Colonial Campaigns Club (CCC)

To the List:

Below is a CORRECTED list of lethality figures for Howitzer-fired canister (specifically the 48 ball canister for 3-pounder artillery). While the new numbers are better, they didn’t change so much that it would change the general shape of the overall lethality curve. It merely changed the length of the curve.

George

I was pondering the lethality of howitzers at fairly short range. Ever since I read AL's alternate scenario with howitzer's having an alternate pdt to reflect the use of canister at short range, instead of ball, I have been pondering how one might "model" the lethality of canister.

We could divide the trajectory of canister into four, maybe five ranges (assuming 48 ball in a 3" diameter canister):

1) the range from cannon to target where the grape or shot "string" is expanding up to the width of an infantry target (approx. 20 inches) - 48 shot in a 20" diameter, or 20" x 20" square if we want to simplify the math;

2) the continued expansion of the "pattern" or "thread" in all directions until the diameter reaches the height of the average infantry man (approx. 55 inches), where the "bite" out of an infantry line is as wide as it is tall - this represents 48 shot in a 55" diameter (or a 55" x 55" square if we want to simplify the math);

3) the continued expansion of the "pattern" or "thread" in all directions, widening the "bite" of an infantry line in a rectangular fashion - representing 48 shot in a rectangle that doesn't get higher than 55" tall, but continues to extend (to the left and right of the artillery sight line). At first, there is a probability of 1 shot per square foot of infantry line. And then the pattern spreads out enough to where there is only a probability of 1 shot per one human profile (say 85% of 20 inches by 55 inches - - or 6.5 square feet);

4) the continued expansion of the pattern where the probability of a "ball" drops to less than 1 ball per one man's 6.5 sq.ft. profile. Within the bounds of this range, the lethality of grape has to be calculated by multiplying how many times 6.5 sq. feet can fit into the total square footage of the line being enveloped by the grape (say 55" by 400 feet = 1,822 sq. ft.) times the average shot per square footage.

5) and, of course, for those who are sticklers for detail, there is finally the part of the trajectory which exceeds the USEFUL range of the artillery, or at least of grape/canister shot. But in this case, I am specifcally examining the very short ranges.

Based on my preliminary math (I will be double-checking my figures this week), I obtained the following estimates for hits from each 3" canister of 48 shot (1 oz per shot), using 125 feet to represent each hex of the typical engine pdt file, and the assumption that once the "plume" of canister shot stabilizes outside of the mouth of the cannon, the approximate expansion in diameter of the pattern is 1" per yard:

1 hex - 2 to 3 men hit
2 hexes – 4 to 5 men hit
3 hexes – 5 to 7 men hit
4 hexes – 7 to 8 men hit
5 hexes – 9 to 10 men hit
6 hexes – 10 to 12 men hit
7 hexes – 12 to 11 men hit (the curve is now headed downward)
8 hexes – 11 to 10 men hit
9 hexes – 9 men hit
10 hexes – 8 men hit

and so on ... until we hits drop off more
suddenly due to passing the useful range of
the artillery piece.

At about 275 yards, the spread pattern has become so dispersed that the odds of hitting a 6.5 square foot target (the human profile) continues to decrease until we reach the end of the useful range of canister (whatever that may be).

In terms of feet, 8 hexes (when hits begin to attenuate) is about 1000 feet or about 333 yards. This approximate 300 yard range is in the middle of the frequently cited useful range of canister that averages 16 shot per inch of cannon diameter.

This analysis assumes that spherical shot, once in its dispersing vector, continues to fly in a straight line at a constant angle from the sight line for the cannon. Specifically, using
one website, I assumed the following:

At 5 yards, the pattern is approximately 7.9 or 8 inches in diameter.
At 10 yards, the pattern is approximately 15.8 inches in diameter
At 15 yards, the pattern is approximately 23.6 inches in diameter
At 20 yards, the pattern is approximately 27.6 inches in diameter.

After 20 yards, it is assumed the trajectory of shot has stabilized (as much as it ever will), and continue to spread at approximately 4 inches for every 5 yards.

Naturally, there is the tendency for individual shot to assume a slightly curved trajectory, due to irregular spin and other factors.. Shot deforms out of shape during the cannon ignition, as one shot pushes against other shot, leading to irregularities in trajectory.

Even non-deformed spherical shot can deviate from the expected trajectory a certain degree (if the center of gravity is not perfectly centered). However, I think we can safely say that these variable trajectory elements will only affect the "shot cone" a small amount, and affect hit rates by +/- a man or less at any given range.

Regards,

Ensign Brooks