## Abstract

The energy cost of running (Cr) is classically determined from steady-state oxygen consumption (V̇o_{2}) at constant speed, divided by running speed. In the present study, Cr was determined during incremental treadmill tests in the course of the assessment of V̇o_{2max} and related parameters as follows. Assume that the running speed is increased by a constant amount (Δv) at regular short intervals (T) and that, during each intensity transient below the gas exchange threshold, V̇o_{2} increases exponentially, without time delay, toward the steady state. If V̇o_{2} is averaged over homologous times within each speed step, neglecting the initial 10 s, the V̇o_{2} difference between corresponding time values becomes constant and equal to the difference between the appropriate steady states. Thus Cr was obtained from the ratio of the difference between the V̇o_{2} averages for any two homologous times, within subsequent periods, to the corresponding speed difference. Since in aerobic conditions, Cr on the treadmill is independent of the speed, and since Δv and T were constant, the relationship between V̇o_{2} and speed is described by straight lines, where the slope yields Cr above resting. This was indeed experimentally observed, the slopes of the linear regressions (*R*^{2} range: 0.78 to 0.97 *n* = 9 to 16) within the three time windows being essentially equal. In six subjects, the grand-average of Cr amounted to 0.177 ± 0.011 ml O_{2}/(kg·m) [3.70 ± 0.23 J/(kg·m)]. This value is essentially equal to that obtained for the same subjects by applying the “classical” procedure [0.177 ± 0.015 ml O_{2}/(kg·m); 3.70 ± 0.31 J/(kg·m)], so confirming the validity of the incremental approach for assessing the energy cost of treadmill running.

- treadmill running
- incremental exercise
- oxygen consumption
- energy requirement

the energy cost of running (Cr), i.e., the amount of energy spent to transport the subject's body over one unit of distance, to the authors' knowledge was first determined by Waller and by Liljestrand and Stenström in 1919 [cited by Margaria (29)]. Despite its obvious relevance and of several studies that followed the pioneering works of Waller and Liljestrand and Stenström (15, 22, 29–31, 36), only in recent years have the many facets of Cr been given the attention they deserve. These are briefly described below and summarized in Table 1.

*1*) Cr is independent of the speed, at least for speeds wherein the air resistance is negligible (15, 19, 31, 32). Indeed, up to ∼5 m/s (18 km/h) the fraction of Cr due to the air resistance, when running outdoors, is ≤5% of the total (21, 34);*2*) Cr depends on the incline and on the characteristics of the terrain (25, 33, 35, 39);*3*) when normalized per unit body mass, Cr above resting, on flat compact terrain shows a 10–20% variability among subjects: the average value reported by di Prampero et al. (10) amounting to 0.182 ± 0.014 ml O_{2}/(kg·m) [3.80 ± 0.29 J/(kg·m)];*4*) after puberty, Cr is independent of the age and sex; before puberty, however, it is larger than in adults, amounting to ∼0.390 ml O_{2}/(kg·m) [8.15 J/(kg·m)] in children of 5 yr and decreasing gradually to attain the adult value at age 14–16 yr;*5*) trained long-distance runners are characterized by lower Crs than less trained ones [e.g., see Jones (20)], although the role of long-term training and of natural endowment are difficult to disentangle (1, 2);*6*) a larger body mass or added loads seem to reduce Cr slightly, when referred to the overall transported mass (24).

Cr is generally expressed as the amount of energy spent above resting to transport 1 kg body mass over 1 m distance. As such it is obtained by subtracting from the steady-state V̇o_{2} the value measured (or estimated) at rest in standing position and then dividing the values obtained by the running speed. This is somewhat arbitrary, so that some authors prefer to stick to the overall energy cost of running, rest included. Throughout this study, however, we will deal with the “net” cost of running, since the “resting” metabolism is a rather minor fraction of the total, particularly so at high speeds.

Generally Cr is determined from the amount of O_{2} consumed; therefore, to express it into energy, the respiratory quotient (RQ) should be known. However, since the energy equivalent of O_{2} varies only from 21.13 to 19.62 kJ/l (from pure glycogen to pure fat oxidation), it is convenient to stick to one single value; often 20.9 kJ/l, which corresponds to an RQ of 0.96, a reasonable value for aerobic exercise below gas exchange threshold.

As mentioned above (see *point 3*) the variability of Cr among subjects is relatively minor, the coefficient of variation amounting to ∼7.5%. Even so, Cr is crucial in setting best performance times over distances between 800 m and the marathon, together with V̇o_{2max}, the fraction of it that can be sustained throughout the race and the maximal capacity of the anaerobic stores (10, 11). Indeed, consider two runners whose physiological characteristics are exactly alike, with one exception: the Cr of *runner A* is 5% less than that of *runner B*, a difference well within the expected variability. If this is so, the performance times of *runner A* will be systematically 5% shorter than those of *subject B*, a colossal difference when dealing with top athletic performances.

A paradigmatic example of this state of affairs was reported by Jones (20) who, over a 5-yr period, observed an 8% increase in the 3,000 m running speed of an Olympic runner, whereas over the same period V̇o_{2max} decreased by 10%. The fall of V̇o_{2max} was more than compensated for by *1*) the decrease of Cr [gross Cr at 1% treadmill incline fell from 0.200 to 0.180 ml O_{2}/(kg·m)] and *2*) the increase in lactate threshold (from 15 to 18 km/h), this last suggesting an increase of the fraction of V̇o_{2max} that could be sustained throughout the 3,000 m race.

## AIM OF THE STUDY

The closing paragraphs of the preceding section showed the role of Cr in setting best running performances, thus highlighting the importance of assessing Cr as well as its changes with training. Therefore, in this study we propose a simple method for determining Cr in the course of the routine assessment of V̇o_{2max} and related parameters during an incremental test, much along the lines put forward very nearly 30 yr ago by Whipp and coworkers (38) to assess the mean response time, as well as the efficiency of cycloergometric exercise.

## THEORY

This section is based on the assumption that, for exercise intensities below the gas exchange threshold, the V̇o_{2} changes during the transients follow a monoexponential time course with no time delay. This assumption is an overt oversimplification, a fact that will be discussed later (see discussion), nevertheless it will allow us to put on clearer grounds the theoretical analysis that follows. Indeed, if this is the case, at the onset of square wave exercise:
_{2}^{t} and V̇o_{2}^{s} indicate V̇o_{2} above resting at *time t* and at steady state and τ is the time constant of the process. *Equation 1* shows that for *t* ≥ 4 τ, V̇o_{2}^{t} ≥ 0.98 V̇o_{2}^{s}.

The “classical” procedure to determine Cr is to have the subject run at a constant speed for ∼5 min. Since τ is on the order of 40 s or less (e.g., see Refs. 18, 38), after ∼160 s (≈4 τ) V̇o_{2}^{t} ≥ 0.98 V̇o_{2}^{s}. So, if V̇o_{2} is measured between the 3rd and 5th min and divided by the speed, Cr is correctly determined. This procedure is somewhat time consuming, even if in trained runners, in whom, because of a faster V̇o_{2} on-response, the steady-state V̇o_{2} is reached in ∼90 s, it can be shortened appreciably: e.g., performing a multi-stage test with 3 min/stage while assessing Cr from V̇o_{2} measured in the 3rd min [e.g., see Carter et al. (7)].

In recent years, the incremental exercise tests for assessing V̇o_{2max} have gained ever increasing acceptance in the scientific community. In this case, the exercise intensity is increased at regular intervals (usually 30 s to 1 min) by a constant amount. Thus V̇o_{2} keeps increasing, without ever attaining a steady state, until volitional exhaustion or until the test is interrupted by the operator. This approach is widely used for assessing V̇o_{2max}, gas exchange threshold, and other metabolic parameters.

However, when the exercise mode is running, this same approach could easily yield Cr as well, a useful information that is often lost. To this aim, we will first show how this can be done when the speed is continuously increased at a constant rate (ramp test); we will then address the more common cases in which the speed is increased by a constant amount at regular intervals (incremental test).

Consider the ramp test first: it will be assumed that the subject is running on the treadmill at a given moderate constant speed. At *time zero* (*t* = 0) the treadmill speed is increased at a constant rate (dv/d*t* = constant = v̇) in a square-wave fashion. As a consequence also the rate of change of O_{2} requirement per unit of time will suddenly increase from dV̇o_{2}/d*t* = V̈o_{2} = 0 (for constant speed steady-state running) to a rate dictated by the rate of change of speed (v̇), where the double dot denotes the second time derivative of the quantity in question. Thus the actual rate of change of V̇o_{2} (V̈o_{2}), assuming a monoexponential time course without time delay will again be described by *Eq. 1*:
_{2}^{t} and V̈o_{2}^{s} are the second time derivatives and the time constant τ is the same.

*Equation 2* is represented graphically in Fig. 1*A*, which shows that, as was the case for a square-wave change of V̇o_{2} (*Eq. 1*), after a time ≥4 τ, V̈o_{2}^{t} = V̈o_{2}^{s}. Thus, after ∼4 τ, the rate at which the O_{2} consumption changes over time (V̈o_{2}^{t}) has become constant (V̈o_{2}^{s}) and proportional to the rate of change of speed (v̇). It should also be noted that V̈o_{2}^{s} is not the actual O_{2} requirement at steady state, which is given by the product of V̈o_{2}^{s} and the time (V̇o_{2}^{s} = V̈o_{2}^{s}·*t*). Rather V̈o_{2}^{s} is the rate at which V̇o_{2} changes per unit of time after the initial delay (≈4 τ), i.e., when it has become proportional to the rate at which the running speed is changing (v̇):

Dimensionally, V̈o_{2}^{s} is the amount of O_{2} consumed and v̇ is the distance covered, both expressed per unit of time squared. Multiplying both sides of *Eq. 3* by
*K*, i.e., the proportionality constant between V̈o_{2}^{s} and v̇ is the energy cost of running, as traditionally defined.

Thus, in a graphical representation such as in Fig. 1*A*, for *t* ≥ 4 τ, the ratio of V̈o_{2} (*left ordinate*) to the (imposed) constant rate of change of velocity (v̇; *right ordinate*) yields the energy cost of running.

Generally, however, the results of the incremental tests are reported plotting the O_{2} consumption rate (V̇o_{2}) as a function of the time, as represented in Fig. 1*B*. In this type of representation, V̇o_{2} at any *time t*, is lower than the V̇o_{2} requirement at the steady state (= V̈o_{2}^{s}·*t*, see above), by an amount (ΔV̇o_{2}^{t}) (see Fig. 1*B*):

In turn, ΔV̇o_{2}^{t} is given by the time integral of the difference between the rate of change of V̇o_{2}, were the process infinitely fast (τ = 0) and its actual rate of change (V̈o_{2}^{t}) (hatched area in Fig. 1*A*):

Since, as mentioned above, the V̇o_{2} response was assumed to be monoexponential and without time delays, ΔV̇o_{2}^{t} can be written as:

Thus, from *Eqs. 5* and *4′*, for any *time t*, the actual V̇o_{2} will be given by:
*t* ≥ 4 τ reduces to:

These two equations show that, for *t* ≥ 4 τ: *1*) the two functions describing the actual V̇o_{2} and the V̇o_{2} requirement at steady state (= V̈o_{2}^{s}·*t*) as a function of time become parallel. Furthermore, *2*) the time lag between the actual V̇o_{2} (V̇o_{2}^{t}) and the true requirement (V̈o_{2}^{s} *t*) is equal, in the ideal case described here (monoexponential response without time delay) to the time constant of V̇o_{2} (τ) or, more realistically, to the mean response time of the process, as originally pointed out by Whipp et al. (38). In addition, *3*) the vertical distance between the steady-state V̇o_{2} requirement at *time t* (V̈o_{2}^{s}·*t*) and the actual V̇o_{2} at *time t* (V̇o_{2}^{t}) is constant and equal to V̈o_{2}^{s}·τ. Thus, once again, for *t* ≥ 4 τ, the slopes of the two straight lines (V̇o_{2} requirement vs. time, ΔV̇o_{2}^{s}/Δ*t*) and actual V̇o_{2} vs. time (ΔV̇o_{2}^{t}/Δ*t*) become equal: V̈o_{2}^{t} = V̈o_{2}^{s}. Therefore, the energy cost of running can be calculated as the ratio of the slope of V̇o_{2} vs. time relationship to the slope of the v vs. time relationship (=ΔV̈o_{2}/Δv̇; see also *Eq. 3*″).

These considerations are reported graphically in Fig. 1*B*.

We will now consider the more common incremental tests in which the running speed is increased by a constant amount (Δv) at regular intervals of duration T, while V̇o_{2} is measured over short periods of time, usually on a breath-by-breath basis. As described above (see *Eq. 1*), it will be assumed that, for aerobic exercise below the gas exchange threshold, V̇o_{2} increases exponentially toward the steady state (V̇o_{2}^{s}) as described by:
_{2}^{0} is the V̇o_{2} immediately preceding the speed transient and V̇o_{2}^{s} is the amplitude of step V̇o_{2} requirement, i.e., the difference between the V̇o_{2} requirement at the new steady state and the actual V̇o_{2} at the moment of the change of speed (V̇o_{2}^{0}). *Equation 8* can be written as:
_{2}^{n,s} is the steady-state V̇o_{2} of the *n*th running period and V̇o_{2}^{n−1,T} is the actual V̇o_{2} at the end of the immediately preceding run of duration T. Thus the first term in parenthesis is the amplitude of the V̇o_{2} increase, over and above the V̇o_{2} prevailing at the end of the preceding period.

It is easy to show that, after a few running periods and provided that the step amplitude of V̇o_{2} requirement (proportional to Δv) is constant, the V̇o_{2} differences between homologous times within each period become constant and equal to the differences that would be attained, were the *time T* sufficiently long to attain the steady state.
*n*, *n*+1, *n*−1, and the time within the period by the letter a, b, or … s (for the steady state) following the comma.

Thus, if Δv (= v^{n}−v^{n−1}) is constant and known, the ratios:
_{2}^{n,i} and v_{n}, where *n* is a given time period T, i is a given time within T, and v_{n} is the speed of the appropriate time period. This approach is represented graphically in Fig. 2.

## METHODS

The experiments were performed on six recreational long-distance runners in view of their participation in the “Etna Marathon” (a 43-km running race from sea level to 3,000 m of altitude). The runners, whose characteristics are reported in Table 2, gave their informed consent, and the procedures were approved by the local ethical committee and were in agreement with the Declaration of Helsinki (1964).

The subjects ran on a treadmill at 8 km/h and zero incline for 4 min. The speed was then increased by 0.5 km/h every 30 s until volitional exhaustion. O_{2} uptake (V̇o_{2}), CO_{2} output (V̇co_{2}), and heart rate (HR) were continuously recorded on a breath-by-breath or beat-by-beat basis by means of a metabolic unit (K4b^{2}, Cosmed, Italy) and by electrocardiogram (ECG; MDF VF, Esaote, Italy). This procedure allowed us to determine gas exchange threshold (GET) and maximal O_{2} consumption (V̇o_{2max}), as from standard procedures (see Table 2). Specifically, the gas exchange threshold was determined by means of the V-slope approach, wherein the inflexion point of the V̇co_{2}/V̇o_{2} regression was estimated by two independent experimenters and V̇o_{2max} was assessed from the V̇o_{2} plateau. In addition, the energy cost of running was calculated in the speed range from the beginning of the incremental phase to GET, as follows. For every 30-s step, the O_{2} uptake was averaged over three time windows 0–10 s (*A*); 10–20 s (*B*); 20–30 s (*C*). The so obtained V̇o_{2} values were plotted as a function of the corresponding speed. This allowed us to obtain three individual relationships between V̇o_{2} and running speed (*A, B, C*) for each subject (see Fig. 3). These were then interpolated by least squares linear regressions, the slopes of which yielded three average Cr values for each subject (see theory and *Eq. 11*). In addition Cr was also determined on all subjects according to the standard protocol, wherein the steady-state V̇o_{2} (between the 3rd and the 4th min of exercise) was measured at four running velocities, all below GET and corresponding to 85, 95, 100, and 110% of the individual best marathon velocity, Cr was then obtained from the ratio of steady-state V̇o_{2} to running velocity.

In a previous study Cr was determined by this same approach following an identical protocol with the same equipment and procedures in seven other subjects before and after a 120-km desert running race (5 stages over 4 days) (16). In this case, however, Cr was not determined by means of the standard steady state protocol, nor was the underlying theory discussed in detail. These data are also reported and discussed below.

## RESULTS

In all six subjects of this study, the relationships between V̇o_{2} over the three selected time windows (*A*: 0–10 s; *B*: 10–20 s; *C*: 20–30 s) and running speed could be appropriately interpolated by linear regressions, the *R*^{2} of which ranged from 0.78 to 0.97, *n* = 9 to 16 (see Fig. 3 and Table 3).

In all subjects, the slopes of the three individual regressions were essentially equal; therefore, individual Cr, as obtained from the incremental protocol (*Eq. 11*), was calculated from the average of the three slopes (Table 4). The intercepts of the three individual relationships between V̇o_{2} and speed (*A, B, C*) show a greater variability than the corresponding slopes (Table 3). The average for all subjects (ml·kg^{−1}·min^{−1}) amounts to *A* = 4.32, *B* = 4.74, *C* = 5.29. They are not significantly different from each other, nor from the O_{2} consumption at rest, standing on the treadmill, which amounted to 4.74 ± 0.42 ml·kg^{−1}·min^{−1}.

The average Cr, as obtained from the standard protocol in the speed range from 85 to 110% of the individual best marathon velocity, was not significantly different from that calculated from the incremental protocol (Table 4).

In the data obtained on the seven subjects (16), on whom Cr was determined from the incremental protocol only, before and after the 120-km desert race, the slopes (and hence the Cr values) as obtained from the 0- to 10-s time windows {0.189 ± 0.017 ml/(kg·m) [3.95 ± 0.36 J/(kg·m)] before and 0.178 ± 0.016 ml/(kg·m) [3.72 ± 0.33 J/(kg·m)] after the race} were significantly larger, albeit slightly so, than those determined from the 20- to 30-s time window {0.177 ± 0.015 ml/(kg·m) [3.70 ± 0.31 J/(kg·m)] before and 0.173 ± 0.025 ml/(kg·m) [3.62 ± 0.52 J/(kg·m)] after the race}. However, the Cr values obtained from the 20- to 30-s time window were not significantly different than those obtained from the immediately preceding one (10–20 s) {0.177 ± 0.017 ml/(kg·m) [3.70 ± 0.36 J/(kg·m)] before and 0.175 ± 0.023 ml/(kg·m) [3.66 ± 0.48 J/(kg·m)] after the race}, which, in turn were not significantly different than those obtained from the first time window (0–10 s).

## DISCUSSION

The data reported in Table 4 as well as those originally obtained by Fusi et al. (16) show that, in all subjects, the values of Cr obtained from *Eq. 11*, wherein the time windows were 10–20 s (*B*) and 20–30 s (C), were essentially equal, amounting on the average to 0.178 ± 0.012 ml/(kg·m) [3.72 ± 0.25 J/(kg·m)], 0.176 ± 0.011 ml/(kg·m) [3.68 ± 0.23 J/(kg·m); Table 4] on the six subjects of this study, and to 0.177 ± 0.017 ml/(kg·m) [3.70 ± 0.36 J/(kg·m)], 0.177 ± 0.015 ml/(kg·m) [3.70 ± 0.31 J/(kg·m)] before and 0.175 ± 0.023 ml/(kg·m) [3.66 ± 0.48 J/(kg·m)], 0.173 ± 0.025 ml/(kg·m) [3.62 ± 0.52 J/(kg·m)] after the desert race in the seven subjects of the previous study (16). In addition, the average of the three individual values (*A, B, C*) in all six subjects of the present study was not significantly different than the corresponding average as obtained from the standard protocol over the four investigated speeds. Indeed the ratio of the individual averages Cr (incremental) to Cr (standard) ranged from 0.94 to 1.044, the grand average amounting to 1.003 ± 0.038 (Table 4). Furthermore, the bias (mean Cr standard-mean Cr incremental): *1*) is not significantly different from zero, amounting to 0.00033 ml/(kg·m) and *2*) it is not affected by the individual average between the two sets of measurement and *3*) five of six data points fall within the 95% confidence limits (Fig. 4).

Finally, the grand average of the absolute values obtained in this study, be it by means of the incremental (where the initial time period 0–10 s is neglected) or standard protocol, amount to 0.177 ± 0.011 ml/(kg·m) [3.70 ± 0.23 J/(kg·m); incremental *B* and *C* slopes] and to 0.177 ± 0.015 ml/(kg·m) [3.70 ± 0.31 J/(kg·m); standard]: a value close to those reported in the literature for treadmill running when the incline is 0% (e.g., see Ref. 4). Therefore, even if the number of subjects of this study was rather small, it can be concluded that Cr can be accurately obtained from incremental running tests, wherein the speed is increased at regular intervals by a constant amount, provided that the steps are sufficiently long (30–60 s) and neglecting the first ∼10 s of each step.

The approach to calculate Cr by means of the incremental protocol, as outlined in theory depends crucially on two assumptions: *1*) the constancy of Cr, independently of the running speed, *2*) the constancy of the time constant of the V̇o_{2} on-response (τ) and the absence of time delays, over the entire range of the investigated energy expenditures. These two assumptions are briefly discussed below.

*Assumption 1* is strongly supported by the observation that Cr (above resting), as calculated by means of the standard protocol, for all subjects, was essentially equal over the four investigated speeds (see Table 4), consistently with the great majority of data on treadmill running at constant speed [e.g., see Weyand et al. (37)].

The second assumption is somewhat more questionable. Indeed, were it rigorously true, the three slopes of the V̇o_{2}/velocity relationships ought to be equal for the three time windows considered (*A, B*, and *C*; see Fig. 3), as predicted from *Eq. 11*. This was indeed the case for the six subjects of this study (see Table 3) where the Cr values obtained from the three slopes were not significantly different from each other, the average ratios of the slopes *A/C* and *B/C* amounting to =1.015 (range 0.954 to 1.093) and to =1.009 (range 0.983 to 1.037), respectively.

At variance with these data, in our previous study we observed that the Cr values obtained from 0- to 10-s time window were significantly, albeit slightly, larger than those obtained in the 20- to 30-s time window. Indeed, the average ratios of the slopes *A/C* and *B/C* amounted to 1.090 (range 1.067 to 1.119) and to 1.020 (range 1.000 to 1.056) before and to *A/C* = 1.078 (range 1.000 to 1.116) and *B/C* = 1.034 (range 0.975 to 1.103) after the desert race (16).

These findings are consistent with the observation that the V̇o_{2} kinetics at the onset of a metabolic transient from rest are characterized by a cardiodynamic phase, characterized by a fast response time, which is followed by a slower metabolic phase with a time constant on the order of 35 s (primary phase). If this were indeed the case, the V̇o_{2} determined over the initial time window (*A*) can be expected to be larger than that determined at later stages, thus yielding larger slopes of the V̇o_{2}/velocity (and hence larger values of Cr).

In view of these observations, the few paragraphs that follow will be devoted to a brief discussion of the effects of exercise mode, intensity, and duration on the V̇o_{2} on-response, considering that the present approach involved an initial phase of running at constant slow speed [V̇o_{2}^{s}≅30 ml/(kg·min); see Fig. 3]. Thus at the onset of the first period of the incremental test and even more so at the onset of all subsequent ones, V̇o_{2} was substantially larger than at rest. Under these conditions, but not exclusively so, the V̇o_{2} on-responses are greatly dependent on exercise intensity and mode (7). Indeed, whereas during cycloergometric (3) and knee extension (27) exercises, the time constant of the V̇o_{2} on-response becomes longer when the exercise is preceded by a milder priming one, rather than by a state of rest, this is not the case during stepping exercise (12, 14). In addition, the amplitude of the slow component of the V̇o_{2} on-response is substantially smaller during treadmill, compared with cycloergometric exercise, and is reduced after prior high-intensity exercise (5, 6, 17, 23), even if this is obviously irrelevant in the present study.

Finally, it should be pointed out that, regardless of the exercise mode, when the exercise transient is preceded by a milder priming one, both the time delay and the cardiodynamic phase of the V̇o_{2} on-response can be expected to become very nearly negligible.

The considerations reported in the preceding paragraphs support the simplifying assumption of a unique V̇o_{2} on-response without time delays over the entire range of the investigated energy expenditures below GET. Even so, it is suggested that the present approach for calculating Cr be applied, neglecting the initial 10–15 s of each constant speed step. It seems also interesting to point out that, in practice, and at least during cycle ergometry exercise diagnostics, the different V̇o_{2} on-responses that can be expected as the workload is progressively increased throughout the test are largely neglected.

In concluding this section it is somewhat surprising that this approach, which, as mentioned above, was put forward in 1981 by Whipp et al. (38) to determine mean response time and efficiency in cycling, at least to the authors' knowledge, was never applied to assess the energy cost of treadmill running.

## CONCLUSIONS

The above reported results and considerations show that the energy cost of running can be estimated from the slope of the V̇o_{2} vs. speed relationship during incremental running tests, albeit with a grain of salt, because of the many assumptions discussed above and provided that, within each running step the single breath V̇o_{2} values be averaged over homologous time periods, and neglecting the initial 10–15 s of each speed step.

Finally, it should be pointed out that the approach described above can be applied only to treadmill running, in which case the speed changes are not associated with any acceleration of the runner's body whose position does not change in a frame of reference centred on the ground. At variance with treadmill running, when running on the terrain, any speed change, be it stepwise or continuous, leads to a proportional acceleration of the runner. During the acceleration phase, the energy cost of running is larger than running at a constant speed by an amount that depends on the acceleration itself (13). Therefore, since the assumption of the constancy of Cr, independent of the speed, is not tenable during accelerated running, the present approach can be meaningfully applied to treadmill running only.

- Copyright © 2009 the American Physiological Society