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interval of space between centres of successive generating spheres will decrease as the shell travels, and the enveloping cone will be modified (fig. 6). The form of the shell-wave will resemble roughly a paraboloid of revolution, the vertex being at the shell as long as the latter has a velocity exceeding that of sound, and consequently travelling with a velocity greater than that of sound. After the velocity of the shell has dropped below that of sound the shell-wave travels out in all directions with the velocity of sound normal to the surface.

FIG. 5.

The exact form of the shell-wave will depend upon the range table of the gun and the interval since the shell left the gun, and cannot be specified as being any familiar surface. The trace of the wave on the plane of the earth's surface, with which the observer is in general concerned, depends further upon the elevation at which the gun is firing. Since the sphere representing the position of the gun-wave is one of the generating spheres the shell-wave will touch this sphere. In fig. 6 where G is the gun, ABC the trace of the gun-wave on the horizontal plane, ASC the trace of the shell-wave, within the cone represented by AGC both sounds will be heard, outside the cone only the sound of discharge. The interval between the two sounds is

FIG. 6

clearly greatest on the line of fire, decreasing as the observer moves to a flank. As the gun is elevated the interval detected by a listener in a fixed position decreases, the trace of the shell-wave approaching that of the gun-wave. This is illustrated in fig. 7. If the gun be sufficiently elevated no shell-wave is heard by a listener at any position on the ground, though it may be heard in an observation balloon. Thus the double sound has been heard by an observer so situated in the case of a g-2-in. howitzer, firing with full charge (M.V. 1,500 f.s.), while observers on the ground heard only the single sound.

Owing firstly to the selective sensitiveness of the human ear, and secondly to the fact that the shell-wave is generated well above the surface of the earth, and travels down to the ear without meeting obstacles and without being hindered by refraction effects, the shell- wave alone is usually heard when the hostile piece is distant, and is spoken of as the sound of the piece by the casual listener. Any attempt to take rough bearings on a gun by estimating the direction from which the sound appears to be coming then leads to a very erroneous result, since it is the normal to the shell-wave that is selected. Unless the listener is on the line of fire such a bearing will pass considerably in front of the piece. To calculate the position of a gun from the intervals between the arrival of the shell-wave at different posts requires a knowledge of the exact form of the wave in question at various times of flight, and this presupposes a knowledge of the range table of the gun, and the elevation at which tt is firing (given by the approximate range). It is clear that to apply the sound- ranging method to records made by the shell-wave is a matter involv- ing information not always available, and considerable preliminary work on the construction of curves representing shell-waves for different hostile guns firing at various elevations when it is available.

FIG. 7.

In the case of howitzers the horizontal component of the muzzle velocity is less than the velocity of sound in all ordinary cases, so that only one sound, the gun-wave, is heard on the ground.

Instruments. The instruments comprise : (a) detectors, placed at each of the six surveyed posts, which give an electrical response to the arrival of the sound, and (b) a recording instrument, placed at a central station and connected by a separate circuit to each detector, which registers the exact time at which each detector responds.

When the method was first tried by the French the detector used was a soldier, who pressed a key when he heard the sound of a hostile piece, the key closing a circuit which actuated a pen on a smoked paper chronograph at a central station. This method

FIG. 8. Hot- Wire Microphone.



involves inevitable errors due to the personal equation of the observer, and is further invalidated by the fact that, in the case of guns, the observer frequently hears only the shell-wave. The diffi- culties of working from records of this kind have already been dis- cussed. Later, carbon microphones with large wooden diaphragms were introduced, small cells being included in circuit with the microphone and a primary coil, all at the post; the circuit leading back to the recording instrument included a secondary coil wound on the primary. These microphones suffered from the fact that they had a range of sensitiveness similar to that of the human ear; they responded readily to chance sounds, such as the clatter of equip- ment, or to shaking, and they registered the shell-wave in preference to the gun-wave. They were superseded (first in the British army, and ultimately in all the Allied armies) by the hot-wire microphone invented by Maj. W. S. Tucker (British patent No. 13123 of 1916,