Metabolic threshold testing on the water

Performance Testing on the Water: Lactate and Ventilatory Thresholds in Canoe Sprint

Why This Article?

The earlier articles in this series dealt with the external side of load: measuring mechanical power in the boat, the power-duration profile built from it, and critical power as the anchor for training prescription. Critical power is a purely mechanical parameter, the asymptote of a hyperbola fitted to maximal efforts of different durations, and it needs neither a blood sample nor a gas exchange measurement (Monod & Scherrer, 1965; Poole et al., 2016). That is also where it stops: a boundary defined in mechanical terms says nothing about the metabolic state an athlete is actually in at that boundary.

This article adds the metabolic side. Lactate and gas exchange were recorded on the water, and every threshold concept the protocol supports was applied to the resulting curves. Methods that need a finer step resolution, much longer steps or a separate series of constant-load trials were left out. What comes back is deliberately not one number but a 37 W spread inside the same athlete on the same test day. Pick a single value out of that range and call it the anaerobic threshold, and the question is whether you measured it or simply chose it.

The Data

The test protocol

Every result reported here comes from on-water testing in the boat. The sequence is shown in Figure 1.

Figure 1. Structure of the test session. Six steps of 240 s with 120 s breaks for blood sampling (red arrows), the dashed step is optional. After 10 min of recovery the ramp test follows, increasing every 60 s until exhaustion.

Why the steps last 240 s. Step duration is a compromise between two demands pulling in opposite directions. Oxygen uptake needs roughly two minutes to settle at a new intensity, but stretch six steps out much further and the top ones can no longer be completed cleanly. Four minutes is therefore the lower methodological limit. The derivation from the time constant, a worked example and the sources are in the appendix. The 120 s break is long enough for a clean capillary blood sample but not for lactate to clear. What the incremental test captures per step is therefore not an isolated steady state but a cumulative metabolic response.

Anthropometry and body composition

Table 1 Anthropometric data and body composition

What blood lactate concentration actually represents

Where lactate is made, and where it is measured. Lactate is formed from pyruvate in the working muscle, and it is formed continuously. Lactate dehydrogenase holds the two in an equilibrium that sits far over on the lactate side, so lactate production climbs in step with glycolytic flux (Heck et al., 2022, p. 38; Poole et al., 2021). Once formed, lactate leaves the fibre through the monocarboxylate transporters. Those carriers are saturable, following Michaelis-Menten kinetics, so their transport rate cannot keep scaling up indefinitely (Heck et al., 2022, p. 243). From the fibre the lactate spreads out into the body’s watery compartments, the lactate distribution space. Blood is only one part of that space, and it is at the same time the delivery route by which heart muscle, liver and working muscle take the lactate back up. A sample from the earlobe therefore never shows production on its own (Beneke, 2003).

Which leads to the one sentence every lactate interpretation rests on: a measured blood lactate concentration is a balance, not a measure of production. It is always what is left over from production, transport and clearance together, so it says nothing directly about how high the energy turnover is (Heck et al., 2022, p. 39). And because it is a concentration, it depends on the volume the lactate is diluted into. Total body water differs between our two participants by roughly eight percentage points of body mass, which means that the same absolute lactate production would show up as a higher measured concentration in Athlete 02. Every concept built around a fixed target concentration ignores that.

What a Physiological Threshold Marks

Three processes need to be kept apart, and everyday language keeps rolling them into one. The distinction decides which methods actually describe the same process and may therefore be pooled into a single value, and Figure 3 already shows how far apart the common concepts land. First, though, the basic curve shape that everything else refers back to.

Figure 2. Schematic blood lactate curve over intensity. The domain boundaries drawn in are conventions placed inside a continuous transition. After Jamnick et al. (2020).

The first rise above resting lactate

Lactate is not something the body only makes under load. At rest the BLC already sits at roughly 0.4 to 1.8 mmol·l^-1, and muscle is not the only tissue producing it (Heck et al., 2022, p. 38). Production and clearance run alongside each other at all times. Under aerobic conditions lactate is not a waste product but a fuel that shuttles between lactate-producing and lactate-consuming tissues, the lactate shuttle (Brooks, 2018).

At low intensities clearance rises faster than production. The measured BLC can therefore dip below the resting value before the steadily rising glycolytic rate pushes it back up. That minimum is not a measurement error, and several of the concepts below are built on it. The intensity at which production first measurably outpaces clearance is where the rise begins: LT₁. Whether the dip shows up at all is another matter: in a large review of ergometer tests the resting value was usually already the lowest, and a value below resting lactate appeared in only about one case in ten (Heck et al., 2022, p. 249 f.). Catching that minimum means setting the opening step low enough, a point we come back to in the results.

The highest steady state

Above LT₁ blood lactate still settles into a steady state, just at a higher level. There is, however, an intensity beyond which production permanently exceeds maximal clearance and the concentration climbs until exhaustion: the maximal lactate steady state (MLSS). It is a genuine physiological state, but by definition it can only be pinned down with several constant-load trials of 20 to 30 min separated by long recovery, never from a single incremental test (Billat et al., 2003; Beneke, 2003). And even this reference standard is not defined uniformly: alongside the standard procedure, Heck et al. (2022, p. 227 f.) list nine further research groups, each with its own MLSS criterion. The gold standard is itself a convention.

What an incremental test delivers instead are surrogate criteria: geometrically defined points on the lactate-power curve, assumed to mark the same state the MLSS marks. Every LT₂ method belongs in that category. Eleven common constructions arriving at clearly different answers is the direct consequence of that indirect definition, and how far apart they sit is shown in Figure 3. Heck et al. (2022, p. 235) conclude that, judged biochemically and in terms of regulation, only the maximal lactate steady state and the crossing point survive as lactate threshold concepts.

The ventilatory response

The ventilatory thresholds do not measure lactate at all. What they pick up is the respiratory answer to the protons (H⁺ ions) that glycolysis releases: buffering those protons through the bicarbonate system sets free extra CO₂, that CO₂ has to be blown off, and it shows up as a disproportionate rise in CO₂ output relative to oxygen uptake (Wasserman et al., 1973; Beaver et al., 1986). They are indirect evidence of the same process, not a second measurement of the same variable. In Figure 3 they are therefore listed as concepts in their own right and not merged with the lactate concepts.

Thresholds are transitions, not sharp boundaries

All three are physiologically transitions, and at every level at once: recruitment shifts gradually towards the more glycolytic fibre types, the fuel mix changes continuously, buffering does not switch on abruptly. Blood lactate, for its part, only ever reflects the gap between production and clearance, so it cannot produce a sharp kink in the first place. The word threshold promises a sharpness the underlying curve does not have (Faude et al., 2009; Jamnick et al., 2020; Poole et al., 2021), as the shape in Figure 2 shows. What the methods really settle is therefore a convention about where inside that transition to draw the line.

Jamnick et al. (2020) count at least 30 published lactate threshold methods and, drawing on the review by Faude et al. (2009), put the spread they produce within one and the same person at around 30%. Jamnick et al. (2018) ran 14 methods on the same measured curve. With four-minute steps, exactly our step duration, the group means ran from 202 W for the log-log method to 291 W for the fixed 4 mmol·l^-1 criterion, against a measured MLSS averaging 265 W. Put plainly: the same curve yields thresholds more than a third apart, and the only thing that changed was which method was applied to it. Nor is the value fixed within a single athlete, because prior training load, fatigue and carbohydrate availability all shift the curve (Impey et al., 2018). Poole et al. (2021) put what a threshold actually tells you into perspective: it marks the intensity from which lactate starts to accumulate in arterial blood, because glycolytic flux rises with load. It is a landmark you can observe, not a cause of fatigue.

For training practice that has one concrete consequence: two athletes handed the same percentage prescription can end up in different physiological states, and a domain boundary is better treated as a band a few watts wide than as a line. Just how far the methods can spread is shown in Figure 3.

Figure 3. Distribution of eleven threshold methods over relative intensity, 42 tests in 21 trained cyclists. The spread of any one method regularly swallows the medians of its neighbours. Figure by Jem Arnold, threshold methods after Jamnick et al. (2020).

Where critical power sits relative to the lactate thresholds

Critical power is a fourth transition, defined differently again: the asymptote of the power-duration relationship (Figure 4). In practice CP, MLSS and LT₂ are often treated as interchangeable. As an approximation that holds, as a definition it does not. Critical power as a rule sits above the MLSS, on average by about 7%, with individual values between 1 and 16% (Jones et al., 2019), and 278 against 239 W in Dekerle et al. (2003). Jamnick et al. (2020) regard critical power as the best-supported method for this domain boundary and place the 30-min MLSS roughly 4% below it. Poole et al. (2021) keep the two apart conceptually: the lactate threshold marks the onset of arterial lactate accumulation, critical power the ceiling for a sustained non-oxidative contribution to energy supply. How little a high correlation says about actual agreement is shown by Lillo-Beviá et al. (2022): between functional threshold power from a 20-min test and the measured MLSS, r > 0.90, and the systematic error was still 12 ± 7 W.

Figure 4. Power-duration relationship with the intensity domains. Below critical power the effort can be held in a steady state, above it the finite work capacity W' is spent down. The two domain boundaries are the same transitions this article determines via lactate: the shift from moderate to heavy corresponds to the first, the shift from heavy to severe to the second lactate threshold.

That is the case for reporting a consensus here rather than a single number. Methods that carry the same label do not necessarily capture the same process, and those that do are tied to it with varying strength. An unweighted mean across all of them would be a number without a defined physiological referent. The sections that follow build the value up the other way round: first the model fitted to the curve, then the methods applied to it, and finally their weighted combination into one value each for LT₁ and LT₂.

Modelling the Lactate-Power Curve

Almost every threshold concept works not on the measured points themselves but on a continuous function fitted through them, because the constructions call for slopes, curvatures and secants that six discrete points simply do not have. The choice of model function is therefore a methodological decision that helps determine the threshold value, and in practice it often goes unreported. Two models are run in parallel here.

The third-order polynomial

BLC(P) = a₃·P³ + a₂·P² + a₁·P + a₀

A cubic polynomial captures the flat start, the inflection point and the steep rise in one smooth function, and it is the established standard model (Heck et al., 2022; Roecker & Dickhuth, 2001). It is tied down at the lower end by entering the measured resting lactate as a data point at 0 W. With four free parameters, a coefficient of determination close to 1.000 is no proof of quality.

The exponential model

BLC(P) = c₁ + c₂ · e^c₃·P

Criteria built on a defined slope or curvature need a curve that rises strictly monotonically and stays convex, and a polynomial can break that locally. Those criteria use the exponential model instead, whose functional form can be derived from the differential equation of lactate kinetics (Hille & Geiger, 1993, cited after Heck et al., 2022, p. 224).

The Threshold Methods Applied 

For the first lactate threshold the protocol supports four methods: one that reads the shape of the curve in a double-logarithmic plot, one that works off oxygen uptake, and two that build on an individually measured baseline.

For the second there are eleven methods, in three groups: secant and tangent constructions that go purely on the shape of the curve, methods that add a fixed increment to an individually measured starting point, and one target concentration that is the same for everybody. That order is also the basis of the weighting, because it reflects how much of a method comes out of the athlete’s own curve. Construction, criticism and base weights are given in the appendix in Table A1 and A2, and where each one sits in the wider field is shown in Figure 3.

Every method on the athlete's own curve

The next two figures pull together everything the article has so far treated separately: the measured lactate values, both model functions and every threshold method as a vertical line on one and the same curve. The two weighted consensus values are drawn bold, the ones thrown out at the plausibility or consistency step are faint. How wide the resulting band is can be read straight off both images.

Figure 5. Blood lactate curve over power, Athlete 01. Vertical lines are the individual concepts, bold the weighted consensus values, faint the rejected ones. The flat branch of the curve rests on a single measured point, because the lowest step sat almost exactly at his resting value.

Figure 6. The same for Athlete 02. Her elevated resting lactate lifts the whole curve upwards.

Three things stand out in both figures, and they carry the rest of this article. First, the LT₂ methods cluster on the steep branch and still spread across a range wider than any sensible training zone. Second, the LT₁ methods fan out further on the flat branch, because there are fewer measured points there and the fitted curve has correspondingly more freedom. Third, the two curves sit at different heights even though both athletes completed the same protocol. What these figures show is not a point but a band, and that is exactly why no single value is reported below.

From a Field of Concepts to a Consensus Value

The consensus threshold reported here is not an arithmetic mean. It is built in four steps:

1. Availability. A concept that returns no result counts as failed and is not replaced by a stand-in value.
2. Plausibility corridor. A candidate has to lie between 35 and 75% (LT₁) or 60 and 100% (LT₂) of the individual reference power, expressed relatively, because a fixed watt window would be far stricter on a weaker athlete than on a stronger one.
3. Consistency check. Candidates that sit far from the median drop out. The tolerance is either 2.5 times the robust median absolute deviation or 8% of the median, whichever is larger.
4. Weighting. Base weight (column "weight" in Table A1 and A2) multiplied by a quality factor built from model fit and data support at exactly the power where the threshold falls. A concept can therefore lose weight on a thinly supported curve without being downgraded in principle.

The reference power itself is not taken from the point of exhaustion in the ramp but calculated from oxygen uptake. The appendix sets out exactly how.

Results of the Lactate Analysis

Table 2 is the results table of this article. It lists every calculated threshold for both athletes in one shared list, ordered by power, which makes it visible how the lactate and ventilatory thresholds actually interleave. The two weighted consensus values are shaded, the ventilatory thresholds blue.

Table 2 All calculated threshold concepts from the on-water test, ascending by power

*Rejected at the plausibility step for falling below 35% of the reference power. The angle bisector after Bunc produced no interpretable solution. Red shading marks the lactate consensus values, blue the kinetics-corrected ventilatory thresholds and grey-blue the uncorrected ones.

The consensus values come out at 120 ± 14 W for LT₁ (CV 11.5%, all four concepts) and 164 ± 11 W for LT₂ (CV 6.5%, ten of eleven) in Athlete 01, and at 73 ± 2 W (CV 2.2%, three of four) and 106 ± 8 W (CV 7.9%, ten of eleven) in Athlete 02. The aerobic-anaerobic transition therefore spans 44 W in one athlete and 33 W in the other. The resulting corridors run from 78 to 166 W and 133 to 222 W in Athlete 01, and from 52 to 112 W and 90 to 150 W in Athlete 02.

The opening step was set too high

The lowest step was set too high, because the entire step scheme had been derived from a critical power that turned out to be badly overestimated.

What we found. Athlete 01 paddled steps from 97 to 220 W against an LT₁ of 120 W, Athlete 02 from 56 to 150 W against an LT₁ of 73 W. In both cases only one of the six steps fell below the first lactate threshold, so no dip in blood lactate appeared. In Athlete 01 the lowest step sits almost exactly at his resting level, which leaves the flat branch of the curve resting on a single measured point. In Athlete 02 the resting value itself is unusually high at 2.74 mmol·l^-1, and the lowest step lands right on it. Both can be read straight off Figure 5 and 6. An incremental test without a dip is not unusual in itself (Heck et al., 2022, p. 249 f.). This is therefore no gross protocol error, but it does mean that the five concepts needing a solid baseline are working from thinner data here. The script accordingly halves the weights of the affected concepts, and in Athlete 02 the lactate minimum drops out of the plausibility corridor altogether.

Putting the lactate levels in context. An aerobic threshold at 3.09 mmol·l^-1, as in Athlete 02, is unusually high. Athlete 01 sits at 1.94 mmol·l^-1 and therefore in the expected range, and an identical session on the kayak ergometer puts her at 2.05 mmol·l^-1. The likeliest cause is her elevated baseline: resting lactate lifts the entire curve, which hits the concentration-based criteria hardest (Heck et al., 2022, p. 252).

What about the 3.74 and 4.52 mmol·l^-1 at LT₂? Two reference points bracket the expected range, and they pull in opposite directions. Upwards pulls the comparatively small muscle mass a kayak stroke recruits. Beneke (2003) describes an inverse relationship between MLSS lactate and the mass of the primarily involved musculature, and across 856 participants mean MLSS values run, depending on the exercise mode, from 2.6 mmol·l^-1 on a rowing ergometer to 7.6 mmol·l^-1 on an arm crank ergometer (Heck et al., 2022, p. 228). Downwards pulls the only kayak-specific on-water measurement there is, an MLSS of 3.06 ± 0.68 mmol·l^-1 in eleven elite kayakers (Pilotto et al., 2019). Our values fall between the two. That a 240 s step is shorter than a constant-load trial and pushes the curve further up fits the picture, but with two participants it cannot be separated out from other influences. Stated conservatively, the point is that numbers like these cannot be read in absolute terms without knowing how much muscle was working, which leaves a target concentration identical for everybody poorly justified in canoe sprint.

The link to critical power. The critical power tests came first, and the step scheme was derived from them afterwards. The load prescriptions came out of the first critical power estimate of 209 W and 144 W, which rested entirely on maximal efforts between 1 s and 6 min. An asymptote fitted to nothing but short efforts comes out systematically too high, because the flat, long-duration branch of the power-duration curve carries no measured points at all. In sprint-oriented athletes such as canoe sprinters that is especially likely, because their short efforts are very strong relative to their endurance capacity. The two values accordingly sit at 94% and 98% of power at V̇O_2max, and therefore 27% and 36% above the second lactate threshold determined here. A sustainable limit above the second lactate threshold makes no physiological sense, and because the whole step scheme hung on that number, it started out systematically too high. The error travelled from the mechanical side of performance testing into the metabolic side, not the other way round. The next two articles follow this up in detail.

What this changes in the protocol. The LT₁ consensus for Athlete 02 should be read as a lower bound. Future tests will therefore add a markedly lower opening step, so that the flat branch of the curve carries measured points again.

The Ventilatory Thresholds

The basic principle is the same as for the lactate thresholds: again the task is to locate a breakpoint in a curve. Two differences matter. First, what is analysed is a continuously recorded signal from the ramp test rather than one measured value per step. Second, several criteria read the same physiological event off different signals. The ventilation side supplies the ventilatory equivalent V̇E/V̇O₂, the cumulative excess CO₂ and ventilation V̇E itself, the gas exchange side the ratio of V̇CO₂ to V̇O₂ and the end-tidal CO₂ partial pressure PetCO₂. Two criteria drawn from the same signal family are not two independent pieces of evidence, and the consensus weighting takes that into account. Six criteria are evaluated, three for VT₁ and three for VT₂, with a seventh shown for illustration only. How each is constructed and weighted is given in the appendix in Table A3.

Correcting the ramp for oxygen uptake kinetics

Our ramp test steps up every 60 s, at a mean rate of 22.6 and 11.0 W·min^-1 respectively. Oxygen uptake never reaches a steady state during a ramp. It trails the load by a constant time offset, and that offset is the athlete’s individual time constant τ (Whipp & Wasserman, 1972). A gas exchange event is therefore read off at too high a power and has to be corrected downwards by ΔP = (S · τ) / 60. Derivation, formula and a worked example are in the appendix.

Table 3 Effect of the kinetics correction

In Athlete 01 the correction at VT₁ comes to almost ten percent. Leaving it out would put his domain boundary nearly 14 W too high. The difference between the two participants follows directly from time constant and ramp rate, and is therefore itself an individual finding. Figure 7 and 8 show the breakpoints in every signal analysed.

Figure 7. Ventilatory analysis of the ramp test, Athlete 01. For each signal, the breakpoint together with the uncorrected and the kinetics-corrected threshold as separate lines.

Figure 8. The same for Athlete 02, with a markedly smaller correction.

Ventilatory and Lactate Thresholds Compared

Table 4 Ratio of the kinetics-corrected ventilatory to the lactate thresholds

In both of our measurements the ventilatory thresholds sit systematically above the corresponding lactate thresholds. At the first threshold the ratio is identical in both athletes at 1.10, at the second it is not. The literature points the same way: in Dekerle et al. (2003) the second ventilatory threshold sat at 286 W, clearly above the measured MLSS of 239 W. Jamnick et al. (2020) therefore advise against using the respiratory compensation point as a stand-in for MLSS or critical power unless the ramp is very long, and their reasoning is exactly the problem the previous section deals with: a wattage read off a ramp does not correspond to the same oxygen uptake as that wattage under constant load. How tightly the ventilatory response and lactate accumulation are coupled also depends on buffering capacity and respiratory control (Cerezuela-Espejo et al., 2018). For this article the practical consequence is that the two families of methods are reported separately rather than pooled.

Calculating a Threshold Instead of Measuring It

Every threshold shown so far was measured. There is another route. The crossing-point model describes the lactate production rate and the maximal oxidative elimination rate as two functions of power (Mader & Heck, 1986; Mader, 2003), and both thresholds fall out of those same two curves. LT₂ is the intersection itself, the point at which production and maximal elimination are equal. Above it, lactate keeps climbing under constant load, which is by definition the MLSS. LT₁, in this model, is the point of maximal pyruvate deficit: below it, glycolysis delivers less pyruvate than the oxidative machinery could use, and the shortfall is covered by fat oxidation. Where that shortfall is largest in absolute terms, fat turnover is highest too, and that is the FAT_max point, which can also be measured spirometrically. The model therefore explains the same trough that the incremental test sees as the lactate minimum. Both are shown across the full power axis in Figure 9 and 10.

Every input is measured: the maximal lactate production rate from a 15 s sprint, V̇O_2max and the slope of oxygen uptake from the on-water test, plus body composition. The lactate distribution volume was derived individually from measured total body water, using the factor of about 0.735 that Mader and Heck (1986) derived on energetic grounds. A few canoe-specific adjustments were made to the original model. They are not spelled out here but held back for the article series devoted to the model.

The next two figures show what the model looks like for our two athletes. Plotted are the lactate production rate, the maximal oxidative elimination rate and the oxidative reserve, that is, the share of energy demand glycolysis does not have to cover. Above the point where the two rates cross, lactate starts to accumulate. The two marked points are set against the measured thresholds in Table 5 below.

The inputs differ considerably between the two participants: the maximal lactate production rate from the 15 s sprint is 0.4479 against 0.2068 mmol·l^-1·s^-1, the lactate distribution space derived from TBW 40.4 against 31.1 l, and the muscle mass taken to be active, here 60% of the SMM from Table 1, 21.1 against 14.9 kg. Substrate rates come out of the same model: at the FAT_max point 48.8 against 46.2 g·h^-1 of fat, and at the calculated MLSS 284 against 230 g·h^-1 of carbohydrate.

Figure 9. Crossing-point model for Athlete 01. The blue line is the measured V̇O₂-power relationship with the step values, the red dashed curve the lactate production rate, the teal dashed one the maximal oxidative elimination rate and the purple one the oxidative reserve. Where the two rates cross is the calculated MLSS at 171 W, and the maximum of the reserve marks FAT_max at 107 W.

Figure 10. The same for Athlete 02, with FAT_max at 81 W and a calculated MLSS of 125 W. Her markedly lower maximal lactate production rate makes the two rate curves cross earlier and at a shallower angle.

Table 5 Crossing-point model compared with the measured thresholds

The comparison is made not against the weighted consensus values but against the two concepts the model is calibrated on: log-log for LT₁ and D_max,mod for LT₂. In Jamnick et al. (2018), D_max,mod from the 4 min test came closest of all tested methods to the measured MLSS, and log-log serves there as the reference for the first threshold.

In Athlete 01 the calculated MLSS lands within 2.6% of the measured second lactate threshold. In Athlete 02 it sits about ten percent above it, and FAT_max is off in the same direction. Whether that is down to the model parameters or to a distortion in her measured thresholds cannot be settled with two participants. A full account of the model is reserved for a series of its own.

Every Value at a Glance

Table 6 Summary of all values from the on-water test

Percentages refer to each athlete's individual power at V̇O_2max.

One observation is worth pulling out, because it points the same way in both data sets. In Athlete 01 the mean of VT₁ and VT₂ is 164.5 W and therefore sits right on his LT₂ consensus of 164 W, with the calculated MLSS of 171 W close by. In Athlete 02 the same calculation gives 98.5 W against an LT₂ of 106 W. That the second lactate threshold falls roughly between the two ventilatory thresholds fits the ordering visible in Table 4. With two participants and two measurements, though, this is not a finding but an observation that could just as easily be coincidence. It would need checking in a larger sample before anyone turned it into a rule of thumb.

Limitations

• Sample size. Two participants, one incremental and one ramp test each, no repeat measurement. Nothing can be said about day-to-day reliability.
• Opening step. The LT₁ consensus for Athlete 02 should be read as a lower bound, and five of the fifteen concepts rest on a stretch of the curve that was only partly captured.
• Step duration. 240 s is the methodological lower limit, and longer steps would have been hard to sustain in a six-step protocol.
• Absolute lactate levels. They cannot be read in absolute terms without knowing how much muscle was involved, and they do not carry across sports.
• Normalised shape criteria. Four concepts only reach a power axis through a normalisation convention, which is why they are weighted low.
• Base weights. Set on expert judgement, with a subjective element, and replaceable in the analysis script.
• No MLSS reference. Every LT₂ value here is a surrogate for the MLSS, and none of them was validated against that criterion.

What Comes Next

Every value in this article needs blood samples, a gas exchange measurement or a metabolic model. In day-to-day training none of that is usually to hand. The power measured in the boat is.

The next article therefore asks what kind of profile can be built from power data alone: critical power, the anaerobic work capacity W' and the fatigue term of the power-duration relationship, including the question of why the 209 and 144 W fitted from efforts between 1 s and 6 min do not hold up. The final article brings both routes together into a canoe-specific intensity scale.

Appendix

What follows is the material that did not fit into the main text: why the steps last as long as they do, how the individual reference power is derived, how the ramp is corrected for oxygen uptake kinetics, and, at the end, a reference section covering every threshold method used, with its construction, weighting and criticism.

Why the steps last 240 s

Kinetics argues for long steps. A measured value can only be read as a steady state if the system has actually reached one. Oxygen uptake approaches the demand of a new load exponentially, and the time constant τ describes how quickly: after one time constant roughly 63% of the step is covered, after four times that roughly 98% (Whipp & Wasserman, 1972; Whipp et al., 1982). τ is individual, and an athlete with a small τ is back in equilibrium sooner after each increase.

Fatigue argues against long steps. Six steps of 240 s already mean 24 min of work, and the 5 to 10 min per step that pure lactate diagnostics calls for (Mader et al., 1976, cited after Heck et al., 2022, p. 211) would have made the upper steps impossible to complete cleanly. Four minutes is therefore the lower methodological limit and at the same time the workable compromise. That longer steps push lactate values upwards, and with them every concentration-based criterion, is well documented (Heck et al., 2022, p. 366 f.; Beneke, 2003).

The individual reference power

All percentages and the plausibility corridor refer to the power at V̇O_2max. The point of exhaustion in the ramp depends on day-to-day form and motivation, which makes it unsuitable as a reference. It is calculated instead from the weighted linear relationship between steady-state oxygen uptake and step power.

Correcting the ramp for oxygen uptake kinetics

What our “ramp” really was. In the literature a ramp test means a load that rises almost second by second. On the water that is not feasible, because power in the boat cannot be dictated by an ergometer brake. The athlete has to hit it herself. Our protocol therefore steps up every 60 s and is, strictly speaking, a fast incremental test. That does not make it unusable, as long as the calculations work with the mean ramp rate: 22.6 W·min^-1 for Athlete 01 and 11.0 W·min^-1 for Athlete 02. Comparisons with the 20 to 30 W·min^-1 common in cycling should be drawn cautiously, because in kayaking the same absolute rate is a considerably larger relative jump in intensity. On top of that, the test was designed first and foremost to elicit the highest possible V̇O_2max. The ventilatory thresholds come out of the same data set, but that is not what it was built for.

Why a correction is needed. A continuously rising load drives energy demand up faster than oxygen uptake can follow. In a first-order system, meaning one whose response to a step change is exponential and captured by a single time constant, the metabolic response settles into trailing the load by a constant time offset, and that offset is exactly τ (Whipp & Wasserman, 1972; Whipp et al., 1982). A gas exchange event at ramp time t was therefore set off by an earlier, lower power, and the threshold is read off at too high a wattage:

ΔP = (S · MRT) / 60    [S in W·min^-1, MRT in s]

Both the correction itself and the permissible kinetics ratio are capped. The breath-by-breath data are deliberately not averaged beforehand, because averaging would systematically distort the estimated time constant (Lamarra et al., 1987).

The individual threshold methods

The three tables that follow are meant as a reference. For each method they give the criterion in the curve or in the ramp signal, the base weight assigned to it and an assessment of where it stands.

Table A1 Concepts for determining the first lactate threshold

Classification and criticism after Heck et al. (2022, ch. 9).

Table A2 Concepts for determining the second lactate threshold

Classification and criticism after Heck et al. (2022, ch. 9).

Table A3 Criteria for determining the ventilatory thresholds

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A note on the citations. For a few of the threshold concepts calculated here, the primary paper is not held in the project bibliography. Those concepts are named by their common designation and cited through the summarising account in Heck et al. (2022, ch. 9). The primary sources listed there are carried over into the reference list.