Power profiling and the power-duration relationship in cycling: a narrative review

Emerging trends in technological innovations, data analysis and practical applications have facilitated the measurement of cycling power output in the field, leading to improvements in training prescription, performance testing and race analysis. This review aimed to critically reflect on power profiling strategies in association with the power-duration relationship in cycling, to provide an updated view for applied researchers and practitioners. The authors elaborate on measuring power output followed by an outline of the methodological approaches to power profiling. Moreover, the deriving a power-duration relationship section presents existing concepts of power-duration models alongside exercise intensity domains. Combining laboratory and field testing discusses how traditional laboratory and field testing can be combined to inform and individualize the power profiling approach. Deriving the parameters of power-duration modelling suggests how these measures can be obtained from laboratory and field testing, including criteria for ensuring a high ecological validity (e.g. rider specialization, race demands). It is recommended that field testing should always be conducted in accordance with pre-established guidelines from the existing literature (e.g. set number of prediction trials, inter-trial recovery, road gradient and data analysis). It is also recommended to avoid single effort prediction trials, such as functional threshold power. Power-duration parameter estimates can be derived from the 2 parameter linear or non-linear critical power model: P(t) = W′/t + CP (W′—work capacity above CP; t—time). Structured field testing should be included to obtain an accurate fingerprint of a cyclist’s power profile.

The Impact of Elevated Body Core Temperature on Critical Power as Determined by a 3-min All-Out Test

Critical power (CP) delineates the heavy and severe exercise intensity domains, and sustained work rates above CP result in an inexorable progression of oxygen uptake to a maximal value and, subsequently, the limit of exercise tolerance. The finite work capacity above CP, W′, is defined by the curvature constant of the power-duration relationship. Heavy or severe exercise in a hot environment generates additional challenges related to the rise in body core temperature (Tc) that may impact CP and W′. The purpose of this study was to determine the effect of elevated Tc on CP and W′. CP and W′ were estimated by end-test power (EP; mean of final 30s) and work above end-test power (WEP), respectively, from 3-min "all-out" tests performed on a cycle ergometer. Volunteers (n = 8, 4 female) performed the 3-min tests during a familiarization visit and two experimental visits (Thermoneutral vs Hot, randomized crossover design). Before experimental 3-min tests, subjects were immersed in water (Thermoneutral: 36°C for 30 min; Hot: 40.5°C until Tc was ≥ 38.5°C). Mean Tc was significantly greater in Hot compared to Thermoneutral (38.5±0.0°C vs. 37.4±0.2°C; mean±SD, P<0.01). All 3-min tests were performed in an environmental chamber (Thermoneutral: 18°C, 45% RH; Hot: 38°C, 40% RH). EP was similar between Thermoneutral (239 ± 57W) and Hot (234 ± 66W; P = 0.55). WEP was similar between Thermoneutral (10.9 ± 3.0 kJ) and Hot (9.3 ± 3.6; P = 0.19). These results suggest that elevated Tc has no significant impact on EP or WEP.

An analysis of temporal scaling behaviour of extreme rainfall in Germany based on radar precipitation QPE data

We investigated the depth–duration relationship of maximum rainfall over all of Germany based on 16 years of radar-derived quantitative precipitation estimates (namely, RADKLIM-YW, German Meteorological Service) with a space–time resolution of 1 km2 and 5 min. Contrary to the long-term historic records that identified a smooth power law scaling behaviour between the maximum rainfall depth and duration, our analysis revealed three distinct scaling regimes of which boundaries are approximately 1 h and 1 d. A few extraordinary events dominated a wide range of durations and deviate to the usual power law. Furthermore, the shape of the depth–duration relationship varied with the sample size of randomly selected radar pixels. A smooth scaling behaviour was identified when the sample size was small (e.g. 10 to 100), but the original three distinct scaling regimes became more apparent as the sample size increases (e.g. 1000 to 10 000). Lastly, a pixel-wise classification of the depth–duration relationship of the maximum rainfall at all individual pixels in Germany revealed three distinguishable types of scaling behaviour, clearly determined by the temporal structure of the extreme rainfall events at a pixel. Thus, the relationship might change with longer time series and can be improved once available.

Honey bees communicate distance via non-linear waggle duration functions

Honey bees (genus Apis) can communicate the approximate location of a resource to their nestmates via the waggle dance. The distance to a goal is encoded by the duration of the waggle phase of the dance, but the precise shape of this distance-duration relationship is ambiguous: earlier studies (before the 1990s) proposed that it is non-linear, with the increase in waggle duration flattening with distance, while more recent studies suggested that it follows a simple linear function (i.e. a straight line). Strikingly, authors of earlier studies trained bees to much longer distances than authors of more recent studies, but unfortunately they usually measured the duration of dance circuits (waggle phase plus return phase of the dance), which is only a correlate of the bees’ distance signal. We trained honey bees (A. mellifera carnica) to visit sugar feeders over a relatively long array of distances between 0.1 and 1.7 km from the hive and measured the duration of both the waggle phase and the return phase of their dances from video recordings. The distance-related increase in waggle duration was better described by a non-linear model with a decreasing slope than by a simple linear model. The relationship was equally well captured by a model with two linear segments separated at a “break-point” at 1 km distance. In turn, the relationship between return phase duration and distance was sufficiently well described by a simple linear model. The data suggest that honey bees process flight distance differently before and beyond a certain threshold distance. While the physiological and evolutionary causes of this behavior remain to be explored, our results can be applied to improve the estimation of honey bee foraging distances based on the decoding of waggle dances.

Effects of Normobaric Hypoxia on Matched-severe Exercise and Power-duration Relationship

We investigated the effects of hypoxia on matched-severe intensity exercise and on the parameters of the power-duration relationship. Fifteen trained subjects performed in both normoxia and normobaric hypoxia (FiO2=0.13, ~3000 m) a maximal incremental test, a 3 min all-out test (3AOT) and a transition from rest to an exercise performed to exhaustion (Tlim) at the same relative intensity (80%∆). Respiratory and pulmonary gas-exchange variables were continuously measured (K5, Cosmed, Italy). Tlim test’s V̇O2 kinetics was calculated using a two-component exponential model. V̇O2max (44.1±5.1 vs. 58.7±6.4 ml.kg-1.min-1, p<0.001) was decreased in hypoxia. In Tlim, time-to-exhaustion sustained was similar (454±130 vs. 484±169 s) despite that V̇O2 kinetics was slower (τ1: 31.1±5.8 vs. 21.6±4.7 s, p<0.001) and the amplitude of the V̇O2 slow component lower (12.4±5.4 vs. 20.2±5.7 ml.kg-1.min-1, p<0.05) in hypoxia. CP was reduced (225±35 vs. 270±49 W, p<0.001) but W’ was unchanged (11.3±2.9 vs. 11.4±2.7 kJ) in hypoxia. The changes in CP/V̇O2max were positively correlated with changes in W’ (r = 0.58, p<0.05). The lower oxygen availability had an impact on aerobic related physiological parameters, but exercise tolerance is similar between hypoxia and normoxia when the relative intensity is matched despite a slower V̇O2 kinetics in hypoxia.

Dating the Bushveld Complex: Timing of Crystallization, Duration of Magmatism, and Cooling of the World’s Largest Layered Intrusion and Related Rocks

The Paleoproterozoic Bushveld Complex, including the world’s largest layered intrusion and host to world-class stratiform chromium, platinum group element, and vanadium deposits, is a remarkable natural laboratory for investigating the timescales of magmatic processes in the Earth’s crust. A framework for the emplacement, crystallization, and cooling of the Bushveld Complex based on integrated U-Pb zircon-baddeleyite-titanite-rutile geochronology is presented for samples of different rock types from the Bushveld Complex, including ultramafic and mafic cumulates, mineralized horizons, granitic rocks from the roof, and a carbonatite from the nearby alkaline Phalaborwa Complex. The results indicate that (1) the Bushveld Complex was built incrementally over a ∼5 million-year interval from 2060 Ma to 2055 Ma with a peak in magma flux at c.2055–2056 Ma, (2) U-Pb zircon crystallization ages do not decrease in an uninterrupted systematic manner from the base to the top of the intrusion indicating that the Bushveld Complex does not represent the crystallized products of a single progressively filled and cooled magma chamber, and (3) U-Pb rutile dates constrain cooling of the intrusion at the level of the Critical Zone through ∼500 °C by 2053 Ma. The c.2060 Ma Phalaborwa Complex (pyroxenite, syenite, carbonatite + Cu-Fe-phosphate-vermiculite deposits) represents one of the earliest manifestations of widespread Bushveld-related magmatism in the northern Kaapvaal craton. The extended range and out-of-sequence U-Pb zircon dates determined for a harzburgite from the Lower Zone (c.2056 Ma), an orthopyroxenite from the Lower Critical Zone (c.2057 Ma), and orthopyroxenites from the Upper Critical Zone (c.2057–2060 Ma) are interpreted to indicate that the lower part of the Bushveld Complex developed through successive intrusions and accretion of sheet-like intrusions (sills), some intruded at different stratigraphic levels. Crystallization of the main volume of the Bushveld Complex, as represented by the thick gabbroic sequences of the Main Zone and Upper Zone, is constrained to a relatively narrow interval of time (∼1 million years) at c.2055–2056 Ma. Granites and granophyres in the roof, and a diorite in the uppermost Upper Zone, constitute the youngest igneous activity in the Bushveld Complex at c.2055 Ma. Collectively, these results contribute to an emerging paradigm shift for the assembly of some ultramafic-mafic magmatic systems from the conventional “big tank” model to an “amalgamated sill” model. The volume-duration relationship determined for magmatism in the Bushveld Complex, when compared to timescales established for the assembly of other layered intrusions and more silica-rich plutonic-volcanic systems worldwide, is distinct and equivalent to those determined for Phanerozoic continental and oceanic flood basalts that constitute large igneous provinces. Emplacement of the 2055–2060 Ma Bushveld Complex corresponds to the end of the Lomagundi-Jatuli Event, the largest magnitude positive carbon isotope excursion in Earth history, and this temporal correlation suggests that there may have been a contribution from voluminous Bushveld ultramafic-mafic-silicic magmatism to disruptions in the global paleoenvironment.