242 
PRINCIPLES OP GUNNERY. 
The resist¬ 
ance of the 
air to a pro¬ 
jectile in 
motion. 
The retard¬ 
ation varies 
directly as 
the resist¬ 
ance op¬ 
posed to the 
motion of 
the pro¬ 
jectile, and 
inversely as 
the weight 
of the pro¬ 
jectile, 
Equation 
of motion 
connecting 
distance 
and velo. 
city. 
nience of calculation; d being the diameter of the projectile in inches, 
and w its weight in lbs.: so that 
_ d* K 
w (1000)8 • 
It was concluded that the resistance of the air to the hemispherical 
head was the greatest, and to the ogival head of 2 diameters the least, 
of the forms experimented on. 
The resistance of the air to the hemispheroidal and ogival heads 
differs so little that there is practically not much to choose between 
them. Professor Bashforth states that “ the slight variations in the 
resistances to the three latter forms le&d to the conclusion that the 
amount of resistance offered by the air to the motion of elongated 
projectiles is little affected by the more or less pointed apex, but 
depends chiefly upon the form of head near its junction with the 
cylindrical body of the projectile. In this neighbourhood the forms of 
the hemispheroidal head and the ogival head struck with a radius of 
2 diameters are the same, and the resistances are little different. - ’'’ 
The resistance which an elongated projectile in motion meets 
WITH IN PASSING THROUGH THE AIR DEPENDS 
(1) On the velocity of the projectile. 
(2) On its sectional area. 
(3) On the form of head. 
For velocities between 1100 f.s. and 1350 f.s. the resistance varies as 
the cube of the velocity ; so that if v = the velocity of projectile, d — its 
diameter, K' a coefficient depending on the form of head, the resist¬ 
ance opposed to its motion, 
or R, varies as v^d^K'. 
For projectiles with similar forms of heads K' is constant; so that 
within the limits of velocity mentioned above, and with ordinary 
service projectiles, 
-n V, 
R oc a d*v 6 — -, suppose. 
9 
The retardation, or the rate of loss of velocity, of the projectile 
owing to this resistance, varies inversely as the tveight of the projectile ; 
so that if w be the weight of the projectile, it follows that 
the retardation = = K'v 3 — 
w w 
For convenience of calculation, suppose K’ = 
relations become 
gz / ,, \3 
resistance ( R ) = K . — 
_ d 2 / v \ 3 
and retardation 
w \1000 
(™T 
. dv _ d 2 Kv 3 . 
0XV ds~ w (1000) 8 ’ 
11 
( 1000 ) 
- s ; then the above 
( 1 ) 
( 2 ) 
