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Optimal pacing strategy: from theoretical modelling to reality in 1500-m speed skating
  1. F J Hettinga1,2,
  2. J J De Koning1,3,
  3. L J I Schmidt1,
  4. N A C Wind1,
  5. B R MacIntosh4,
  6. C Foster3
  1. 1Research Institute MOVE, Department of Human Movement Sciences, VU University Amsterdam, Amsterdam, The Netherlands
  2. 2Center for Human Movement Sciences, University Medical Center Groningen/University of Groningen, Groningen, The Netherlands
  3. 3Department of Exercise and Sports Science, University of Wisconsin-LaCrosse, LaCrosse, Wisconsin, USA
  4. 4Human Performance Laboratory, Department of Kinesiology, University of Calgary, Calgary, Canada
  1. Correspondence to Florentina J Hettinga, Center for Human movement Sciences, University Medical Center Groningen/University of Groningen, Antonius Deusinglaan 1, Groningen 9713, The Netherlands; f.j.hettinga{at}


Purpose Athletes are trained to choose the pace which is perceived to be correct during a specific effort, such as the 1500-m speed skating competition. The purpose of the present study was to “override” self-paced (SP) performance by instructing athletes to execute a theoretically optimal pacing profile.

Methods Seven national-level speed-skaters performed a SP 1500-m which was analysed by obtaining velocity (every 100 m) and body position (every 200 m) with video to calculate total mechanical power output. Together with gross efficiency and aerobic kinetics, obtained in separate trials, data were used to calculate aerobic and anaerobic power output profiles. An energy flow model was applied to SP, simulating a range of pacing strategies, and a theoretically optimal pacing profile was imposed in a second race (IM).

Results Final time for IM was ∼2 s slower than SP. Total power distribution per lap differed, with a higher power over the first 300 m for IM (637.0 (49.4) vs 612.5 (50.0) W). Anaerobic parameters did not differ. The faster first lap resulted in a higher aerodynamic drag coefficient and perhaps a less effective push-off.

Conclusion Experienced athletes have a well-developed performance template, and changing pacing strategy towards a theoretically optimal fast start protocol had negative consequences on speed-skating technique and did not result in better performance.

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Athletes seem to choose their pacing strategy from the starting point of exercise, adjusted to their physiological condition.1 Apparently, the trade-off between benefits of extra power early in the race versus the liability of earlier fatigue is solved by the athlete by performing a virtual calculation. Homeostatic disturbances are balanced against the goal of competition, a process of trial and error. Continuous adjustments in power output within an event are apparently associated with information processing between the brain and peripheral physiological systems,2 3 reflected in the rating of perceived exertion (RPE). Even when incorrect distance feedback is provided, RPE patterns do not change over the course of a self-paced (SP) 20-km race.4 Athletes follow a predetermined exercise template with a growth in RPE proportional to the event distance,5 6 which is important in preventing unacceptably large disturbances in homeostasis7 8 and maximising performance. Developing and using this template has been referred to as teleoanticipation,9 an internal negotiation regarding estimation of task remaining, momentary power output, estimated energetic reserves10 11 and already-performed exercise.12

Though several studies focussed on pacing strategies in endurance performance, the present study evaluates anaerobic energy distribution during middle distance performance, where anaerobic energy represents a quantitatively large percentage of total energy requirement. Performance can be modelled using an energy flow model.13,,18 Different pacing strategies can be simulated to determine the value of different strategies1 14 19 predicting that middle distance athletic events (<2 min) can be improved with a relatively fast initial pace.1 14 18 Although experienced athletes are apparently well equipped to determine pacing strategy, they do not always follow the theoretical optimal pacing profile. In the present study, the performance template of SP 1500-m speed skating was “overridden” by imposing a pacing strategy based on a theoretically optimal profile.1 14 18 This allowed us to test the hypothesis emerging from modelling studies that a faster initial pace would result in better performance.



Seven national-level male speed skaters provided written informed consent and participated in the study. The protocol was approved by the University of Calgary Conjoint Health Research Ethics Board. Mean participant height was 181 (6) cm, mean body mass was 77 (5) kg and mean age was 20 (3) years.


Four skating trials were performed at an indoor 400-m skating oval at 1035 m above sea level (Calgary, Canada). On separate days, athletes performed two competitive 1500-m races: one SP and one with an imposed pacing strategy (IM) based on calculations from the energy flow model. To obtain the individual characteristics necessary as input for the energy flow model, gross efficiency (GE) was determined during submaximal skating by measuring oxygen consumption (V̇O2) and mechanical power output. V̇O2 response was measured in a preliminary 1500-m trial. Both trials preceded SP and IM. Before every trial, barometric pressure was measured. Mean ice temperature was measured at eight locations on the track, and ice friction coefficient was estimated.20 To obtain knee and trunk angles for determination of mechanical power output,14 digital video recordings were made on the straight segments of the track. Timing was done by digital cameras at the entry and exit of each corner, and average velocity and power output of each segment were calculated.15 Because of the large acceleration in the initial 100 m, velocity at the first measurement camera (at 100 m) was assumed to be 1.3 times the mean velocity over the first 100 m, based on second-by-second high-speed recorded velocity profiles obtained at the 1500-m Salt Lake City Olympics (unpublished).

Submaximal trial

Athletes skated nine laps at a submaximal intensity intended to be sustainable for 30–60 min. V̇O2 was measured using a portable metabolic system (Cosmed K4b2, Rome, Italy). The gas analyser was calibrated with room air and reference gas (15.19% O2, 6.06% CO2). Volume measurement was calibrated using a 3-l syringe. Skating velocity, knee and trunk angles were obtained to calculate mechanical power output. GE was determined15 based on calculations of mechanical power output and V̇O2 with the respiratory exchange ratio (RER)21: metabolic power attributable to aerobic sources (Pmet) was calculated from the V̇O2 and V̇CO2 data as follows:

Embedded Image

where Pmet is the aerobic metabolic power output in W, V̇O2 is the oxygen consumption in l• min−1 and RER is the respiratory exchange ratio. Constants are based on the energy equivalence of V̇O2, taking into consideration the mixture of substrate metabolised. An RER in excess of 1.0 was attributable to buffering; thus, RER >1.0 was treated as if equal to 1.0 relative to calculating metabolic work. GE was calculated as follows:

Embedded Image

where Ptot is the mechanical power produced by the skater.14

V̇O2 response

To describe the mechanical power achieved by aerobic energy (Paer) over time, necessary for modelling performance, V̇O2 data were collected in a 1500-m trial preceding the experimental trials and interpolated to 1s values. Participants were instructed to finish as fast as possible as in competition. The V̇O2 response was fit by a least squares mono-exponential model22 that has previously been applied to time-trial exercise.14,,16 23 The cardiodynamic phase was omitted from the fitting fields based on visual inspection. By multiplying the V̇O2 response by the energy equivalent of oxygen (20.98 kJ/l O2, since RER >1) and GE, Paer was calculated, resulting in a rate constant (λ) and a maximal aerobic power output (Paermax; equation 1). Equation 1 is presented without the time delay that was taken up into fitting the V̇O2 response, because for modelling performance, it will not be used.

Embedded Image(1)

Experimental trials

The first race was SP and part of a national competition. SP was used to obtain the remaining model parameters (ie, the description for calculated Pan over time) necessary to simulate different pacing strategies. Based on the prediction of the energy flow model, the coaches' advice and 300-m sprint times, skaters were instructed to start IM at a relatively fast pace outside their normal pacing range, conforming to the results of De Koning et al14 and Hettinga et al23 This strategy was closer to the theoretically optimal strategy but still within the range of commonsense possibilities, particularly considering that the start of 1500 m is very close to their top skating velocity for 300 m already. To get acquainted with the “feel” of the faster start, the skaters practiced the faster start in two training sessions, completing 3 × 300 and 2 × 700 m at maximal velocity.

Velocity and power output were compared per lap, and anaerobic power profile parameters were compared. To represent differences in pacing strategy, correcting for possible differences in external conditions, velocity was normalised to mean velocity. To identify the effect of a changing skating posture during the race, air friction coefficient (kair)24 was compared.

The energy flow model

By using the energy flow model including expressions for mechanical power produced by the speed skater (Ptot) and mechanical power used to overcome frictional forces (Pfriction), SP and IM were modelled, and different pacing profiles were simulated.14,,18 The interplay between Ptot and Pfriction results in temporal changes in kinetic energy (dEkin/dt) of the skater (equation 2), leading to a certain velocity profile over the race.

Embedded Image(2)

Pfriction can be described by the summation of power used to overcome air frictional forces (Pair, equation 3) and ice resistance (Pice, equation 4).

Embedded Image(3)

The air friction coefficient (kair) is affected by postural changes over the race and is calculated according to van Ingen Schenau (26) using the measured trunk and knee angles; v equals velocity in a no wind situation, as in the present (indoor) study. Pair is adjusted for barometric pressure. Pice was calculated from the skater's body weight (m · g), coefficient of ice friction (µ) and v25 (equation 4); µ was estimated using on-ice temperature.20

Embedded Image(4)

Ptot equals the sum of mechanical power production by the aerobic (Paer) and anaerobic (Pan) energy system (equation 5).

Embedded Image(5)

Both Paer and Pan can be described over time, as already described for Paer (equation 1). Paer was determined during a supramaximal preceding effort. The time-course of this energy delivery was assumed to be identical in each trial. Pan was calculated by subtracting Paer from Ptot. This difference was fit to equation 6.

Embedded Image(6)

Pan decreases monoexponentially from a peak (Panpeak) at the beginning of the race to a constant level described by Pancon, the asymptote of equation 6. Peak anaerobic power (Panpeak) is the sum of Pancon and Panmax, which is more relevant to performance than either Pancon or Panmax separately. The anaerobic rate constant γ14 23 dictates the rate of decline from Panpeak to Pancon. For comparing individual datum, the instantaneous value of Pan at the end of exercise is taken.

Optimal pacing strategy

Because pacing strategy in the supramaximal domain is mainly determined by the distribution of anaerobic energy,19 the effect of manipulating anaerobic parameters Pancon, Panmax and γ was studied by simulating different performances. The parameters of Pan were varied with the restriction that total anaerobic work generated over the race, and all other variables, were kept constant. The combination of Panmax, γ and Pancon leading to the fastest time corresponds to optimal pacing strategy.


SP and IM were compared per lap with ANOVA repeated measures (strategy × lap). The parameters of the anaerobic power profiles were compared with a paired sample t test (p<0.05).


Submaximal trial

Mean GE was 18.7% (1.0%), skated at a mean power output of 185.7 (16.0) W, with a mean velocity of 9.59 (0.40) m/s and a mean RER of 0.98 (0.04). Mean knee angle was 110.7º (9.8º), and mean trunk angle was 18.5º (6.0º).

V̇O2 response

The mean amplitude of the V̇O2 response, that is, the highest V̇O2 observed during the pretrial, was 3.3 (0.3l)·min−1, with a mechanical equivalent Paermax of 218.7 (20.6) W. Mean λ (equation 1) was 0.125 (0.37) s. Times were relatively slow (121.99 (2.94) s). A typical example of V̇O2 response of a representative participant is shown (fig 1).

Figure 1

Typical example of the V̇O2 response of a representative individual for the 1500-m time trial (left panel). Residuals were calculated by subtracting the measured V̇O2 from the mono-exponential fit (right panel).

SP trial versus imposed strategy trial

Estimated ice-friction coefficient was slightly higher in IM (0.0047 (0.0000)), where ice temperature was −4.5 ºC (0.0ºC) compared to SP (0.0044 (0.0002)), where ice temperature was −6.2ºC (1.1ºC). Barometric pressure was also slightly higher in the IM (897.9 (1.2) hP) compared to SP (896.6 (0.4) hP).

Final times of SP (115.39 (4.45) s) were significantly faster than IM (117.29 (3.53) s). Lap times and velocity profiles are shown (table 1). Main effects for absolute (vabs) and relative velocity normalised to mean velocity (vrel) were significantly different between pacing strategies. Values for the aerodynamic drag coefficient (kair; table 2) were higher throughout the entire race for IM. Ptot was significantly greater during the opening 300 m of IM and decreased significantly per lap in both SP and IM (table 3). An interaction (strategy × lap) effect was found for the distribution of Ptot per lap, demonstrating that the values for Ptot varied by lap, and this change was dependent on which trial was considered. Essentially, this means the change in Ptot through the race was different between trials, resulting in different (relative) velocity profiles over the race.

Table 1

Mean lap times, absolute velocity (vabs) per lap and relative velocity normalised to mean velocity (vrel) per lap

Table 2

Mean air friction coefficient (kair) per lap, mean knee angles per lap and mean trunk angles per lap

Table 3

Total power output (Ptot) per lap

Energy flow model prediction of the theoretically optimal pacing strategy

Optimal pacing strategy was predicted using GE, the response V̇O2 and the velocity profile from the SP trial. This trial allowed calculation of the Pan. For all participants, the theoretically optimal performance could be achieved by skating a faster initial pace, conforming to previous data.1 14 18 Less mechanical energy, which is related to the value of Pancon, must be left at the finish, and more energy must have been used early in the race, shown by a higher Panpeak. Predicted final times resulting from the different simulated pacing strategies (different anaerobic parameters) for a representative participant are presented in fig 2.

Figure 2

Different combinations of the anaerobic parameters: γ and Pancon are shown for a representative individual, with corresponding final times (upper panel). The shallow area of the mesh represents the fastest final time. Contour plots of these graphs are also shown (bottom panel). The space between adjacent contour lines represents 0.1 s. Only Pancon and γ are displayed, because the amount of anaerobic work is the same in all simulations, meaning that Panpeak, Pancon and γ are interdependent. Displaying different combinations will lead to comparable plots. SP of a representative individual is marked with an “x”.

Anaerobic power distribution

In IM, Pan changed towards the as optimal predicted direction but did not differ from anaerobic parameters of SP (table 4).

Table 4

Individual data for the anaerobic parameters are presented: maximal anaerobic power (Panmax), peak anaerobic power (Panpeak), anaerobic rate constant (γ), the instantaneous value of Pan attained at the end of exercise (Panend) and total anaerobic work (Ean)


A more nearly optimal pacing strategy was imposed on athletes competing at national level: conforming with predictions,1 14 18 a higher initial peak power output was recommended and predicted to lead to better performance. Athletes indeed demonstrated a relatively faster initial pace over the first 300 m, caused by a significant difference in the distribution of Ptot, with a higher Ptot over the first 300 m. Vrel over the last lap was lower, though Ptot was not. Though Panpeak and γ changed towards the predicted direction, no differences were found between strategies for these parameters individually. Differences in Ptot over time are suggested to be caused by combined effects of changes in Panpeak and γ. However, Paer was assumed to be equal in both SP and IM but is apparently influenced by starting effort23: a larger peak power over the first ∼15 s of the race accelerates V̇O2 response. Though the start of IM was faster, SP was already performed with a relatively fast start, so this is not expected to greatly influence results. V̇O2 Unfortunately, response was not obtained during the experimental trials, because athletes could not wear the measurement system during competition. A separate trial was performed, where final times were somewhat slower than during the experimental trials, probably attributable to extra air resistance and breathing resistance from the metabolic system. Because all trials were performed at supra-maximal effort, this is not expected to largely influence the results.

Another issue in modelling the speed skating performance is that though speed-skating race performance can be accurately predicted based on data per 100 m,15 the modelling of speed-skating performance based on relatively few data points leads to an error compared to the observed performance (table 5). Unfortunately, it was not possible to measure power output directly on a second by second basis, as in cycling.1 Pan was thus fit based on measurement once per 100 m. This affected the determination of total mechanical power output, particularly in the first 100 m, where acceleration was large. Consequently, the estimation of the anaerobic parameters that were varied to simulate different pacing strategies was affected. Based on second-by-second high-speed recorded velocity profiles obtained at the 1500-m Salt Lake City Olympics, this was corrected for. The modelled SP time trial had a final time of 116.27 (4.42) s (about 0.88 s slower than observed performance), and the modelled IM time trial had a final time of 118.11 (3.54) s (about 0.81 s slower than observed performance). Deviations of observed performance were equally large over the first 300 m (table 5) and were not expected to influence differences between trials. Anaerobic parameters were in the same range as cycling and speed skating,1 15 and differences with previous studies were as expected based on the level of the athletes and differences between the sports. Velocity profiles had about the same error over the race; thus, pacing strategy was represented well, though model performance was absolutely slower than observed performance.

Table 5

Individual differences between modelled performance and observed performance are presented per lap

Lastly, it has to be raised that only seven participants participated, a consequence of having the unique opportunity of measuring national level elite athletes. For the modelling, this is enough, but performing conventional statistics to compare results is more difficult. Though this has to be kept in mind in interpreting the results, we believe that in combination with modelling, we obtained valuable information on optimal performance in elite athletes.

Though pacing strategies shifted towards the predicted profiles, athletes could not be drawn far from their self-selected pacing strategy. This is in agreement with Hulleman et al,26 showing that SP performance was rather stable and a monetary incentive did not change pacing strategy compared to non-incentivised trials. Athletes seem to have a very robust system of determining pacing strategy, based on endpoint knowledge, previous experience,3 9 10 physiological condition1 27 and peripheral factors.3 27 Based on the awareness of metabolic reserves and homeostatic disturbance in the current exercise bout, this predetermined template is compared to previous experiences, a process that is not easily overridden.26 Though ratings of perceived exertion would have been a valuable addition to the present study, recording RPE would distract the athletes from performing optimally. It could be expected that RPE followed a predetermined exercise template with a growth proportional (scalar) to the estimated event distance6 in a SP trial. By overriding this template by imposing a faster start, ratings of perceived exertion would be expected to increase sooner, and a difference between IM and SP would be expected.

Another point is that more than two training sessions may be necessary to “learn” a different pacing pattern. During an entire speed-skating season, no differences in Wingate test performance were found,28 suggesting little change in the anaerobic contribution in the initial part of the race. Over a longer period of time and training (four seasons), successful speed skaters distinguished themselves by the ability to produce higher peak powers.25 Though natural growth was involved, it also suggests that it might be possible to “train” optimal pacing strategy.

Though Pan shifted towards a theoretically optimal pacing profile, IM was ∼2 s slower than SP. Mean vabs was higher for SP compared to IM, mainly because velocity was maintained better in the latter half of the race. The worse results for IM could not be explained by differences in mean power output between trials. Differences in motivation were assumed to be minor because there were no differences in total work. External conditions (barometric pressure and ice friction) varied slightly in favour of SP and could account for only part of the difference between performances. The explanation for the worse performance for IM thus must be found in the technical nature of speed skating; a predefined movement where maintaining body position is of large importance and body weight has to be carried continuously. It is important to avoid early fatigue, because loss of technical ability results in a postural change, increasing frontal area and thus increasing air friction coefficient (kair). A horizontal trunk position and a small angle in the knee-joint during gliding reduce air resistance and are important for a proper timing and direction of the push-off.29 As athletes fatigue throughout the race, body position changes towards a less crouched position,15 which may lessen the restriction of blood flow to the thigh muscles30 but is less favourable aerodynamically. The present study showed that in IM, kair was higher throughout exercise, possibly caused by the summation of increased knee and trunk angles, though individually, these were not differing. It seems that the effort of increasing initial pace results in unfavourable technical changes in speed skating, overriding the potential benefit of the faster start. Additionally, although data are limited, the assumption of a constant GE throughout the entirety of both skating trials is suspect. Given the difficulty in producing an effective push off in speed skating, it is almost inevitable that GE decreases throughout competition, particularly in situations such as IM where fatigue would reasonably interfere with the coordination required to produce the push off efficiently. As discussed, athletes seem to have a well-developed sense of physical condition,27 and metabolic rate can be accurately adjusted by a feedback control system.9 By comparing their awareness of metabolic reserves and homeostatic disturbance in the current exercise bout relative to previous experience, a well-evolved system seems to exist, making it possible for the athlete to skate a 1500-m without losing the technical ability.


Experienced athletes seem to possess a well-developed performance template, and changing pacing strategy towards a theoretically optimal fast start protocol did not result in better performance. Earlier fatigue seems to affect technique; slight deviations from the template apparently have relatively large consequences, because timing and direction of the push off and maintaining body position are of large importance for optimal speed-skating performance.

What is already known on this topic

Modelling techniques have resulted in reasonably accurate predictions of performance in both cycling and speed skating. By varying anaerobic energy distribution, different pacing strategies can be evaluated to predict optimal performance. So far, predicted optimal strategies have never been tested in real-life settings by actually imposing them.

What this study adds

The present study was designed to test modelling predictions by actually imposing a theoretically optimal pacing strategy. The results suggested that the predicted optimal degree of “all-out” start was not ideal in practice, perhaps because of an unaccounted for effect of fatigue on skating technique.


The authors would like to thank the Calgary Olympic Oval, the Sport Science Association of Alberta, the speed skaters participating in this project and their coaches for their cooperation. The authors would also like to thank Shane Esau and Jared Fletcher for their technical assistance.



  • Competing interests None.

  • Ethics approval The approval was obtained from the University of Calgary Conjoint Health Research Ethics Board.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Patient consent Obtained.