'All the King's horses and all the King's men couldn't put Humpty together again'. Such is how it goes in the nursery rhyme books about Humpty Dumpty and his great fall from the top of a wall. Oddly enough, that is how it seems also to be going now in respect of efforts to piece together the dynamics of Felix Baumgartner's great fall (flight) from the capsule of a very high altitude balloon at nearly 40 km MSL (above Mean Sea Level). During his flight he reached a maximum velocity fairly early on, after which he slowed down until deployment of a drogue that arrested his free fall. Graham Hoare raised issues in the Letters column of Mathematics Today [1] about the mathematical modelling of the fall and this stimulated discussions that resulted in.. various efforts seeking to reconcile the dynamics of the fall to facts that were known about it. Such facts have been refined over time and the purpose of this note is to present a very simple mathematical model incorporating the latest data that an A level student familiar with Newton's laws of motion can well understand. Briefly, the problem is treated as one of gravitational motion through a series of adjacent, horizontally stratified layers wherein resistance to motion at any point within a layer is presumed to vary with the square of the velocity at that point. To this end, a multiplicative motion resistance factor is introduced as a staircase type function, one which is presumed to be constant within each layer but varying from one layer to the next. Following a description based on Newton's equations of motion, outputs from one layer provide inputs to the next, and so on. In this respect the approach to the problem is much the same as one commonly adopted in other sciences, for example in Electromagnetic Theory, where plane wave propagation through a layered media, such as a Radome used to protect an antenna, is treated in a similar fashion, again to very good effect.
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