Does the preferred walk-run transition speed on steep inclines minimize energetic cost, heart rate or neither?

Humans prefer to walk at slow speeds and to run at fast speeds. In
between, there is a speed at which people choose to transition between
gaits, the Preferred Transition Speed (PTS). At slow speeds, it is
energetically cheaper to walk and at faster speeds, it is cheaper to run.
Thus, there is an intermediate speed, the Energetically Optimal Transition
Speed (EOTS). Our goals were to determine: 1) how PTS and EOTS compare
across a wide range of inclines and 2) if the EOTS can be predicted by the
heart rate optimal transition speed (HROTS). Ten healthy, high-caliber,
male trail/mountain runners participated. On day 1, subjects completed
0&[deg] and 15&[deg] trials and on day 2, 5&[deg]
and 10&[deg]. We calculated PTS as the average of the walk-to-run
transition speed (WRTS) and the run-to-walk transition speed (RWTS)
determined with an incremental protocol. We calculated EOTS and HROTS from
energetic cost and heart rate data for walking and running near the
expected EOTS for each incline. The intersection of the walking and
running linear regression equations defined EOTS and HROTS. We found that
PTS, EOTS, and HROTS all were slower on steeper inclines. PTS was slower
than EOTS at 0&[deg], 5&[deg], and 10&[deg], but
the two converged at 15&[deg]. Across all inclines, PTS and EOTS
were only moderately correlated. Although EOTS correlated with HROTS, EOTS
was not predicted accurately by heart rate on an individual basis.