Relation 
between 
angle of 
spiral and 
twist of 
rifling. 
Determin¬ 
ation of 
the twist 
of rifling at 
any point 
in the bore. 
84 
PRINCIPLES OP GUNNERY.' 
with the increasing twist, it is estimated at any point by the distance 
in which the spiral would make one tarn had the angle of spiral 
remained uniform, and the same as at the given point. 
Suppose a the angle of spiral at any point in the bore; also suppose 
the twist of rifling at the same point to be one turn in n calibres. 
Then 
tan a = ;* 
n 
which expresses the relation between the angle of spiral and twist of 
rifling at any point in the bore. 
Problem. —To find the twist at any point of the bore of a gun rifled 
with increasing twist. 
Let a and a be the angles of spiral at the muzzle and at the breech 
respectively ) n and m the number of calibres in which the spiral 
makes one turn at the muzzle and at the breech respectively. 
y 
} 
^ 
o a e 
5 a: 
In the figure, OP represents the curve (increasing twist )—0 at the 
muzzle and P at the breech end of the rifling. The curve OP is a 
parabola, whose vertex is at A ; and is referred to vertical and horb 
zontal co-ordinates, whose origin is at 0. Then 
tan a — — , and tan a = - . 
n vi 
Let y — bx + cx 3 be the equation to the curve. 
Differentiating, 
tvhere x = 0, 
dx 
~ — tan a — b. 
dx 
h -f 2 cx; 
(i) 
Let OQ (the length of rifling in the bore) — l. Then from equa¬ 
tion (1) 
tan a = tan a + 2cl; 
7r 7r 
tan a — tan a _ m n 
b l 
or 
2c 
* See “Treatise on the Construction and Manufacture of Ordnance in the British Service/’ 
