Validating the PaddlePulse On the Water

Does the power measured by PaddlePulse hold up?
A metabolic validation on the water

Mechanical power in watts describes what an athlete actually produces. Heart rate and blood lactate describe what that production costs internally. In sprint canoe there is still no accepted gold standard for the power produced on the water. Training is steered by boat speed, heart rate, stroke rate or blood lactate instead, and each of these has its own systematic weakness. Boat speed depends heavily on wind and current, so the same speed can mean very different mechanical demands. Heart rate responds with a delay, drifts during long efforts and is influenced by temperature, hydration or caffeine (Achten & Jeukendrup, 2003).

PaddlePulse is a sensor mounted on the hull that derives propulsive power from the acceleration and deceleration phases of the kayak. That raises the question whether the numbers it reports describe a physically real quantity. Since no absolute gold standard exists on the water, the question cannot be settled by comparing the sensor with another system such as a paddle based device. The validation therefore needs a reference that is completely independent of the sensor. That role is taken by the athlete's own metabolism.

Why oxygen uptake works as a reference

Below the intensity at which oxygen uptake reaches its maximum, the energy demand rises in proportion to the mechanical power produced. Every additional watt requires a proportionally higher oxygen turnover. This property is exactly what the established metabolic prediction equations for ergometer work are built on (Sietsema et al., 2020; Ettema & Lorås, 2009a). The regularity holds only within a clearly bounded intensity range. Above the anaerobic threshold, meaning above LT₂ or VT₂, a slow component of oxygen uptake can appear, and close to maximal oxygen uptake the relationship flattens out. The linearity test therefore applies primarily to those intensity ranges in which a stable metabolic steady state can be reached.

Within that range a test criterion emerges that needs no second technical device. If the sensor signal is proportional to the work actually performed, then plotting steady state oxygen uptake against the measured power has to produce a straight line. A noisy signal would scatter the points into a cloud, a systematically distorted signal would bend the relationship, and a meaningless signal would show no recognisable pattern at all. What matters is that the oxygen uptake is recorded independently of the sensor. It responds only to the work that is physically done and cannot be influenced by a faulty power signal.

Test setup

Two former competitive athletes who still train at a high level took part, Athlete 01 (male) and Athlete 02 (female).

Table 1 Anthropometry, maximal oxygen uptake and efficiencies

Gross efficiency relates the mechanical power to the total metabolic rate. Net efficiency subtracts the resting metabolic rate first. Both figures span all stages of the water session.

Both athletes completed five separate test sessions.

• Tests 01 to 03: Sprints over 15 s as well as all out efforts over 1, 3 and 6 min. These served the power duration profile only, and we cover the details in a separate article.
• Tests 04 and 05: Step tests in the laboratory and on the water. After a 5 min warm-up came stages of 240 s with 120 s rest, then 10 min of active recovery, and finally a ramp test with 60 s stages to exhaustion.

The stage intensities were derived from Tests 01 to 03. The maximal efforts over different durations form the power duration profile, from which the critical power is estimated. That estimate set the range of the step test.

Table 2 Power duration profile from Tests 01 to 03

Table 3 Prescribed loads of the metabolic tests

Figure 1. Course of the metabolic diagnostics with warm-up, step test and closing ramp test. The red arrows mark the blood lactate sampling points.

The stage duration of 240 s is the core of the design. Only a stage long enough allows the oxygen uptake to reach a plateau, and only that plateau can be assigned unambiguously to a mechanical power. A pure ramp test would save time but never reaches a metabolic steady state, because the oxygen uptake would lag behind the mechanical load throughout. The ramp test therefore sits as a separate block at the end and serves one purpose only, the determination of maximal oxygen uptake (V̇O_2max).

Gas exchange was recorded breath by breath with a portable MetaMax 3B. Heart rate was captured with a Polar H10 chest strap plus a Polar Verity Sense armband as a backup. Blood was sampled minimally invasively from the earlobe after hyperaemisation and disinfection, and analysed enzymatically and amperometrically with a Biosen S-Line. Additionally, body composition (fat-free mass, body fat) was determined using bioelectrical impedance analysis (BIA, Nutri Duplex).

Where the oxygen values come from

A single breath is a very noisy signal. The path to a usable measurement point runs through four steps:

1. Cleaning: Outliers in the breath by breath signal are filtered out statistically.
2. Modelling: The exponential rise model of oxygen uptake is fitted to every stage.
3. Reading: The steady state value (V̇O_2ss) is taken as the model mean over the final 60 seconds.
4. Weighting: More precise stages carry more statistical weight in the final regression.

The corresponding mechanical power is averaged over exactly the same time window, so that numerator and denominator always describe the same physiological state.

Results of the water tests

Both athletes held the prescribed target intensities precisely. Plotting steady state oxygen uptake against the power reported by the sensor produces a clean straight line for both of them across the whole range evaluated.

Figure 2. Time course of the water session of Athlete 01. The left axis shows oxygen uptake (light blue) and carbon dioxide output (red), the right axis heart rate (green), stroke rate (violet), power (black) and blood lactate (dark red points, scaled by 10^-1 for display). All curves are rolling means.

Figure 3. Athlete 01 on the water. The light blue line is the linear regression of steady state oxygen uptake against the sensor power, the fine dotted and dashed lines are the curvilinear models of oxygen uptake and carbon dioxide output. The dark red points show the exponential rise in blood lactate, which leaves the oxygen uptake on this axis untouched. Green crosses and violet triangles are heart rate and stroke rate, both scaled by 10^-1 for the right hand axis.

Figure 4. Time course of the water session of Athlete 02, presented as in Figure 2.

Figure 5. Athlete 02 on the water, presented as in Figure 3. The linear relationship holds right up to the metabolic limit. The highest stage sits visibly below the line because maximal oxygen uptake had already been reached there. That stage is therefore excluded from the linear regression and drawn semi transparent.

Table 4 Parameters of the linear V̇O₂ power relationship

Under open water conditions the PaddlePulse sensor produces a signal whose link to the athlete's metabolic rate is as tight as on a stationary ergometer. The remaining deviations of the individual stages from the line, shown as the largest relative error, are of the same order as the measurement uncertainty of the gas analysis itself.

Mechanical efficiency as the second test

Linearity shows that the sensor signal is proportional to the work actually performed. It says nothing about whether the reported watts are also of the right magnitude. A straight line stays a straight line if the power axis is compressed or stretched by a constant factor, so a systematically mis-scaled signal would still pass the linearity test. Proportionality is proven, the scale is still open. That gap is closed by the slope efficiency, because the slope of the line states directly what one additional watt costs in oxygen.

For slope efficiency in kayaking there are no reliable reference values so far, which means the values around 16 % measured here cannot be checked against an established range. Gross efficiency does allow a comparison, because kayak specific studies exist for it. In twelve elite sprint kayakers on the kayak ergometer, a gross efficiency of 10.1 ± 1.1 % at maximal oxygen uptake was reported (Gomes et al., 2012). The 8.6 to 13.3 % measured here are of the same order. For paddling on the water, mechanical efficiencies of roughly 4 to 6 % have been derived from the towing drag of the boat (Pendergast et al., 1989). That figure is not directly comparable, because it counts only the drag power actually turned into propulsion as useful work and therefore comes out systematically lower.

Gross and net efficiency, at 8.6 to 13.3 % and 10.6 to 14.2 %, come out systematically lower than the slope efficiency, because they include the non propulsive baseline costs in the quotient (see Table 1). The three measures are therefore not convertible into one another and should not be expected to agree. What matters is that all three stay in a range that is plausible for upper body work, and that they sit clearly below the values of sports such as cycling. There, typical gross efficiencies are 19 to 22 %, net efficiencies 19 to 24 % and delta efficiencies 23 to 28 % (see Ettema & Lorås, 2009a; Francescato et al., 1995).

A sensor signal that systematically over or underestimates power would immediately produce implausible efficiencies. Watt values reported too high would imply a mechanical efficiency that paddling cannot reach. The consistency found here, around 16 %, points instead to a sensor that quantifies the work performed on a correct physical scale. What is proven is therefore not only the shape of the relationship but also its magnitude.

The intercept as a measure of movement economy

Where the regression line meets the y-axis it gives the calculated oxygen uptake at zero watts of propulsive power. This value collects the physiological costs that never reach the propulsion, among them the resting metabolic rate, the work of breathing, trunk stabilisation, keeping the boat balanced and the internal work of the paddling movement, meaning the acceleration and deceleration of arms, trunk and paddle, which produces no propulsion of its own (see Francescato et al., 1995). On the water this oxygen demand at zero propulsive power came to 769 and 946 ml/min.

This extrapolated value carries a certain statistical uncertainty, with standard errors of 144 and 124 ml/min. One additional stage at very low intensity would have anchored the lower part of the line more firmly and sharpened the estimate further. Even so, the intercept offers a valuable quantitative way to compare the movement economy of the same athlete objectively over time.

Cross-check in the laboratory

On the kayak ergometer a mechanical reference is available, so the measurement can be checked a second time. There too the oxygen uptake runs strictly linear with the measured power, with comparable slopes and efficiencies to the water (see Table 4).

Figure 6. Time course of the laboratory session of Athlete 01 on the kayak ergometer, presented as in Figure 2. The black power curve shows the sensor signal converted to the ergometer scale.

Figure 7. Athlete 01 in the laboratory, presented as in Figure 3. The linear relationship is confirmed on the ergometer with even less scatter than on the water.

Figure 8. Time course of the laboratory session of Athlete 02, presented as in Figure 6.

Figure 9. Athlete 02 in the laboratory, presented as in Figure 3.

One striking finding is a systematic difference in the power scale between water and ergometer. This result is physically coherent and not a measurement error. On a fixed ergometer the hydrodynamic gliding phase of the boat disappears entirely, and the resistance of a flywheel follows completely different laws than a hull moving through water. The relationship itself stays strictly linear. On a stationary ergometer the conversion only requires a device specific calibration factor.

Context and methodological limits

Combining internal and external data exposes systematic limitations of purely field based methods:

• Overestimation of critical power: Without exhaustive efforts lasting more than twelve minutes, the model estimates CP too high, here 209 W and 144 W. Comparing it with the lactate and gas exchange data makes that visible.
• Specifics of lactate production: Pure upper body work activates less muscle mass, which generally produces higher lactate values. Fixed mmol thresholds are often of limited validity here.
• Missing values at low intensity: One additional stage at very low mechanical power would have been extremely valuable in hindsight. It would have anchored the intercept of the V̇O₂ regression more firmly and would also have improved the calculation of the first lactate threshold (LT₁) and the first ventilatory threshold (VT₁) considerably.

Note. The topics touched on briefly here are covered in depth in their own articles. Planned are pieces on the critical power tests and the power duration profile as well as on the various lactate and ventilatory thresholds in sprint canoe.

Practical value

• Training prescriptions become verifiable: A target such as 3 min at 200 W is an exact load whose metabolic response is known and can be checked afterwards against heart rate and lactate.
• Movement economy becomes measurable: Slope and intercept separate quantitatively how much of the metabolic energy reaches the propulsion and how much is lost to stabilisation and technique.
• Performance models can be corrected: Only the physiological comparison with metabolic data shows when and by how much a short field test overestimates the threshold.

Conclusion

Across a broad power range the steady state oxygen uptake rises strictly linearly with the power reported by PaddlePulse, both on the water and on the kayak ergometer. The oxygen cost derived from it corresponds to a slope efficiency of around 16 % and sits in a range that is plausible for the upper body work of kayaking and consistent with the kayak specific efficiency data available.

Together the two findings answer the opening question. The sensor measures a quantity that is proportional to the mechanical work actually performed, and it measures it on the correct scale. The power measurement describes what the athlete produces, the physiology describes what that work costs him. Only both quantities together make sure that the training planned is the training completed.

Appendix: thresholds of the water session

For completeness, the following tables document every threshold calculated for the open water session. Since the individual concepts rest on very different assumptions and sometimes differ considerably, a weighted consensus value is reported as well, which balances the concepts by model quality and physiological individualisation.

Table A1 Blood lactate thresholds, sorted ascending

Table A2 Ventilatory thresholds from the ramp test

The raw values come from the ramp test with 60 s stages. Because oxygen uptake follows a rising load with an individual delay, every threshold determined in a ramp appears at a slightly too high power. The kinetics corrected value removes that delay using the individually measured time constant.

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