+-----------------------+-----------------+-----------------+-----------------+-----------------+ | | Cast-iron Common| Palliser Shell | Solid Steel | Solid Lead | | | Shell [f] = 2/3,| [f] = ½, S.G. 8.| Bullet | Bullet [f] = 0, | | | S.G. 7.2. | | [f] = 0, S.G. 8.| S.G. 10.9. | +--------+--------------+--------+--------+--------+--------+--------+--------+--------+--------+ | x |[beta]-[alpha]|[delta] | n |[delta] | n |[delta] | n |[delta] | 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 [delta] of the rifling is given by tan [delta] = [pi]d/nd = ½ dp/u, (10) which is the ratio of the linear velocity of rotation ½dp to u, the velocity of advance, c1 C2d² tan² [delta] = [pi]²/n² = d²p²/4u² = (c2 - c1) -- ---- c2 C1² W´ / W´ \ / k2 \² 1 + --- [alpha] ( 1 + ---[epsilon] ) ( -- ) W´ W \ W / \ d / = --- ([beta] - [alpha]) --------------- · -----------------------------. (11) W W´ / k1 \^4 1 + ---[beta] ( -- ) W \ d /