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The advent of high-speed scanning radars which yield but a few pulses per scan element and displays which collapse the range co-ordinate has necessitated an analytical approach to the problem of radar range performance, as empirical methods have proven inadequate. An analysis is made which yields several graphs from which the radar detection range can be calculated for any desired detection probability, and from which computations of the probability of false target echoes can be made. Methods are also indicated which permit dark-tube operation and video pulse stretching. Statistical concepts involved in the effect of receiver noise are introduced.