This paper presents a transition-flight mathematical model of a civil tilt-rotor VTOL unmanned aerial vehicle (UAV) TURAC. Forces and moments acting on the UAV body are calculated using Newton's second law. Aerodynamic effects of free airstream and propeller airstream are defined separately. CFD analyses are performed to specify aerodynamic coefficients for transitional flight regime. The trim point is mathematically defined with respect to angle of attack, tilt angle, airspeed, thrust of tilt-rotor and coaxial fan are defined during transitional flight. A transitional flight scenario is developed with force and moment equations.