Principles Of Flight (Aerodynamics¨Forces Acting on the Aircraft¨) II

Forces Acting on the Aircraft
Thrust, drag, lift, and weight are forces that act upon all aircraft in ﬂight. Understanding how these forces work and knowing how to control them with the use of power and ﬂight controls are essential to ﬂight. This chapter discusses the aerodynamics of ﬂight—how design, weight, load factors, and gravity affect an aircraft during ﬂight maneuvers.

The four forces acting on an aircraft in straight-and-level, unaccelerated ﬂight are thrust, drag, lift, and weight. They are deﬁned as follows:

Thrust—the forward force produced by the powerplant/ propeller or rotor. It opposes or overcomes the force of drag. As a general rule, it acts parallel to the longitudinal axis. However, this is not always the case, as explained later.
Drag—a rearward, retarding force caused by disruption of airﬂow by the wing, rotor, fuselage, and other protruding objects. Drag opposes thrust, and acts rearward parallel to the relative wind.
Weight—the combined load of the aircraft itself, the crew, the fuel, and the cargo or baggage. Weight pulls the aircraft downward because of the force of gravity. It opposes lift, and acts vertically downward through the aircraft’s center of gravity (CG).
Lift—opposes the downward force of weight, is produced by the dynamic effect of the air acting on the airfoil, and acts perpendicular to the ﬂightpath through the center of lift.

In steady ﬂight, the sum of these opposing forces is always zero. There can be no unbalanced forces in steady, straight ﬂight based upon Newton’s Third Law, which states that for every action or force there is an equal, but opposite, reaction or force. This is true whether ﬂying level or when climbing or descending.

It does not mean the four forces are equal. It means the opposing forces are equal to, and thereby cancel, the effects of each other. In Figure 4-1 the force vectors of thrust, drag, lift, and weight appear to be equal in value. The usual explanation states (without stipulating that thrust and drag do not equal weight and lift) that thrust equals drag and lift equals weight. Although basically true, this statement can be misleading. It should be understood that in straight, level, unaccelerated ﬂight, it is true that the opposing lift/weight forces are equal. They are also greater than the opposing forces of thrust/drag that are equal only to each other. Therefore, in steady ﬂight:

The sum of all upward forces (not just lift) equals the sum of all downward forces (not just weight).
The sum of all forward forces (not just thrust) equals Correct relationship of forces acting on an airplane

Figure 4-1. Relationship of forces acting on an airplane.

This reﬁnement of the old “thrust equals drag; lift equals weight” formula explains that a portion of thrust is directed upward in climbs and acts as if it were lift while a portion of weight is directed backward and acts as if it were drag. [Figure 4-2]

Figure 4-2. Force vectors during a stabilized climb.

In glides, a portion of the weight vector is directed forward, and, therefore, acts as thrust. In other words, any time the ﬂightpath of the aircraft is not horizontal, lift, weight, thrust, and drag vectors must each be broken down into two components.

Discussions of the preceding concepts are frequently omitted in aeronautical texts/handbooks/manuals. The reason is not that they are inconsequential, but because the main ideas with respect to the aerodynamic forces acting upon an airplane in ﬂight can be presented in their most essential elements without being involved in the technicalities of the aerodynamicist. In point of fact, considering only level ﬂight, and normal climbs and glides in a steady state, it is still true that lift provided by the wing or rotor is the primary upward force, and weight is the primary downward force.

By using the aerodynamic forces of thrust, drag, lift, and weight, pilots can ﬂy a controlled, safe ﬂight. A more detailed discussion of these forces follows.

Thrust
For an aircraft to move, thrust must be exerted and be greater than drag. The aircraft will continue to move and gain speed until thrust and drag are equal. In order to maintain a constant airspeed, thrust and drag must remain equal, just as lift and weight must be equal to maintain a constant altitude. If in level ﬂight, the engine power is reduced, the thrust is lessened, and the aircraft slows down. As long as the thrust

Figure 4-3. Angle of attack at various speeds.

is less than the drag, the aircraft continues to decelerate until its airspeed is insufﬁcient to support it in the air.

Likewise, if the engine power is increased, thrust becomes greater than drag and the airspeed increases. As long as the thrust continues to be greater than the drag, the aircraft continues to accelerate. When drag equals thrust, the aircraft ﬂies at a constant airspeed.

Straight-and-level ﬂight may be sustained at a wide range of speeds. The pilot coordinates angle of attack (AOA)—the acute angle between the chord line of the airfoil and the direction of the relative wind—and thrust in all speed regimes if the aircraft is to be held in level ﬂight. Roughly, these regimes can be grouped in three categories: low-speed ﬂight, cruising ﬂight, and high-speed ﬂight.

When the airspeed is low, the AOA must be relatively high if the balance between lift and weight is to be maintained. [Figure 4-3] If thrust decreases and airspeed decreases, lift becomes less than weight and the aircraft starts to descend. To maintain level ﬂight, the pilot can increase the AOA an amount which will generate a lift force again equal to the weight of the aircraft. While the aircraft will be ﬂying more slowly, it will still maintain level ﬂight if the pilot has properly coordinated thrust and AOA.

Straight-and-level ﬂight in the slow-speed regime provides some interesting conditions relative to the equilibrium of forces

because with the aircraft in a nose-high attitude, there is a vertical component of thrust that helps support it. For one thing, wing loading tends to be less than would be expected. Most pilots are aware that an airplane will stall, other conditions being equal, at a slower speed with the power on than with the power off. (Induced airﬂow over the wings from the propeller also contributes to this.) However, if analysis is restricted to the four forces as they are usually deﬁned during slow-speed ﬂight the thrust is equal to drag, and lift is equal to weight.

During straight-and-level ﬂight when thrust is increased and the airspeed increases, the AOA must be decreased. That is, if changes have been coordinated, the aircraft will remain in level ﬂight, but at a higher speed when the proper relationship between thrust and AOA is established.

If the AOA were not coordinated (decreased) with an increase of thrust, the aircraft would climb. But decreasing the AOA modiﬁes the lift, keeping it equal to the weight, and the aircraft remains in level ﬂight. Level ﬂight at even slightly negative AOA is possible at very high speed. It is evident then, that level ﬂight can be performed with any AOA between stalling angle and the relatively small negative angles found at high speed.

Some aircraft have the ability to change the direction of the thrust rather than changing the AOA. This is accomplished either by pivoting the engines or by vectoring the exhaust gases. [Figure 4-4]

Figure 4-4. Some aircraft have the ability to change the direction of thrust.

Drag
Drag is the force that resists movement of an aircraft through the air. There are two basic types: parasite drag and induced drag. The ﬁrst is called parasite because it in no way functions to aid ﬂight, while the second, induced drag, is a result of an airfoil developing lift.

Parasite Drag Parasite drag is comprised of all the forces that work to slow an aircraft’s movement. As the term parasite implies, it is the drag that is not associated with the production of lift. This includes the displacement of the air by the aircraft, turbulence generated in the airstream, or a hindrance of air moving over the surface of the aircraft and airfoil. There are three types of parasite drag: form drag, interference drag, and skin friction.

Form Drag Form drag is the portion of parasite drag generated by the aircraft due to its shape and airﬂow around it. Examples include the engine cowlings, antennas, and the aerodynamic shape of other components. When the air has to separate to move around a moving aircraft and its components, it eventually rejoins after passing the body. How quickly and smoothly it rejoins is representative of the resistance that it creates which requires additional force to overcome. [Figure 4-5]

Figure 4-5. Form drag.

Notice how the ﬂat plate in Figure 4-5 causes the air to swirl around the edges until it eventually rejoins downstream. Form drag is the easiest to reduce when designing an aircraft. The solution is to streamline as many of the parts as possible.

Interference

Drag Interference drag comes from the intersection of airstreams that creates eddy currents, turbulence, or restricts smooth airﬂow. For example, the intersection of the wing and the fuselage at the wing root has signiﬁcant interference drag. Air ﬂowing around the fuselage collides with air ﬂowing over the wing, merging into a current of air different from the two original currents. The most interference drag is observed when two surfaces meet at perpendicular angles. Fairings are used to reduce this tendency. If a jet ﬁghter carries two identical wing tanks, the overall drag is greater than the sum of the individual tanks because both of these create and generate interference drag. Fairings and distance between lifting surfaces and external components (such as radar antennas hung from wings) reduce interference drag. [Figure 4-6]

Figure 4-6. A wing root can cause interference drag.

Skin Friction Drag Skin friction drag is the aerodynamic resistance due to the contact of moving air with the surface of an aircraft. Every surface, no matter how apparently smooth, has a rough, ragged surface when viewed under a microscope. The air molecules, which come in direct contact with the surface of the wing, are virtually motionless. Each layer of molecules above the surface moves slightly faster until the molecules are moving at the velocity of the air moving around the aircraft. This speed is called the free-stream velocity. The area between the wing and the free-stream velocity level is about as wide as a playing card and is called the boundary layer. At the top of the boundary layer, the molecules increase velocity and move at the same speed as the molecules outside the boundary layer. The actual speed at which the molecules move depends upon the shape of the wing, the viscosity (stickiness) of the air through which the wing or airfoil is moving, and its compressibility (how much it can be compacted).

The airﬂow outside of the boundary layer reacts to the shape of the edge of the boundary layer just as it would to the physical surface of an object. The boundary layer gives any object an “effective” shape that is usually slightly different from the physical shape. The boundary layer may also separate from the body, thus creating an effective shape much different from the physical shape of the object. This change in the physical shape of the boundary layer causes a dramatic decrease in lift and an increase in drag. When this happens, the airfoil has stalled.

In order to reduce the effect of skin friction drag, aircraft designers utilize flush mount rivets and remove any irregularities which may protrude above the wing surface. In addition, a smooth and glossy ﬁnish aids in transition of air across the surface of the wing. Since dirt on an aircraft disrupts the free ﬂow of air and increases drag, keep the surfaces of an aircraft clean and waxed.

Induced Drag

The second basic type of drag is induced drag. It is an established physical fact that no system that does work in the mechanical sense can be 100 percent efﬁcient. This means that whatever the nature of the system, the required work is obtained at the expense of certain additional work that is dissipated or lost in the system. The more efﬁcient the system, the smaller this loss.

In level ﬂight the aerodynamic properties of a wing or rotor produce a required lift, but this can be obtained only at the expense of a certain penalty. The name given to this penalty is induced drag. Induced drag is inherent whenever an airfoil is producing lift and, in fact, this type of drag is inseparable from the production of lift. Consequently, it is always present if lift is produced.

An airfoil (wing or rotor blade) produces the lift force by making use of the energy of the free airstream. Whenever an airfoil is producing lift, the pressure on the lower surface of it is greater than that on the upper surface (Bernoulli’s Principle). As a result, the air tends to ﬂow from the high pressure area below the tip upward to the low pressure area on the upper surface. In the vicinity of the tips, there is a tendency for these pressures to equalize, resulting in a lateral ﬂow outward from the underside to the upper surface. This lateral ﬂow imparts a rotational velocity to the air at the tips, creating vortices, which trail behind the airfoil.

When the aircraft is viewed from the tail, these vortices circulate counterclockwise about the right tip and clockwise about the left tip. [Figure 4-7] Bearing in mind the direction of rotation of these vortices, it can be seen that they induce an upward ﬂow of air beyond the tip, and a downwash ﬂow

behind the wing’s trailing edge. This induced downwash has nothing in common with the downwash that is necessary to produce lift. It is, in fact, the source of induced drag. The greater the size and strength of the vortices and consequent downwash component on the net airﬂow over the airfoil, the greater the induced drag effect becomes. This downwash over the top of the airfoil at the tip has the same effect as bending the lift vector rearward; therefore, the lift is slightly aft of perpendicular to the relative wind, creating a rearward lift component. This is induced drag.

Figure 4-7. Wingtip vortex from a crop duster.

In order to create a greater negative pressure on the top of an airfoil, the airfoil can be inclined to a higher AOA. If the AOA of a symmetrical airfoil were zero, there would be no pressure differential, and consequently, no downwash component and no induced drag. In any case, as AOA increases, induced drag increases proportionally. To state this another way—the lower the airspeed the greater the AOA required to produce lift equal to the aircraft’s weight and, therefore, the greater induced drag. The amount of induced drag varies inversely with the square of the airspeed.

Conversely, parasite drag increases as the square of the airspeed. Thus, as airspeed decreases to near the stalling speed, the total drag becomes greater, due mainly to the sharp rise in induced drag. Similarly, as the airspeed reaches the terminal velocity of the aircraft, the total drag again increases rapidly, due to the sharp increase of parasite drag. As seen in Figure 4-8, at some given airspeed, total drag is at its minimum amount. In ﬁguring the maximum endurance and range of aircraft, the power required to overcome drag is at a minimum if drag is at a minimum.

Figure 4-8. Drag versus speed.

Lift/Drag Ratio
Drag is the price paid to obtain lift. The lift to drag ratio (L/D) is the amount of lift generated by a wing or airfoil compared to its drag. A ratio of L/D indicates airfoil efﬁciency. Aircraft with higher L/D ratios are more efﬁcient than those with lower L/D ratios. In unaccelerated ﬂight with the lift and drag data steady, the proportions of the CL and coefﬁcient of drag (CD) can be calculated for speciﬁc AOA. [Figure 4-9]

The L/D ratio is determined by dividing the CL by the CD, which is the same as dividing the lift equation by the drag equation. All terms except coefﬁcients cancel out.
L = Lift in pounds
D = Drag

Where L is the lift force in pounds, CL is the lift coefﬁcient, ρ is density expressed in slugs per cubic feet, V is velocity in feet per second, q is dynamic pressure per square feet, and S is the wing area in square feet.

CD= Ratio of drag pressure to dynamic pressure. Typically at low angles of attack, the drag coefﬁcient is low and small changes in angle of attack create only slight changes in the drag coefﬁcient. At high angles of attack, small changes in the angle of attack cause signiﬁcant changes in drag.

L = CL . ρ . V2 . S

D = CD . ρ . V2 . S

The above formulas represent the coefﬁcient of lift (CL) and the coefﬁcient of drag (CD) respectively. The shape of an airfoil and other life producing devices (i.e., ﬂaps) effect the production of lift and alter with changes in the AOA. The lift/drag ratio is used to express the relation between lift and drag and is determined by dividing the lift coefﬁcient by the drag coefﬁcient, CL/CD.

Notice in Figure 4-9 that the lift curve (red) reaches its maximum for this particular wing section at 20° AOA, and then rapidly decreases. 15° AOA is therefore the stalling angle. The drag curve (yellow) increases very rapidly from 14° AOA and completely overcomes the lift curve at 21° AOA. The lift/drag ratio (green) reaches its maximum at 6° AOA, meaning that at this angle, the most lift is obtained for the least amount of drag.

Note that the maximum lift/drag ratio (L/DMAX) occurs at one speciﬁc CL and AOA. If the aircraft is operated in steady ﬂight at L/DMAX, the total drag is at a minimum. Any AOA lower or higher than that for L/DMAX reduces the L/D and consequently increases the total drag for a given aircraft’s lift. Figure 4-8 depicts the L/DMAX by the lowest portion of the orange line labeled “total drag.” The conﬁguration of an aircraft has a great effect on the L/D.

Figure 4-9. Lift coefficients at various angles of attack.

Weight

Gravity is the pulling force that tends to draw all bodies to the center of the earth. The CG may be considered as a point at which all the weight of the aircraft is concentrated. If the aircraft were supported at its exact CG, it would balance in any attitude. It will be noted that CG is of major importance in an aircraft, for its position has a great bearing upon stability.

The location of the CG is determined by the general design of each particular aircraft. The designers determine how far the center of pressure (CP) will travel. They then ﬁx the CG forward of the center of pressure for the corresponding ﬂight speed in order to provide an adequate restoring moment to retain ﬂight equilibrium.

Weight has a deﬁnite relationship to lift. This relationship is simple, but important in understanding the aerodynamics of flying. Lift is the upward force on the wing acting perpendicular to the relative wind. Lift is required to counteract the aircraft’s weight (which is caused by the force of gravity acting on the mass of the aircraft). This weight (gravity) force acts downward through the airplane’s CG. In stabilized level ﬂight, when the lift force is equal to the weight force, the aircraft is in a state of equilibrium and neither gains nor loses altitude. If lift becomes less than weight, the aircraft loses altitude. When lift is greater than weight, the aircraft gains altitude.

Lift

The pilot can control the lift. Any time the control yoke or stick is moved fore or aft, the AOA is changed. As the AOA increases, lift increases (all other factors being equal). When the aircraft reaches the maximum AOA, lift begins to diminish rapidly. This is the stalling AOA, known as CL-MAX critical AOA. Examine Figure 4-9, noting how the CL increases until the critical AOA is reached, then decreases rapidly with any further increase in the AOA.

Before proceeding further with the topic of lift and how it can be controlled, velocity must be interjected. The shape of the wing or rotor cannot be effective unless it continually keeps “attacking” new air. If an aircraft is to keep ﬂying, the lift-producing airfoil must keep moving. In a helicopter or gyro-plane this is accomplished by the rotation of the rotor blades. For other types of aircraft such as airplanes, weightshift control, or gliders, air must be moving across the lifting surface. This is accomplished by the forward speed of the aircraft. Lift is proportional to the square of the aircraft’s

velocity. For example, an airplane traveling at 200 knots has four times the lift as the same airplane traveling at 100 knots, if the AOA and other factors remain constant.

Actually, an aircraft could not continue to travel in level ﬂight at a constant altitude and maintain the same AOA if the velocity is increased. The lift would increase and the aircraft would climb as a result of the increased lift force. Therefore, to maintain the lift and weight forces in balance, and to keep the aircraft straight and level (not accelerating upward) in a state of equilibrium, as velocity is increased, lift must be decreased. This is normally accomplished by reducing the AOA by lowering the nose. Conversely, as the aircraft is slowed, the decreasing velocity requires increasing the AOA to maintain lift sufﬁcient to maintain ﬂight. There is, of course, a limit to how far the AOA can be increased, if a stall is to be avoided.

All other factors being constant, for every AOA there is a corresponding airspeed required to maintain altitude in steady, unaccelerated ﬂight (true only if maintaining “level ﬂight”). Since an airfoil always stalls at the same AOA, if increasing weight, lift must also be increased. The only method of increasing lift is by increasing velocity if the AOA is held constant just short of the “critical,” or stalling, AOA.

Lift and drag also vary directly with the density of the air. Density is affected by several factors: pressure, temperature, and humidity. At an altitude of 18,000 feet, the density of the air has one-half the density of air at sea level. In order to maintain its lift at a higher altitude, an aircraft must ﬂy at a greater true airspeed for any given AOA.

Warm air is less dense than cool air, and moist air is less dense than dry air. Thus, on a hot humid day, an aircraft must be ﬂown at a greater true airspeed for any given AOA than on a cool, dry day.

If the density factor is decreased and the total lift must equal the total weight to remain in ﬂight, it follows that one of the other factors must be increased. The factor usually increased is the airspeed or the AOA, because these are controlled directly by the pilot.

Lift varies directly with the wing area, provided there is no change in the wing’s planform. If the wings have the same proportion and airfoil sections, a wing with a planform area of 200 square feet lifts twice as much at the same AOA as a wing with an area of 100 square feet.

Two major aerodynamic factors from the pilot’s viewpoint are lift and velocity because they can be controlled readily and accurately. Of course, the pilot can also control density by adjusting the altitude and can control wing area if the aircraft happens to have ﬂaps of the type that enlarge wing area. However, for most situations, the pilot controls lift and velocity to maneuver an aircraft. For instance, in straight-andlevel ﬂight, cruising along at a constant altitude, altitude is maintained by adjusting lift to match the aircraft’s velocity or cruise airspeed, while maintaining a state of equilibrium in which lift equals weight. In an approach to landing, when the pilot wishes to land as slowly as practical, it is necessary to increase lift to near maximum to maintain lift equal to the weight of the aircraft.

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