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 they 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). The prevailing scientific thinking prior to the 1990s was that at a given speed, humans and other species choose the gait that minimizes energy expenditure, i.e. that PTS=EOTS. But more recent research indicates that the PTS occurs at a speed slower than the EOTS in humans (Abe et al., 2019; Ganley et al., 2011; Hreljac, 1993; Minetti et al., 1994; Rotstein et al., 2005). Curiously, in horses, the walk–trot transition does occur near the EOTS (Griffin et al., 2004) but the trot–gallop transition is triggered by mechanics, not energetics (Farley and Taylor, 1991).

Consequently, researchers have proposed various neuromechanical hypotheses to explain the human walk–run gait transition speed, but no clear consensus has emerged (Kung et al., 2018). Several researchers have hypothesized that the walk–run transition is triggered by impending fatigue of specific muscles, notably the tibialis anterior (Abe et al., 2019; Bartlett and Kram, 2008; Hreljac, 1995; Hreljac et al., 2001, 2008). Neptune and Sasaki (2005) implicated force insufficiency resulting from the muscle force–length and force–velocity relationships as another walk–run gait transition trigger. They found that when walking at the PTS, the plantar flexor muscle force production was insufficient, despite an increase in muscle excitation as indicated by electromyography (EMG). The physics of the body's center of mass inverted pendulum-like motion is another proposed trigger (Kram et al., 1997; Usherwood, 2005).

The PTS is slower on inclines relative to flat terrain (Diedrich and Warren, 1998; Hreljac, 1995; Hubel and Usherwood, 2013; Minetti et al., 1994). Further, the PTS is slower than the EOTS on inclines up to 8.5 deg and the difference between the PTS and EOTS (∼0.2 m s⁻¹) remains fairly constant on those moderate grades (Minetti et al., 1994). Inclined locomotion is a promising tool for scientists trying to understand what triggers the walk–run transition in general (Hreljac, 1995) because, compared with level locomotion, uphill locomotion has a greater energetic cost and places different demands on specific muscle groups (Vernillo et al., 2017).

On an applied note, the walk–run gait transition on inclines is of great interest to competitive trail/mountain runners, who often ponder whether they should walk or run when racing uphill. It is obvious that competitors should nearly always run during flat and downhill sections of any race. But variable factors such as incline, speed and ground surface, as well as the length of the climb and the overall duration of the race all add complexity to an individual's gait selection process. Many trail/mountain runners use GPS watches and heart rate monitors to guide their training and racing (Koop and Rutberg, 2016). If heart rate is an accurate proxy for energetic cost, heart rate monitors combined with GPS sensors could allow athletes to identify their EOTS during a race or in training, choose their gait accordingly, and thus enhance performance by minimizing energetic cost. Even though a physiological steady state is unlikely to occur during trail/mountain running due to the variable factors listed above, at a certain speed and incline, one specific gait will minimize energetic cost.

The purpose of this study was to determine how the PTS and EOTS change over a wide range of inclines. Specifically, we investigated how incline affects the PTS, EOTS and the relationship between the two. We also determined how heart rate is influenced by gait selection. Our first hypothesis was that PTS and EOTS would both be slower on steeper inclines. We also tested the null hypothesis that the absolute difference in speed between the PTS and EOTS would be independent of incline. We anticipated rejecting that hypothesis because we thought that with the greater energetic demand on steeper inclines, there would be a greater impetus to minimize energetic cost. That is, we expected that PTS and EOTS would converge on steeper inclines. Finally, we hypothesized that the EOTS would equal the heart rate optimal transition speed (HROTS) at each incline. We thought this would occur because energetic cost generally correlates with heart rate during steady-state endurance exercise (Arts and Kuipers, 1994).

Ten healthy, high-caliber, male trail/mountain runners (28.7±5.7 years, 67.6±4.9 kg, 1.79±0.06 m; means±s.d.) volunteered and provided informed consent as per the requirements of the University of Colorado Institutional Review Board. All subjects had placed in the top 10% in a trail/mountain running competition within the previous 2 years.

The study consisted of two sessions. On day 1, we collected data for walking and running at 0 deg and then at 15 deg (26.8% grade). On day 2, we collected data for walking and running at 5 deg (8.7% grade) and then at 10 deg (17.6% grade). We did not randomize the trial order to avoid having a subject complete the more difficult 10 and 15 deg trials back-to-back on the same day. For each incline, we first determined PTS and then collected energetics and heart rate data simultaneously to calculate EOTS and HROTS. For each subject, we randomly assigned half the subjects to the ‘walk-first’ gait order and half to the ‘run-first’ gait order. Subjects walked and ran on a classic Quinton 18-60 motorized treadmill with a rigid steel deck (Quinton Instrument Company, Bothell, WA, USA).

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⁻¹ (increased during WRTS trials, decreased during RWTS trials). The process was repeated until a gait transition occurred and was sustained for 30 s.

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 mass loss due mostly to sweating. Thus, each subject maintained a nearly constant mass 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, USA). 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 (V̇_O2) and carbon dioxide production (V̇_CO2) and we averaged the last 2 min of each 5 min trial. We then calculated metabolic power using the equation of Péronnet and Massicotte (1991), as clarified by Kipp et al. (2018). We only included trials with a respiratory exchange ratio (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 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⁻¹, and the process was repeated. If running was the more economical gait, we decreased the treadmill speed by 0.1 m s⁻¹, and the process was 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.

We used R Studio (https://rstudio.com/) for all statistical analysis. For the three speeds at which the differences between metabolic rates for 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 speed at which the two equations intersected defined the EOTS and HROTS for each subject.

Overall, we analyzed 10 subjects at four different inclines, i.e. 40 determinations of EOTS and HROTS. Of those 80 linear regression analyses, the walking versus running regressions intersected at a speed <3 m s⁻¹ for all but two subjects (one subject for EOTS at 15 deg and a different subject for HROTS at 10 deg). Essentially, those individuals’ regression lines for walking and running were nearly parallel. We chose to exclude those two conditions from further statistical analysis and aggregate data compilation. We then determined the linear regression equations and R² values for PTS, EOTS and HROTS as functions of incline. Furthermore, we compared PTS versus EOTS, PTS versus HROTS, and EOTS versus HROTS at each incline by computing P-values (from paired t-tests), R² values (from linear regression analysis) and effect sizes (from Cohen's d statistic).

As expected, on the level and at all inclines, walking generally required less metabolic power at slow speeds and running required less at faster speeds. Thus, regression lines for metabolic power versus speed in the two gaits generally intersected (intersection = EOTS). An example for one subject at 15 deg is depicted in Fig. 1A. Heart rate also generally showed similar patterns and an example of the HROTS is shown in Fig. 1B.

A minor limitation occurred with our EOTS and HROTS calculations. The goal was to measure energetic cost for at least one speed faster and at least one speed slower than the subjects’ EOTS. However, at 15 deg, three subjects were unable to complete the faster trials with a RER <1.0. As a result, those three subjects’ EOTS regression analyses failed to capture the linear regression equation intersection point and some extrapolation was required. This extrapolation may have increased the variability of the calculated EOTS at 15 deg. There were 16 instances in which we failed to capture the linear regression intersection point and thus needed to extrapolate the HROTS value (typically by ∼0.1 m s⁻¹).

Our data indicate that the mean PTS was slower than the mean EOTS at 0, 5 and 10 deg, but not at 15 deg (P-values of 0.002, 0.107, 0.007 and 0.931, respectively; Cohen's d effect sizes of 1.77, 1.04, 1.17 and 0.02, respectively). The correlations between PTS and EOTS were weak to moderate at all inclines (R² values of 0.045, 0.478, 0.193 and 0.498 at 0, 5, 10 and 15 deg, respectively; Fig. 5; P-values comparing these slopes with zero were 0.555, 0.027, 0.204 and 0.034, respectively). Note: at 5 deg, the regression slope was significantly different from zero but the slope was inexplicably negative.

Our data indicate that the mean PTS was slower than the mean HROTS at 0 deg, but not at 5, 10 and 15 deg (P-values of 0.001, 0.366, 0.271 and 0.946, respectively; Cohen's d effect sizes of 1.48, 0.54, 0.44 and 0.03, respectively). The correlations between PTS and HROTS were weak to moderate at all inclines (R² values of 0.270, 0.371, 0.133 and 0.002 at 0, 5, 10 and 15 deg, respectively; Fig. 6; P-values comparing these slopes with zero were 0.124, 0.062, 0.335 and 0.898, respectively). Note: at 5 deg, the regression slope was significantly different from zero but the slope was again inexplicably negative.

The relationship between EOTS and HROTS was inconsistent across inclines. Our data indicate that the mean EOTS was not different from the mean HROTS at 0 deg, was faster than the mean HROTS at 5 deg, was similar at 10 deg, and was not different at 15 deg (P-values of 0.818, 0.002, 0.124 and 0.503, respectively; Cohen's d effect sizes of 0.05, 0.77, 0.40 and 0.21, respectively). The correlations between EOTS and HROTS were moderate to strong at all inclines (R² values of 0.658, 0.708, 0.567 and 0.376 at 0, 5, 10 and 15 deg, respectively; Fig. 7; P-values comparing these slopes with zero were 0.004, 0.002, 0.019 and 0.079, respectively).

We retain our first hypothesis that PTS and EOTS would both be slower on steeper inclines. This is consistent with previous research. Minetti et al. (1994) determined that both PTS and EOTS were slower on inclines up to 8.5 deg. Diedrich and Warren (1998), Hreljac (1995) and Hubel and Usherwood (2013) all determined that PTS was slower on moderate inclines (but none measured EOTS).

Hubel and Usherwood (2013) also developed a prediction for the walk–run transition on inclines using the physics-based limits of an inverted pendulum/compass gait model for walking. Their prediction reduces to a simple rule of thumb whereby the PTS slows by about 1% for every 1% increase in incline (or ∼1.8% per degree). In the present study, the mean preferred transition speeds at 5, 10 and 15 deg were 1.78, 1.62 and 1.47 m s⁻¹, respectively. Using Hubel and Usherwood's (2013) rule of thumb, with the baseline PTS at 0 deg found in the present study (1.95 m s⁻¹), the predicted preferred transition speeds at 5, 10 and 15 deg are 1.78, 1.63 and 1.49 m s⁻¹, respectively. Our empirical measurements coincide remarkably well with the predicted values. This supports Hubel and Usherwood's (2013) conclusion that the inverted pendulum/compass gait model for walking informs the qualitative understanding of why PTS slows with incline and also has predictive ability in quantifying PTS across inclines. However, on an individual level, the predictive ability was less accurate. Using Hubel and Usherwood's (2013) rule of thumb, with the baseline PTS at 0 deg for each subject used to predict their PTS at 5, 10 and 15 deg, the average absolute percent differences between predicted and actual preferred transition speeds were 8.8%, 7.1% and 11.7% at 5, 10 and 15 deg, respectively.

We also retain our second hypothesis that PTS and EOTS would converge at steeper inclines. The difference between the average PTS and EOTS was 0.19 m s⁻¹ at 0 deg, 0.21 m s⁻¹ at 5 deg, 0.16 m s⁻¹ at 10 deg and 0.04 m s⁻¹ at 15 deg, with PTS always numerically slower than EOTS (Fig. 8). Statistical analysis indicated that the PTS was slower than the EOTS at 0, 5 and 10 deg but not at 15 deg. At 5 deg, the difference between PTS and EOTS had inexplicably large inter-subject variability; the standard deviation at 5 deg was approximately twice that at 0 deg and 10 deg (Table 2).

The finding that PTS was slower than EOTS on level terrain was previously well established (Abe et al., 2019; Ganley et al., 2011; Hreljac, 1993; Minetti et al., 1994; Rotstein et al., 2005), with just one study finding that PTS equaled EOTS (Mercier et al., 1994). Only Minetti et al. (1994) have previously studied how the relationship between PTS and EOTS is affected by incline. They concluded that the absolute difference (m s⁻¹) between PTS and EOTS does not change with gradient, but they studied more moderate inclines, up to 8.5 deg.

Our data demonstrate that the difference between PTS and EOTS remained roughly constant up to 10 deg, but not at 15 deg. Clearly, optimizing energetic economy does not solely determine PTS at moderate grades that do not involve a high rate of exertion. As grade steepens, energetic cost may become more influential. However, the equation for the regression of PTS versus EOTS at 15 deg (Table 2, Fig. 5) has an R² value of only 0.498, i.e. PTS only explained half of the variance in EOTS. Despite the fact that PTS and EOTS did converge at 15 deg, further investigation of the relationship between PTS and EOTS at even steeper inclines would be interesting. However, doing so would require subjects/athletes with exceptional aerobic capacities.

The relationship between PTS and EOTS, and thus whether energetic cost serves as a trigger for gait transitions, has been studied in horses as well. Like humans, the evidence for PTS equaling EOTS in these quadrupeds is nuanced. Hoyt and Taylor (1981) concluded that at their preferred speed within each gait, horses choose the gait that minimizes energetic cost. Griffin et al. (2004) built upon that idea and found that energetics also seem to trigger the walk–trot transition. But Farley and Taylor (1991) clearly demonstrated that the trot–gallop transition was triggered by musculoskeletal forces and not energetics. In humans, there is also evidence for kinetic factors triggering the level walk–run transition (Raynor et al., 2002; Hreljac et al., 2008).

Our third hypothesis was that EOTS would equal HROTS at all inclines. Statistical analysis indicated that the EOTS and HROTS were not different at 0 deg, diverged at 5 deg, were similar at 10 deg, and were again not different at 15 deg. Furthermore, the correlations between EOTS and HROTS were not consistent enough to have practical predictive application for competitive trail/mountain runners (Fig. 7). Thus, we reject our third hypothesis given our mixed results. Rotstein et al. (2005) and Mercier et al. (1994) found that PTS equals HROTS on level terrain, although Mercier et al. (1994) also found that PTS equals EOTS, which differs from the rest of the research done on this topic. At 0 deg, we found that EOTS and HROTS were equal and both were faster than PTS (Table 2). No previous research has studied HROTS on inclines.

Our lab's previous research on steep uphill running and walking has focused on 30 deg (Giovanelli et al., 2016; Ortiz et al., 2017; Whiting et al., 2020) because it is the optimal incline for vertical kilometer races, and it maximizes the vertical rate of ascent for a given metabolic power (Giovanelli et al., 2016). If we extrapolate our Eqn 1 to 30 deg, it predicts a PTS of 0.983 m s⁻¹. Using the rule of thumb from Hubel and Usherwood (2013), a 1% decrease in PTS per 1% incline, with the baseline PTS at 0 deg found in the present study (1.95 m s⁻¹), the predicted PTS at 30 deg would be 1.09 m s⁻¹. There is currently no published research regarding the PTS at 30 deg. Extrapolating the EOTS to 30 deg using Eqn 2 yields a value of 0.909 m s⁻¹ for the EOTS. From Ortiz et al. (2017), this predicted EOTS closely corresponds to the data for the lone subject who had the aerobic fitness needed to reach EOTS at such a steep incline. Ultimately, these equations and predictions provide information on the relationship between PTS and EOTS on extremely steep inclines, which is often difficult to determine empirically (Ortiz et al., 2017).

Our study has some limitations. First, when trail/mountain runners walk on inclined terrain outdoors, they often push with their hands on their quadriceps to facilitate knee extension during late stance. However, because of the constraints of the mouthpiece and breathing tube used to collect the expired air, subjects were unable to flex at the waist in order to place their hands on their knees during inclined walking. This may have influenced metabolic cost and discomfort in walking, especially at 10 and 15 deg, and thus slightly distorted the calculated EOTS.

Unlike previous studies of the walk–run transition (Diedrich and Warren, 1998; Hreljac, 1995; Hubel and Usherwood, 2013; Minetti et al., 1994), we focused on well-trained trail/mountain runners with high aerobic fitness. Our results may not be applicable to less aerobically fit individuals simply because they cannot sustain the exercise intensities that our subjects could maintain in steady state.

Many interesting questions remain around the topic of human gait transition on inclines. For example, one could more explicitly explore the idea that energetics have a greater influence on PTS at higher exercise intensities. Considering the strong evidence for a neuromechanical trigger for the PTS during level locomotion, future inclined gait transition research should study the influence of biomechanical parameters. Determining whether any joint kinetic or kinematic variables trigger the uphill PTS is a logical future aspect to study. Likewise, pairing the kinetic and kinematic investigation with a neuromuscular component, measuring EMG activity of surface leg muscles, would be helpful in determining how biomechanical parameters influence gait transition speed (Whiting et al., 2020). Finally, performing more sophisticated biomechanical measurements concurrently with EMG measurements would allow for follow-up of Neptune and Sasaki's (2005) findings that muscle force–length and force–velocity properties hinder the plantar flexors when walking at the PTS.

Over a range of inclines, we found that the preferred (PTS), energetically optimal (EOTS) and heart rate optimal (HROTS) walk–run transitions speeds are slower on inclines. PTS is slower than EOTS up to 10 deg but they converge at 15 deg. EOTS is not accurately predicted by heart rate. Energetic, biomechanical and neuromuscular factors all influence gait transitions and should be studied in further detail, especially on inclines commonly experienced by trail/mountain runners, for whom the question of optimal gait transition has large performance implications.

We thank Robbie Courter and Derek Wright for their help with statistical analysis and results compilation, respectively; Kyle Stearns, Clarissa Whiting, Ross Wilkinson and Lance Perkins for help with data collection; and all of the subjects for their willingness to participate.