The total solar eclipse over the continental United States on 21 August 2017 offered a unique opportunity to study the dependence of the ionospheric density and morphology on incident solar radiation at different local times. The Super Dual Auroral Radar Network (SuperDARN) radars in Christmas Valley, Oregon, and Fort Hays, Kansas, are located slightly southward of the line of totality; they both made measurements of the eclipsed ionosphere. The received power of backscattered signal decreases during the eclipse, and the slant ranges from the westward looking radar beams initially increase and then decrease after totality. The time scales over which these changes occur at each site differ significantly from one another. For Christmas Valley the propagation changes are fairly symmetric in time, with the largest slant ranges and smallest power return occurring coincident with the closest approach of totality to the radar. The Fort Hays signature is less symmetric. In order to investigate the underlying processes governing the ionospheric eclipse response, we use a ray-tracing code to simulate SuperDARN data in conjunction with different eclipsed ionosphere models. In particular, we quantify the effect of the neutral wind velocity on the simulated data by testing the effect of adding/removing various neutral wind vector components. The results indicate that variations in meridional winds have a greater impact on the modeled ionospheric eclipse response than do variations in zonal winds. The geomagnetic field geometry and the line-of-sight angle from each site to the Sun appear to be important factors that influence the ionospheric eclipse response.