C,

CHAPTER IV.

C, The Ballistic Coefficient.

THE ballistic coefficient, measures the ability

of the projectile to overcome the resistance of the air. It is the important factor in determining the elements of the trajectory, and if increased intentionally or unintentionally the ballistic qualities of the projectile will be greatly exaggerated, for the greater its value the greater the ballistic properties.

Fortunately, it is within our province to determine the value of C to a high degree of accuracy, and therefore determine the ballistics of any projectile, if the muzzle velocity is known.

in which c, the coefficient of form or reduction, see Chap. V. and d the effective diameter of the projectile. The effective diameter equals the caliber plus the depth of one groove.

C is determined more accurately by experiment, because then the errors of construction do not enter the formula. Or more broadly speaking, by experiment the value of C is determined irrespective of the shape or construction of the head of the projectile.

Briefly, the method is to set two chronographs, one near the muzzle to determine the muzzle velocity, the other at a short known distance to determine the remaining velocity.

S(v) and S(V) are space functions, Table 1.

S(v) S (2465)=3415.5

S(V) S (2700)=2644.8

770.7

.. faXC=300÷÷770.7.389+, when fa 1

Using formula 10, omitting fa, and obtaining from any gun catalog V and v, C is readily determined for that particular projectile having that velocity.

Formula 10 is imperative in determining the projectile of greatest efficiency, see Vol. 11.

For the definition of fa and the method of determining it: q. v. Chap. X. formula 30, and problem 17.

In some catalogs the muzzle velocity only is given

with the height, H, for a given range.

With these

data the calculation of C is more laborious, but involves only part of the problems in Chapter II. Hence, only an outline of the method of procedure will be given, for it involves no new problems.

Problem 10.

Given V 2330, X 200 yds., H

Remington 25 cal., pointed, wt. 101 grs.

To determine the value of C.

0.331 ft.

1st. Select, if possible, a pointed projectile of same caliber with C known, say the 250 savage, 87 gr. C=.276.

2nd. By simple proportion,

:

C-276 C-( )=87: 101, whence C equals approximately .32.

3rd. Calculate the actual time, T, from H, formula 5A.

4th. Calculate v for 200 yds. using the value of C found by 2, or ASSUMED, formula 1.

5th. Calculate first experimental time, T', formula 4. T' will usually be found greater or less than T, the actual time. If greater, assume a greater value for C and if less, assume a less value for C, differing from the first value by at least .04 or .06.

6th. With this new assumed value of C, following the 4th and 5th steps, calculate the second experimental time, T". T" will usually be found to be greater or less than T. The difference between T'

and T" will be the difference in time for the different values of C.

7th. By simple interpolation find another working value for C, and repeat, calculating the third experimental time, T".

By continuing the same method a value for C as exact as the reader wishes may be found. For this projectile the value of C is found to be .3401.

If by formula 10 we were to compute the values of C for a given projectile having different muzzle velocities, we should find these values of C vary as the velocities. For example, the value of C for the 38-40-180-1775 is .156 and its value for the same projectile having a muzzle velocity of 1324 f. s. is .129.

It follows then, that the value of C varies as the velocity and hence has several values during the flight of the projectile. This fact is taken into consideration in the construction of ballistic tables I and A, and in determining the maximum horizontal and maximum vertical ranges.

All of which means that one must not assume the same value for C for a given projectile at different velocities, as he would be prone to do in reloading.

This variation in the value of C is due to the variations in the resistance of the air; and as proven by Bashford, Mayevski and others the resistance of the air varies as some power of the velocity.

In the following table n denotes that power of the velocity.

For the 150-2700-C-.389 the resistance offered by the air at first is as the 1.55th power of the velocity, then as the 1.7th power, and so on, changing for all the values of n during the flight of the projectile.

Plotting a curve for the value of n as taken from the preceding table, the curve would indicate that a vacuum lies in the wake of the projectile when its velocity is between 970 and 1230 f.s. and increases. See killing power of bullets, Vol. 11, which is so intimately connected.

A study of the velocity curves, Fig. 2 from the standpoint of C will show that the .256-140-3000C-.548 maintains its velocity the best of this group, although the others having a less value for C have a greater muzzle velocity.

These illustrations are not given for adverse criticism of any projectile, but merely for the sake of comparative study.

Note also that the .250-87-3000-C-.276 loses its velocity more rapidly than the others, its value of C being the least.