|MadSci Network: Physics|
1. Landolt-Bornstein , Oceanography, New Series, group 5, Volume 3, part A.
2. Cureio, Petty, Optical absorption of pure water,
Journal of the Optical Society of America, (JOSA) V41, pp 302-304
Your question revolves around the basic concepts of the science and laws of
THERMODYNAMICS and the transfer of heat.
There are three ways heat can be transferred form a submarine; by conduction,
by convection and by radiation. For a submarine operating in the sea, all three
of these methods of heat transfer must be taken into account.
Conduction: If one end of a metal rod is placed in a flame while the other
end is held in your hand, you will feel the rod becoming hotter and hotter
even though your hand is not in direct contact with the flame. Heat is said
to flow along or through the material by conduction.
Convection: The transfer of heat from one place to another by the actual
motion of material is called convection. Examples are water cooling or air
cooling of a hot engine.
Radiation: When we hold a hot body near our hand in still air or a vacuum,
we feel the heat by radiation. In the design of satellites operating in the
vacuum of space, convection and conduction cannot be used to remove heat
from the spacecraft, only radiation can be used to dissipate waste heat.
The data in References 1 and 2 for clear fresh water and clear sea water show
that the water is most transparent at visible blue - green wavelengths between
0.4 to 0.5 micrometers (micrometers are 1/1,000,000 of a meter) where the
attenuation (loss) of electromagnetic energy is about - 0.1 dB per meter
(about 2% loss, 98% transmission). However, the attenuation rapidly increases
for both longer and shorter wavelengths.
A submarine's propulsion system operates at very high temperatures of several
thousand degrees C and all three methods of heat transfer must be taken into
account. However, convection and conduction of the waste heat to seawater is
the primary way of cooling a submarine. However, remote sensing usually relies
on monitoring the heat radiation from an object including it's heating of the
surrounding environment, which in this case is the seawater around the submarine.
Let us assume that the submarine is expelling boiling water at 100 degrees
The wavelength for the peak of the thermal radiation spectrum (Black body
radiation) for a material at a temperature of 100 degrees C is determined by:
Max Wavelength (in micrometers) = 2897 divided by the temperature in degrees K
0 degrees C = 273.16 degrees K, thus boiling water is
at 273.16 + 100 = 373 degrees K.
Max Wavelength = 2897 / 373 = 7.8 micrometers in the infrared.
From References 1 and 2 we find that at 7.8 micrometer wavelength the attenuation
of water is greater than -30 dB per meter. This means that for a given amount of energy
entering a meter of length of water only 0.1% passes through the meter and the
99.9% of the energy is absorbed or scattered. The second meter of water will
attenuate 99.9% of the original 0.1% entering and an insignificant amount of
thermal radiation would remain. Thus we conclude that we will only be able to
detect a submarine by thermal radiation only a few meters under the water.
If the submarine were traveling on or near the surface, the surface radiation from
the water heated by the submarine might leave a thermal wake which might be
detectable. However, detecting thermal radiation directly from the submarine at a
depth greater than a few meters would be very difficult if not impossible and
submarines usually travel at much greater depths.
We know that in clear water we can visually see a submarine at a much greater depth
than a few meters because of the blue - green "window" in water; however, the
thermal radiation from the submarine at these wavelengths is negligible.
After the invention of powerful blue - green lasers during the 1960s there has
been a great deal of research in using LIDAR (laser radar) to detect submarines
at depth; however, information about how well this works is not pubically available.
Best regards, Your Mad Scientist
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