A Comparison of Methodological Approaches to Measuring Cycling Mechanical Efficiency

The study included 14 subjects (12 males and 2 females) from different sport backgrounds, and they were sport science students or members of local sport clubs. Practically, all of them used cycling as their training mode in some part of the year. Six of them could be classified as cyclists (i.e., active cyclist or triathlete). The intensity of 150 W was chosen to be the power output at which the different efficiency indices were compared. This was thought to be intensity high enough so that the internal energy expenditure does not interfere with the outcome. To make sure that this load of 150 W was completed mostly aerobically, a candidate was accepted to the study only if the following criteria were fulfilled: respiratory exchange ratio (RER) at 150 W was not more than 1.00 and the aerobic threshold was at least 150 W, determined by Finnish standards based on the first clear increase of lactate level from baseline [34]. By the terminology of Seiler [35], these criteria ensure that 150 W was in a light intensity training zone, making it a relatively easy load for each participant. Two educated testers defined independently aerobic thresholds for the participants. Of the 17 tested subjects, 14 participants (12 men and 2 women) fulfilled the inclusion criteria. For them, the mean (± SD) increase in lactate at 150 W load from its lowest value was 0.38 ± 0.29 mmol/l. Their further information is given in Table 2.

Each subject was taken into a test room separately, and the temperature (20–22 °C) and humidity (25–30%) were quite stable during and between each test. Subjects were asked to refrain from strenuous exercise 2 days prior to a test. First, the body height and weight were measured. The weight was measured with cycling clothes without shoes and, in addition, 300 g was subtracted from this as weight for the clothes and to anticipate the weight reduction due to perspiration.

The ergometer test began with 10-min resting gas exchange measurement (MasterScreen CPX, CareFusion, San Diego, USA) by sitting still on the cycling ergometer (Monark Ergomedic 839E), which is a customary way to measure E_rest in efficiency literature [7, 32]. After this, to measure E_0,m, the participant cycled 5 min against zero load. The initial load for the incremental test was chosen between 90 and 150 W depending on the fitness level of the participant, but in such a way that each subject performed the demanded 150 W. The load was increased by 30 W (men) or 25 W (women) at every 5 min. The gas exchange was measured by breath-by-breath method and analyzed with Lab Manager V5.32.0 (Laboratory Systems Group Pty. Ltd., Melbourne, Australia) with the average of last minute, except with E_rest two last minutes, of each load was taken into analyses. Lactate was taken from the fingertip immediately after each load, and it was analyzed by Biosen C_line Sport 2 (EKF Diagnostic lactate/glucose, Cardiff, UK). The test was progressed in this fashion until the lactate was increased by 1 mmol/l from the initial level, after which, to measure VO_2max, the load was increased every 2 min until voluntary exhaustion or until cadence reduced irrevocably (> 15 s) below 60 rpm. During these final loads, the participants were strongly encouraged. Participants were free to choose their favored cadence (the realized range was 70–95 rpm), but it was instructed to keep constant during the 5-min loads, as cadence affects the efficiency [28]. A metronome was offered for maintaining a constant cadence. Moreover, the test conductors kept watching over the cadence inspecting visually the cadence meter. Further, during the 5-min loads, the participants were instructed to stay seated and keep their hand on the same spot on the handlebar, as the position on the bike may affect efficiency [8]. The cadence, shoes, and riding position were freely chosen by the participants, as we were interested in subjects’ efficiency indices as they appear in their regular cycling practices.

Aerobic energy expenditure was calculated by applying the equation from [34]:

Furthermore, lactate measurements were utilized to estimate the anaerobic energy expenditure during the 5-min loads by applying the formula from [36]:

Here, ΔLa is the difference of the lactate concentrations between the observed and the previous load. The total energy expenditure was the summation of these two components: E_tot = E_tot,Aer + E_tot,Anaer. For each subject, an individual regression line E_tot = aW_ext + b was calculated by using observation points from the first load up to the aerobic threshold. This led to 3–5 observation points ranged between 90 and 210 W to be used for the regression line, which is quite the typical amount of points in literature [37‐39].

It is quite customary to verbally argue how the role of internal energy expenditure E₀ comes negligible when external work W_ext increases arbitrarily large [8]. Next, we show how this can be calculated strictly and how the theoretical consequence is that every efficiency indices approach to DE. In other words, it is shown mathematically that regardless of their definitions and starting points, every considered mechanical efficiency indices unite as external work rate increases.

The following is the standing assumption.

Assumption 1 Assume that W_ext-E_tot function is linear, i.e., that E_tot = aW_ext + b, for some a, b ∈ R₊.

By definition, DE is an inverse of a slope of W_ext-E_tot regression line, which is linear by Assumption 1. That is \( \mathrm{DE}=\frac{1}{a} \), where E_tot = aW_ext + b. Furthermore, by definition \( \mathrm{GE}=\frac{W_{\mathrm{ext}}}{E_{\mathrm{tot}}} \), so that when applying Assumption 1, one can derive

Here, the last expression approaches to \( \frac{1}{a}=\mathrm{DE} \) when W_ext approaches to infinity, as \( \frac{b}{W_{\mathrm{ext}}} \) approaches to zero. This gives and proves that GE approaches to DE as W_ext approaches to infinity. Using similar deduction, it can also be concluded that NE and WE approach to DE as W_ext approaches to infinity.

The following Table 3 contains the measured efficiency index values. At 150 W, the measured E_tot,Anaer was 0.25 ± 0.18 kJ/min, while E_tot,Aer was 44.8 ± 1.8 kJ/min.

The efficiency indices can be divided into three groups by Spearman’s rank correlation (Fig. 1): I (GE, NE, T), II (DE, WE_e) and III (WE_m). Grouping was done by selecting two efficiencies into the same group, if their rank correlation exceeded 0.66 (limit for p < 0.01 significance). None of the six indicators of efficiency belonged to a more than one group, so that the groups did not overlap with each other. In other words, correlations within a group are strongly significant (group I, p ranges between 1×10⁻⁶ – 0.0008; group II, p = 10⁻¹³), while there are no significant correlations between groups (see Fig. 1).

In the present study, the GE and DE were not very close to each other: the shortest distance between GE and DE were 3.4± 1.7% points, the range being 0.7–7.2% points. It should be mentioned that 10/14 participants had maximal GE value at a higher intensity level than 150 W. Furthermore, for each subject, a regression line E_tot = aW_ext + b can be constructed. This can be substituted into the ratio \( \mathrm{GE}=\frac{W_{\mathrm{ext}}}{E_{\mathrm{tot}}} \) in order to estimate in which theoretical intensities GE would be near DE, if one could pedal infinitely high intensities aerobically. In this study, GE would be theoretically in a 0.5% point environment of DE at intensities of 1350 ± 750 W.

Energy expenditures E_0,m, E_0,e, and E_rest are plotted in Fig. 2. Measured zero load energy expenditure E_0,m was on average 142% greater than extrapolated E_0,e, and they differed from each other significantly (p = 4 × 10⁻⁹). Furthermore, E_rest did not differ significantly from E_0,e (p = 0.60). E_0,e and E_0,m correlated only weakly (r = 0.45, p = 0.11). Lastly, to estimate a reliability and accuracy of DE and WE_e, the length of subjects’ 95% confidence interval (CI) for DE and E_0,e were calculated and they were 6.9 ± 5.2% and 47± 32 kJ/min, respectively, while the mean values for DE and E_0,e were 22.6% and 6.9 kJ/min, respectively.

In general, group I can be interpreted to illustrate the mechanical efficiency of a whole body in a cycling work. GE and T belong to the same group, understandably, as the former one is a refined version of the latter one. The fact that NE belongs to this group indicates that there are no great differences nor adaptations in resting energy expenditure between individuals. On the other hand, in theory, groups II and III try to grab the efficiency of an isolated musculoskeletal system in a cycling work by subtracting, in a one form or another, zero load energy expenditure from the examination. Hence, it seems that E₀ plays a role, and a bigger one than E_rest, when trying to explain why efficiency indices fall into different groups. The importance of E₀ is well in line with a previous study [41], in which it was argued that differences in zero load cycling between individuals explain some of the observed variation in GE between individuals. Another possible reason for the differences between the groups lies in the difficulty and uncertainty of determining WE_e and DE from W_ext-E_tot regression line.

DE and WE_e belong to the same group as they are both calculated from the same W_ext-E_tot regression line. Furthermore, at each observation point, WE_e can be seen as an inverse of a slope of a line through that observation point and E_0,e, so that WE_e can be interpreted, more or less, as a local delta efficiency. If all the observation points would fall on the same straight line, WE_e and DE would coincide.

One can find indirect support from literature to this grouping. When studying correlations between different physiological factors to indicators of mechanical efficiency, it has been demonstrated that physiological factors affect differently to indicators from different groups. For example, a measure from group I has been reported to be significantly affected while the measure from group II has not, e.g., by the temperature of the skin [32], VO_2max [10], and body weight [26]. In addition, group I has been reported to be affected while group III has not, e.g., by training [41]. Thus, the literature shows that, based on correlation to physiological factors, there seem to be some groupings for mechanical efficiency indices supporting indirectly our grouping.

It has been observed that the repeatability of DE is significantly weaker than GE [10], but this phenomenon has eluded explanations. Here, we argue that this phenomenon can be explained by the weak accuracy of W_ext-E_tot regression line, which is caused mainly by using too few observation points, typically 3 [37, 38], 4 [39], or at most 6 [32, 42]. In the present study, we replicated the usual way to calculate efficiency indices, which was the reason to include only 3–5 points to our W_ext-E_tot regression line. As the value (95% CI) for DE was 22.6% (19.2–26.1%) and for E_0,e 6.9 kJ/min (− 16.6–30.4 kJ/min), it is plainly clear that more observation points would be required for a reliable W_ext-E_tot regression line, and hence, reliable DE and E_0,e estimates. Noteworthy, the coefficient of determination, R², is unable to distinguish this problem, as R² value for W_ext-E_tot regression line in our study was 0.996± 0.004. It means that R² is far from a sufficient test for explaining the accuracy of W_ext-E_tot regression line when there are too few observation points; after all, R² with two observation points is always 1.00, although this kind of estimation contains huge potential error. Another factor, besides the number of observation points, affecting reliability of W_ext-E_tot regression line is cadence. It affects energy expenditure, and applying linear regression from [8] we can, purely theoretically, estimate that using four observation points DE can change as much as 1.1 %-points by only altering cadence from 80 by ±1 rpm. As keeping cadence closer than ± 1 rpm to a target cadence during the test is very challenging, it becomes clear that there is quite large built-in imprecision potential in DE measurements. In contrast, keeping cadence 80 ± 1 rpm affects theoretically GE only by 0.1% points.

A clear proposal to improve the accuracy of W_ext-E_tot regression line would be to use more data points. For example, in the study of Medbø et al. [43], it has been suggested to use at least 10 observation points when estimating W_ext-E_tot regression line. Another way to improve the estimation would be to include only aerobic intensities. For example, some efficiency studies have included 270 W loads for women [42] and 300 W loads for men [32] when calculating DE. However, without measuring blood lactates, the amount of anaerobic energy expenditure cannot accurately be estimated for these intensities. Not to mention about the potential impact of slow VO₂ component, which can be present already when the intensity exceeds 50% VO_2max [18, 19] skewing the linearity of W_ext-E_tot relation. Last proposal to get more precise DE would be to monitor accurately the used cadence.

It should be clear in mind that the accuracy of W_ext-E_tot regression line has more profound meaning than only that of determining DE and E_0,e as it is also used, e.g., to extrapolate theoretical energy (or oxygen) consumption at high-intensity works [43, 44].

It has been widely recognized how E_0,m is much greater than E_0,e, the difference ranging from 20 to 350% [16, 17], being 140% in the present study. This means that they both cannot accurately describe E₀ which they supposedly illustrate. Above, we have argued how the accuracy of E_0,e is quite weak based on CI. Another, often ignored, charge against E_0,e is that it does not differ from E_rest (p = 0.60, Fig. 2), with half of the subjects in the present study having smaller E_0,e than E_rest, which sounds abnormal. Similar values can be seen, e.g., in [27]. One explanation might be that E_0,e does not actually illustrate the energy expenditure which it has been thought to illustrate. For example, it has been observed in [15] that internal work is neither constant nor independent from external work. This can be interpreted so that, although W_ext-E_tot connection would be linear, the energy expenditure of a zero load is not found at the intersection with y-axis, as we do not know how the internal work is related to the total energy expenditure at different loads. One could also try to explain the possibility of E_rest to be truly higher than E₀, as starting an exercise against zero load could in principal increase the work load of the heart and legs but at the same time reduce even more the work load of other parts of the body, e.g., the digestive system and internal organs, but this is highly speculative.

On the other hand, also E_0,m has many problems. Firstly, there are all the theoretical explanations, shown in the “Background” section, how E_0,e offers better approximation for E₀ than E_{0, m}. Moreover, in literature, E_0,m (and thus WE_m) has been discarded because of its too high values [7, 8]. An isolated muscle has theoretically been discussed to have mechanical efficiency at most 30% [12, 13]. In the present study, WE_m was 32.0± 2.9% (range 28.0–38.3%) and hence, too high for a mechanical efficiency of an isolated musculoskeletal system in a cycling work where the usage of elastic energy is minimal [45]. All in all, E_0,e seems too small to be true energy expenditure for zero load and E_0,m too large, and hence, both of them (and thus WE_e and WE_m) seem to contain unanswered methodological problems. More specifically, as was reported above, WE_e and DE are quite parallel measurements for a mechanical efficiency, and as such, if the problems related to WE_e cannot be solved, it casts doubts also on DE, even though its theoretical base would otherwise be firm enough.

To bring the discussion to a conclusion, we have now seen how methodologically DE, WE_e, and WE_m all contain problems casting some serious doubts on sensibility of baseline subtractions. The previous doubts against NE, WE, and DE are essentially theoretical considerations based on the facts that energy expenditure cannot be divided into separated components and that the baseline subtractions are not invariant with different work intensities [8, 12, 13, 25]. The doubts of the present study are based on the methodological outcomes: essentially that WE_m is too large, that E_0,e is too similar to E_rest, and that 95% CI of DE and E_0,e are too wide. Based on these findings, NE would be the only methodologically sound mechanical efficiency index with a baseline subtraction. However, both NE and GE belong to the same group I. Thus, one can argue that GE carries basically the same information than NE, but without an additional inconvenience and possible source of error by having to measure E_rest. In this way, the present study suggests methodologically that also the need for NE is questionable.

Although the outcome of our study is quite distinctive with three separated groups for mechanical efficiency indices, some weaknesses could affect this conclusion. Letting each participant choose their own natural cadence could have influenced the outcome, as cadence is known to affect the efficiency indices [8]. Although we acknowledged this, the same cadence was not chosen to impose for everyone, as we were interested in individual differences and dividing individuals into different classes based on their natural cycling patterns. We felt that imposing an unnatural cadence to subjects could interfere with that aim. It should be also mentioned that we did not record cadence from pedal revolution to another, which means there might be a small load to load sway in cadence for each participant. This deviation then mostly affects W_ext-E_tot regression line, and hence, values of DE and WE_e.

In this study, both male and female subjects were included, as our main interest was to compare different indices of mechanical efficiency for subjects of broad backgrounds. We acknowledge that there is a mild gender difference in GE, E_0,m, and E_0,e, but that they can be explained mostly by the difference in lean leg volume [17]. As interindividual variation in GE and E₀ can in general be explained mostly by body mass and especially by leg mass [11, 14, 26], we felt that gender question was not too restricting in our approach: allowing also female subjects to take part, we felt that we mainly expanded our study to include also lighter body masses. It should be mentioned that the results are unaltered when analyzed with men only (data not shown).