How do you account for the effects of compressibility and shock waves on drag and lift?

1 Compressibility and shock waves

Compressibility is the property of air that allows it to change its density and pressure when it is subjected to a force or a change in speed. When the air around your aircraft is moving faster than the speed of sound, it cannot adjust smoothly to the shape of your aircraft, and it forms shock waves. Shock waves are sudden changes in pressure and density that propagate through the air and create a sonic boom. Shock waves increase the drag on your aircraft, because they create a high-pressure region in front of your aircraft and a low-pressure region behind it. This pressure difference reduces the net force that pushes your aircraft forward.

2 Drag and lift coefficients

To account for the effects of compressibility and shock waves on drag and lift, you need to use some aerodynamic coefficients that measure how much drag and lift your aircraft generates per unit of area and dynamic pressure. The drag coefficient (Cd) is the ratio of the drag force to the product of the area and the dynamic pressure. The lift coefficient (Cl) is the ratio of the lift force to the same product. These coefficients depend on the shape, size, and orientation of your aircraft, as well as the Mach number, which is the ratio of the airspeed to the speed of sound.

3 Critical Mach number

The critical Mach number (Mc) is the Mach number at which the air around your aircraft reaches the speed of sound for the first time. This is where the compressibility effects start to become significant and affect the drag and lift coefficients. The critical Mach number depends on the shape of your aircraft, especially the curvature and thickness of the wings. The more curved and thick your wings are, the lower the critical Mach number will be. For example, a typical subsonic aircraft has a critical Mach number of about 0.8, while a supersonic aircraft has a critical Mach number of about 1.2.

4 Drag divergence Mach number

The drag divergence Mach number (Mdd) is the Mach number at which the drag coefficient starts to increase rapidly due to the formation of shock waves. This is where the drag force becomes a major factor that limits the performance and efficiency of your aircraft. The drag divergence Mach number depends on the shape and smoothness of your aircraft, as well as the angle of attack, which is the angle between the direction of the airspeed and the wing chord. The more streamlined and smooth your aircraft is, and the lower the angle of attack is, the higher the drag divergence Mach number will be. For example, a typical subsonic aircraft has a drag divergence Mach number of about 0.9, while a supersonic aircraft has a drag divergence Mach number of about 1.4.

5 Lift curve slope

The lift curve slope (a) is the rate of change of the lift coefficient with respect to the angle of attack. It measures how much lift your aircraft generates per unit of angle of attack. The lift curve slope depends on the aspect ratio, which is the ratio of the wing span to the wing chord, and the Mach number. The higher the aspect ratio and the lower the Mach number are, the higher the lift curve slope will be. However, when the Mach number approaches or exceeds the critical Mach number, the lift curve slope starts to decrease due to the compressibility effects and the formation of shock waves. This reduces the lift force and the stability of your aircraft.

6 Design considerations

To account for the effects of compressibility and shock waves on drag and lift, you need to consider some design aspects that can help you optimize your aerodynamic performance and efficiency. For example, you can use a swept wing, which is a wing that angles backward from the fuselage, to delay the onset of shock waves and increase the critical and drag divergence Mach numbers. You can also use a supercritical airfoil, which is a wing shape that has a flatter upper surface and a rounder lower surface, to reduce the drag coefficient and increase the lift coefficient at high Mach numbers. You can also use a variable geometry wing, which is a wing that can change its shape and angle during flight, to adapt to different speed regimes and flight conditions.