AAWSAP DIRD, Detection and High-Resolution Tracking of Vehicles at Hypersonic Velocities, November 2010

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These equations can be expressed in a form where the ratio of density, temperature, and
pressure across the normal shock are a function of the upstream Mach number, M1.
(11)
(12)
Pz = 1+ ~(M12 - 1)
(13)
P1
r+ 1
Pi
<r + t) M 12
= ----­
(14)
Pi
2 + (y - 1) M i2
As an example, if the object shown in figure 4 is traveling at Mach 3 through air at sea level,
the pressure in the region between the nose of the object and the shock changes as shown in
the following table:
Table 1: Normal Shock Values for Mach 3 Flow
Freestream
Ratio of
Values
Values
Properties
Downstream
Across the
of the
Normal Shock
Normal Shock
M1 =3
M2/M1 = 0.158
M2 = 0.475
p1 = 101,325 Pa
p/p1 = 10.333
p2 = 1,047,000 Pa
T1 = 293 K
Ti/T1 = 2.679
T2 = 785.0 K
= (2o·q
= (s12·q
p1 = 1.293 kg/m 3
p/p1 = 3.857
p2 = 4.976 kg/m3
For a normal shock, the Mach number on the downstream side of the shock is always
subsonic, and in this example, the Mach number abruptly drops from M1 = 3 to M2 = 0.475.
The temperature always increases across a shock, and for a Mach 3 flow, the temperature
rises from room temperature at 20° C up to 512° C.
It is apparent that, for supersonic
aircraft traveling at this speed, the fuselage and wings will need to be made of materials that
can withstand the high temperatures and the dramatic pressure increase of 10.333. Shocks
are always accompanied by significant increases in pressure, temperature, and density in the
flow across the shock.
Flow about an Ogive or wedge-shaped airfoil as shown in Figure 4 can be analyzed in a
similar fashion; however, the wall deflection angle, e, will affect the flow and the formation of
the oblique shock wave that surrounds the airfoil.
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