In this paper we examine the detailed magnetic structure of ropes and quantitatively compare it with a general flux rope model. First, the seemingly chaotic ionospheric magnetic signature is shown to be ordered in a local coordinate system unique to each rope. This signature is also consistent with that expected of a flux rope. We have selected a special subset of the flux rope data that provides detailed information on rope magnetic structure. This subset, referred to as the small impact parameter subset, consists of flux rope traversals on which the spacecraft passed through the center of the structure. We have formulated a model of flux rope structure and have fit it successfully to cases from the small impact parameter subset. From these modeled cases we have inferred that flux ropes are comprised of primarily field-aligned currents with maximum current densities of a few tens of microamps/m2 and that parallel electric fields of less than a microvolt/m can drive these currents given the background ionospheric conductivity. We have also found that Joule heating rates within flux ropes are much smaller than ambient photoelectron heating. These modeled cases also suggest that flux ropes are stable to pinch-related instabilities like the sausage and planar kink modes, but are unstable to the long-wavelength helical kink mode.