MAXIMUM ALTITUDE FOR A SUCCESSFUL SPACE DIVE

Abstract

In this paper, we attempt to find the maximum altitude from sea level from which a person could successfully and safely descend to the surface of the Earth. We also analyse and highlight the challenges and dangers in such a descent which is also a proof of how only a handful of people have ever tried doing this pragmatically, notably Felix Baumgartner in 2012 and Alan Eustace in 2014. With a range of variables, conditions, and velocities, we investigate the problem using a density-barometric perspective and one solely based upon forces and using simple onedimensional motion equations to analyse the scenario. We use Newton’s second laws to determine the maximum velocity a skydiver can achieve which would be when the resultant forces acting on it must be 0. Then we analyse the different drag forces the skydiver goes through before reaching this velocity and found the relative acceleration. Equating this into the motion equations gave the displacement and thereby the maximum altitude possible for the skydiver. In the barometric approach, we formulate a relation between the terminal velocity at different heights (terminal velocities change due to the changing drag forces due to different air densities of regions in atmospheres) and the density of those heights. Then we formulated an equation for the maximum height which involved scale height, a logarithmic equation of the terminal constants and some constants. From these methods we find that the maximum altitude for a skydiver to descend from and reach the ground safely is 45,818m, whereas the true value must be somewhere between 41,261m and 45,818m.