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Applied Sciences: Biodynamics

Running velocity at ˙VO2max


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Medicine & Science in Sports & Exercise: January 1996 - Volume 28 - Issue 1 - p 114-119
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Several authors have defined running velocities which may, as a group, be described as the velocity associated with ˙VO2max. Although several names, definitions, methods, and abbreviations have been introduced, in this paper we shall use ν˙VO2max for them all. This abbreviation was first introduced by Daniels et al.(8). Some authors have used the same definition and methods (7,15) or the same name and abbreviation(5,7,15), while others have used other terms which represent a similar parameter which may best be described as an integrated product of ˙VO2max and running economy.

Regardless of their actual definition, method of determination, or form of abbreviation, these ν˙VO2max have been shown to serve as an indicator of performance in middle- and long-distance running events. For example, ν˙VO2max is related to performance by high school female athletes in a 5-km cross country race (7); to performance by elite male distance runners in 1500-m, 3000-m, and 5000-m track events (11); to performance by a heterogenous groups of men and women runners in 1500-m track events (12); to performance by subelite male distance runners in 5000-m track races(18), 10-km road races (15) and 21.1-km road races (3); and also to performance by a heterogenous group of male runners in 10-km, 21.1-km, and 42.2-km road races(16, 17). Daniels et al. (8) have also suggested that ν˙VO2max is higher in elite versus subelite women distance runners and that ν˙VO2max is very similar to the velocity that can be sustained by these women over 3000 m.

The time that ν˙VO2max can be sustained (tLIM atν˙VO2max) is related to the lactate threshold, the lactate steady state velocity, and the average velocity in a 21.1-km race, when these velocities are expressed as a percentage of ν˙VO2max(3,6). It has been suggested that tLIM atν˙VO2max may be related to anaerobic capacity(5).

Since ν˙VO2max incorporates maximal aerobic power and running economy in one term, ν˙VO2max is used in monitoring athletes' training. Since tLIM at ν˙VO2max may provide information about the anaerobic capacity of an individual (5), it too may be of value in evaluating the effectiveness of a training program.ν˙VO2max and tLIM at ν˙VO2max can also be used in the prescription of training for distance runners(1,2): if ν˙VO2max is the minimal velocity necessary to elicit ˙VO2max, it should describe the ideal training intensity when the goal of training is to increase maximal aerobic power by training for as long as possible at ν˙VO2max or by repeating shorter bouts at ν˙VO2max with minimal fatigue.

In most of the published studies in which a ν˙VO2max has been determined, by whatever method, subjects were only men(3-6,11,16-18), although some data from women have been reported(7,8,12). To date, the determination ofν˙VO2max in women runners, using the definition of treadmill speed at which ˙VO2max is elicited(3-6), has apparently not been attempted.

Inspection of the methods and definitions of ν˙VO2max used in the various studies suggested to us that several different parameters have been calculated, even though we may broadly refer to them as the velocity at˙VO2max. Billat et al. (3-6) defined ν˙VO2max as the treadmill speed at which an athlete was running when ˙VO2max was elicited. diPrampero(9) calculated a velocity by dividing ˙VO2max by the oxygen cost of running at a submaximal intensity (C). Lacour et al.(11,12) modified the method of diPrampero(9) and subtracted ˙VO2 at rest from˙VO2max and C before dividing. In the methods used by Cunningham(7), Daniels et al. (8), and Morgan et al. (15), ν˙VO2max was determined by extrapolation from the submaximal velocity: ˙VO2 relationship to predict the velocity that would be associated with ˙VO2max; in the two studies in which the methods were described, this ˙VO2max was measured during uphill treadmill running (7,15). Noakes et al. (16) and Scrimgeour et al.(17) reported the final treadmill speed that was sustained by an athlete for at least 1 min, regardless of the actual speed at which ˙VO2max was elicited. Similarly, Tanaka et al.(18) described their ν˙VO2max as the maximal running velocity achieved on the treadmill, although the length of time that the velocity had to be sustained to qualify asν˙VO2max was not reported.

The definitions used by Billat et al.(3-6), Noakes et al.(16), Scrimgeour et al., (17), and Tanaka et al. (18), while not all exactly the same, describe parameters with an anaerobic component as they define velocities that are above the anaerobic threshold. Parameters defined as a ratio of maximal aerobic power to the oxygen cost of running(9,11,12) represent running velocities that could be sustained aerobically if there were no anaerobic contribution(although 100% of ˙VO2max cannot in fact be elicited without an anaerobic contribution); therefore, we refer to these as purely aerobic indices. It is not so clear whether the parameter defined by Cunningham(7), Daniels et al. (8), and Morgan et al. (15) has an anaerobic component. We believe it should since, although it is determined by extrapolation from steady-state fully aerobic submaximal data points, it describes a velocity above the anaerobic threshold.

Our hypothesis was that the different authors were not using different methods to determine one parameter; based on the nature of their definitions, we hypothesized that the velocities calculated in the various studies represented different parameters. The primary purpose of this study was to test that hypothesis. Specifically, the goal was to compare estimates ofν˙VO2max derived using the definitions provided by Billat et al.(3-6); diPrampero(9); Lacour et al. (11,12); Cunningham (7), Daniels et al. (8), and Morgan et al. (15); and Noakes et al.(16) and Scrimgeour et al. (17). A secondary purpose was to evaluate the usefulness of these parameters, based on theoretical considerations.



Twenty-two members of a university women's track team volunteered to participate in this study. These women specialized in running distances from 400 m to 5000 m. They were of mean (±SD) age 19 ± 1 yr, height 167.6 ± 7.5 cm, and weight 56.8 ± 4.7 kg. Their mean˙VO2max was 52.0 ± 5.0 ml·kg-1·min-1. The study was approved by the Institutional Review Board of the University of North Texas, and all of the subjects provided written voluntary informed consent.


Subjects performed a speed-incremented 0%-slope treadmill test to exhaustion for the determination of ν˙VO2max using five different definitions(3-6; 9; 11,12; 7,8,15; 16,17), although not the same testing protocols as in those studies. The ν˙VO2max values were compared using repeated measures analysis and correlations.

Data Collection Procedures

The treadmill exercise tests began with three 5-min stages during which the speeds were usually 6.0 miles·h-1 (9.7 km·h-1 or 161 m·min-1), 7.0 miles·h-1 (11.3 km·h-1 or 188 m·min-1), and 8.0 miles·h-1 (12.9 km·h-1 or 215 m·min-1). Each of these stages was followed by a 5-min rest. For some of the less fit subjects, the treadmill speed for the third stage was reduced, compared with the majority of subjects, to 7.5 miles·h-1 (12.9 km·h-1 or 215 m·min-1). All subsequent stages were of 2-min duration and were performed in a continuous fashion, with no rest periods. The first of these 2-min stages was at 9.0 miles·h-1 (14.5 km·h-1 or 241 m·min-1). Increments for these stages were relatively small(0.5 miles·h-1 or 0.8 km·h-1 or 13 m·min-1) to allow a more precise identification of the treadmill speed at which ˙VO2max was elicited. In all cases, actual speed at each stage was calculated from repeated clockings of the time for 20 treadmill belt revolutions.

On another day, subjects performed three other 5-min submaximal stages, again with each followed by a 5-min rest. For most of the subjects, speeds for these stages were 6.5 miles·h-1 (10.5 km·h-1 or 174 m·min-1), 7.5 miles·h-1 (12.1 km·h-1 or 201 m·min-1), and 8.5 miles·h-1 (13.7 km·h-1 or 228 m·min-1). For some of the less fit subjects, slower treadmill speeds were used. The purpose of these six submaximal stages was to obtain data for use in defining the velocity:˙VO2 relationship; for the less fit subjects, the protocol was altered to ensure that steady state˙VO2 would be obtained and that the values would not exceed 90% of˙VO2max(10).

Throughout all of the tests, metabolic data were obtained using a MedGraphics CPMax metabolic cart (St. Paul, MN) which was calibrated prior to each test according to the manufacturer's instructions. Data were reduced to 15-s averages, and rolling 30-s averages were calculated. For our diPrampero definition, the energy cost of running (C) was determined as the ratio of˙VO2 (ml·kg-1·min-1) to velocity(m·min-1) during the 5th minute at 7.0 miles·h-1(11.3 km·h-1 or 188 m·min-1), which was the speed during the second stage in the incremental test. For our Lacour definition,˙VO2 at rest was subtracted from the steady state ˙VO2 before the ratio (C′) was calculated; ˙VO2 at rest was calculated to be 5 ml · min-1(11-13). The velocity:˙VO2 relationship was determined using the linear regression procedure on SPSS(Chicago, IL) and the velocity that would be associated with˙VO2max was derived using this relationship and the measured˙VO2max. ˙VO2max was identified as the highest 30-s value during the test.

ν˙VO2max values were determined using five different definitions. In this paper, the five values for ν˙VO2max are identified using the name of one author who has published data using the specific definition. When two or more authors have used the same definition(e.g., Cunningham (7), Daniels (8), and Morgan et al. (15)), one name was arbitrarily selected. The five values compared in this study were:

  1. ν˙VO2max[Billat]: the (lowest) treadmill speed at which˙VO2max was elicited(3-6);
  2. ν˙VO2max[diPrampero]: calculated as˙VO2max·C-1(9);
  3. ν˙VO2max[Lacour]: calculated as (˙VO2max -˙VO2 at rest) · (C′)-1(11,12);
  4. ν˙VO2max[Daniels]: calculated using the slope and y-intercept of the velocity:˙VO2 relationship by setting by˙VO2 equal to ˙VO2max and solving for velocity(7,8,15);
  5. ν˙VO2max[Noakes]: the highest treadmill speed that was sustained for at least 1 min (16,17).

Data Analyses

The null hypothesis was that there would be no difference in the values ofν˙VO2max determined using the different definitions and that the values would be highly correlated in this sample of nonelite women track and field athletes. The working hypothesis was that, because of the anaerobic contribution during treadmill running when ˙VO2max is elicited or fatigue occurs, the values obtained using the definitions used previously by Billat et al. (3-6), by Noakes et al.(16) and scrimgeour et al. (17), and by Cunningham (7), Daniels et al.(8), and Morgan et al. (15) would produce parameters with higher values than the parameters generated using the definitions of diPrampero (9) and of Lacour et al.(11,12).

The five values for ν˙VO2max that were obtained for each of the subjects were compared using a repeated measures ANOVA and Tukeypost-hoc tests. Intraclass and bivariate correlations between the parameter values were also calculated. Statistical significance was set at the 0.05 level.


The mean values for ν˙VO2max that were derived using the five different definitions are presented in Table 1. Results of the repeated measures ANOVA revealed a significant difference among the means (F4,84 = 7.80, P < 0.001). Results of the Tukey post-hoc tests are summarized in Table 1. Intraclass r for the methods was 0.872. Bivariate correlations between values from all pairs of definitions are presented in Table 2.


The main finding in this study was that the different definitions ofν˙VO2max describe five different parameters; they do not provide different ways of determining the value of one parameter. This conclusion is based on three facts: first, theoretically the definitions describe different parameters, since some of the velocities must include an anaerobic component; second, ANOVA and follow-up comparisons determined differences in the mean values obtained using the different definitions; and third, and perhaps most importantly, there were large intraindividual differences in values obtained using the different definitions, as evidenced by the relatively low correlations between the sets of values. This finding does not invalidate the conclusion that has been drawn in several published papers thatν˙VO2max is related to running performance(3,6-8,11,12,15-18). It does indicate that, in these various papers, running performances have been compared to quite different parameters.

Our sample was not exceptionally large and representated a heterogenous group of trained nonelite athletes who specialized in events from 400 m to 5000 m. The diversity of the training backgrounds and race specialities of the subjects may have contributed to the interindividual differences in the five values, and perhaps also to the intraindividual differences. However, such effects would in no way detract from the interpretation that the five parameters were different. We saw no consistent effect of race speciality on the intraindividual differences.

Values in the present study were consistently lower than the men's values that have been reported previously(3-6,11,12,15-18). The mean values for ν˙VO2max[Daniels] for our subjects were also lower than the 277 m·min-1 reported by Cunningham(7) or the 329 m·min-1 reported by Daniels et al. (8). Cunningham's young female subjects specialized in distance events, had a higher ˙VO2max than our women(61.7 ml·kg-1·min-1 vs 52.0 ml·kg-1·min-1) and were tested within 2 wk of the state cross-country championships. The women studied by Daniels et al.(8) were successful distance runners with mean values for˙VO2max of 67.0 ml·kg-1·min-1. The eight women athletes among the 32 subjects evaluated by Lacour et al.(12) had higher ν˙VO2max[Lacour] values than our subjects (324 m·min-1 versus 257 m·min-1). These differences would be expected, as our subjects were not all distance specialists, and were tested before the competitive season.

Some differences between values in this study and those reported in the literature may be due to the fact that the protocol used in this study was not exactly the same as any used in previous studies. The protocol was designed to allow estimation of C, extrapolation from the submaximal velocity:˙VO2 relationship, and fairly precise identification of both the velocity at which ˙VO2max was elicited and the highest velocity that could be sustained for 1 min. We believe that, in these regards, our protocol was similar enough to those used in the other studies for us to generate comparable values.

It was hypothesized that the ν˙VO2max[Billat],ν˙VO2max[Daniels], and ν˙VO2max[Noakes], which should each involve an anaerobic component since each represents a running velocity above the anaerobic threshold, would be consistently higher thanν˙VO2max[diPrampero] and ν˙VO2max[Lacour], which represent running velocities that could be sustained aerobically if there were no anaerobic contribution. Our results generally supported this hypothesis, although not all differences reached statistical significance and we would haved expected ν˙VO2max[Daniels] to be higher thanν˙VO2max[Lacour]. The relatively low correlations(Table 2) between sets of values further demonstrated that there were five definitions of five different parameters, not five different methods of determining one parameter.

Is any one definition “best”? Is any one parameter“right”? No-one yet has tested individuals, calculated fiveν˙VO2max using the different definitions, and seen whether any particular parameter was more highly correlated with running performance. So, with respect to the ability to predict running performance, there is little evidence to suggest that any one definition is, in that sense, better than another. However, each definition does have its own logical appeal and each parameter has its strengths and weaknesses. We might say that each is“best” for what it describes.

For example, the strength of the Billat ν˙VO2max is that this running velocity is “real”... it is the velocity actually associated with the measurement of ˙VO2max. The method is simple; no calculations are involved; whatever the treadmill speed is,ν˙VO2max is. The potential drawback to using this definition lies in precision...the values for ν˙VO2max are only as precise as the increments used in testing, and the values may be influenced by the length and number of stages. This ν˙VO2max parameter should be useful in the prescription of training for distance runners(1,2) when the object is to achieve and sustain˙VO2max, because it is the velocity (or, at least, a velocity) at which ˙VO2max is elicited.

Like the Billat ν˙VO2max, the Noakes parameter represents a velocity actually sustained by the athlete, and is simple to measure. In fact,ν˙VO2max[Noakes] could be determined without any metabolic analyses and would be easily adapted to overground running and field testing at the track. While it does not necessarily describe the velocity at which˙VO2max is attained, it might well be best related to performance since it itself is a performance measure. However, like the Billat parameter, the Noakes values are limited in precision to the increments used in testing.

Theoretically, the velocities generated using the diPrampero(9) and Lacour et al.(11,12) definitions should be lower than the velocity at which ˙VO2max is actually elicited (seeTable 1) and actual exercise at these calculated velocities would not be associated with the attainment of ˙VO2max. The advantage of using these definitions is that they provide uniquely aerobic indices which are not influenced by anaerobic capacity. Furthermore, the values for these ν˙VO2max parameters are not constrained by the magnitude of the increments used in the exercise test. However, the values are susceptible to the effects of day-to-day variations of biological or technical origin in the calculated values for ˙VO2max or the energy cost of running and may also be affected by the choice of which stage to use in the calculation of the energy cost of running. It is noted that the coefficients of variation (CV) for values obtained using these latter definitions were higher than the CV for the values determined directly from treadmill velocities (Table 1) and probably reflect the combined variability in ˙VO2max (CV, 10%) and the oxygen cost of running(CV, 10%). Since resting ˙VO2 (Lacour parameter) is not actually measured, any theoretical advantage to including it may be balanced by the practical problems associated with estimating this value(11,12).

The definition of the ν˙VO2max[Daniels] parameter also requires estimation of the oxygen cost of running. It has the advantage of tracking economy over a range of intensities, although the difficulty in precisely extrapolating oxygen cost from submaximal velocity:˙VO2 points has been discussed (10,13,14). This may be the primary weakness of this definition.

The lack of precision in ν˙VO2max obtained using any of these definitions might seem small. However, a variation of 0.6 km·h-1(less than the increment used in our testing) is a difference of 2 s per 400 m. If ν˙VO2max is to be used as a guide for determining training intensity (1,2), such an error is meaningful. If the parameter is being used to monitor training, a variation of 0.6 km·h-1 for an individual with a ν˙VO2max of 20.0 km·h-1 may appear to represent an error of only 3%. However, since the actual ranges of values in an athletic population might be less than 4 km·h-1, an error of 0.6 km·h-1 would be problematic.

In summary, five definitions of ν˙VO2max were found to yield different values and, in fact, describe five different parameters. Therefore, interpretation and comparison of the results of previous studies is difficult. One might argue that, because they are purely aerobic indices and not“contaminated” by an anaerobic component,ν˙VO2max[diPrampero] and ν˙VO2max[Lacour] are the most meaningful parameters to use to monitor training...when their values improve, maximal aerobic power or efficiency has increased. But whenν˙VO2max[Billat], ν˙VO2max[Daniels], orν˙VO2max[Noakes] improves, the reason may be an increase in maximal aerobic power, the lactate threshold, anaerobic capacity, or efficiency; of course, all these factors also influence performance and reflect training status. If ν˙VO2max is to be used as a guide in prescribing training intensity, with the rationale being that it is the lowest speed that will elicit ˙VO2max(1,2), then ν˙VO2max[Billat] would appear to be the logical choice. However, it is noted that it has yet to be proven thatν˙VO2max[Billat] actually does represent the lowest velocity that will elicit ˙VO2max. In addition, it could be argued thatν˙VO2max[Daniels] should describe the lowest velocity to elicit˙VO2max; in this study it was 4% (NS) lower thanν˙VO2max[Billat].

The velocity associated with ˙VO2max is an interesting and potentially useful parameter. It is concluded that the different definitions of the running velocity associated with ˙VO2max(“ν˙VO2max”) generate distinctly different parameters, some with and some without an anaerobic component. Individuals involved with the concept of determining an integrated product of˙VO2max and running economy must be aware that the way of defining and determining a parameter can have a considerable effect on its value. Perhaps the different parameters should have different, specific, consistent, and descriptive labels. Regardless, it is clear that individuals must exercise care in comparing results from various studies or in applying the parameters in scientifically based training programs. Finally, values for the five parameters for a group of competitive but nonelite women athletes have been provided and compared to values reported in men and successful women distance runners. These means, and the effects of definition of ν˙VO2max on the value of the parameter, may be provide useful comparisons for future studies involving ν˙VO2max and women.


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