treespider
Posts: 9796
Joined: 1/30/2005 From: Edgewater, MD Status: offline
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quote:
ORIGINAL: el cid again quote:
el cid again, I'm interested in your source for bomb effectiveness, especially this square root relation. What is your book/scholarly paper source for this formula? Actually, it is just physics. It is the way an explosion works. Energy dissipates as the square of the distance. For a soft target (which is something not hard like made of concrete or steel - wood is more or less soft), the damage area is inversely proportional to the distance from the detonation, squared. A larger bomb does release more energy - actually not in direct relation to its weight - but in direct relation to the explosive on board multiplied by a factor for the efficiency of the explosive (thus, for example, Torpex is worth more pound for pound than TNT). But the amount of exposive is roughly proportional to the bomb (or shell) weight - not a horrible simplification for our purposes if you don't want to look up the details of each bomb. Anyway - a bigger bomb is useful ONLY when there is something that NEEDS a bigger bomb as a target. For most targets, you are better off dropping more smaller bombs. [This is why bomblets are so popular]. It appears we have a model that says "two attacks by 500 pound bombs = 1 attack by a 1000 pound bomb" and, in general, this is false. There is a reason our standard bomb load was 500 pound bombs, not 2000 pound bombs. The chances of a hit by fewer bombs is significantly lower. But IF you score a hit, the bigger bomb usually does not do as much damage as more than one (even just two) smaller hits. On the other hand, there are exceptions, and you also can get lucky, if you start a fire (common) or cause an explosion (rare). A bigger bomb matters when hitting a battleship - and the 16 inch shells dropped from Kates at Pearl Harbor were effective. In that case, you needed something bigger than even a thousand pounder to reliably penetrate a deck. And one bomb got lucky - causing a secondary explosion which sank Arizona. No smaller bomb would have done that. If you are interetsed in blast effects: There are two main effects which can cause damage to targets: the high energy fragments of the casing and the shock (or blast) wave. Warheads are usually designed to maximize one of these effects. Fragments tend to be lethal to a greater range than the blast effects, but it depends on the particular target. Aircraft are particularly vulnerable to fragment damage as are personnel. On the other hand, buildings can only be brought down by extensive blast effects. We now turn to a detailed account of each type. Blast Effects The rapid expansion of the gaseous products after the casing has burst creates a shock wave. The shock wave is an acoustic wave like ordinary sound, but of limited duration and great energy. Recall that the energy of the acoustic wave was a function of the amplitude, or peak pressure. In shock waves, the peak pressure is achieved only once, and is called the peak overpressure. The peak overpressure is reached very quickly as the shock wave passes, after which the pressure subsides more slowly. As the wave passes the pressure oscillates one or more times between positive and negative phases. When the pressure is above the ambient, the shock wave is considered to be in the positive phase. The opposite condition is called the negative phase. Due to the pressure differential within the shock wave, the air will flow from high to low pressure. This creates a blast wind, which can be of substantial velocity, well over 100 mph. The blast wind only lasts for a fraction of a second and changes direction during the negative phase. As the wind flows against objects, they will feel dynamic pressure from the drag. The dynamic pressure felt by an object follows the familiar equation for drag: Pdyn = Cd ½rv(2), (2) =squared where: Cd is the coefficient of drag for the particular object, r is the density of air (normally ~1.2 kg/m3) , and v is the velocity of the blast wind. Figure 2. Peak overpressure and dynamic pressure in a shock wave.
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< Message edited by treespider -- 1/27/2006 3:00:13 PM >
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