A method for determining the maximum control moments required for an aircraft to perform a velocity vector roll is investigated. The velocity vector roll is assumed to occur at constant angle of attack, constant velocity, and zero sideslip. A simplified set of equations is developed for the non dimensional control moments about the three principal body axes. These equations take on a form well suited for numerical optimization methods. The Schittkowski sap optimization code is used to provide fast, accurate solutions. The numerical method also shows the advantage of being adaptable to changing the airframe and flight performance parameters. An exercise to find the global control moment maxima was performed for a an F-18 with constant aerodynamic derivatives and a load factor of one. The optimization was run for a range of discrete steady state roll rates, roll mode time constants and velocities. The results showed trends for the maxima to occur at the highest steady state roll rate parameter, smallest roll mode time constant and lowest velocity. Each control axis maximum is specific to a particular orientation and angle of attack. For the roll axis, the maximum occurs at nearly zero angle of attack and 270 of wind axis bank angle. The yaw axis maximum occurs at the largest angle of attack (70) and 90 of wind axis bank angle. The pitch maximum occurs near 270 of wind axis bank and 55 angle of attack, but is highly sensitive to the selection of Cma . All control moment maxima occur at a flight path angle of O. The roll and yaw control moment maxima occur upon a maximum roll input starting from rest at the specified orientation and angle of attack. The pitch control maximum occurs at the steady state roll rate when the proper orientation and angle of attack is encountered. / Master of Science