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

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In this equation, q represents the amount of radiant energy emitted in watts, E is the
emissivity (a dimensionless quantity that gauges the relative ability of an object's surface to
emit energy by radiation), A is the surface area, a is the Stefan-Boltzmann constant (a
= 5.67 x 10-s J-s- 1-m- 2 -K-4 ), and T is the temperature of the object's surface. A simple
example of emission of heat as radiant energy is an infrared bathroom heater where electric
current is passed through a metallic element that reaches several thousand degrees and
emits considerable thermal radiation.
All objects in the environment exchange radiant heat with each other and seek equilibrium
temperatures. At high temperatures, many objects behave as "black body radiators" defined
by their surface emissivity, E = 1. The surface temperature of an object causes
electromagnetic radiation to be emitted with a spectrum given by Planck's Distribution Law,
equation 18, where the energy density is emitted by the surface of the object per
wavelength per unit volume:
8 ;r h c
u(i.T) = ,, -,~"--
A
The terms in this equation are as follows:
• c: speed of light, (3 x 10 8 m/s).
• h: Planck's constant, (6.62 x 10-34 J-s).
• A: wavelength of the emitted radiation, (m).
• k: Boltzmann constant, (1.38 x 10· 23 J/K).
• T: surface temperature, (K).
• u(A,T): spectral energy density, (J-m- 3 -m- 1).
( 18)
The surface of the sun behaves as a black body radiatora with a surface temperature of
5,778 K. For the sun, the Planck distribution of energy versus wavelength looks like that of
Figure 12. The horizontal axis is the wavelength in units of meters and shows that peak
energy occurs at a wavelength of about 5.02 x 10- 7 meters or 0.502 microns (1 micron = 10·6
meters). This falls within the visible band (0.38 microns to 0.65 microns) and corresponds to
the yellow color of our sun. The peak wavelength, equation 19, is given by Wien's
Displacement Law:
).""' = 2.8977685 x 10--1
(m - K)/ T ( 19)
This shows that as the temperature of an object increases, the amount of radiant energy
released by the surface increases and the value of the peak wavelength becomes smaller.
"A black body is an idealized object that absorbs all electromagnetic radiation that falls on it.
Since a black body is a perfect absorber of radiant energy, by the laws of thermodynamics it must
also be a perfect emitter of radiation.
18
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