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Optimisation of a variable pacing strategy in road cycling

-By: Tomas Swift-Metcalfe

Last modified: July 9, 2016

This piece is a literature review I did for my final piece in university on pacing strategy in cycling, it covers some of the maths involved in pacing and includes some hypotheses on how to get the most from your performance in a particular environmental context. You can find the final piece (experimental write up) here:

Surprised by Chris Froome’s downhill victory? There may be thought (science) behind it!

Optimisation of a variable pacing strategy in road cycling


This literature review looks at performance assessment methods in road cycling, what constitutes an optimal pacing strategy and whether performance models can predict real world performance and hence suggest an optimal pacing strategy.

Due to the nature of training for road cycling, time trials and the cycling segment of a triathlon, coaches rarely work with athletes in person and as such rely heavily on data collected remotely to prescribe training. For the purpose of this review only field based performance assessment methods that can be applied remotely using power data are considered.

Performance analysis aims to quantify exercise load, which is a product of intensity and time (Skiba and Clarke, 2013) and refers to the amount of training or ‘dose’ of training (Wallace et al., 2014). Intensity is usually defined by what training metrics are used: power (W), heart rate (HR), rate of perceived exertion (RPE). Generally coaches focus on the indirect inference of lactate threshold or other analogous phenomena, as the key value upon which to base their training prescriptions (intensity and time). Functional Threshold Power™ (FTP) (Peaksware Inc, Boulder, USA), or critical power (CP) (Monod and Scherrer, 1965) are metrics analogous with with power at lactate threshold, commonly used in the by cyclists and coaches. This literature review explores the ecological validity of FTP, CP and how these can be applied to pacing strategy.

Pacing strategy is defined here as how an athlete distributes effort over the duration of a performance. From Abbiss and Laursen (2008), it is possible to identify the main pacing strategies pertinent to endurance cycling: variable or dynamic pacing (VP), where intensity is varied; even or linear pacing (EP), where effort is kept steady; negative pacing, where an athlete goes faster as the event progresses; positive pacing, where an athlete slows as the event progresses. Sustainable power is often measured through a self paced effort (SP) and used as a baseline in research.

It is clear some argument exists as to whether variable pacing (VP), utilizing work rates above FTP or CP during longer effort constitutes a more effective pacing strategy than even paced (EP) efforts. From mathematical models of forces acting on a cyclist (Martin et al. 1998), it is possible to analyse the different force in different situations and what implications these will have on pacing strategy raising the following questions: Should pacing strategy vary depending on context? Are efforts not contemplated by CP or FTP relevant to pacing strategy?

This review is broken into three main sections: pacing strategy, a mathematical examination of pacing strategy and performance analysis methods.

Pacing strategy

Theoretical and laboratory based research

While researching the reliability of laboratory based tests on pacing strategy, Thomas et al. (2013) found that despite high variance at the beginning and end of the test, lab TT efforts were reliable. Athletes adopted a parabolic-shaped pacing strategy for SP.

For a 60 min effort where environmental conditions remain stable such as in a velodrome, or on an ergometer, Padilla et al. (2000) suggest, based on a mathematical model itself based case study of a specific 1 h world record attempt that an even pacing strategy is optimal due to less extra energy being expended through acceleration. Stable situations such as that in a velodrome are seldom encountered in normal road cycling.

Thomas et al. (2012) examined the effect of EP, SP and VP strategies on cycling performance and found that EP caused the least amount physiological disturbance and lower perceived effort as measured through the 20 point Borg scale. For testing variable pacing, their design presented a 1:1.5 ratio of high intensity versus low intensity efforts, where those efforts equated to 142% and 72% of the mean value obtained in a simulated self paced 20 km time trial (TT) on an indoor ergometer. There is no mention why the values of 142% and 72% were chosen, although the total workload would equal that of SP precisely and was well tolerated by the participants in the study. EP power was set as the average for SP. The authors suggest EP might be optimal for endurance events based on lower perceived effort and smallest degree of physiological perturbation observed in their study. The authors themselves admit the need to investigate more ecologically valid models.

Outside of the stated aims of the study, Thomas et al. (2012) found that for the self paced trial, participants adopted a fast start, or positive pacing strategy, however this might not be a so much a deliberate strategy, as the authors suggest as a decline in gross efficiency.

Atkinson et al. (2007) similarly tested VP in a simulated hilly TT, set to work (800 kJ) and not distance, where power varied by +5% on uphill sections to -5% on downhill sections in relation to the average power established in self paced trial with the same amount of work. In this situation, uphill sections tended to be much longer (mean 714 s) in duration than downhill (190 s), inverse to the study by Thomas et al. (2010) with longer periods above mean power for SP. While this study did find a reduction in time to complete the task for five of the seven participants, it appear this strategy is not useful for all people. While no mention is made of how uphill sections are simulated and since only over all time for each section is given and work done is the same for both uphill and downhill sections, it can only assume that acceleration due to gravity on a slope is summed to the power produced by the cyclist, be it positive or negative. There is also no mention of how changes in air resistance are quantified.

In assessing mean power in a self paced trial Atkinson et al. (2007) also observed participants tended to a positive pacing strategy.

Inference from real world performances

Abbiss et al. (2006) looked at pacing strategies employed in actual performances by well trained, experienced triathletes taking part in an Ironman triathlon. The key external variable affecting the athletes during the event was the wind and the authors found that the athletes tended to slight increase power output into the wind and that there was a greater variability in power output into a headwind, in line with what Swain (1997) proposes as optimal. Like observed in Atkinson et. al. (2007), the participants observed by Abbiss et. al. (2006) showed a positive pacing strategy with mean lap time increasing as they progressed.

Johnson et al. (2013) looked at pacing strategy from the perspective of relative success in the Hawaii Ironman World Championships. Success was determined by the percentage difference between the prior goal of the competitor and the outcome. This definition of success is dependent on the subjective appraisal by participants of their goals. The researchers looked at the relative intensities of exercise for the cycling section using heart rate (HR) and found that the most successful athletes according to their definition produced a more even effort and sustained higher HR on descents and increasing intensity on the downhill. From this the authors conclude uphill sections should be approached with caution. None of the sections the authors analyzed were descent or ascent only. Sections were defined according to whether net descent was positive or negative, as such do not explicitly detail a specific type of geography, but rather net ascent over relatively long distances. Johnson et al. (2013) mention that the successful group adopted a slightly negative pacing strategy.

Mathematical examination of terrain and pacing strategy

Martin et al. (1998) produced a mathematical model for power while cycling, from which results highly correlated (R2 = .97) with actual values as measured with an SRM (SRM GMBH, Jülich, Germany) power meter and presented with a standard error of only 2.7 W. This model was reviewed by Debraux et al. (2011) and found in terms of aerodynamic drag to be accurate. The SRM power meter has itself been shown to be valid and reliable in laboratory and field tests (Nimmerichter et al. 2009).

Using the model from Martin et al. (1998) it is possible to test the effect of various factors on performance. If wind direction is ignored, power needed to overcome drag force is given by the following equation, where rho is air density and CdA is coefficient of drag:

Power (W) = 0.5 * rho * CdA * velocity

It can be seen from the equation that rho and CdA remaining constant that power increases to the cube of speed. From Martin et al. (1998), changes in potential energy are given by the following equation:

Power (W) = slope * velocity * mass * g (-9.81 m.s-2)

Ignoring factors such as rolling and mechanical resistance, accounted for by Martin et al. (1998), when the sum of these equations equal zero, we get an approximation of terminal velocity for a given slope. For a slop with -5% is approximately 16.01 m.s-1 where CdA is equal to 0.5 and rho is 1.266 kg/m3 and the weight of the cyclist and equipment is 80 kg. The same equation can be used to calculate the added speed of producing more force on a descent. As an illustration, a cyclist obeying the aforementioned characteristics, using the same equations with the same limitations producing an extra 300 w of power would travel at 18.23 m.s-1 versus 16.01 m.s-1 coasting, providing a time benefit of 6.7 sec per kilometer. This might not be the best use of effort: In real world scenarios, an equivalent increase in speed can be achieved through an aerodynamic tuck reducing frontal area potentially improving if drag coefficient remains constant or improves (Peterman et al., 2015). Swain (1997) found increasing effort on uphill segments and decreasing it on downhill segments to provide a benefit in time to completion, supporting these conclusions.

Sprinting up to terminal velocity for a given situation, so as to spend the least time accelerating and take advantage of the ATP-PC reserve may provide a valuable benefit to a cyclist going from an uphill to a downhill scenario. For this situation, change in kinetic energy become the predominant force acting against the cyclist. The illustration below, using a formula also from Martin et al. (1998) ignores energy stored in the wheels:

Power (W) = ½ * mass (kg) * velocity (m.s.-1 ) / time (s)

From this equation it is possible to calculate time to reach a given terminal velocity. Ignoring factors such as the exponential increase in air resistance and the contribution by gravity, for a cyclist of the aforementioned characteristics acceleration to terminal velocity (18.23 m.s-1) for a power of 300 W on a -5% incline is 37.9 sec, whereas for the same cyclist producing 500 W it would require 22.7 sec. Average time savings over a 1000 m descent between 300 W acceleration and 500 W is 4.7 sec.

Conclusions on pacing strategy

Given the exponential increase in drag given velocity and constant acceleration due to gravity, more effort is best applied on uphill sections and less on downhill sections. These variations in effort also appear to be tolerated physiologically (Thomas et al. 2012).

Between Atkinson et al. (2007) and Thomas et al. (2012) it seems clear that the magnitude and duration of intensities relative to mean power from a self paced test and the ratio of hard efforts to soft efforts have a great impact on what degree of variation can be tolerated.

From the mathematical model proposed by Martin et al. (1998), it is possible to understand the implications of different intensities of effort at different point on a variable course. Sprinting at certain points on a variable course may be relevant to pacing strategy, if these efforts are well tolerate by the individual and exercise on the following section is below “anaerobic” threshold.

How the ATP-PC system relates to sustained performance and pacing

None of the studies on pacing reviewed mention efforts deriving energy from the ATP-PC energy system, a factor that in real world scenarios might prove significant. Menaspà et al. (2015a), found that 12 sec sprint power was not affected by 12 min of prior variable and non-variable high intensity exercise, deemed to simulate the intensity of the finish of a cycling road race, hence the capacity of the system is unlikely to be impaired by a sustained high intensity effort of 12 min duration. Menaspà et al. (2015b) found in an experimental setting that neither 10 min of variable high intensity exercise or constant high intensity exercise impaired sprint performance in elite cyclists.

The ATP-PC presents with a high effort to recovery ratio, with Bogdanis et al. (1995) observing a half life of 56.6 +/- 7.3 s for PC resynthesis. Hence recovery periods need to be considered is it it to be applied as part of a pacing strategy. Hazell et al. (2010) found in a study looking at the effect of 10 s sprint interval performance that a 2 min active recovery period allowed participant to maintain achieve a very similar percentage of peak power in subsequent sprints as a 4 min active recovery period, 95% and 96% of peak power respectively.

Stevens and Dascomb (2015) found that in TT type tests that sprints within these do not affect the repeatability of a result, when looking at mean power for the effort indicating that these are tolerated.

Assessing performance

Currently FTP and CP are two common assessments of performance in the field. These tests all use TT type efforts to assess mean power values given time, from this calculate sustainable power or power at lactate threshold.

Factors affecting the reliability of field tests

Maximal TT like efforts are a reliable and ecologically valid method of evaluating performance in the field and are tolerant to sprint efforts during a TT effort (Stevens and Dascombe, 2015). For short maximal efforts of 4 min, such as those required by the CP formula for the quantification of anaerobic work capacity, Nimmerichter et al. (2009) found small TT effort of this duration to be reliable, over various courses with a small degree of undulation and the effect of familiarisation with the course and protocol. A TT as a method of assessing average power was found by Stephens and Dascombe (2015), to provide repeatable results, with a coefficient of variance of <1% where the test were conducted by relatively fit athletes, familiar with the environment and the test procedure.

Peterman et al. (2015) while examining the drag area and performance found field testing with a power meter to more accurately determine performance than lab based tests, including VO2 peak, lactate threshold and economy and that power alone poorly predicted performance in TTs due to inter-individual differences in aerodynamic resistance.

Other environmental factors that can affect the reliability of field testing include temperature (Peiffer and Abbiss, 2011), air pressure and humidity and the degree of acclimatisation (Racinais et al., 2015).

Functional threshold power (FTP)

Due to it’s ease of application and ecological validity, FTP is widely used by cyclists and coaches for defining training intensities. FTP requires a simple, single field test to evaluate. Either average power for 20 min (P20) or average power for 60 min (P60) is used to determine FTP, with P60 being equal to FTP and 95% of P20 average power being an approximation of FTP.

FTP is said to be analogous with power at lactate threshold (Allen and Coggan, 2006). Due to the proprietary nature of the concepts, little is published in the academic literature testing and evaluating FTP, normalized power™ (NP) and training stress score™ (TSS). It is not clear from the available literature how LT was determined, however, it can be inferred. Coggan (2003) states “(LT is) defined as a 1 mmol/L increase in blood lactate over exercise baseline”. From this we can assume Coggan (2003) is referring to MLSS. MLSS is defined by Schuylenbergh et al. (2004) as “the highest constant workload during which lactate increased no more than 1 mmol x 1-1 from min 10 to 30” in a constant-load 30 min test”.

FTP was found by Gavin et al. (2012) to be equivalent to power where lactate is measured at 4 mmol and not MLSS. This result is in itself is strange since the definition of lactate threshold being where blood lactate is measured at 4 mmol·L-1 does not take into account inter individual differences in blood lactate kinetics. Also, in Gavin et al. (2012) used a different protocol than the protocol based on either P20 or P60 typically used to identify FTP, using an 8 min TT.

Miller et al. (2014) found CP to be a better predictor of mountain bike race performance. However Millar et al. (2014) did not define FTP from either P20 or P60 methods, but rather performed a normal lactate test and defined FTP as the power at 4 mmol·L-1 blood lactate. This does not match any definition of FTP, hence it is not actually test whether FTP can predict exercise performance.

Miller et al. (2014) compared intermittent power (IP) and FTP for predicting performance outcome in a cross-country mountain biking (XCO). The rationale for comparing IP to FTP was that it might better at predicting performance in XCO, due to the intermittent and high intensity nature of the sport. The authors followed the normal procedure for calculating FTP taking 95% of P20, while the intermittent power test includes 20 intervals of 45 sec interspersed with 15 sec recovery. The IP protocol was based on observations of the ratio of work to recovery in actual XCO race. Both models used linear regression to predict performance in an actual XCO race and were able to do so with significant accuracy (p < 0.01), with the IP model produced a not significant smaller error. This study support the notion that contextual testing might be more accurate in predicting performance, while at the same time finding that FTP is useful in predicting performance in events with highly variable power outputs.

Critical Power

CP is specifically defined as the power-asymptote of the power to time to exhaustion curve. This curve requires at least three points of power for a given duration to be plotted. In a simplified form, this curve can be reduced to a straight line between two points with CP being equal to the slope of the line. Originally Monod and Scherrer (1965) who conceived the concept stated that exhaustion will not occur at exercise intensities below critical power. This statement, while intuitively wrong, is also discredited by Vanhatalo et al. (2011), who state that cannot typically sustained for durations greater than 30 min.

Anaerobic work capacity, or W’ is specifically the curvature constant of the CP curve and can be understood to equal the “anaerobic reserve” or the finite amount of work that can be done above CP (Vanhatalo et al. 2011). This concept was tested by Dekerle et al. (2015) who had participants deplete 70% of W’ over 3 min and 10 min, followed by a period exercising at CP + 10%, for which the hypothesized would equal 30% of W’ should W’ equal anaerobic reserve. While for the 10 min test work completed was close to that predicted by the critical power model, for the 3 min test there was a greater degree of variability, with an average 49% more work being done in the 3 min test than predicted by the CP model. Dekerle et al. (2015) also found that a positive pacing strategy to be beneficial for exercise intensities above CP. While Dekerle et al. (2015) list a number of mechanism affecting such a strategy, such as the accumulation of hydrogen ions, or inorganic phosphates, it seems the greater relative contribution of ATP-PC system to powering an effort within this time frame is relevant, but not considered.

Jones et al. (2008) tested exercise capacity 10% above and below critical power for leg extension. Using P magnetic resonance spectroscopy to measure metabolites and hence changes in homeostasis, the researchers found that 3 min after the beginning exercise, levels of phosphocreatine (PC) and remained elevated, and no further changes in metabolites (phosphate) and pH occurred. By contrast exercise 10% above CP resulted in a shorter exercise duration, a drop in PC, pH and an increase in hydrogen ion concentration and inorganic phosphates from this the authors conclude that CP does mark the highest constant work rate for a muscle.

While CP does provide a method for quantifying an anaerobic reserve it does not account for efforts shorter than 2 min. For short efforts (Dekerle et al. 2015), CP does not accurately model performance. Morton and Billat (2004) adapted the model to account for this limitation, however this variation is widely used and also has a number of inherent constraints.

In real world situations rate of recovery of W’ needs to be considered.

Comparing CP and FTP, Miller et al. (2014b) found CP to better predict mountain bike race times and with less error. Issues with the definition of FTP used are evident, as it was taken to be power where blood lactate equals 4 mmol·L-1 during an incremental lab test.

Power curves and longitudinal data collection

Added to these methods of assessing performance, modern software and equipment allows the on going collection of mean power for maximal efforts given time, negating the need for specific testing in certain circumstances.


Both FTP and CP provide good methods of assessing cycling performance and can be used to predict race outcomes and as such, pacing strategy, yet longitudinal analysis of performance data may also provide an alternative in situations that call on an athlete to produce maximal effort.

Varying power output over long efforts tends to reduce performance where environmental variables are constant (Marwood et al., 2013), however on a course with variable profile this may not be the case (Swain, 1997).

Limitations to FTP and CP performance models occur where recovery between intermittent efforts is a factor and when short, high intensity efforts (< 2 min) are involved. Neither FTP nor CP account for sprint efforts using ATP-PC energy systems directly. No quantification of capacity in this exercise domain occurs, aside from in the form the W’ in CP. No method of assessing performance mentioned herein addressed the rate of recovery of W’.

No clear answer seems to exist on what constitutes an ideal pacing strategy is complex due to the breath of intrinsic and extrinsic constraints affecting an outdoor performance.

It is hypothesised that the ATP-PC system is relevant to performance outcome in TTs and as such should be contemplated as part of testing and a pacing strategy that varies depending on environmental context and an athlete’s relative abilities.


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