One of the major problems in space physics is the limitation of measurements. We present here one way to infer global characteristics of the magnetosphere from only a single satellite position. Several consistent orbit-tracing (COT) models of fast flows in thin plasma sheets were constructed. The resulting ion distribution functions were examined to see if there are any features which can distinguish a uniform earthward flow of plasma from flows which are confined in a narrow channel in the dawn-dusk direction. The model distribution functions during uniform flows had the appearance of an initially isotropic f(v) that had simply been shifted by the earthward flow speed. The model f(v) exhibited lima bean--shaped features when the flow was confined to a region comparable to the diameter of a cyclotron orbit based on Bz. Distribution functions observed by the Geotail satellite were examined for comparisons, and the measured distributions were found to exhibit features similar to those obtained in the COT model. We are able to demonstrate that the distributions measured by Geotail may only be reproduced in our technique if the convective electric field is confined in the dawn-dusk direction.