The Extreme Skydiver: Universal Jump Parameter, Critical Path Points, and Flight Instabilities

The problem of high-altitude skydivers experiencing large variations in atmospheric density is investigated. Past efforts have mostly concentrated on finding altitude and velocity solutions to match recorded data. The procedure here goes past altitude and velocity and includes calculating the higher derivatives of acceleration and its derivative, the jolt, and the jolt’s derivative. It is shown the peaks in acceleration and jolt provide insight to the dynamics of the problem and explain instabilities seen in one case where no small stabilizing parachute was used, specifically, instabilities coincide with the skydiver reaching peak positive acceleration. The analysis was accomplished by dividing the jump profile into five regions based on air densities at approximately 10,000 m increments and using Taylor series expansions in each increment. A parameter in the derivations, referred to as a universal jump parameter, was useful in simplifying and organizing the analysis. Calculated quantities, important in documenting freefall records, such as peak velocity and total free-fall time, agree very well with recorded data.