A rule of the French engineers states that a charge which will produce a common mine with L. L. R. = l will produce a camouflet if the L. L. R. is increased to 7/4l. At this depth C´ = 0.187C, and the formula gives a crater radius of 25/49.
As a safe “rule of thumb,” we may assume that a charge which will give a common mine with L. L. R. = l will give a camouflet with L. L. R. = 2l (r´ from formula = (3/7)l). Conversely, a camouflet will be produced by ⅛ of the charge which will produce a common mine.
9. Radius of Rupture.—The determination of the radius of rupture is an important consideration in underground warfare, since, when it is known, miners may so place their chambers as to break in the galleries of the enemy without injuring their own.
As different mining galleries, however, differ from each other so much in strength to resist crushing, and as the cost of an exhaustive series of experiments to determine their relative strength would be so great both in time and money, but little well-established data exist upon which to found a rule for determining the radius of rupture.
10. The rule deduced by Gumpertz and Lebrun, however, from the material available at their time corresponds very nearly with the results of later experiments and observations, and is generally admitted as sufficiently near correct for practical use.
This rule is based upon the theory that the surface of rupture is an oblate spheroid, ([Pl. XI], Fig. 3), with its axis of revolution vertical and its centre at the centre of the charge; the intersection with the surface of the ground AD coinciding with the edge of the crater. The ratio between the semi-transverse axis CF and the semi-conjugate axis CH of the generating ellipse of this assumed spheroid is the same as that between the radius of explosion CD and L. L. R., CK. The rule is, that the radius of rupture in any direction is equal the corresponding radius of this spheroid.
From the conditions assumed the following values of the semi-transverse and semi-conjugate axes h and v (which are the horizontal and vertical radii of rupture) are obtained, viz.:[10]
| h = l√(1 + 2(r/l)2); |
| v = l√[(1 + 2(r/l)2)/(1 + (r/l)2)]. |
For common mines these formulas give: