We propose a fixed wing unmanned aerial vehicles (UAV)-based millimeter wave (mmWave) backhaul links, that is offered as a cost effective and easy to deploy solution, to connect a disaster or remote area to the nearest core network. First, we fully characterize the single relay fixed-wing UAV-based communication system by taking into account the effects of realistic physical parameters, such as the UAV's circular path, critical points of the flight path, heights and positions of obstacles, flight altitude, tracking error, the severity of UAV's vibrations, the real 3D antenna pattern, mmWave atmospheric channel loss, temperature and air pressure. Second, we derive the distribution of the signal-to-noise ratio (SNR) metric, which is based on the sum of a series of Dirac delta functions. Using the SNR distribution, we derive closed-form expressions for the outage probability and the ergodic capacity of the considered system as a function of all system parameters. To provide an acceptable quality of service for longer link lengths, we extend the analytical expressions to a multi-relay system. The accuracy of the closed-form expressions are verified by Monte-Carlo simulations. Finally, by providing sufficient simulation results, we investigate the effects of key channel parameters such as antenna pattern gain and flight path on the performance of the considered system; and we carefully analyze the relationships between these parameters in order to maximize the average channel capacity.