# High-Speed Aerodynamics - Aircraft Theory of Flight

## Compressibility Effects

When air is flowing at subsonic speed, it acts like an incompressible fluid. As discussed earlier in this chapter, when air at subsonic speed flows through a diverging shaped passage, the velocity decreases and the static pressure rises, but the density of the air does not change. In a converging shaped passage, subsonic air speeds up and its static pressure decreases. When supersonic air flows through a converging passage, its velocity decreases and its pressure and density both increase. [Figure 1] At supersonic flow, air acts like a compressible fluid. Because air behaves differently when flowing at supersonic velocity, airplanes that fly supersonic must have wings with a different shape.

 Figure 1. Supersonic airflow through a venturi

## The Speed of Sound

Sound, in reference to airplanes and their movement through the air, is nothing more than pressure disturbances in the air. As discussed earlier in the Sound post, it is like dropping a rock in the water and watching the waves flow out from the center.

 Figure 2. Altitude and temperature versus speed of sound

As an airplane flies through the air, every point on the airplane that causes a disturbance creates sound energy in the form of pressure waves. These pressure waves flow away from the airplane at the speed of sound, which at standard day temperature of 59 °F, is 761 mph. The speed of sound in air changes with temperature, increasing as temperature increases. Figure 2 shows how the speed of sound changes with altitude.

## Subsonic, Transonic, and Supersonic Flight

When an airplane is flying at subsonic speed, all of the air flowing around the airplane is at a velocity of less than the speed of sound, which is known as Mach 1. Keep in mind that the air accelerates when it flows over certain parts of the airplane, like the top of the wing, so an airplane flying at 500 mph could have air over the top of the wing reach a speed of 600 mph. How fast an airplane can fly and still be considered in subsonic flight varies with the design of the wing, but as a Mach number, it will typically be just over Mach 0.8.

When an airplane is flying at transonic speed, part of the airplane is experiencing subsonic airflow and part is experiencing supersonic airflow. Over the top of the wing, probably about halfway back, the velocity of the air will reach Mach 1 and a shock wave will form. The shock wave forms 90 degrees to the airflow and is known as a normal shock wave. Stability problems can be encountered during transonic flight, because the shock wave can cause the airflow to separate from the wing. The shock wave also causes the center of lift to shift aft, causing the nose to pitch down. The speed at which the shock wave forms is known as the critical Mach number. Transonic speed is typically between Mach 0.80 and 1.20.

When an airplane is flying at supersonic speed, the entire airplane is experiencing supersonic airflow. At this speed, the shock wave which formed on top of the wing during transonic flight has moved all the way aft and has attached itself to the wing trailing edge. Supersonic speed is from Mach 1.20 to 5.0. If an airplane flies faster than Mach 5, it is said to be in hypersonic flight.

## Shock Waves

Sound coming from an airplane is the result of the air being disturbed as the airplane moves through it, and the resulting pressure waves that radiate out from the source of the disturbance. For a slow-moving airplane, the pressure waves travel out ahead of the airplane, traveling at the speed of sound. When the speed of the airplane reaches the speed of sound, however, the pressure waves, or sound energy, cannot get away from the airplane. At this point the sound energy starts to pile up, initially on the top of the wing, and eventually attaching itself to the wing leading and trailing edges. This piling up of sound energy is called a shock wave. If the shock waves reach the ground, and cross the path of a person, they will be heard as a sonic boom. Figure 3A shows a wing in slow speed flight, with many disturbances on the wing generating sound pressure waves that are radiating outward. View B is the wing of an airplane in supersonic flight, with the sound pressure waves piling up toward the wing leading edge.

 Figure 3. Sound energy in subsonic and supersonic flight

### Normal Shock Wave

When an airplane is in transonic flight, the shock wave that forms on top of the wing, and eventually on the bottom of the wing, is called a normal shock wave. If the leading edge of the wing is blunted, instead of being rounded or sharp, a normal shock wave will also form in front of the wing during supersonic flight. Normal shock waves form perpendicular to the airstream. The velocity of the air behind a normal shock wave is subsonic, and the static pressure and density of the air are higher. Figure 4 shows a normal shock wave forming on the top of a wing.

 Figure 4. Normal shock wave

### Oblique Shock Wave

An airplane that is designed to fly supersonic will have very sharp edged surfaces, in order to have the least amount of drag. When the airplane is in supersonic flight, the sharp leading edge and trailing edge of the wing will have shock waves attach to them. These shock waves are known as oblique shock waves. Behind an oblique shock wave the velocity of the air is lower, but still supersonic, and the static pressure and density are higher. Figure 5 shows an oblique shock wave on the leading and trailing edges of a supersonic airfoil.

 Figure 5. Supersonic airfoil with oblique shock waves and expansion waves

### Expansion Wave

Earlier in the discussion of high-speed aerodynamics, it was stated that air at supersonic speed acts like a compressible fluid. For this reason, supersonic air, when given the opportunity, wants to expand outward. When supersonic air is flowing over the top of a wing, and the wing surface turns away from the direction of flow, the air will expand and follow the new direction. An expansion wave will occur at the point where the direction of flow changes. Behind the expansion wave the velocity increases, and the static pressure and density decrease. An expansion wave is not a shock wave. Figure 5 shows an expansion wave on a supersonic airfoil.

## High-Speed Airfoils

Transonic flight is the most difficult flight regime for an airplane, because part of the wing is experiencing subsonic airflow and part is experiencing supersonic airflow. For a subsonic airfoil, the aerodynamic center, or the point of support, is approximately 25 percent of the way back from the wing leading edge. In supersonic flight, the aerodynamic center moves back to 50 percent of the wing’s chord, causing some significant changes in the airplane’s control and stability.

If an airplane designed to fly subsonic, perhaps at a Mach number of 0.80, flies too fast and enters transonic flight, some noticeable changes will take place with respect to the airflow over the wing. Figure 6 shows six views of a wing, with each view showing the Mach number getting higher.

 Figure 6. Airflow with progressively greater Mach numbers

The scenario for the six views is as follows:
1. View A - The Mach number is fairly low, and the entire wing is experiencing subsonic airflow.
2. View B - The velocity has reached the critical Mach number, where the airflow over the top of the wing is reaching Mach 1 velocity.
3. View C - The velocity has surpassed the critical Mach number, and a normal shock wave has formed on the top of the wing. Some airflow separation starts to occur behind the shock wave.
4. View D - The velocity has continued to increase beyond the critical Mach number, and the normal shock wave has moved far enough aft that serious airflow separation is occurring. A normal shock wave is now forming on the bottom of the wing as well. Behind the normal shock waves, the velocity of the air is subsonic and the static pressure has increased.
5. View E - The velocity has increased to the point that both shock waves on the wing, top and bottom, have moved to the back of the wing and attached to the trailing edge. Some airflow separation is still occurring.
6. View F - The forward velocity of the airfoil is greater than Mach 1, and a new shock wave has formed just forward of the leading edge of the wing. If the wing has a sharp leading edge, the shock wave will attach itself to the sharp edge.

The airfoil shown in Figure 6 is not properly designed to handle supersonic airflow. The bow wave in front of the wing leading edge of view F would be attached to the leading edge, if the wing was a double wedge or biconvex design. These two wing designs are shown in Figure 7.

 Figure 7. Double wedge and biconvex supersonic wing design

## Aerodynamic Heating

One of the problems with airplanes and high-speed flight is the heat that builds up on the airplane’s surface because of air friction. When the SR-71 Blackbird airplane is cruising at Mach 3.5, skin temperatures on its surface range from 450 °F to over 1,000 °F. To withstand this high temperature, the airplane was constructed of titanium alloy, instead of the traditional aluminum alloy. The supersonic transport Concorde was originally designed to cruise at Mach 2.2, but its cruise speed was reduced to Mach 2.0 because of structural problems that started to occur because of aerodynamic heating. If airplanes capable of hypersonic flight are going to be built in the future, one of the obstacles that will have to be overcome is the stress on the airplane’s structure caused by heat.

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