Practical 
examples. 
280 
PRINCIPLES OP GUNNERY. 
Example (1).-—What is the range and time of flight of a 12-lb. 
shot fired with a ninzzle velocity of 1680 f.s. at 3° of quadrant eleva¬ 
tion the jump being taken at 20', and the diameter of the shot 3 ins. ? 
Here 
angle of departure, a, = 3 ° 20 ', 
d? 
w 
3. 
- 4- 
The whole ascending branch of the trajectory may be taken, and at 
the vertex 
/5 = 0 ; 
hence D = a — ft = 3° 20'. 
In applying the formula for small angles of departure, 
Dq sec $ — d) 
a n _ 
'v sec <f> + D sec d>. 
* w 
sec may be neglected, and p sec may be taken equal to V , the 
muzzle velocity, and q sec <fi = v, the remaining velocity at the end of 
the arc under consideration; so that the above formula becomes 
D, = Dy + ~ D = D lm + f x 3-333 
= •0588 + 2-5 = 2-5538 ; 
or 0 = 1188. 
The formula for computing <f> is in this case^ where ft = 0> 
- a p — q a 
and since p = V and q = v nearly, 
1680 — 1168 300' 
£= 1° 40' + 
1680 + 1168 X 3 
1° 40' + 12' = 1° 02'. 
The formula for computing X is 
cl g 
“ X = COS <p (Sq sec ^ —■• Sjj sec \ 
which may be written in this case 
X = cos $(S B -S V ); 
w 
or X = -— (#1168 — #168o) S ^ nce #1168 = 2665 
#1680 = ^3 
= 3443 cos 1° 52' 
= 3441 ft. 
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