A predicted relationship between auroral electron energy flux (&egr;) and the inferred accelerating potential drop (V) for accelerated Maxwellian distributions has been derived by R. Lundin and I. Sandahl. This relationship (&egr;∝V2) has been favorably tested with sounding rocket data by Lundin and Sandahl for the limiting case of eV/Ec≫1 (where Ec is the characteristic energy of the accelerated Maxwellian distribution) and by L. Lyons for a single inverted-V observed by the Injun 5 satellite. The study reported in this paper has utilized data from Atmosphere Explorer D to extend these studies over the range. 2>eV/Ec>5 and for a wide range of latitudes and local times on both the nightside and the dayside. Our results show good agreement with the full accelerated Maxwellian model. We have further derived an analytical approximation to the electron energy flux which much better describes the data over the range. 2c<3 than does the &egr;∝3V2 approximation. In addition, analyses of individual energy spectra at small and large pitch angles through well-defined inverted-V structures suggest that the altitude of the inferred potential drop maximizes near the center of the inverted-V's.