266 
PRINCIPLES OE GUNNERY. 
Maximum The maximum height of the trajectory may also be approximated to 
trajectory, thus :—If T be the total time of flight, 
maximum height of trajectory = 
{Vide p. 262). 
09.9 
= -jf- (3'39) 2 = 46-26 ft. 
O 
Method of If y — PN is the height of the object to be struck, t the time of 
the “clan- flight over OP, and T the time of flight over the given range, OB, 
See/’ or St ’ then from equation (6), 
the distance 
in which an 
object of 
given height 
would be 
y = ^{T-t). 
under given Solving the quadratic, it is found that 
conditions. 
( 8 ) 
the upper sign to be taken for the second half of the trajectory. 
Hence t is known in terms of the total time of flight, and the height 
of the object fired at. 
The time over OP being known, the velocity at P can be found, 
whence the distance ON is known, and consequently NB —the “ dan¬ 
gerous distance ;; —is known. 
Example 2.—The 12‘5-in. M.L. gun is fired with a battering charge 
so as to strike a ship on the water-line at a distance of 3000 ft. What 
would be the “ dangerous distance/’’ or the distance short of 3000 ft. 
in which the'ship whose side was 8*05 ft. above the water-line would be 
struck somewhere on its side, under the given conditions ? Muzzle 
velocity = 1420 f.s., weight of projectile = 802 lbs., diameter of pro¬ 
jectile = 12*42 ins., OB = 3000 ft., PN= 8*05 ft. 
The remaining velocity at B can be found thus: 
S„ = Sr + - S = S li% + X 3000 
w ■ 802 
= 1251*1 + 576*9 = 1828 ; 
or v = 1307 f.s. (Table I.) 
The time over OB can be found thus : 
T = = I= 2-2 secs 
d* *1923 
w 
