Economic Speed Research Articles

Normalized economical speed is influenced by aging and not by exercise habituation

ObjectiveA U-shaped relationship between energy cost of walking (Cw) and walking speed indicates that there is a specific speed minimizing the Cw, called economical speed (ES). It is mostly slower in older adults than young adults; however, effects of leg length on the ES have been ignored. We investigated effects of aging and exercise habituation on the normalized ES by leg length (ESnormalized). We quantified time delay of stride length and step frequency in sedentary young (SY), active young (AY), and active elderly (AE) adults in response to sinusoidal gait speed change at 30-s and 180-s periods with an amplitude of ± 0.56 m･s− 1.ResultsThe ES was significantly slower in the following sequence: AE, SY, and AY, whereas ESnormalized was slower in the AE than in other young groups, with no difference between AY and SY. AE and SY showed greater step variabilities at the 180-s period, whereas AY showed relatively smaller step variabilities at both periods. Collectively, the ESnormalized slowed due to aging, not due to exercise habituation. When optimizing the appropriate SL-SF combination for sinusoidal speed changes, young and elderly adults may adopt different strategies. Exercise habituation may reduce step variabilities in young adults.

Dynamic Spatial General Equilibrium

We incorporate forward‐looking capital accumulation into a dynamic discrete choice model of migration. We characterize the steady‐state equilibrium; generalize existing dynamic exact‐hat algebra techniques to incorporate investment; and linearize the model to provide an analytical characterization of the economy's transition path using spectral analysis. We show that capital and labor dynamics interact to shape the economy's speed of adjustment toward steady state. We implement our quantitative analysis using data on capital stocks, populations, and bilateral trade and migration flows for U.S. states from 1965–2015. We show that this interaction between capital and labor dynamics plays a central role in explaining the observed decline in the rate of income convergence across U.S. states and the persistent and heterogeneous impact of local shocks.

Economical and preferred walking speed using body weight support apparatus with a spring-like characteristics

BackgroundA specific walking speed minimizing the U-shaped relationship between energy cost of transport per unit distance (CoT) and speed is called economical speed (ES). To investigate the effects of reduced body weight on the ES, we installed a body weight support (BWS) apparatus with a spring-like characteristics. We also examined whether the 'calculated' ES was equivalent to the 'preferred' walking speed (PWS) with 30% BWS.MethodsWe measured oxygen uptake and carbon dioxide output to calculate CoT values at seven treadmill walking speeds (0.67–2.00 m s− 1) in 40 healthy young males under normal walking (NW) and BWS. The PWS was determined under both conditions on a different day.ResultsA spring-like behavior of our BWS apparatus reduced the CoT values at 1.56, 1.78, and 2.00 m s− 1. The ES with BWS (1.61 ± 0.11 m s− 1) was faster than NW condition (1.39 ± 0.06 m s− 1). A Bland-Altman analysis indicated that there were no systematic biases between ES and PWS in both conditions.ConclusionsThe use of BWS apparatus with a spring-like behavior reduced the CoT values at faster walking speeds, resulting in the faster ES with 30% BWS compared to NW. Since the ES was equivalent to the PWS in both conditions, the PWS could be mainly determined by the metabolic minimization in healthy young males. This result also derives that the PWS can be a substitutable index of the individual ES in these populations.

Combined effects of exposure to hypoxia and cool on walking economy and muscle oxygenation profiles at tibialis anterior

ABSTRACTWe investigated combined effects of ambient temperature (23°C or 13°C) and fraction of inspired oxygen (21%O2 or 13%O2) on energy cost of walking (Cw: J·kg−1·km−1) and economical speed (ES). Eighteen healthy young adults (11 males, seven females) walked at seven speeds from 0.67 to 1.67 m s−1 (four min per stage). Environmental conditions were set; thermoneutral (N: 23°C) with normoxia (N: 21%O2) = NN; 23°C (N) with hypoxia (H: 13%O2) = NH; cool (C: 13°C) with 21%O2 (N) = CN, and 13°C (C) with 13%O2 (H) = CH. Muscle deoxygenation (HHb) and tissue O2 saturation (StO2) were measured at tibialis anterior. We found a significantly slower ES in NH (1.289 ± 0.091 m s−1) and CH (1.275 ± 0.099 m s−1) than in NN (1.334 ± 0.112 m s−1) and CN (1.332 ± 0.104 m s−1). Changes in HHb and StO2 were related to the ES. These results suggested that the combined effects (exposure to hypoxia and cool) is nearly equal to exposure to hypoxia and cool individually. Specifically, acute moderate hypoxia slowed the ES by approx. 4%, but acute cool environment did not affect the ES. Further, HHb and StO2 may partly account for an individual ES.

Energy cost and lower leg muscle activities during erect bipedal locomotion under hyperoxia

BackgroundEnergy cost of transport per unit distance (CoT) against speed shows U-shaped fashion in walking and linear fashion in running, indicating that there exists a specific walking speed minimizing the CoT, being defined as economical speed (ES). Another specific gait speed is the intersection speed between both fashions, being called energetically optimal transition speed (EOTS). We measured the ES, EOTS, and muscle activities during walking and running at the EOTS under hyperoxia (40% fraction of inspired oxygen) on the level and uphill gradients (+ 5%).MethodsOxygen consumption left(dot{V}{mathrm{O}}_2right) and carbon dioxide output left(dot{V}{mathrm{CO}}_2right) were measured to calculate the CoT values at eight walking speeds (2.4–7.3 km h−1) and four running speeds (7.3–9.4 km h− 1) in 17 young males. Electromyography was recorded from gastrocnemius medialis, gastrocnemius lateralis (GL), and tibialis anterior (TA) to evaluate muscle activities. Mean power frequency (MPF) was obtained to compare motor unit recruitment patterns between walking and running.Results dot{V}{mathrm{O}}_2 , dot{V}{mathrm{CO}}_2 , and CoT values were lower under hyperoxia than normoxia at faster walking speeds and any running speeds. A faster ES on the uphill gradient and slower EOTS on both gradients were observed under hyperoxia than normoxia. GL and TA activities became lower when switching from walking to running at the EOTS under both FiO2 conditions on both gradients, so did the MPF in the TA.ConclusionsES and EOTS were influenced by reduced metabolic demands induced by hyperoxia. GL and TA activities in association with a lower shift of motor unit recruitment patterns in the TA would be related to the gait selection when walking or running at the EOTS.Trial registrationUMIN000017690 (R000020501). Registered May 26, 2015, before the first trial.

Impact of ambient temperature on energy cost and economical speed during level walking in healthy young males

ABSTRACTWe measured oxygen consumption and carbon dioxide output during walking [per unit distance (Cw) values] for 14 healthy young human males at seven speeds from 0.67 to 1.67 m s−1 (4 min per stage) in thermoneutral (23°C), cool (13°C), and hot (33°C) environments. The Cw at faster gait speeds in the 33°C trial was slightly higher compared to those in the 23°C and 13°C trials. We found the speed at which the young males walked had a significant effect on the Cw values (P<0.05), but the different environmental temperatures showed no significant effect (P>0.05). Economical speed (ES) which can minimize the Cw in each individual was calculated from a U-shaped relationship. We found a significantly slower ES at 33°C [1.265 (0.060) m s−1 mean (s.d.)] compared to 23°C [1.349 (0.077) m s−1] and 13°C [1.356 (0.078) m s−1, P<0.05, respectively] with no differences between 23°C and 13°C (P>0.05). Heart rate and mean skin temperature responses in the 33°C condition increased throughout the walking trial compared to 23°C and 13°C (all P<0.05). These results suggest that an acutely hot environment slowed the ES by ∼7%, but an acutely cool environment did not affect the Cw and ES.

Walking economy at simulated high altitude in human healthy young male lowlanders.

ABSTRACTWe measured oxygen consumption during walking per unit distance (Cw) values for 12 human healthy young males at six speeds from 0.667 to 1.639 m s−1 (four min per stage) on a level gradient under normobaric normoxia, moderate hypoxia (15% O2), and severe hypoxia (11% O2). Muscle deoxygenation (HHb) was measured at the vastus lateralis muscle using near-infrared spectroscopy. Economical speed which can minimize the Cw in each individual was calculated from a U-shaped relationship. We found a significantly slower economical speed (ES) under severe hypoxia [1.237 (0.056) m s−1; mean (s.d.)] compared to normoxia [1.334 (0.070) m s−1] and moderate hypoxia [1.314 (0.070) m s−1, P<0.05 respectively] with no differences between normoxia and moderate hypoxia (P>0.05). HHb gradually increased with increasing speed under severe hypoxia, while it did not increase under normoxia and moderate hypoxia. Changes in HHb between standing baseline and the final minute at faster gait speeds were significantly related to individual ES (r=0.393 at 1.250 m s−1, r=0.376 at 1.444 m s−1, and r=0.409 at 1.639 m s−1, P<0.05, respectively). These results suggested that acute severe hypoxia slowed ES by ∼8%, but moderate hypoxia left ES unchanged.

Economical Speed and Energetically Optimal Transition Speed Evaluated by Gross and Net Oxygen Cost of Transport at Different Gradients.

The oxygen cost of transport per unit distance (CoT; mL·kg-1·km-1) shows a U-shaped curve as a function of walking speed (v), which includes a particular walking speed minimizing the CoT, so called economical speed (ES). The CoT-v relationship in running is approximately linear. These distinctive walking and running CoT-v relationships give an intersection between U-shaped and linear CoT relationships, termed the energetically optimal transition speed (EOTS). This study investigated the effects of subtracting the standing oxygen cost for calculating the CoT and its relevant effects on the ES and EOTS at the level and gradient slopes (±5%) in eleven male trained athletes. The percent effects of subtracting the standing oxygen cost (4.8 ± 0.4 mL·kg-1·min-1) on the CoT were significantly greater as the walking speed was slower, but it was not significant at faster running speeds over 9.4 km·h-1. The percent effect was significantly dependent on the gradient (downhill > level > uphill, P < 0.001). The net ES (level 4.09 ± 0.31, uphill 4.22 ± 0.37, and downhill 4.16 ± 0.44 km·h-1) was approximately 20% slower than the gross ES (level 5.15 ± 0.18, uphill 5.27 ± 0.20, and downhill 5.37 ± 0.22 km·h-1, P < 0.001). Both net and gross ES were not significantly dependent on the gradient. In contrast, the gross EOTS was slower than the net EOTS at the level (7.49 ± 0.32 vs. 7.63 ± 0.36 km·h-1, P = 0.003) and downhill gradients (7.78 ± 0.33 vs. 8.01 ± 0.41 km·h-1, P < 0.001), but not at the uphill gradient (7.55 ± 0.37 vs. 7.63 ± 0.51 km·h-1, P = 0.080). Note that those percent differences were less than 2.9%. Given these results, a subtraction of the standing oxygen cost should be carefully considered depending on the purpose of each study.

Comparisons of energy cost and economical walking speed at various gradients in healthy, active younger and older adults

Background/ObjectiveOxygen consumption during walking per unit distance (Cw; mL/kg/m) is known to be greater for older adults than younger adults, although its underlying process is controversial. MethodsWe measured the Cw values at six gait speeds from 30 m/min to 105 m/min on level ground and gradient slopes (±5%) in healthy younger and older male adults. A quadratic approximation was applied for a relationship between Cw and gait speeds (v; m/min). It gives a U-shaped Cw–v relationship, which includes a particular gait speed minimizing the Cw, the so-called economical speed (ES). The age-related difference of the Cw–v relationship was assessed by comparisons of ES and/or Cw. ResultsA significantly greater Cw at 30 m/min and slower ES were found for older adults at the downhill gradient, suggesting that a combination of leftward and upward shifts of the Cw–v relationship was found at that gradient. Only a slower ES was found for older adults at the uphill gradient, suggesting that a leftward shift was found for older adults at that gradient. Neither a significant leftward nor an upward shift was found at the level gradient. Leg length significantly correlated to the ES for younger adults at the level and downhill gradients, while such a significant relationship was observed only at the level gradient for older adults. The maximal quadriceps muscle strength significantly correlated to the ES for older adults at all gradients, but not for younger adults. ConclusionThe age-related alteration of the Cw–v relationship depends on the gradient, and its related factors were different between age groups.

Energy cost of pushing a wheelchair on various gradients in young men

This study investigated the effects of pushing a wheelchair on the energy cost of walking (Cw; defined as the ratio of the steady-state oxygen consumption to the walking speed) and economical speed (ES) on the level and ±5% gradients. Eight pairs were formed from twelve young men to minimize variation in body weight between pushing and assisted participants. The State Trait Anxiety Inventory (STAI) test was conducted to evaluate wheelchair occupants' anxiety before and after each trial. The Cw values were significantly higher when pushing a wheelchair on the uphill gradient at more than 45 m/min. ES was significantly lower when pushing a wheelchair on the level (−8.5%) and uphill gradient (−9.1%), but not on the downhill gradient (−0.3%). Individual ES was also estimated using the concept of “Froude number”, and “estimated” ES was significantly correlated with “measured” ES even when pushing a wheelchair on the downhill gradient. The STAI score was not significantly increased except at 105 m/min, regardless of gradient. These results indicated that the fastest walking speed without an enhancement in wheelchair occupants' anxiety corresponds to ES when pushing a wheelchair with a seated occupant on all gradients, at least in young fit men. Relevance to industryThis study provides information on alterations in ES while pushing a wheelchair on different gradients, with the associated perspective of wheelchair occupants' anxiety. The results are useful for reducing energy expenditure and/or avoiding the early onset of fatigue in wheelchair assistants without increasing wheelchair occupants' anxiety.

Ergonomic effects of load carriage on energy cost of gradient walking

We examined the effects of load on the energy cost of walking ( C w), being defined as the ratio of the 2-min steady-state oxygen consumption to the speed, and economical speed (ES) during level and gradient walking. Ten men walked on a treadmill at various speeds with and without a load on their back at 0% and ±5% gradients. Significantly lower C w values were observed only when the load was carried on the back during level walking at slower speeds. The ES was significantly decreased by less than 5% when the load was carried on the back. Significant gradient differences were also observed in the ES in the load and no load conditions. These results would be applicable to a wider range of occupational and leisure tasks.