The propagation model of the Ionospheric Communications Analysis and Predictions Program (IONCAP) program, which is designed for fast throughput calculations in the prediction of high-frequency sky wave system performance, makes use of virtual heights, as calculated from known height profiles of the electron density. Use of these for oblique path calculations relies on the well known flat Earth theorems of Breit-Tuve and Martyn, with additional curved Earth correction terms. These approximate corrections are examined in the light of exact results from other models, and alternative strategies are discussed.