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.

Subjects walked and ran on a classic Quinton 18-60 motorized treadmill with a rigid steel deck (Quinton Instrument Company, Bothell, WA).

Determination of PTS: The average of the walk-to-run transition speed (WRTS) and run-to-walk transition speed (RWTS) defined the PTS as per Hreljac et. al. (2007). We first determined the WRTS in the walk-first group and then their RWTS and vice versa for the run-first group. Based on pilot experiments, we selected starting speeds such that there was no doubt which gait would be preferred at the initial speed. Once the speed of the treadmill was correctly set, subjects mounted the treadmill and chose their gait ad libitum. After we determined the preferred gait at the particular speed, the subject straddled the treadmill belt while we changed the speed by 0.1 m/s (increased during WRTS trials, decreased during RWTS trials). The process repeated until a gait transition occurred and was sustained for 30 seconds.

Determination of EOTS and HROTS: For the energetics and heart rate trials, we set the initial speed based on pilot experiments that indicated it would be near the EOTS. Subjects in the walk-first group walked at the incline-specific initial speed for 5 min, rested for ∼5 min and then ran at that speed for 5 min. Subjects in the run-first group did the opposite. During the rest periods, we re-weighed the subject and they drank just enough water to compensate for the weight loss due mostly to sweating. Thus, each subject maintained a nearly constant weight throughout all the trials.

To measure metabolic rate during walking and running, we used an open-circuit, expired gas analysis system (TrueOne 2400; ParvoMedics, Sandy, UT). Subjects wore a mouthpiece with a one-way breathing valve and a nose clip allowing us to collect their expired air. The ParvoMedics software calculated the STPD rates of oxygen consumption (V□O₂) and carbon dioxide production (V□CO₂) and we averaged the last 2 minutes of each 5-minute trial. We then calculated metabolic power using the equation of Péronnet and Massicotte (1991) equation, as clarified by Kipp et al. (2018). We only included trials with respiratory exchange ratios (RER) <1.0 to ensure that metabolic energy was predominantly being provided from oxidative pathways. We used an R7 Polar iWL (Polar Electro Oy, Kempele, Finland) to measure heart rate in beats per minute (bpm) and averaged the values for the last 2 min of each trial.

Immediately after both gait trials were completed for the initial speed, we calculated and compared the metabolic power required for walking and running. If walking was the more economical gait, we increased the treadmill speed by 0.1 m/s, and the process repeated. If running was the more economical gait, we decreased the treadmill speed by 0.1 m/s, and the process repeated. Each subject performed three speeds, both walking and running at each incline. However, some subjects needed to complete walking and running trials at a fourth speed so that we could obtain energetics data for one speed faster and one speed slower than their EOTS.

For the three speeds at which the differences between metabolic rates between walking and running were least, we calculated linear regression equations for both metabolic power and heart rate as functions of speed for both walking and running for each subject and incline. The speeds at which the two equations intersected defined the EOTS and HROTS for each subject.

Overall, we analyzed ten subjects at four different inclines, i.e. 40 determinations of EOTS and HROTS. Of those 80 linear regression analyses, the walking vs. running regressions intersected at a speed < 3 m/sec for all but two subjects (one subject for EOTS at 15° and a different subject for HROTS at 10°). Essentially, those individuals’ regression lines were nearly parallel. We chose to exclude those two conditions from further statistical analysis and aggregate data compilation.

There are two missing values, as noted in the methods: HROTS for subject 5 at 10 degrees and EOTS for subject 4 at 15 degrees.