In order to address the need for an affordable reduced gravity test platform, this work focuses on the analysis and implementation of atmospheric acceleration tracking with an autonomous aerial vehicle. As proof of concept, the vehicle is designed with the objective of flying accurate reduced-gravity parabolas. Suggestions from both academia and industry were taken into account, as well as requirements imposed by a regulatory agency. The novelty of this work is the Proportional Integral Ramp Quadratic PIRQ controller, which is employed to counteract the aerodynamic forces impeding the vehicles constant acceleration during the maneuver. The stability of the free-fall maneuver under this controller is studied in detail via the formation of the transverse dynamics and the application of the circle criterion. The implementation of such a controller is then outlined, and the PIRQ controller is validated through a flight test, where the vehicle successfully tracks Martian gravity 0.378 G's with a standard deviation of 0.0426.