capable of doing, a foot-pound of work. A rifle ball having an energy of 2000 ft. lbs. is capable of raising 2000 lbs. one foot high or 1 lb. 2000 feet high. In measuring work done, no consideration is given to the time required. Too great stress cannot be put upon the statement that the time employed in doing a certain amount of work has nothing whatever to do with the amount of work done.

However, time is a factor in power which is the rate of doing work. One horse-power represents the ability to raise 33,000 lbs. one foot in one minute. Foot-second is the velocity expressed in feet per

second.

The Plane of Fire, or Plane of Departure, is the vertical plane passing through the line of departure.

Direct fire pertains to fire in which the angle of departure does not exceed 15 degrees.

High Angle Fire pertains to fire in which the angle of departure is greater than 15 degrees.

Recoil is the backward movement of the rifle caused by the reaction of the powder gases upon the projectile, and the reaction of both powder gases and projectile upon the air.

When the expansion of gases takes place the projectile is driven into and through the barrel, the friction of the barrel upon the projectile equals the friction of the projectile upon the barrel. The oarsman urges the water backward with the same force that he urges his boat forward. The friction

of the boat upon the water equals the friction of the water upon the boat.

The primary phase takes place while the projectile is moving through the barrel. It is the primary recoil that makes the angle of departure greater than the angle of elevation. It causes the jump of the rifle, which varies with the drop of the stock, the weight and velocity of both projectile and powder, the construction of the rifle, and the firmness with which the rifle is held.

The velocity of free recoil of the rifle due to the primary cause is expressed by

=

w+1⁄2w'
W

X v

For. D

in which v' is the velocity of recoil, W the weight of rifle, w the weight of projectile, w' the weight. of powder, and v the velocity of the projectile at any place in the bore, which velocity is determined from the formulas of Interior Ballistics, Vol. II. At the muzzle v equals the muzzle velocity.

The value of v' as determined by the above formula is approximately 7/10 of the total or maximum free recoil of the rifle, the remaining 3/10 is the result of the secondary phase.

The secondary phase is that which takes place after the projectile leaves the barrel, and is due to the reaction of the gases from the rifle upon the atmosphere, and varies as the caliber, velocity and shape of the projectile. The velocity of free recoil due to the secondary phase has been determined by experiment with the Sebert velocimeter, the value of which being added to formula D gives the for

mula for the total or maximum free recoil of the rifle as expressed

in which V' is the total, or maximum, velocity of free recoil of the rifle. W, w, and w' are expressed in grains.

The velocity of free recoil having been calculated, the energy of recoil is calculated by formula 2, Chap. II.

Since the recoil of a rifle is a function of the weight of the powder charge as well as the rate of burning of the powder, and as the pressure and burning curves of different smokeless powders vary, those powders having the longer pressure and burning curves produce greater recoil. For the same reasons recoils produced by black powder are greater than those produced by smokeless powders.

22 NEWTON

N.A.CO.

CHAPTER II.

The Fundamental Elements and Their Practical

T

Applications.

HOSE elements of ballistics which are of the

most practical interest to the rifleman, enabling him to know his rifle and its possibilities, are the muzzle velocity V, the remaining velocity v, the energy at any place in its flight E, the time of flight T, the maximum height of the trajectory H, and incidentally the horizontal distance x, from the muzzle to the summit of the trajectory for any range X, (in feet).

The following arrangement of data is suggested as being convenient. The name and figures within the parentheses therein and hereafter in tables and problems are those of the Springfield '06-150-2700-C .389 and are used only for illustration.

Ballistics.

Name of cartridge (Springfield, 1906).

Descrip

tion, caliber (.30). Wt. of bullet (150 grs.). Dia. of bullet (.304). C (.389). c (.595). Barometer (30′′). Temperature (60 F).

in which X is the range in FEET, S(v) and S(V) space functions found in Table 1 in the vertical column under S(u), S(V) opposite the V in column under (u), and S(v) opposite v in column under (u). X 300

771.2

Interpolation is simple proportion, as herein used. The difference between the space functions of 2470 and 2460 is 34.8, which difference represents an increment in velocity of 10 feet. The difference found

17.4

above is 17.4; hence -X 10 f. s. = 5 f. s. to be 34.8 subtracted.

Similarly, v for all ranges may be computed.

Problem 2.

Given V (2700) and wt. of bullet (150 grs.)

in which m is the weight in POUNDS, V the ve

locity in f. s., and g=32.16.