A series of treadmill experiments is described concerned with a runner
's speed, heart-rate and the gradient. Together with the results of si
milar experiments, some of them carried out over 50 years ago, the res
ults suggest that for a given heart-rate, log(speed) is linearly relat
ed to gradient, and that for a given gradient, heart-rate is linearly
related to speed. The results suggest:(1) that athletes who run p% fas
ter on the level will run p% faster up a slope, if they maintain the s
ame heart-rate; (2) that athletes will use the same number of heart be
ats running up a hill of uniform slope no matter how fast or slowly th
ey run; (3) that athletes should run directly up any slope of less tha
n about 20-degrees and try to zigzag up slopes greater than this.