2: Aerodynamics

The Four Forces

Lift and Drag

Wing-Tip Vortices and Load Factor

Turns

Axes of Rotation

Trim

Stability

Angle of Incidence and Aspect Ratio

Optimum Cruise Altitude

Mach Number Cruise Control

Critical Mach Number

Sweep Back

True Airspeed

The Four Forces

The four forces acting on an aircraft in flight are lift, weight, thrust and drag. Weight always acts vertically toward the center of the earth. Lift acts perpendicular to the relative wind (not always vertically). Thrust and drag act opposite each other and parallel to the relative wind.

When the aircraft is in a state of equilibrium, there are no accelerations and it continues in steady flight. An acceleration exists if the aircraft's speed is increasing or decreasing, the rate of climb or descent is increasing or decreasing, or the aircraft is turning.

In steady state flight, the sum of the four forces is equal to zero. In straight and level flight, thrust is equal to drag and lift is equal to weight. In a climb or descent, the upward forces are equal to the downward forces and the horizontal accelerating forces are equal to the decelerating forces. See Figure 2-1.

Figure 2-1. Relationship of forces in flight

Lift and Drag

Lift is produced by air flowing over the curved wing surfaces. The air flowing over the upper surface of the wing is deflected further than that flowing across the lower surface and so is accelerated. Bernoulli's Principle states that when a gas is accelerated, its pressure decreases. Thus, the pressure on the upper wing surface is lower than that on the lower surface and lift is produced.

Angle of attack is the angle between the relative wind and chord line of the wing. At zero angle of attack, though the pressure on the upper surface of the wing is less than atmospheric, the wing is producing minimum lift. As the angle of attack is increased, the lift developed by the wing increases proportionately due to the downward deflection of the air. This is true until the angle of attack exceeds a critical value, when the air flowing over the top of the wing breaks up into a turbulent flow and the wing stalls. See Figure 2-2.

Angle of attack and airspeed determine the total lift. An increase in either airspeed or angle of attack increases total lift (up to the stalling angle of attack), and a decrease in either decreases total lift. To maintain the same total lift (i.e., maintain level flight) a pilot has to change the angle of attack anytime airspeed is changed. For example, as airspeed decreases, the angle of attack must be increased to compensate for the loss of lift.

A wing will always stall at the same angle of attack. The load factor, weight and density altitude will cause the stalling true airspeed to vary but the stall angle of attack will always be the same.

The total lift developed by an airfoil can be thought of as acting through a single point called the center of pressure (CP). The center of pressure moves forward and aft on the wing as the angle of attack changes. When the angle of attack increases, the center of pressure moves forward due to loss of lift on the trailing edge of the wing and increased lift on the leading edge. When the angle of attack is lowered, the center

of pressure moves aft. The location of an airplane's center of pressure (especially relative to the center of gravity) has a major influence on its aerodynamic balance and controllability. See Figure 2-3.

There are two types of drag—induced and parasite. Parasite drag is the resistance of the air to the aircraft's movement through it. Parasite drag increases with the square of the aircraft's airspeed. Induced drag is a byproduct of lift and is proportional to the angle of attack of the wing.

A curve comparing total drag to angle of attack reveals an angle of attack at which drag is at a minimum value. At lower angles of attack (higher airspeeds) total drag increases because of increasing parasite drag. At higher angles of attack (lower airspeeds), increasing induced drag increases the total drag. Since the lift stays constant (equal to weight), the low point on the curve is the angle of attack that produces the best lift to drag (L/D) ratio. See Figure 2-4.

Figure 2-2. Angle of attack

Figure 2-3. Angle of attack vs. stall

Figure 2-4. Drag curve

Wing-Tip Vortices and Load Factor

On every wing there is a flow of air around the wing tip from the high pressure on the bottom of the wing to the lower pressure on the top of the wing. These wing-tip vortices trail behind the aircraft in flight and can be a hazard to other aircraft. The vortices will be the most intense when the angle of attack is the highest. The most intense vortices will be generated when an aircraft is heavy, slow and with the gear and flaps up.

Load factor is the ratio of the weight supported by the wings to the actual weight of the aircraft. On the ground or in unaccelerated flight, the load factor is 1. Conditions which can increase the load factor are vertical gusts (turbulence) and level turns.

Turns

The horizontal component of lift turns the airplane and the vertical component of lift opposes gravity. Rudder and aileron must be coordinated when entering a turn. If there is too much bank for the rudder deflection, a slip will develop. If too much rudder is used for the bank angle, a skid is the result. Swept wing turbojet airplanes are naturally very well balanced in turns and any rudder input will usually result in a skid.

Axes of Rotation

An airplane rotates about three axes. Control about the longitudinal axis (roll) is obtained by use of ailerons, and occasionally flight spoilers. Control about the lateral axis (pitch) is obtained by elevators or stabilators. Control about the vertical axis (yaw) is obtained by use of the rudder. All three axes intersect at the center of gravity (CG) of the aircraft, thus the aircraft maneuvers around the CG.

Trim

Besides the primary flight controls, a method to trim the aircraft in each of its axes is provided. The trim relieves any control pressures for the existing airspeed and load configuration. An aircraft is in trim when the roll, pitch and yaw moments are equal to zero.

The most common method of trim control is with trailing edge trim tabs on the control surfaces. The trim tab for a given control surface always moves in the opposite direction of the surface itself. For example, if you want an elevator or aileron to move up, the trim tab on that surface must be trimmed down.

Stability

Static stability describes the initial reaction of an aircraft after it has been disturbed from equilibrium in one or more of its axes of rotation. If the aircraft has an initial tendency to return to its original attitude of equilibrium it has positive static stability. When it tends to diverge, it exhibits negative static stability. If an aircraft tends to remain in its new, disturbed state it has neutral static stability. Most airplanes have positive static stability in pitch and yaw, and are close to neutrally stable in roll. See Figure 2-5.

When an aircraft exhibits positive static stability in one of its axes, the term dynamic stability describes the long term tendency of the aircraft. When an aircraft is disturbed from equilibrium and then tries to return, it will invariably overshoot the original attitude and then pitch back. This results in a series of oscillations. If the oscillations become smaller with time, the aircraft has positive dynamic stability. If the aircraft diverges further away from its original attitude with each oscillation, it has negative dynamic stability. See Figure 2-6.

The entire design of an aircraft contributes to its stability (or lack of it) in each of its axes of rotation. However, the vertical tail is the primary source of directional stability (yaw), and the horizontal tail is the primary source of pitch stability. The center of gravity location also affects stability. If the CG is toward its rearward limit, the aircraft will be less stable in both roll and pitch. As the CG is moved forward, the stability improves. Most aircraft wings have a certain degree of dihedral to increase the lateral stability of the aircraft.

Power changes tend to disturb equilibrium especially in pitch. The greatest change in airplane trim and stability will occur when power is added at slow speed. This sort of situation occurs on a go around from a power approach.

Figure 2-5. Static stability

Figure 2-6. Dynamic stability

Angle of Incidence and Aspect Ratio

The angle of incidence is the angle between the chord line of the wing and the longitudinal axis of the aircraft.

Aspect ratio is the ratio of wingspan to the mean aerodynamic chord of the wing. Airplanes with a high aspect ratio (long thin wings) have increased lift and decreased drag at high angles of attack. They have the disadvantage of increased drag at high airspeeds. Aircraft with low aspect ratios have poor drag characteristics at low speed, but are more efficient at higher airspeeds.

Optimum Cruise Altitude

Turbojet engines have a strong preference for operations at high altitudes and airspeeds. Both lower temperatures and higher altitudes increase engine efficiency by requiring a lower fuel flow for a given thrust. Besides increased engine efficiency, lift and drag both decrease at higher altitudes, therefore less thrust is required.

Turbine engines are much more efficient when operated at the upper end of their RPM range. Generally, the optimum cruise altitude for a turbojet airplane is the highest at which it is possible to maintain the optimum aerodynamic conditions (best angle of attack) at maximum continuous power. The optimum altitude is determined mainly by the aircraft's gross weight at the beginning of cruise.

Absolute altitude is the altitude at which maximum climb power can just maintain level flight and there is zero rate of climb.

As an aircraft burns fuel and becomes lighter, the optimum cruise altitude slowly increases and the speed that yields the optimum cruise performance slowly decreases. Since it is seldom practical to change speed and altitude constantly, it is common procedure to maintain a constant Mach cruise at a Flight Level close to optimum. As fuel is burned, thrust is reduced to maintain the constant Mach number.

Mach Number Cruise Control

Mach number is the ratio of the true airspeed to the speed of sound (TAS Speed of Sound). For example, an aircraft cruising at Mach .80 is flying at 80% of the speed of sound. The speed of sound is Mach 1.0.

The speed of sound in the atmosphere varies only with the temperature. As the temperature increases the speed of sound also increases. An aircraft descending at a constant Mach number will experience an increase in TAS as the temperature increases at lower altitudes. Similarly, an airplane climbing at constant Mach number will experience a decrease in TAS as the temperature decreases.

With respect to Mach cruise control, flight speeds can be divided into four regimes—subsonic, transonic, supersonic, and hypersonic. The subsonic regime can be considered to occur at aircraft Mach numbers less than .75 Mach. The transonic range is at Mach numbers between .75 and 1.2. Supersonic flight occurs at Mach numbers from 1.2 to 5.0, and the hypersonic range is Mach numbers above 5.0.

Critical Mach Number

A large increase in drag occurs when the air flow around the aircraft exceeds the speed of sound (Mach 1.0). Because lift is generated by accelerating air across the upper surface of the wing, local air flow velocities will reach supersonic speeds (Mach 1.0) with the aircraft Mach number considerably below the speed of sound.

A limiting speed for subsonic transport aircraft is its critical Mach number (Mcrit). It is the speed at which airflow over the wing first reaches, but does not exceed, the speed of sound. At Mcrit there may be sonic but no supersonic flow. See Figure 2-7.

When an airplane exceeds its critical Mach number, a shock wave forms on the wing surface that can cause a phenomenon known as shock stall. If this shock stall occurs symmetrically at the wing roots, the loss of lift and loss of downwash on the tail will cause the aircraft to pitch down or "tuck under." This tendency is further aggravated in swept wing aircraft because the center of pressure moves aft as the wing roots shock stall.

Figure 2-7. Local Mach numbers

Sweep Back

The less airflow is accelerated across the wing, the higher the critical Mach number (i.e., the maximum flow velocity is closer to the aircraft's Mach number). Two ways of increasing Mcrit in jet transport designs are to give the wing a lower camber or increase wing sweep. A thin airfoil section (lower camber) causes less airflow acceleration. The swept wing design has the effect of creating a thin airfoil section by inducing a spanwise flow, thus increasing the effective chord length.

Although a swept wing design gives an airplane a higher critical Mach number (and therefore a higher maximum cruise speed), it results in some undesirable flight characteristics. One of these is a reduced maximum coefficient of lift. This requires that swept wing airplanes extensively employ high lift devices, such as slats and slotted flaps, to get acceptably low takeoff and landing speeds. The purpose of high lift devices such as flaps, slats and slots is to increase lift at low airspeeds and to delay stall to a higher angle of attack.

Another disadvantage of the swept wing design is the tendency for the wing tips to stall first. This results in loss of aileron control early in the stall and in very little aerodynamic buffet on the tail surfaces.

Dutch roll tendency is typical of swept wing designs. If such an airplane yaws, the advancing wing is at a higher angle of attack and presents a greater span to the airstream than the retreating wing. This causes the aircraft to roll in the direction of the initial yaw and simultaneously to reverse its direction of yaw. When the yaw reverses, the airplane then reverses its direction of roll and yaw again. This roll-yaw coupling is usually damped out by the vertical stabilizer. But, at high speeds and in turbulence this may not be adequate, so most aircraft are also equipped with a yaw damper to help counteract any Dutch roll tendency.

True Airspeed

True Airspeed (TAS) is the actual speed of the aircraft through the air. True airspeed is determined by correcting Equivalent Airspeed (EAS) for density altitude error. Most modern airliners have a direct readout of TAS from the air data computer.

True airspeed increases relative to EAS as altitude and/or temperature increases. This means that at higher altitudes, the TAS will be higher for any given takeoff, landing, or cruise indicated airspeed.

Ground speed is the aircraft's TAS plus any tailwind or minus any headwind. For example, if an airplane has a 25 knot headwind and then makes a 180° turn, its ground speed will increase by 50 knots.