1°

previously translated. The right line representing mean velocity curve after powder gases cease to act is drawn first. From it the velocity of bullet at from 30 to 40 feet from muzzle is obtained and used in Eq. (1) to obtain V. With first point thus established it remains only to draw a curve which shall pass through it, take the mean position of intermediate points, and be tangent to the right line already drawn. The ordinate and abscissa of point of tangency give maximum velocity of recoil and the corresponding recoil. The formula given by Sébert and Hugoniot (Construction Note No. 62, page 10) can be used when the velocity is approaching a maximum very slowly (Curve No. 5, Plate II); but for small arm curves the graphical method is preferred.

From the adjusted mean velocity curve the values in columns 10, 12 and 15 are obtained.

From column 18, we observe a very slight increase in velocity of bullet for the first twenty feet. It begins to lose in velocity after passing a point about 30 feet from muzzle and thereafter loses at a mean rate of about 7 feet for every 10 feet of range. This loss is greater than the value (about 4.7 feet) given by ballistic formulas for this bullet and range. This was to be expected, for the more rapidly moving gases compress the atmosphere in front of the bullet, and the small wires in target screens offer a slight resistance.

The piece has recoiled only 1".59 when it has its maximum velocity, and 2".345 when the bullet is 20 feet away. It thus appears that the piece is the first to suffer retardation.

The two values of mean velocity for whole range, given by the two instruments, furnish a satisfactory check.

The recoil corresponding to maximum velocity, of recoil, the range corresponding to maximum velocity of bullet and the retardation of bullet over the remaining short range are shown only approximately in the tables submitted. A slight variation in efficiency of powder will materially affect these data.

To determine accurately the retardation of bullet, the photochronograph, or the polarizing photo-chronograph referred to in the introduction, should be used.

In investigating free recoil of cannon, it is customary to assume friction to be negligible; but, inasmuch as the negative furnishes the necessary data, it is thought best to obtain at least an approximate correction for loss in maximum velocity of recoil through friction.

The piece is mounted on small iron wheels whose circumferences are grooved to fit the track formed by letting brass rods

into longitudinal grooves in top and bottom of wooden box. The weight of piece is supported (Fig. 7, Plate I) by the two lower wheels, front and rear, while the upper wheel keeps the piece in a vertical plane. The tracks can, without sensible error, be assumed as horizontal.

By removing rear of box, Fig. 7 Plate I, and carrying a silk thread attached to rear of piece, over a very light pulley at rear of box, the force just necessary to start piece rolling was measured. The pulley was made from a light clock wheel and, with thread from pulley to piece parallel to track, the force was measured by dropping bird shot into a cup attached to end of thread until piece began to move. The weight of cup and shot was 3600 grains, giving for coefficient of friction.

From curve No. 1, Plate II, we find the velocity of recoil 11.291 f.s. for recoil = 1′′.590 and 11.130 f.s. for recoil = 7′′. 179. Substituting in the expression

It is held by some authorities* that the coefficient of friction increases with increase of velocity where the pressure is light and velocity moderate.

In this case the increase may be due to abnormal and irregular variations in pressure caused by balloting of piece during recoil, this balloting being due to the fact that the center of gravity of piece (mounted) was o".72 below axis of bore, and to the slight vertical play of wheels necessary to prevent binding.

The coefficient of friction is often found to vary even under similar conditions. For our purpose the coefficient as given by Eq. (4) will be used.

The position of center of gravity of piece was determined by the usual method of suspending it as a pendulum (three points. of suspension being used to insure accuracy).

See Appleton's Cyclopaedia of Applied Mechanics, Volume 1, page 849.

+ See Construction Note No. 56, Part I.

The component of weight supported by front wheel, w', is 4.7139 and by rear wheel, w", 5.1758 pounds.

Let

P = Mean pressure on base of bore during first stage of recoil.

P' Mean pressure on base of bore during second stage of recoil.

w Weight of projectile.

= Weight of powder charge.

W'➡ Pressure of front wheel (a) on track due
to weight of piece = 4.7139 pounds.

W" Pressure of rear wheel (b) on track due
to weight of piece 5.1758 pounds.
R' Reaction of track on front wheel (c) due
to moment of powder pressure.

R" Reaction of truck on rear wheel (6) due
to moment of powder pressure.

x, Distance passed over by piece during first stage of recoil.

E Recoil energy lost through friction dur ing first stage of recoil.

E' Recoil energy lost through friction dur-
ing second stage of recoil.

V=Velocity of recoil at exit of projectile.
V1 Maximum velocity of recoil from mean

curve.

V Maximum velocity of recoil corrected for

e

During first stage of recoil we have the following sequence of equations leading up to determination of V for this negative:

e

to determine V and thence muzzle energy of recoil;

m

and two other equations corresponding to (7) and (8) to find P',

R' and R";

E' = μ (R' — W')(X,−x,) + μ (R" + W")(X,−x1),

(11)

Substituting 11.351 for V,, 1265 for v and the proper values of W1, w and л,-69225, 500, and 68, respectively,—we find

A 2254.

The errors in measured values of V1, due to neglecting friction amount to about 1⁄2 of 1 per cent.

Corrections are applied before calculating the values of A given in table of condensed data.

The explanations given for Table I, together with the information furnished by headings in following tables (inclusive) will enable the reader to understand the remaining data submitted. The tuning fork used gives 247.76 complete vibrations per second.

CONCLUSIONS.

Energies of Recoil.

1. A black powder charge of 68 grains and a smokeless powder charge of 29 grains give to a 500 grains, o".45 caliber bullet, mean maximum velocities of 1279 and 1235 feet per second respectively, and to the piece, mean maximum engeries of free recoil of 20.172 and 16.231 foot pounds respectively.

Assuming that a 29 grains charge from a more efficient lot of Rifleite would give the velocity 1279 f. s. without change in A, the energy of recoil would become 17.086 foot pounds.

The ratio of recoils from black and smokeless powders is therefore,

1. 18 to 1.

2.

The maximum energies of tree recoil of small arms decrease rapidly with increase of weight of piece.

With weights 8.540 and 11.319 pounds, o".30 caliber rifle, the maximum energies, for same cartridge, are 11.050 and 8.185 foot pounds respectively.

When weight of piece becomes infinitely great, energy of recoil reduces to zero. When it is desirable to reduce recoil, it may be done by increasing weight of piece.

3.

Velocity of bullet increases as weight of piece increases. For 8.540 and 11.319 pounds weight of piece, o".30 caliber, the mean maximum velocities of bullets, for same cartridge, are 1915 and 1934 feet per second respectively.

In a fixed rest these cartridges gave a mean maximum velocity of 1987 f. s. at 50 feet range.

Dynamometer records of energies of recoil are between 60% and 70% of the true energies of free recoil. This illustrates the effect of initial brakes in keeping down the recoil of heavy guns.

Values of Coefficient A.

1. This coefficient is affected by almost any change made in conditions of loading.

2. It decreases with increase in weight of piece, dropping from 2956 for 8.540 pounds to 2690 for 11,050 pounds, weight of piece, o". 30 caliber. o".30

3. It decreases with the charge, dropping from 2258 for 68 grains black powder, to 1716 for 58 grains. A part of this decrease in A is due to increase in weight of piece, which was 9.889 for the 68 grains and 10.963 for the 58 grains charge.

4.

5.

It is larger for smokeless powders than for black powders. The coefficient, A, is sometimes defined as the mean velocity of powder gases. This definition is inaccurate and is liable to produce the impression that there is such a thing as a powder coefficient which in the simple equation

will permit the calculation of the maximum velocity of free recoil,
V1, for any value of W,, w and, provided the powder for which
A was determined be used and the value of v be measured.
The above table shows this to be untrue.

The value of A, determined experimentally, is not applicable to different conditions of loading and to different weights of piece. The above table however will enable the reader to obtain, by applying corrections, an approximate value for A, for given conditions that do not differ materially from tabular conditions.