T-45 Aerodynamics Student Workbook
Aero Chapter 02, High-Speed Flight
As acceleration continues, the normal
compression wave will strengthen and move
aft. At some speed, approximately 5% above
the Critical Mach Number, there is a rapid
rise in the drag coefficient due to the
Total Drag
formation of the normal compression wave.
This speed is the Force Divergent Mach
Number (Mfd), also known as the Drag
Divergence Mach number (Figure 20).
CD
Additional drag arises from flow separation
DRAG
COEFFICIENT
CD
when it occurs.
As flight speed is increased further, a bottom
M
CRIT
shock wave will appear (Figure 21). The
Force Divergent Mach Number
compression wave on the lower surface is
0.8
0.85
1.0
1.2
usually weaker than the one on the upper
VELOCITY
surface because acceleration over the lower
Figure 20: FORCE DIVERGENT MACH NUMBER
surface is much less. Wave drag will
continue to increase as the compression
waves strengthen. Flight controls on the
trailing edge of the airfoil begin to lose their
Normal Shock Wave
effectiveness. In subsonic flight, flight control
Supersonic
displacement affects the pressure distribution
Flow
about the entire airfoil. With a normal wave
present, the controls may be operating in a
separated or “dead” layer air.
Separation
OBLIQUE COMPRESSION WAVES
As airflow velocity continues to increase, the
Normal Shock Wave
waves continue to move aft and eventually
attach to the trailing edge and become
Figure 21: COMPRESSION WAVE AT MACH 0.92
“OBLIQUE” waves (Figure 22). An oblique
angle is an angle greater than 90 which is
measured from the airstream and, therefore,
describes the oblique wave. A supersonic
airstream, as it passes through oblique shock
wave, slows down. However, the change in
velocity through an oblique wave is not as
Supersonic Flow
Oblique
great as through the normal wave and the
Shock Wave
velocity will remain supersonic. The airflow
will experience an increase in static pressure,
Separation
density, and temperature. Kinetic energy is
converted to heat and lost. The angle of the
oblique wave increases with an increase in
Oblique
the airstream Mach Number. Because the
Supersonic Flow
Shock Wave
airflow is not perpendicular to the pressure
wave, the airflow changes direction.
Figure 22: OBLIQUE WAVE AT MACH 0.99
Eventually, the airflow decelerates and
becomes subsonic passing through a normal
shock wave.
(7-99) Original
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