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An optimal load allocation approach is presented for measurement and data reporting in wireless sensor networks with a single level tree network topology. The measurement problem investigated involves a measurement space, part of which can be sampled by each sensor. We seek to optimally assign sensors part of the measurement space to minimize reporting time and energy usage. Three representative measurement and reporting strategies are studied. This work is novel as it considers, for the first time, the measurement capacity of processors and assumes negligible computation time which is radically different from the traditional divisible load scheduling research to date. Aerospace applications include satellite remote sensing and monitoring and sensor networks deployed and monitored from the air.