This paper addresses the problem of an aerial moving target search with a radar on an airborne platform. An observation of the radar is a modeled as a cone covering a set of regions of the search area. We assume overlapping cones of observation, and we want to find the discrete allocation plan of search effort to the cones in order to optimize target detection. For the stationary target search with overlapping cones, we present a dynamic programming algorithm that computes the optimal allocation. An approximate greedy heuristic, which is more appropriate in a real time context, is also presented and assessed. The moving target search problem is solved with the Forward And Backward (FAB) algorithm coupled with the different stationary search algorithms. In this paper, we use radar detection model that has been shown to be more realistic than the ones usually considered. Also, several models of movement of the target are considered with different Markovian transition matrices. We compare the performance of the mentioned algorithms on several scenarios.