Speed, gradient and workrate in uphill running

A series of treadmill experiments is described concerned with a runner’s speed, heart-rate and the gradient. Together with the results of similar experiments, some of them carried out over 50 years ago, the results suggest that for a given heart-rate, log(speed) is linearly related to gradient, and that for a given gradient, heart-rate is linearly related to speed. The result suggest: (1) that athletes who run p% faster on the level will run p% faster up a slope, if they maintain the same heart-rate; (2) that athletes will use the same number of heart beats running up a hill of uniform slope no matter how fast or slowly they run; (3) that athletes should run directly up any slope of less than about 20° and try to zigzag up slopes greater than this.