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For a fixed-weight explosive, the peak pressure and positive impulse decrease with distance from the explosion. This is due to the attentuation of the blast wave. The rate of attenuation is proportional to the rate of expansion of the volume of gases behind the blast wave. In other words the blast pressure is in-versely proportional to the cube of the distance from the blast center (1/R3). When a bomb is detonated at some distance above the ground, the reflected wave catches up to and combines with the original shock wave, called the incident wave, to form a third wave that has a nearly vertical front at ground level. This third wave is called a "Mach Wave" or "Mach Stem," and the point at which the three waves intersect is called the "Triple Point." The Mach Stem grows in height as it spreads laterally, and as the Mach Stem grows, the triple point rises, describing a curve through the air. In the Mach Stem the incident wave is reinforced by the reflected wave, and both the peak pressure and impulse are at a maximum that is considerably higher than the peak pressure and impulse of the original shock wave at the same distance from the point of explosion. Using the phenomenon of Mach reflections, it is possible to increase considerably the radius of effectiveness of a bomb. By detonating a warhead at the proper height above the ground, the maximum radius at which a given pressure or impulse is exerted can be increased, in some cases by almost 50%, over that for the same bomb detonated at ground level.
Approximately 30% of the energy released by the explosive detonation of a General Purpose bomb fragments the case and impart kinetic energy to the fragments. The balance of available energy is used to create a shock front and blast effects. The fragments are propelled at high velocity, and after a short distance they overtake and pass through the shock wave. The rate at which the velocity of the shock front accompanying the blast decreases is generally much greater than the decrease in velocity of fragments, which occurs due to air friction. Therefore, the advance of the shock front lags behind that of the fragments. The radius of effective fragment damage, although target dependent, thus exceeds considerably the radius of effective blast damage in an air burst. Whereas the effects of an idealized blast payload are attenuated by a factor roughly equal to 1/R3 (R is measured from the origin), the attenuation of idealized fragmentation effects will vary as 1/R2 and 1/R, depending upon the specific design of the payload. Herein lies the principle advantage of a fragmentation payload: it can afford a greater miss distance and still remain effective because its attenuation is less.