#### Acknowledgement:

Most of this stuff is from the *Journal of Hazardous Materials*,
A74 (2000) 149-161.

#### Fireball:

Associated with the detonation of an explosive is a
fireball. In general, the dimension of the fireball is given by:

*D = 8.5 x W*^{0.341}

Where *W* is the weight of the explosive in pounds and *D*
is the diameter of the fireball in feet. So, for example, if there is an
explosion of 10 pounds there will be a fireball of diameter 18.64 feet.
This does not seem to match well with my experiments. My results indicate
much smaller fireballs. In fact, unless there is some effort put into
making a fireball there is none. But that could be because my explosives
use ammonium nitrate as their principle ingredient which is typically a very
'cool' explosive.

#### Blast effects:

Trees are sensitive to drag forces, such as wind from the blast
wave. Broad leaf trees are more sensitive than coniferous trees. The
ground drainage, soil type, tree girth, etc. are also big variables. There
are also different levels of damage, these have been characterized as:

Category 1: ground completely cleared, all trees uprooted or
snapped off near the root, leaving stumps not greater than 6 feet in height.

This damage can be approximated by the equation:

*D = 3.65 x W*^{0.425}

Where *W* is the weight of the explosive in pounds and *D* is the
diameter of the category 1 damage in feet.

Category 2: trees heavily damaged, with trunk or major branches broken off;
the limit of this area will be fixed by the distance at which trees are
structurally complete, though minor twigs and leaves are removed.

*D = 5.17 x W*^{0.425}

Where *W* is the weight of the explosive in pounds and *D* is the
diameter of the category 2 damage in feet.

Category 3: trees have lost twigs and leaves only; the limit of the area
will be fixed by the distance at which leaves remain on the trees at all
levels, although they may be torn by the blast; it will usually be found that
some leaves will remain on the upper branches of a high tree, almost up to the
limit of Category 2, but this will not count for this purpose.

*D = 7.73 x W*^{0.425}

Where *W* is the weight of the explosive in pounds and *D* is the
diameter of the category 3 damage in feet.

Category 4: undergrowth, bracken, et., uprooted or sufficiently badly
damaged to cause fading.

*D = 10.31 x W*^{0.425}

Where *W* is the weight of the explosive in pounds and *D* is the
diameter of the category 4 damage in feet.

I have no experience with trees, however the result on grass and small brush
seems to compare well with these numbers.

#### Crater

The size of the craters formed depends on the soil type (soft, hard, sandy,
clay, rocky, etc.) and the position of the explosive compared to ground
level. The following equation is for the explosive touching the ground at
the time of detonation.

*D = k x W*^{1/3}

Where *k* is 1.7 for very hard and 6.0 is for very soft ground, *W*
is the weight of the explosive in pounds, and *D *is the diameter of the
crater in feet.

This appears to match my results very closely.

#### Fatal injuries

This is due to the brick and concrete 'throw' from an explosive
magazine. The fragmentation effects from a steel magazine are less than
for brick and concrete structures. This doesn't take into account a lot of
variables such as how much air space in the magazine (loading density), details
of magazine construction, the effects of the blast wave (lung hemorrhage for
example), and lots of other stuff. But it's a rough estimate.

*P = 0.286 x ln (0.022 x W) x e *^{-3.05E-3 x D}

Where *W* is the weight of the explosive in pounds and *D* is the
distance from the explosion, and P is the probability of a fatal injury.

220.25 < *W* <= 165,000 pounds

**Air Pressure**

This is from
__http://www.navweaps.com/index_tech/tech-048.htm__

*p = 4120/z*^{3}_{ } - 105/z^{2} + 39.5/z

where:

*z = R/W*^{1/3}

*R* is the outward radial distance in feet from the target

*W* is explosive mass in lb (equivalent TNT).

The pressure appears to be the overpressure in PSI, but I am unable to find
confirmation of that. The lethal dose (50%) for large animals varies from
about 50 to 200 PSI depending on the species and duration of the
overpressure. For small animals it is 30 to 80 PSI, again depending on the
species and duration.