Defense Intelligence Reference Document Detection And High Resolution Tracking Of Vehicles At Hypersonic

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Chapter 1: Theory Governing Objects in Flight
Many of the detection technologies for hypersonic aircraft are based on the properties of the
air flow around the object. The fluid mechanics affecting supersonic and hypersonic aircraft
are well described in textbooks on compressible flow by J.D. Anderson; 2,3 subsonic flow,
including the affect of boundary layers, is covered in the textbook by F. M. White. 4
Hypersonic flow usually refers to the regime where objects are moving faster than Mach 5,
but technically refers to the Mach range where pressure, temperature, and density ratios
across shock waves reach constant values, and this does happen at about Mach 5. Fluid flow
changes dramatically at Mach 1 defined at the point where the velocity of a projectile, V,
equals the local speed of sound, a, in the atmosphere:
M ~ V ( 1)
a
Flow regimes are defined by the following:
• M 1, supersonic flow
• M > 5, hypersonic flow
The speed of sound varies with temperature and with the type of gases in the atmosphere. A
simple equation for the speed of sound includes the ratio of specific heats, y, the gas
constant, R, and the temperature, T:
(2)
For air at room temperature, y = 1.4, R = 287 J/kg·K, and T = 20° C or 293 K. The
subsequent speed of sound is 343 m/s (1,125 ft/s or 767 mph). It is easier for a projectile
to exceed the speed of sound at higher elevations since the temperature of the atmosphere
is lower, reducing the speed of sound and the subsequent velocity necessary to break the
sound barrier.
The viscosity of the fluid flowing around an object induces drag and retards its forward
motion. Supersonic flow has some of the viscous characteristics of subsonic flow, but adds in
the complication of shock waves. To understand the nature of how a projectile affects the
flow of fluid around it, consider the case of a subsonic projectile.
SUBSONIC FLOW AND DRAG
Subsonic flows, such as the flow shown in Figure 1, are heavily influenced by collisions
between molecules of air and the surface of the projectile. The equations for this interaction
were first developed by Sir Isaac Newton in the seventeenth century, where he determined
that fluids have a property called "viscosity" that is the cause of drag on projectiles. The key
parameter that affects subsonic fluid flow is the ratio of viscous forces to inertial forces,
where inertial forces are associated with the tendency for a moving fluid to keep moving in
the same direction. The ratio of these two forces is defined as the Reynolds Number, Re.
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