It has been suggested that the conventional air data probes used on modern high performance aircraft can be eliminated by exploiting the capabilities of the Inertial Navigation System (INS) and obtaining analytic estimates of angle-of-attack (α), sideslip angle (β), and possibly of dynamic pressure (q). The reasons for wanting to eliminate the probes are that they are vulnerable to ground handling damage, bird strikes, icing, and hostile action in the case of combat aircraft. To determine the feasibility of this approach, three methods for obtaining α and β estimates from INS information were programmed into a nonlinear simulation of a relaxed stability aircraft which requires a high level of artificial stability augmentation through its flight control system. It was found that none of the three methods provided satisfactory stabilizing feedbacks to the control system when the subject aircraft was disturbed by severe atmospheric turbulence. This was due to the inability of the INS to determine the airframe orientation relative to the motion of the atmosphere. Simulation results for each of the three methods were compared with the results obtained when conventional probes were used to obtain direct measurements of α and β. An alternate method for determining α and β analytically that would be satisfactory for use in turbulence is presented.