An extension and numerical analysis of the Hohmann spiral transfer

This paper extends previous work on the Hohmann Transfer Spiral (HST) by introducing a plane change into the analysis. An analytical expression determining the critical specific impulse incorporating a plane change is
derived for both a circular and elliptical initial orbit. This expression determines the point at which the HST is equivalent in terms of fuel mass fraction to the compared Hohmann transfer. The expression assumes that the inclination change is performed by the high-thrust system. The numerical approach uses a blending method coupled with optimised weighting constants to deliver a locally optimal low-thrust trajectory. By comparing the analytical and numerical approaches, it is shown that the analytical can deliver a good estimation of the HST characteristics so long as little orbit eccentricity control is required. In the cases where orbit eccentricity control is required, the numerical approach should be used. A case study from an inclined Geostationary Transfer Orbit,
equivalent to a high-latitude launch site, to Geostationary Earth Orbit has shown that the HST can offer a fuel mass saving approximately 5% of the launch mass. This equates to the mass penalty associated with this high-latitude launch site and therefore mimics the advantages of a low-latitude launch site at the expense of a longer transfer duration.