Marathon pacing and elevation change
  An analysis of marathon pacing and elevation change is presented. It is based on an empirical observation of how the pace of elite and non-elite marathon runners change over the course of the marathon and a simple approximation of the energy cost of ascent and decent. It was observed that the pace of the runners slowed in a regular manner that could be broken up into four regions. That observation can be used to project target paces for a desired marathon finish time. However, that estimate fails to take in to account the energetic costs of elevation changes (hills) along the marathon course. Several approximations are made to give a coarse estimate of target paces for marathon run on courses with significant elevation changes, i.e. a hilly course. The 2012 Oakland Marathon course is used as and example of a hilly course and the times of 23 finishers are examined. 
J. B. Elliott
physics.pop-ph physics.bio-ph