In this paper we investigate the effect of changes in the interplanetary magnetic field (IMF), solar wind dynamic pressure, and dipole tilt angle on the position of the ionospheric projection of the open-closed field line boundary (OCB) in a magnetohydrodynamic (MHD) model. We carry out a large number of steady state global MHD simulations in order to parameterize the OCB as a function of the solar wind By and Bz which we find to have the largest effect on the OCB location. We interpolate between the values produced by the simulations, which allows us to evaluate the location of the OCB projection into the ionosphere for any values of ∣By∣ 0 nT. We also find that the polar cap area increases with the increasing solar wind dynamic pressure. The Bx component of the IMF and the dipole tilt angle are found to have relatively small effects on the location of the OCB.