This work uses Arizona State University’s (ASU) newly developed high-speed vehicle stability and control screening methodologies to reverse-engineer famous United States Air Force (USAF) flight tests from the 1950s and 1960s. This thesis analyzes the root cause of Chuck Yeager's fateful 1953 supersonic spin in the Bell X-1A to become the "Fastest Man Alive". This thesis then takes a look back at Neil Armstrong's inadvertent atmospheric skip in the North American X-15 and his subsequent hypersonic flight months later. The fundamental flying qualities assessment shown in this work begins with calculating rigid-body frequencies and damping ratios of an aircraft to Military Standard (MIL) requirements, and uses these to create a full, classical stability and control analysis of a high-speed vehicle. Through reverse engineering the flight envelopes and missions for the above aircraft, it appears that the near-disasters of each flight were due to a confluence of then overlooked, yet fundamental, aerodynamic instabilities.