182
5 Miscellaneous Calculations
form a cloud of solid debris particles; the fireball also picks up water from the
atmosphere. All of this material will eventually become fallout, sometimes in the
form of radioactive rain. As the fireball ascends, cooling of its outside and air drag
often creates a toroidal (doughnut-like) shape. At this stage, the cloud will often have
a reddish appearance due to the presence of nitrogen-oxide compounds at its surface.
The air inside the fireball cools by successive radiation and re-absorption of Xrays. When the air has cooled to a temperature of about 300,000
o , a “hydrodynamic
shock” forms, a so-called “front” of compressed air. The shock front travels faster
than energy can be transported by successive absorption and re-emission of radiation,
so it “decouples” from the hot sphere and moves out ahead of the latter, leaving behind
a region of relatively cool air which “eats into” the central hot sphere. For outside
observers, visible radiation comes from the shock wave. As the shock front cools, its
observable temperature bottoms out at a minimum of about 2,000
o . The shock front
also becomes transparent; an observer, if he or she still has eyes, can now look into
higher-temperature air, which results in a second brightness maximum. During this
time, however, the central fireball is still hot enough to be essentially opaque, and
hence invisible.
The brightness of the Trinity test was impressive, but perhaps even more staggering
was the amount of radioactivity generated: An estimated one trillion Curies (see
Exercise 5.1). However, nuclear weapons derive their military value not from their
radioactivity, but rather from blast and burn effects; militarily, the radioactivity can
be a nuisance if you want to move your own troops into the bombarded area. Many of
the monitoring instruments deployed for the Trinity test were destroyed by the blast,
but one pressure gauge located at 208 feet from the base of the 100-foot high tower
atop which the device was mounted gave a reading of about 5 tons per square inch,
or nearly 700 atmospheres. On considering that reinforced multistory buildings will
be demolished by a pressure excess of 20 lb per square inch (~1.4 atmospheres), one
can get a sense of the immense destruction caused by nuclear weapons; at Nagasaki,
an area of about three square miles was essentially totally destroyed. The situation
becomes even more sobering when one learns that postwar improvements resulted
in drastically higher weapon yields. The largest pure fission weapon ever detonated
by the United States, the Ivy King test of November, 1952, generated a yield of 500
kt. This, however, paled in comparison to the February, 1954, Castle Bravo test of a
“thermonuclear” device which yielded 15 megatons. Such fusion-based “hydrogen
bombs” use fission bombs as triggering mechanisms. At the opposite extreme, the M28 “Davy Crockett” nuclear device could be fired from a tripod-mounted recoilless
rifle in battlefield conditions; its yield was on the order of “only” 10–20 tons TNT
equivalent.
A side-effect of nuclear weapons which can act against friendly forces as well as
an adversary is the so-called “electromagnetic pulse,” which arises from gamma-rays
emitted by the explosion ionizing the surrounding air. Negatively-charged electrons
move outward more rapidly than the much heavier positively-charged ions, leading to
a strong and rapidly time-varying electric field which can induce damaging currents
in electronic equipment. In one spectacular case, detonation of a 1.4-megaton weapon
at an altitude of 400 km near Johnston Island in the Pacific Ocean in 1962 caused
5 Miscellaneous Calculations
form a cloud of solid debris particles; the fireball also picks up water from the
atmosphere. All of this material will eventually become fallout, sometimes in the
form of radioactive rain. As the fireball ascends, cooling of its outside and air drag
often creates a toroidal (doughnut-like) shape. At this stage, the cloud will often have
a reddish appearance due to the presence of nitrogen-oxide compounds at its surface.
The air inside the fireball cools by successive radiation and re-absorption of Xrays. When the air has cooled to a temperature of about 300,000
o , a “hydrodynamic
shock” forms, a so-called “front” of compressed air. The shock front travels faster
than energy can be transported by successive absorption and re-emission of radiation,
so it “decouples” from the hot sphere and moves out ahead of the latter, leaving behind
a region of relatively cool air which “eats into” the central hot sphere. For outside
observers, visible radiation comes from the shock wave. As the shock front cools, its
observable temperature bottoms out at a minimum of about 2,000
o . The shock front
also becomes transparent; an observer, if he or she still has eyes, can now look into
higher-temperature air, which results in a second brightness maximum. During this
time, however, the central fireball is still hot enough to be essentially opaque, and
hence invisible.
The brightness of the Trinity test was impressive, but perhaps even more staggering
was the amount of radioactivity generated: An estimated one trillion Curies (see
Exercise 5.1). However, nuclear weapons derive their military value not from their
radioactivity, but rather from blast and burn effects; militarily, the radioactivity can
be a nuisance if you want to move your own troops into the bombarded area. Many of
the monitoring instruments deployed for the Trinity test were destroyed by the blast,
but one pressure gauge located at 208 feet from the base of the 100-foot high tower
atop which the device was mounted gave a reading of about 5 tons per square inch,
or nearly 700 atmospheres. On considering that reinforced multistory buildings will
be demolished by a pressure excess of 20 lb per square inch (~1.4 atmospheres), one
can get a sense of the immense destruction caused by nuclear weapons; at Nagasaki,
an area of about three square miles was essentially totally destroyed. The situation
becomes even more sobering when one learns that postwar improvements resulted
in drastically higher weapon yields. The largest pure fission weapon ever detonated
by the United States, the Ivy King test of November, 1952, generated a yield of 500
kt. This, however, paled in comparison to the February, 1954, Castle Bravo test of a
“thermonuclear” device which yielded 15 megatons. Such fusion-based “hydrogen
bombs” use fission bombs as triggering mechanisms. At the opposite extreme, the M28 “Davy Crockett” nuclear device could be fired from a tripod-mounted recoilless
rifle in battlefield conditions; its yield was on the order of “only” 10–20 tons TNT
equivalent.
A side-effect of nuclear weapons which can act against friendly forces as well as
an adversary is the so-called “electromagnetic pulse,” which arises from gamma-rays
emitted by the explosion ionizing the surrounding air. Negatively-charged electrons
move outward more rapidly than the much heavier positively-charged ions, leading to
a strong and rapidly time-varying electric field which can induce damaging currents
in electronic equipment. In one spectacular case, detonation of a 1.4-megaton weapon
at an altitude of 400 km near Johnston Island in the Pacific Ocean in 1962 caused