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Table of Rifling for Stability of an Elongated Projectile, x Calibres long, giving δ the Angle of Rifling, and n the Pitch of Rifling in Calibres.

Cast-iron Common Shell
ƒ = 2⁄3, S.G. 7.2.		Palliser Shell
ƒ = ½, S.G. 8.		Solid Steel Bullet
ƒ = 0, S.G. 8.		Solid Lead Bullet
ƒ = 0, S.G. 10.9.
x β − α δ n δ n δ n δ n
1.0 0.0000 0°   0′ Infinity 0°   0′ Infinity 0°   0′ Infinity 0°   0′ Infinity
2.0 0.4942 2   49 63.87 2   32 71.08 2   29 72.21 2   08 84.29
2.5 0.6056 3   46 47.91 3   23 53.32 3   19 54.17 2   51 63.24
3.0 0.6819 4   41 38.45 4   13 42.79 4   09 43.47 3   38 50.74
3.5 0.7370 5   35 32.13 5   02 35.75 4   58 36.33 4   15 42.40
4.0 0.7782 6   30 27.60 5   51 30.72 5   45 31.21 4   56 36.43
4.5 0.8100 7   24 24.20 6   40 26.93 6   32 27.36 5   37 31.94
5.0 0.8351 8   16 21.56 7   28 23.98 7   21 24.36 6   18 28.44
6.0 0.8721 10   05 17.67 9   04 19.67 8   56 19.98 7   40 23.33
10.0 0.9395 16   57 10.31 15   19 11.47 15   05 11.65 13   00 13.60
Infinity 1.0000 90   00 0.00 90   00 0.00 90   00 0.00 90   00 0.00

If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle δ of the rifling is given by

tan δ = πd / nd = ½ dp / u,

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which is the ratio of the linear velocity of rotation ½dp to u, the velocity of advance,

tan2 δ = π2= d2p2= (c2 − c1) c1 C2d2
n2 4u2c2 C12
= W′(β − α)
1 + W′α
W
·
( 1 + W′ε ) ( k1) 2
W d
.
W
1 + W′β
W
( k1) 4
W

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