Chelyabinsk Fragmentation Pressure: At What Altitude Did Ram Pressure Overwhelm a Stony Body?

This paper computes a complete entry budget for the Chelyabinsk fireball, working only from published values and stated assumptions. The nominal body has a diameter of 19 metres at a bulk density of 3.30e+03 kilograms per cubic metre, giving an incoming mass of 1.19e+04 tonnes. At the published entry speed of 19.2 kilometres per second its kinetic energy is 520 kilotonnes of TNT equivalent. At the characteristic altitude of 29.7 kilometres the exponential atmosphere has a density of 0.0198 kilograms per cubic metre, the ram pressure on the body is 7.27 megapascals, the stagnation heating flux is 6.96e+04 megawatts per square metre, and the aerodynamic deceleration is 17.7 times terrestrial gravity. The ram pressure first reaches representative material strengths at computed altitudes of 60.6, 44 and 32.4 kilometres for the weakest, intermediate and strongest cases examined. The recovered material, the main recovered fragment raised from Lake Chebarkul, amounts to 654 kilograms, which is 5.52e-03 percent of the computed incoming mass. For scale, a single spherical fragment carrying that recovered mass would have a diameter of 71.6 centimetres, a terminal velocity of 235 metres per second, a fall time of 59.5 seconds from the end of the luminous path at 14 kilometres, and a wind drift of 595 metres under a representative wind. All values are computed by the deposited program from the stated inputs; scenario calculations accompany every headline figure so that the sensitivity of each conclusion to its inputs is visible in the same record.