High Altitude Free Fall: Theoretical Analysis of G-Forces Impacting Human Subjects

Abstract

The physical problem of object varying mass and cross-sectional area falling from high altitudes is analyzed. The equation of motion for velocities in the atmosphere with exponentially growing density (Laplace’s isothermal atmospheres) is resolved analytically and reasonable approximations are found for numerical analysis. The purpose of this project was to estimate maximal drag decelerations impacting objects in free fall, and find altitudes where these decelerations are reached. Estimates are conducted for the range of object masses between 75 Kg and 140 Kg, and altitudes between 10 and 100 Km. Preliminary results of the analysis show: - Maximum drag accelerations (G-forces for human subjects) caused by dense atmosphere grow up with free fall altitude and in range of masses and altitudes considered do not exceed 15-16 g; - Altitude of maximal drag acceleration is increasing with free fall altitude increase and asymptotically approaching certain limit which is determined by the properties of atmosphere and free fall acceleration (for Earth atmosphere this limit is calculated as 28.67 Km); - Parachuting from high altitudes would decrease G-forces for human subjects to the tolerable levels, this effect is specifically sensible for sky-diving from highest altitudes. Based on suggested approach acceptable survival corridors (such as maximal altitudes and initial velocities of free fall) and Life Support (LS) systems requirements for emergency escape during space operations could be formulated. Further general schematics are outlined to support in direct tests the data from theoretical analysis.