This paper describes a complete six-degree-of-freedom nonlinear mathematical model of a tilt rotor unmanned aerial vehicle (UAV). The model is specifically tailored for the design of a hover to forward flight and forward flight to hover transition control system. In that respect, the model includes the aerodynamic effect of propeller-induced airstream which is a function of cruise speed, tilt angle and angle of attack. The cross-section area and output velocity of the propeller-induced airstream are calculated with momentum theory. The projected area on the UAV body that is affected by the propeller-induced airstream is specified and 2D aerodynamic analyses are performed for the airfoil profile of this region. Lookup-tables are generated and implemented in the nonlinear mathematical model. In addition, aerodynamic coefficients of the airframe are calculated by using CFD method and these data are embedded into the nonlinear model as a lookup-table form. In the transition flight regime, both aerodynamic and thrust forces act on the UAV body and the superimposed dynamics become very complex. Hence, it is important to define a method for hover-to-cruise and cruise-to-hover transitions. To this end, both transition scenarios are designed and a state-schedule is developed for flight velocity, angle of attack, and thrust levels of each of the thrust-propellers. This transition state schedule is used as a feedforward state for the flight control system. We present the simulation results of the transition control system and show the successful transition of TURAC in experiment.