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Various

"Scientific American Supplement, No. 803, May 23, 1891"


The best weight for a projectile is found by the formula
w = d cubed (0.45 to 0.5)
w being the weight in pounds, d the diameter in inches and 0.45 to 0.5
having been determined by experiment.
With a light projectile we get a flat trajectory, and accuracy at
short ranges is increased. With a heavy projectile the resistance of
the air has less effect and the projectile is advantageously employed
at long ranges.
In the following formulae, used in calculating the penetration of
projectiles in rolled iron armor,
g = the force of gravity.
w = the weight of projectile in pounds.
d = the diameter of projectile in inches.
v = the striking velocity in feet per second.
P = the penetration in inches.

Major Noble, R.A., gives
_________________
1.6 / w v squared
P = /\ / ----------------
\/ [pi] g d 11334.4
[TEX: P = \sqrt[1.6]{\frac{w \ v^2}{\pi \ g \ d \ 11334.4}}]
U.S. Naval Ordnance Proving Ground uses
________________
2.035/ w v squared
P = /\ / ---------------
\/ [pi] g d 3852.8
[TEX: P = \sqrt[2.035]{\frac{w \ v^2}{\pi \ g \ d \ 3852.8}}]
Col. Maitland gives
w v squared
P = ------------
g d squared 16654.4
[TEX: P = \frac{w \ v^2}{g \ d^2 \ 16654.4}]
Maitland's latest formula, now used in England, is
_
v /w
P = ----- \/ - - 0.


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