A six-month design study for a future high energy hadron collider was initiated by the Fermilab director in October 2000. The request was to study a staged approach where a large circumference tunnel is built that initially would house a low field ({approx}2 T) collider with center-of-mass energy greater than 30 TeV and a peak (initial) luminosity of 10{sup 34} cm{sup -2}s{sup -1}. The tunnel was to be scoped, however, to support a future upgrade to a center-of-mass energy greater than 150 TeV with a peak luminosity of 2 x 10{sup 34} cm{sup -2} sec{sup -1} using high field ({approx} 10 T) superconducting magnet technology. In a collaboration with Brookhaven National Laboratory and Lawrence Berkeley National Laboratory, a report of the Design Study was produced by Fermilab in June 2001. 1 The Design Study focused on a Stage 1, 20 x 20 TeV collider using a 2-in-1 transmission line magnet and leads to a Stage 2, 87.5 x 87.5 TeV collider using 10 T Nb{sub 3}Sn magnet technology. The article that follows is a compilation of accelerator physics designs and computational results which contributed to the Design Study. Many of the parameters found in this report evolved during the study, and thus slight differences between this text and the Design Study report can be found. The present text, however, presents the major accelerator physics issues of the Very Large Hadron Collider as examined by the Design Study collaboration and provides a basis for discussion and further studies of VLHC accelerator parameters and design philosophies.