dissipate the energy of the airstream, slowing it down. The laminar boundary layer increases in thickness with increased distance from the wing leading edge. Some distance back from the leading edge, the laminar flow begins an oscillatory disturbance which is unstable. A waviness occurs in the laminar boundary layer which ultimately grows larger and more severe and destroys the smooth laminar flow. Thus, a transition takes place in which the laminar boundary layer decays into a turbulent boundary layer. The same sort of transition can be noticed in the smoke from a cigarette in still air. At first, the smoke ribbon is smooth and laminar, then develops a definite waviness, and decays into a random turbulent smoke pattern.
Boundary layer control devices are additional means of increasing the maximum lift coefficient of a section. The thin layer of air adjacent to the surface of an airfoil shows reduced local velocities from the effect of skin friction. At high angles of attack, the boundary layer on the upper surface tends to stagnate (come to a stop). When this happens, the airflow separates from the surface and stall occurs.
Boundary layer control devices for high-lift applications feature various devices to maintain high velocity in the boundary layer and delay separation of the airflow. Control of the boundary layer's kinetic energy can be accomplished using slats and the application of suction to draw off the stagnant air and replace it with high-velocity air from outside the boundary layer.
Slats (figure 2-32) are movable control surfaces attached to the leading edge of the wing. When the slat is closed, it forms the leading edge of the wing.
When in the open position (extended forward), a slot is created between the slat and the wing leading edge. Thus, high-energy air is introduced into the boundary layer over the top of the wing. This is known as "boundary layer control." At low airspeeds this improves handling characteristics, allowing the aircraft to be controlled laterally at airspeeds below the otherwise normal landing speed.
Controlling boundary layer air by surface suction allows the wing to operate at higher angles of attack. The effect on lift characteristics is similar to that of a slot, because the slot is essentially a boundary layer control device ducting high-energy air to the upper surface.
Boundary layer control can also be accomplished by directing high-pressure engine bleed air through a narrow orifice located just forward of the wing Fixed slot Automatic slot
• Slat Boundary layer control by upper surface suction Boundary layer control by flap augmentation FIGURE 2-32. Methods of controlling boundary layer air.
flap leading edge. This directs a laminar flow (air in layers) of air over the wing and flaps when the flaps have opened sufficiently to expose the orifice.
The high-temperature, high-velocity laminar air passing over the wing and flaps delays flow separation (the airstream over an airfoil no longer follows the contour of the airfoil), hence reduces turbulence and drag (see figure 2-29). This results in a lower stall speed and allows slower landing speeds.
FORCES ACTING ON A HELICOPTER One of the differences between a helicopter and a fixed-wing aircraft is the main source of lift. The fixed-wing aircraft derives its lift from a fixed airfoil surface while the helicopter derives lift from a rotating airfoil called the rotor. Aircraft are classified as either fixed-wing or rotating wing. The word helicopter comes from a Greek word meaning "helical wing" or "rotating wing."
During any kind of horizontal or vertical flight, there are four forces acting on the helicopter-lift, 49
thrust, weight, and drag. Lift is the force required to support the weight of the helicopter. Thrust is the force required to overcome the drag on the fuselage and other helicopter components.
During hovering flight in a no-wind condition, the tip-path plane is horizontal, that is, parallel to the ground. Lift and thrust act straight up; weight and drag act straight down. The sum of the lift and thrust forces must equal the sum of the weight and drag forces in order for the helicopter to hover.
During vertical flight in a no-wind condition, the lift and thrust forces both act vertically upward.
Weight and drag both act vertically downward.
When lift and thrust equal weight and drag, the helicopter hovers; if lift and thrust are less than weight and drag, the helicopter descends vertically;
if lift and thrust are greater than weight and drag, the helicopter rises vertically.
For forward flight, the tip-path plane is tilted forward, thus tilting the total lift-thrust force forward from the vertical. This resultant lift-thrust force can be resolved into two components--lift acting vertically upward, and thrust acting horizontally in the direction of flight. In addition to lift and thrust, there are weight, the downward acting force, and drag, the rearward acting or retarding force of inertia and wind resistance.
In straight-and-level, unaccelerated forward flight, lift equals weight and thrust equals drag.
(Straight-and-level flight is flight with a constant heading and at a constant altitude.) If lift exceeds weight, the helicopter climbs; if the lift is less than weight, the helicopter descends. If thrust exceeds drag, the helicopter speeds up; if thrust is less than drag, it slows down.
In sideward flight, the tip-path plane is tilted sideward in the direction that flight is desired thus tilting the total lift-thrust vector sideward. In this case, the vertical or lift component is still straight up, weight straight down, but the horizontal or thrust component now acts sideward with drag acting to the opposite side.
For rearward flight, the tip-path plane is tilted rearward tilting the lift-thrust vector rearward. The thrust component is rearward and drag forward, just the opposite to forward fight. The lift component is straight up and weight straight down.
Torque Newton's third law of motion states, "To every action there is an equal and opposite reaction." As the main rotor of a helicopter turns in one direction, the fuselage tends to rotate in the opposite direction. This tendency for the fuselage to rotate is called torque. Since torque effect on the fuselage is a direct result of engine power supplied to the main rotor, any change in engine power brings about a corresponding change in torque effect. The greater the engine power, the greater the torque effect.
Since there is no engine power being supplied to the main rotor during autorotation, there is no torque reaction during autorotation.
The force that compensates for torque and provides for directional control can be produced by means of an auxiliary rotor located on the end of the tail boom. This auxiliary rotor, generally referred to as a tail rotor, or anti-torque rotor, produces thrust in the direction opposite to torque reaction developed by the main rotor (figure 2-33).
Foot pedals in the cockpit permit the pilot to increase or decrease tail-rotor thrust, as needed, to neutralize torque effect.
Other methods of compensating for torque and providing directional control are illustrated in figure 2-33.
The spinning main rotor of a helicopter acts like a gyroscope. As such, it has the properties of gyroscopic action, one of which is precession. Gyroscopic precession is the resultant action or deflection of a spinning object when a force is applied to this object. This action occurs approximately 90° in the direction of rotation from the point where the force is applied (figure 2-34). Through the use of this principle, the tip-path plane of the main rotor may be tilted from the horizontal.
The movement of the cyclic pitch control in a two-bladed rotor system increases the angle of attack of one rotor blade with the result that a greater lifting force is applied at this point in the plane of rotation. This same control movement simultaneously decreases the angle of attack of the other blade a like amount thus decreasing the lifting force applied at this point in the plane of rotation. The blade with the increased angle of attack tends to rise; the blade with the decreased angle of attack tends to lower. However, because of the gyroscopic precession property, the blades do not rise or lower to maximum deflection until a point approximately 90° later in the plane of rotation.
As shown in figure 2-35, the retreating blade angle of attack is increased and the advancing blade angle of attack is decreased resulting in a tipping forward of the tip-path plane, since maxi- 50
Vane in rotor slipstream Anti-torque rotor Differential torque between two rotors Differential tilt of rotor thrusts FIcURE 2-33. Methods for achieving directional control.
mum deflection takes place 90° later when the blades are at the rear and front respectively.
In a three-bladed rotor, the movement of the cyclic pitch control changes the angle of attack of each blade an appropriate amount so that the end result is the same, a tipping forward of the tip-path plane when the maximum change in angle of attack is made as each blade passes the same points at which the maximum increase and decrease are made for the two-bladed rotor as shown in figure 2-35.
As each blade passes the 90° position on the left, the maximum increase in angle of attack occurs. As each blade passes the 90° position to the right, the maximum decrease in angle of attack occurs. Maximum deflection takes place 90° later, maximum upward deflection at the rear and maximum downward deflection at the front, and the tip-path plane tips forward.
Dissymmetry of Lift The area within the tip-path plane of the main rotor is known as the disk area or rotor disk. When hovering in still air, lift created by the rotor blades at all corresponding positions around the rotor disk is equal. Dissymmetry of lift is created by horizontal flight or by wind during hovering flight, and is the difference in lift that exists between the advancing blade half of the disk area and the retreating blade half.
At normal rotor operating r.p.m. and zero air- 51
As the helicopter moves into forward flight, the relative wind moving over each rotor blade becomes a combination of the rotational speed of the rotor and the forward movement of the helicopter. As Reaction occurs shown in figure 2-37, the advancing blade has the combined speed of the blade velocity plus the speed here of the helicopter. On the opposite side, the retreating blade speed is the blade velocity less the speed of the helicopter.
Force applied here It is apparent that the lift over the advancing New axis Old axis Gyro tips up here Gyro tips - down here FIGURE 2-34. Gyroscopic precession principle.
speed, the rotating blade tip speed of most helicopter main rotors is approximately 400 m.p.h. When hovering in a no-wind condition, the speed of the relative wind at the blade tips and at any specific point along the blade is the same throughout the tip-path plane (figure 2-36). However, the speed is reduced as this point moves closer to the rotor hub as indicated in figure 2-36 by the two inner circles.
blade half of the rotor disk will be greater than the lift over the retreating blade half during horizontal fight or when hovering in a wind.
Due to the greater lift of the advancing blade the helicopter would roll to the left unless something is done to equalize the lift of the blades on both sides of the helicopter.
Blade Flapping In a three-bladed rotor system, the rotor blades are attached to the rotor hub by a horizontal hinge which permits the blades to move in a vertical plane, t.e., flap up or down, as they rotate (figure 2-38). In forward flight and assuming that the blade-pitch angle remains constant, the increased lift on the advancing blade will cause the blade to flap up decreasing the angle of attack because the relative wind will change from a horizontal direction to more of a downward direction. The decreased lift on the retreating blade will cause the blade to flap down increasing the angle of attack because the relative wind changes from a horizontal direction to more of an upward direction. The com- Low pitch applied High flap result Low flap result High pitch applied FICURF. 2-35. Rotor disk acts like a gyro.
Direction of rotation ===== FIcURE 2-38. Blade flapping action (vertical plane).
Advancing blade half to equalize the lift over the two halves of the rotor disk.
The amount that a blade flaps up is a compromise 400 300 100 100 300 400 between centrifugal force, which tends to hold the
m.p.h. Tip speed blade straight out from the hub, and lift forces which tend to raise the blade on its flapping hinge.
As the blades flap up they leave their normal tip- Retreating blade half path plane momentarily. As a result, the tip of the blade which is flapping must travel a greater dis tance. Therefore, it has to travel at a greater speed for a fraction of a second, in order to keep up with the other blades.
The blade flapping action creates an unbalance FIGURE 2-36. Comparison of rotor blade speeds for the advancing blade and retreating blade during hover. condition with resulting vibration. To prevent this vibration, a drag hinge (figure 2-39) is incorpo.
rated which permits the blade to move back and forth in a horizontal plane.
Direction of flight Hub (100 m.p.h.)
- Drag hinge FIGURE 2-39. Action of drag hinge (horizontal plane).
500 tection of rotation FIcURE 2-37. Comparison of rotor blade speeds for the advancing and retreating blade during forward fight.
bination of decreased angle of attack on the advancing blade and increased angle of attack on the retreating blade through blade flapping action tends With the blades free to move back and forth on the drag hinges, an unbalanced condition is created since the c.g. (center of gravity) will not remain fixed but moves around the mast. This c.g. move ment causes excessive vibration. To dampen out the vibrations, hydraulic dampers limit the movement of the blades on the drag hinge. These dampers also tend to maintain the geometric relationship of the blades.
A main rotor which permits individual movement of the blades from the hub in both a vertical and
• horizontal plane is called an articulated rotor. The hinge points and direction of motion around each hinge are illustrated in figure 2-40.
In a two-bladed system, the blades flap as a unit.
As the advancing blade flaps up due to the increased lift, the retreating blade flaps down due to the decreased lift. The change in angle of attack on 53
Lead or lag Drag hinge Flap Flap hinge Pitch Axis of rotation FIGURE 2-40. Articulated rotor head.
each blade brought about by this flapping action tends to equalize the lift over the two halves of the rotor disk.
The position of the cyclic pitch control in forward flight also causes a decrease in angle of attack on the advancing blade and an increase in angle of attack on the retreating blade. This together with blade flapping equalizes lift over the two halves of the rotor disk.
Coning Coning (figure. 2-41) is the upward bending of the blades caused by the combined forces of lift and centrifugal force. Before takeoff, the blades rotate in a plane nearly perpendicular to the rotor mast, since centrifugal force is the major force acting on them.
As a vertical takeoff is made, two major forces are acting at the same time centrifugal force acting outward perpendicular to the rotor mast, and lift acting upward and parallel to the mast.. The result of these two forces is that the blades assume Before takeoff lift Centrifugal force During takeoff FICURE 2-41. Blade coning.
a conical path instead of remaining in the plane perpendicular to the mast.
Coning results in blade bending in a semirigid rotor; in an articulated rotor, the blades assume an upward angle through movement about the flapping hinges.
Ground Effect When a helicopter is in a hovering position close to the ground, the rotor blades will be displacing air downward through the disk faster than it can escape from beneath the helicopter. This builds up a cushion of dense air between the ground and the helicopter (figure 2-42). This cushion of more dense air, referred to as ground effect, aids in supporting the helicopter while hovering. It is usually effective to a height of approximately one-half the rotor disk diameter. At approximately 3 to 5 m.p.h. groundspeed, the helicopter will leave its ground cushion.
FICURE 2-42. Ground effect.
Autorotation Autorotation is the term used for the flight condition during which no engine power is supplied and the main rotor is driven only by the action of the relative wind. The helicopter transmission or power train is designed so that the engine, when it stops, is automatically disengaged from the main rotor system to allow the main rotor to rotate freely in its original direction.
When engine power is being supplied to the main rotor, the flow of air is downward through the rotor. When engine power is not being supplied to the main rotor, that is, when the helicopter is in autorotation, the flow of air is upward through the rotor. It is this upward flow of air that causes the rotor to continue turning after engine failure.
The portion of the rotor blade that produces the forces that cause the rotor to turn when the engine is no longer supplying power to the rotor, is that 54
portion between approximately 25% and 70% of the radius outward from the center. This portion is often referred to as the autorotative or driving region." Aerodynamic forces along this portion of the blade tend to speed up the blade rotation.
The inner 25% of the rotor blade, referred to as the "stall region," operates above its maximum angle of attack (stall angle), thereby contributing little lift but considerable drag which tends to slow the blade rotation.
The outer 30% of the rotor blade is known as the "propeller or driven region." Aerodynamic forces here result in a small drag force which tends to slow the tip portion of the blade.
The aerodynamic regions as described above are for vertical autorotations. During forward flight autorotations, these regions are displaced across the rotor disk to the left.
Rotor r.p.m. stabilizes when the autorotative forces (thrust) of the "driving region" and the autorotative forces (drag) of the "driven region" and the "stall region" are equal.
Forward speed during autorotative descent permits a pilot to incline the rotor disk rearward, thus causing a flare. The additional induced lift created by the greater volume of air momentarily checks forward speed as well as descent. The greater volume of air acting on the rotor disk will normally increase rotor r.p.m. during the flare. As the forward speed and descent rate near zero, the upward flow of air has practically ceased and rotor r.p.m.
again decreases; the helicopter settles at a slightly increased rate but with reduced forward speed. The fare enables the pilot to make an emergency landing on a definite spot with little or no landing roll or skid.
HELICOPTER AXES OF FLIGHT As a helicopter maneuvers through the air, its attitude in relation to the ground changes. These changes are described with reference to three axes (figure 2-43) of fight: (1) Vertical, (2) longitudinal, and (3) lateral.
Movement about the vertical axis produces yaw, a nose swing. (or change in direction) to the right or left. This is controlled by the directional-control pedals. The various methods of achieving directional control were discussed earlier in this section.
Movement about the longitudinal axis is called roll. This movement is effected by moving the cyclic pitch control to the right or left. The cyclic pitch control is similar to the control stick of a conventional aircraft. It acts through a mechanical linkage (figure 2-44) to change the pitch of each main-rotor blade during a cycle of rotation.
holl Longitudinal axis Vertical axis
• Lateral axis Pitch FIGURE 2-43. Axes of flight.
Swash plate FIGURE 2-41. Cyclic pitch control mechanism.
The rapidly rotating rotor blades create a disk area that can be tilted in any direction with respect to the supporting rotor mast. Horizontal movement 55
is controlled by changing the direction of tilt of the main rotor to produce a force in the desired direction.
Movement about the lateral axis produces a noseup or nosedown attitude. This movement is effected by moving the cyclic pitch control fore and aft.
The collective pitch control (figure 2-45) varies the lift of the main rotor by increasing or decreasing the pitch of all blades at the same time. Raising the collective pitch control increases the pitch of the blades, thereby increasing the lift. Lowering the control decreases the pitch of the blades, causing a loss of lift. Collective pitch control is also used in coordination with cyclic pitch control to regulate the airspeed of the helicopter.
FIGURE 2-45. Collective pitch control mechanism.
Many factors determine the amount of lift available in helicopter operation. Generally speaking, the pilot has control of two of these. One is the pitch angle of the rotor blades; the other is the power de.
livered to the rotor, represented by r.p.m. and manifold pressure. By controlling the pitch angle of the rotor blades, the pilot can establish the vertical flight of the helicopter. By manipulating the throttle control, a constant engine speed can be maintained regardless of the increase or decrease in blade pitch. The throttle is mounted on the collective pitch grip and is operated by rotating the grip. The throttle is synchronized with the main-rotor pitch control in such a manner that an increase of pitch increases power and a decrease in pitch decreases power. A complete control system of a conventional helicopter is shown in figure 2-46.
HIGH-SPEED AERODYNAMICS Developments in aircraft and powerplants are yielding high-performance transports with capabilities for very high speed flight. Many significant differences arise in the study of high-speed aerodynamics when compared with low-speed aerodynamics.
It is quite necessary, therefore, that persons associated with commercial aviation be familiar with the nature of high-speed airflow and the peculiarities of high-performance airplanes.
General Concepts of Supersonic Flow Patterns At low flight speeds, air experiences small changes in pressure which cause negligible variations in density, greatly simplifying the study of low-speed aerodynamics. The flow is called incompressible since the air undergoes small changes in pressure without significant changes in density. At high flight speeds, however, the pressure changes that take place are quite large and significant changes in air density occur. The study of airflow at high speeds must account for these changes in air density and must consider that the air is compressible, or that there are compressibility effects.
The speed of sound is very important in the study of high-speed airflow. The speed of sound varies with the ambient temperature. At sea level, on a standard day, the speed of sound is about
661.7 knots (760 m.p.h.).
As a wing moves through the air, local velocity changes occur which create pressure disturbances in the airfow around the wing. These pressure disturbances are transmitted through the air at the speed of sound. If the wing is traveling at low speed, the pressure disturbances are transmitted and extend indefinitely in all directions. Evidence of these pressure disturbances is seen in the typical subsonic flow pattern illustrated in figure 2-47 where upwash and flow direction change well ahead of the wing leading edge.
If the wing is traveling above the speed of sound, the airhow ahead of the wing is not infuenced by the pressure field of the wing, since pressure disturbances cannot be propagated faster than the speed of sound. As the flight speed nears the speed of sound, a compression wave forms at the leading edge and all changes in velocity and pressure take place quite sharply and suddenly. The airflow ahead of the wing is not influenced until the air molecules are suddenly forced out of the way by the wing. Evidence of this phenomenon is seen in the typical supersonic flow pattern shown in figure
2-48.
Compressibility effects depend not on airspeed, but rather on the relationship of airspeed to the 56
Rotor blade pitch control horn Flapping axis - Blade thrust bearing .
Upper link (adjustable for tracking blades) Rotating rocker arm (upper links move up together when center of rocker arms is moved up by collective pitch sleeve, and move cyclically when swash plates are tilted) Upper swash plate Lower link (tilts and rotates) Lower swash plate (mounted on gimbals which allow -Pilot's collective pitch lever it to tilt but not to rotate or to move vertically) Throttle linkage - - Throttle twist grip Pilot's control stick Gear case (phantom) fixed to fuselage Co-pilot's collective Collective pitch sleeve vertical positioning mechanism and throttle control Shaft , Co-pilot's control Collective pitch sleeve (moves up and stick down while rotating with shaft) FICURE 2-46. Control system of conventional helicopter.
Flow direction changes well ahead of leading edge Subsonic accelerating flow Subsonic decelerating flow FIcURE 2-47. Typical subsonic flow pattern, subsonic wing.
Trailing edge oblique shock wave Initial expansion wave Leading edge oblique shock wave Final expansion wave Flow direction does not change ahead of leading edge FICURE 2-18. Typical supersonic flow pattern, supersonic wing.
speed of sound. This relationship is called Mach number, and is the ratio of true airspeed to the speed of sound at a particular altitude.
Compressibility effects are not limited to flight speeds at and above the speed of sound. Since any airplane is made up of aerodynamic shapes, air accelerates and decelerates around these shapes and attains local speeds above the flight speed. Thus, an aircraft can experience compressibility effects at flight speeds well below the speed of sound. Since it is possible to have both subsonic and supersonic flows on the airplane at the same time, it is best to define certain regimes of flight. These approximate regimes are defined as follows:
(1) Subsonic--flight Mach numbers below
0.75.
(2) Transonic--flight Mach numbers from
0.75 to 1.20.
(3) Supersonic--fight Mach numbers from
1.20 to 5.00.
(4) Hypersonic-flight Mach numbers above
5.00.
While the flight Mach numbers used to define these regimes are approximate, it is important to appreciate the types of flow existing in each area.
In the subsonic regime, subsonic airflow exists on all parts of the aircraft. In the transonic regime, the flow over the aircraft components is partly subsonic and partly supersonic. In the supersonic and hypersonic regimes, supersonic flow exists over all parts of the aircraft. Of course, in supersonic and hypersonic flight some portions of the boundary layer are 58
subsonic, but the predominating flow is still supersonic.
Difference Between Subsonic and Supersonic Flow In a subsonic flow every molecule is affected more or leas by the motion of every other molecule in the whole field of flow. At supersonic speeds, an air molecule can influence only that part of the flow contained in the Mach cone formed behind that molecule.
The peculiar differences between subsonic flow and supersonic flow can best be seen by considering airflow in a closed contracting/expanding tube, as depicted in figure 2-48.
Decreasing air density Increasing air density Contracting tube Expanding tube Increasing air velocity Decreasing air velocity
(a) Subsonic flow Increasing air density Decreasing air dersity Contracting tube Expanding tube Decreasing air velocity Increasing air velocity
(b) Supersonic flow FIGURE 2-49. Comparison of subsonic and supersonic airflow through a closed tube.
Unlike subsonic flow, a supersonic airstream accelerates along an expanding tube, causing the air density to decrease rapidly to compensate for the combined effects of increased speed and increased cross sectional area.
Unlike subsonic flow, a supersonic airstream decelerates along a contracting tube, causing the air density to increase rapidly to compensate for the combined effects of decreased speed and decreased cross sectional area.
In order to clarify these fundamenta. points, ngure 2-50 lists the nature of the two types of tubes. An understanding of figures 2-49 and 2-50 is essential if one is to grasp the fundamentals of supersonic flow.
Contracting tube Expanding tube Accelerates and Decelerates and Subsonic fow rarefies slightly compresses slightly Decelerates and Accelerates and Supersonic flow compresses greatly rarefies greatly FIGURE 2-50. High-speed flows.
TYPICAL SUPERSONIC FLOW PATTERNS With supersonic flow, all changes in velocity, pressure, temperature, density, and flow direction take place suddenly and over a short distance. The areas of flow change are distinct and the phenomena causing the flow change are called wave formations. All compression waves occur abruptly and are wasteful of energy. Compression waves are more familiarly known as shock waves. Expansion waves result in smoother flow transition and are not wasteful of energy like shock waves. Three types of waves can take place in supersonic flow: (1) The oblique (inclined angle) shock wave (compression), (2) the normal (right angle) shock wave (compression), and (3) the expansion wave (no shock). The nature of the wave depends on the Mach number, the shape of the object causing the flow change, and the direction of flow.
A supersonic airstream passing through the oblique shock wave experiences these changes:
(1) The airstream is slowed down. Both the velocity and the Mach number behind the wave are reduced, but the flow is still supersonic.
(2) The flow direction is changed so that the airstream runs parallel to the new surface.
(3) The static pressure behind the wave is increased.
(4) The static temperature behind the wave is increased (and hence the local speed of sound is increased).
(5) The density of the airstream behind the wave is increased.
(6) Some of the available energy of the airstream (indicated by the sum of dynamic and static pressure) is dissipated by conversion into unavailable heat energy.
Hence, the shock wave is wasteful of energy.
The Normal Shack Wave If a blunt-nosed object is placed in a supersonic airstream, the shock wave which is formed is detached from the leading edge. The detached wave 59
- Subsonic region ~ Oblique shock Normal shock Normal shock - Subsonic region- -Oblique shock
(a) Blunt-nosed object (b) Wedge or cone FIGURE 2-51. Normal shock-wave formation with a detached wave.
also occurs when a wedge or cone half angle exceeds some critical value. Figure 2-51 shows the formation of a normal shock wave in the above two cases. Whenever a shock wave forms perpendicular to the free stream flow, the shock wave is termed a normal (right angle) shock wave and the flow immediately behind the wave is subsonic. No matter how high the free stream Mach number may be, the flow directly behind a normal shock is always subsonic. In fact, the higher the supersonic free stream Mach number (M) is in front of the normal shock wave, the lower the subsonic Mach number is aft of the wave. For example, if M, is 1.5, M2 is 0.7;
while if My is 2.6, M2 is only 0.5. A normal shock wave forms immediately in front of any relatively blunt object in a supersonic airstream, slowing the airstream to subsonic so that the airstream may feel the presence of the blunt object and thus flow around it. Once past the blunt nose, the airstream may remain subsonic or it may accelerate back to supersonic, depending on the shape of the nose and the Mach number of the free stream.
A normal wave may also be formed when there is no object in the supersonic airstream. It so happens that whenever a supersonic airstream is slowed to subsonic without a change in direction, a normal shock wave forms as the boundary between the supersonic and subsonic regions. This is why airplanes encounter compressibility effects before the flight speed is sonic. Figure 2-52 illustrates the manner in which an airfoil at a high subsonic speed has local fow velocities which are supersonic. As the local supersonic flow moves aft, a normal shock wave forms so that the flow may return to subsonic and rejoin the subsonic free stream at the trailing edge without discontinuity. The transition of flow from subsonic to supersonic is smooth and is not accompanied by shock waves if the transition is made gradually with a smooth surface. The transition of flow from supersonic to subsonic without direction change always forms a normal shock wave.
A supersonic airstream passing through a normal shock wave experiences these changes:
(1) The airstream is slowed to subsonic. The local Mach number behind the wave is approximately equal to the reciprocal of the Mach number ahead of the wave. For example, if the Mach number ahead of the wave is 1.25, the Mach number of the flow behind the wave is about 0.8 (more exactly 0.81264).
(2) The airfow direction immediately behind the wave is unchanged.
(3) The static pressure behind the wave is greatly increased.
(4) The static temperature behind the wave is 60