelerated, straight-and-level flight, which is coordinated flight at a constant altitude and heading, lift equals weight and thrust equals drag. Nevertheless, lift and weight will not equal thrust and drag. In everyday vocabulary, the upward forces balance the downward forces, and forward forces balance the rearward forces. This statement is true whether or not the contributions due to weight, drag, lift, and thrust are calculated separately. Any inequality between lift and weight will result in the airplane entering a climb or descent. Any inequality between thrust and drag while maintaining straight-and-level flight will result in acceleration or retardation until the two forces become balanced. However, there are a couple of paradoxes surrounding this information. The first paradox is that in a low-speed, high-power climb, the amount of lift is less than the amount of weight. In this situation, thrust is supporting part of the weight. The second paradox is that in a low-power, high-speed descent, the amount of lift is again less than the amount of weight. In this situation, the drag is supporting part of the weight. In light aircraft, the amount of lift ordinarily is approximately ten times the amount of drag.

The motion of an aircraft through the air depends on the size of these four forces. The weight of an airplane is determined by the size and material used in the airplane’s construction and on the payload and fuel that the airplane carries. The lift and drag are aerodynamical forces that depend on the shape and the size of the aircraft, air conditions, and the flight speed and direction relative to the air velocity. The thrust is determined by the size and type of the propulsion system used in the airplane and on the throttle setting selected during the flight.

The relative wind velocity acting on the airplane contributes a certain amount of force, called total aerodynamic force. This force can be resolved into two components perpendicular to each other along the directions of lift and drag. Lift is the component of aerodynamic force directly perpendicular to the relative wind velocity. Drag is the component of aerodynamic force acting parallel to the relative motion of the wind. Weight is the force directed always downward toward the center of the earth. It is equal to the mass of the airplane multiplied by the acceleration due to the gravity, or the strength of the gravitational field. Thrust is the force produced by the engine and is usually more or less parallel to the long axis of the airplane.

Weight, or gravity, is the force which always acts downward, toward the center of the earth. It is the total sum of the masses of all its components and contents multiplied by the strength of the gravity, commonly referred to as the number of g’s. The weight may be considered to act as a single force, representing all its components and contents, through a single point called the center of gravity.

Weight is the most reliable force, which always acts in the same direction and gradually decreases as airplane fuel is used. The center of gravity shifts as the weight is redistributed.

Although the terms “mass” and “weight” are often confused with each other, it is important to distinguish between them. Mass is a property of a body itself and measures a body’s quantity of matter. Weight, in contrast, is a force representing the force of gravity acting on a body. It is also loosely called gravity.

To illustrate the difference, one could describe an object that is taken to the Moon, where the force of gravity is weaker, about one-sixth that on Earth. On the Moon, the object will weigh only about one-sixth as much as it did on Earth. The mass of the object will be the same on the Moon or anywhere else. In other words, it will continue to have the same amount of matter.

When an object moves relative to a fluid, either a gas or a liquid, the fluid exerts a frictional force on the object. This force which is referred to as a drag force, is due to the viscosity, or stickiness, of the fluid and also, at high speeds, to the turbulence behind and around the object. To characterize the motion of an object at different speeds relative to the fluid and to understand the associated drag, it is useful to understand Reynolds numbers.

The Reynolds number depends on the properties, such as length and velocity, of the fluid and the object relative to the fluid. In case of an airplane, which flies through air, the Reynolds number for air is smaller than that for water because of the lower density of the air. For example, an object of one millimeter long moving with a speed of 1 millimeter per second through water has the same Reynolds number as an object 2 millimeters long moving at a rate of 7 millimeters per second in the air. The drag manifests itself differently for different Reynolds numbers associated to it.

When the Reynolds number is less than 1, as in the case of fairly small objects, such as raindrops, the viscous force is directly proportional to the speed of the object. For large Reynolds numbers, usually above a value between about 1 and 10, there will be turbulence behind the body, known as wake, and hence, the drag force will be larger and it increases as the square of the velocity instead of its linear dependence on the velocity. When the Reynolds number approaches a value of around 1,000,000, the drag force increases abruptly. For above this value, turbulence exits in the layer of fluid lying next to the body all along its sides. For streamlined objects, however, there will be less turbulence and, hence, less drag. The flow is said to be streamlined of laminar flow if the flow is smooth, such that neighboring layers of the fluid slide by each other smoothly.

There are several types of drag, subdivided and classified according to their action on an airplane. Pressure drag is the force pushing a horizontally moving object against the front vertical surface of the object. Friction drag is produced on a horizontally moving object by applying a force along the surface of the object. Friction drag is proportional to the viscosity of the fluid. Fortunately, air has rather low viscosity, so in most situations the amount of friction drag is small compared to that of pressure drag. In contrast, pressure drag does not depend very strongly on viscosity. Instead, it depends on the density of the air.

Both friction drag and pressure drag create a force proportional to the area involved and the square of the airspeed. Part of the pressure drag that a wing produces depends on the amount of lift it is producing. This part of the drag is called induced drag. The rest of the drag is called parasite drag. The part of the parasite drag that is not due to friction is called form drag, because it is extremely sensitive to the detailed form and shape of the airplane.

A streamlined object can have ten times less form drag than a nonstreamlined object of comparable frontal area. The peak pressure in front of the two shapes will be the same. However, the streamlined shape causes the air to accelerate, so the region of highest pressure is smaller, and more importantly, the streamlined shape cultivates high pressure behind the object that pushes it forward, thus canceling most of the pressure drag. This situation is called pressure recovery. An object moving through the air has a high-pressure region in front, but a properly streamlined object will have a high-pressure region in back as well. However, streamlining is never perfect; there is always at least some net pressure drag.

Induced drag also contributes to pressure drag whenever lift is being produced, even for perfectly streamlined objects in the absence of separation. The flow pattern near a nonstreamlined object is not symmetric fore and aft because the streamlines separate from the object as they go around the sharp corners of the plate. Except in the cases of very small objects or very low speeds, pressure drag is larger than friction drag, even for well-streamlined objects.

The pressure drag of a nonstreamlined object is much larger still. For this reason even the smallest parts of high-performance aircraft, such as fuel-cap handles, are precisely aligned with the airflow. An inevitable exception involves the air that has to flow through the engine compartment to cool the engine. A lot of the air has to flow through narrow channels. The resulting friction drag, called cooling drag, amounts to 30 percent of the total drag in some airplanes.

Unlike pressure drag, friction drag cannot possibly be canceled. It can, however, be minimized. The way to minimize friction drag is to minimize the total area, called wetted area, that has high-speed air flowing along it. The way to reduce form drag is to minimize separation by streamlining all parts.

It is often convenient to express the drag force as a dimensionless quantity by the coefficient of drag. In that case, the drag force is proportional to the coefficient of drag, the density of the air, the square of the true airspeed, and the relevant area, which is typically taken to be the wing area excluding the surface area of the fuselage.

In the mushing regime, most of the drag is induced drag. As the airplane goes more slowly, induced drag increases dramatically, and parasite drag becomes almost neglible. At high airspeeds, parasite drag is dominant, and induced drag becomes almost negligible. In a high-speed regime that includes normal cruise, the power required increases rapidly with increasing airspeed.

Parasite drag is the dominant contribution to the coefficient of drag, and it is more or less independent of airspeed. Induced drag decreases as the airspeed increases, but this is a relatively minor contribution in this regime. Ways of reducing induced drag include wing tapering, wingtip modification, and employing washout and a high aspect ratio. The aspect ratio is defined as the ratio between the span and the mean chord. The mean chord, in turn, is the ratio between the wing area and the wingspan.

Airplane wings and other airfoils are designed to deflect the air so that, although streamline flow is largely maintained, the streamlines are crowded together above the wing. Just as the flow lines are crowded together in a pipe constriction where the velocity is high, so the crowded streamlines above the wing indicate that the airspeed is greater than below the wing. Hence, according to Bernoulli’s principle which states that velocity increases as pressure decreases, the air pressure above the wing is less than that below the wing, and there is a net upward force, which is called dynamic lift, or lift.

In fact, Bernoulli’s principle is only one aspect of the lift on a wing. Wings are usually tilted slightly upward so that air striking the bottom surface is deflected downward. The change in momentum, a product of mass and velocity, of the rebounding air molecules results in an additional upward force on the wing. As the air passes over the wing, it is bent down. The bending of the air is the action; the reaction is the lift on the wing. To generate sufficient lift, a wing must divert air down. To increase the lift, either or both the diverted air and downward velocity must be incremented.

The downward velocity behind the wing is called downwash. The vertical downward airspeed varies as the angle of attack. The angle of attack is the angle of the chord line. The direction of the relative airflow on the wing, along the chord line, or chord length, is the distance from the loading edge of the wing to the trailing edge. As the wing moves along while the air is diverted at the rear end of the wing, it is pulled up at the leading edge, also giving rise to upwash. This upwash contributes negatively to the lift. Turbulence also plays an important role in contributing to the lift.

Like drag, lift can also be expressed in a dimensionless quantity in terms of the coefficient of lift. In that way, the lift force is proportional to the coefficient of lift and the density of the air, the square of true airspeed and relevant area. The coefficient of lift is a ratio that basically measures how effectively the wing turns the available dynamic pressure into a useful average suction over the wing. The dynamic pressure is the product of the air density and the square of the velocity. This is the difference between total pressure and static pressure. The total pressure is the pressure in air that has been brought to rest from the free stream, and the static pressure is the ambient pressure at the same level as the aircraft. In actual flight, pilots are not free to make any amount of lift they want. The lift is nearly always equal to the weight multiplied by the load factor; the coefficient of lift depends directly on the load factor, and inversely, on the square of the airspeed. Because of the airspeed squared, the airplane must fly at a very high coefficient of lift in order to support its weight at low airspeeds.

As there is a center of gravity, there is also a center of pressure, which is a point through which the resultant lift acts. The center of pressure changes with change of wing shape. A number, called the lift-drag ratio, is considered best when it produces the most efficient speed for maximum range with minimum drag.

A force pushing an airplane, or any object, forward is called thrust. The thrust is produced 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, countering drag.

Since the Wright brothers first flew in 1903, aeronautical engineers have created a multitude of airplane types, every one of which has dealt with the same four forces of weight, drag, lift, and thrust. All people have to deal with the challenges of stability with respect to these forces. Flying faster than the speed of sound has its own special demands, but the underlying forces of weight, drag, lift, and thrust remain the same.

In some sense, it is easier to fly in space, which is devoid of air, than it is to fly in air. However, spaceflight has its own special challenges. In space, one must deal with only two forces, weight and thrust. Thrust provides the force to lift a rocket into space. Once in orbit, a spacecraft no longer needs propulsion. Short bursts from smaller rockets are used to maneuver the spacecraft. To change its orientation, a spacecraft applies torque, a twisting force, by firing small rockets called thrusters or by spinning internal reaction wheels.

• Barnard, R. H., and D. R. Philpott. Aircraft Flight. 2d ed. Essex, England: Addison-Wesley Longman, 1995. An excellent, nonmathematical text on aeronautics, in which illustrations and physical descriptions, rather than equations, are used to explain virtually all aspects of airplane flight.
• Craig, Gail. Stop Assuming Bernoulli! How Airplanes Really Fly. Anderson, Ind., Regenerative Press, 1997. A vivid description of airplane flight that clarifies some misconceptions about the forces of flight.
• Giancoli, D. C. “Fluids.” In Physics with Application. 3d ed. Englewood Cliffs, N.J.: Prentice Hall, 1991. A brief description of underlying physical principles of forces of flight with simple equations and good illustrations.
• Wegener, Peter P. What Makes Airplanes Fly? History, Science, and Applications of Aerodynamics. New York: Springer-Verlag, 1991. A well-written and wellillustrated but slightly technical review of the historical development of aerodynamics and airplanes.

Aerodynamics

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Gravity

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Microgravity

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Roll and pitch

Spaceflight

Wind tunnels