In UAV networks, route discovery time is the duration from network deployment until the time when each UAV finds a route to every other UAV. It is a critical metric that shows how long a UAV network can be formed and used. Existing methods for calculating route discovery time are to conduct simulations, and it is unclear how parameters in routing protocols influence the final result. In this paper, we propose an analytical approach for route discovery time estimation instead of simulations. We focus on the classic protocol, Optimized Link State Routing (OLSR) protocol, and treat the network formation process as continually adding nodes to the diametral path. We present a general algorithm for computing route discovery time for arbitrary topologies, and provide formulas for special topologies. We show that our analytical results are close to those obtained by simulations.