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==Underwater explosions== [[File:Nuclear_depth_charge_explodes_near_USS_Agerholm_(DD-826)_on_11_May_1962.jpg|thumb|[[USS Agerholm (DD-826)|USS ''Agerholm'' (DD-826)]] launches an [[ASROC]] anti-submarine rocket, armed with a nuclear depth bomb, during [[Operation Dominic|Dominic Swordfish]] (1962)]] The high explosive in a depth charge undergoes a rapid chemical reaction at an approximate rate of {{cvt|8000|m/s|order=flip}}. The gaseous products of that reaction momentarily occupy the volume previously occupied by the solid explosive, but at very high pressure. This pressure is the source of the damage and is proportional to the explosive density and the square of the detonation velocity. A depth charge gas bubble expands to equalize with the pressure of the surrounding water.<ref name="proceedings">{{harvnb|Jones|1978|pp=50β55}}</ref> This gas expansion propagates a shock wave. The density difference of the expanding gas bubble from the surrounding water causes the bubble to rise toward the surface. Unless the explosion is shallow enough to vent the gas bubble to the atmosphere during its initial expansion, the momentum of water moving away from the gas bubble will create a gaseous void of lower pressure than the surrounding water. Surrounding water pressure then collapses the gas bubble with inward momentum causing excess pressure within the gas bubble. Re-expansion of the gas bubble then propagates another potentially damaging shock wave. Cyclical expansion and contraction can continue for several seconds until the gas bubble vents to the atmosphere.<ref name="proceedings"/> Consequently, explosions where the depth charge is detonated at a shallow depth and the gas bubble vents into the atmosphere very soon after the detonation are quite ineffective, even though they are more dramatic and therefore preferred in movies. A sign of an effective detonation depth is that the surface just slightly rises and only after a while vents into a water burst. Very large depth charges, including nuclear weapons, may be detonated at sufficient depth to create multiple damaging shock waves. Such depth charges can also cause damage at longer distances, if reflected shock waves from the ocean floor or surface converge to amplify radial shock waves. Submarines or surface ships may be damaged if operating in the convergence zones of their own depth charge detonations.<ref name="proceedings"/> The damage that an underwater explosion inflicts on a submarine comes from a primary and a secondary shock wave. The primary shock wave is the initial shock wave of the depth charge, and will cause damage to personnel and equipment inside the submarine if detonated close enough. The secondary shock wave is a result of the cyclical expansion and contraction of the gas bubble and will bend the submarine back and forth and cause catastrophic hull breach, in a way that can be likened to bending a plastic ruler rapidly back and forth until it snaps. Up to sixteen cycles of secondary shock waves have been recorded in tests. The effect of the secondary shock wave can be reinforced if another depth charge detonates on the other side of the hull in close time proximity to the first detonation, which is why depth charges are normally launched in pairs with different pre-set detonation depths.{{citation needed|date=February 2015}}<!--nearby shock would trigger second depth charge?--> The killing radius of a depth charge depends on the depth of detonation, the payload of the depth charge and the size and strength of the submarine hull. A depth charge of approximately {{cvt|100|kg|lb|order=flip}} of TNT (400 [[megajoule|MJ]]) would normally have a killing radius (resulting in a hull breach) of only {{cvt|3|-|4|m|ft|order=flip|0}} against a conventional 1000-ton submarine, while the disablement radius (where the submarine is not sunk but is put out of commission) would be approximately {{cvt|8|-|10|m|order=flip}}. A larger payload increases the radius only slightly because the effect of an underwater explosion decreases as the cube of the distance to the target.
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