VARIABLE POWER PACING

FROM CYCLING POWER LAB

Very few cycling events are run off in flat, windless, velodrome-like conditions. Almost always the rider has to contend with hills, headwinds and other factors which ought to have him thinking about a pacing strategy. 

At it’s simplest a pacing strategy might be “to ride the course as hard as a I can”. This is equivalent to saying “I’ll estimate the best constant power I can maintain for however long the course will take me at that power, and that’s the power I’ll use”. But things are not so simple. This is a naive pacing strategy as we will outline below. 

Effort is not equally valuable on all sectors of a variable course. In general, a power increase of 1 watt on an uphill or headwind sector will buy more time than will be lost due to a compensating power reduction of 1 watt on an easier, downhill or tailwind sector. Even if a riders effort (think in terms of average power for now, although we will expand on this a bit below) sums to exactly the same number at the finish line, there are faster ways to cover most courses than to ride at a constant power from start to finish.

Intuition based pacing

Many good cyclists, time triallists in particular, have developed an intuitive feel for this concept and use it regularly. They make aggressive efforts on uphill or headwind sectors, always within their limit considering the length of the sector and any that might be coming up, and then compensate a bit on easier sectors, allowing themselves just enough recovery. As a result of this intelligent pacing they cover the course faster than if they crawled on the hard sectors and flew on the easy sectors, yet their best effort for 30 or 60 minutes or however long the course may be is a limitation they live within.

Pacing by numbers

All riders are limited by their current fitness and a duration based profile of that fitness. A typical rider might be able to maintain 300 watts for an hour, 315 watts for 20 minutes, and 400 watts for 5 minutes. The Monod (Critical Power) Calculator reveals how these inputs can be fed into a model which will deliver a good estimate of the riders best power output for any duration. This can provide 2 essential inputs into the pacing problem

1. The riders best power expectation for the duration of the course

2. The limits of his flexibility on any sector or stretch of sectors within the course.
   
   

Now suppose the rider mentioned above rode a 60 minute course with a 20 minute hill. He might choose to ride the hill at 315 watts, the limit of his ability for 20 minutes, and then adjust his output on the other 40 minutes below 300 watts, such that his average power at the finish line came in at his best ability for 60 minutes, 300 watts. His time would almost certainly be faster than if he’d stuck with 300 watts all the way. Now we are starting to understand the pacing problem in a more useful, measurable way that isn’t lost in a tired riders “intuition”.

Cost of Power and Intensity Scaling

There is more to the problem than working with average power. Not all watts have the same physiological cost because riding at relatively high power outputs is more costly, watt for watt, than at relatively lower ones. For example, few would argue that a minute ridden at 500 watts would not cause more fatigue than 2 times a minute ridden at 250 watts. Various approaches have been proposed to model more representatively the physiological costs of variable power delivery in a way that can be quantified with a number that compares directly with average power and a riders duration specific power limitations. A popular solution is known as "Normalised Power" and forms the default method of power intensity scaling in this model. The interested reader may wish to Google "Coggan Normalised Power" for further detail. Suffice to say that the pacing problem, as in this model, is better considered using some form of intensity scaled power numbers to properly constrain the cost of variable effort within the riders limitations.

Solving the Problem

So how does one combine all of the smart ideas above to figure out

The best pacing strategy for a course of varying difficulty

1. How much time can be saved compared to a constant power effort?

2. There are a lot of “what ifs” in the problem, so much so that it cannot be solved well without a bit of computing power. 

Think again about the naïve pacing strategy “I’ll estimate the best constant power I can maintain for however long the course will take me at that power, and that’s the power I’ll use”. Because rider Critical Power increases as course duration decreases, and because course duration simultaneously decreases as power output increases, even this number has to be found using some sort of iterative computer algorithm. The constant power calculation in the pacing model uses exactly this approach. 

Optimising sector specific power outputs to bring the course time down, within the limits of a riders critical (intensity scaled) power across any one or continuous group of sectors is magnitudes more complicated and demands even more computing. The approach taken by this model is to calculate the relative profitability of power changes on each course sector. In other words, which sector, if ridden a bit harder, offers the greatest reduction in time for the least impact on the intensity scaled power at the course level? And which sector, if ridden a bit easier, offers the least time cost for the greatest impact on intensity scaled power. 

If all sectors can be ranked according to a profitability measure, then sector specific power outputs can be iteratively adjusted to bring the course time down, while holding the course level intensity scaled power unchanged. And one can continue making these adjustments until the riders flexibility to adjust is effectively halted by his sector duration specific critical (intensity scaled) power limits.

In Practise

The pacing model on this site follows the principles covered above. It allows you to model a course with up to 10 sectors, to see a constant power pacing estimate (i.e. power choice and estimated course time) based on your critical power profile (inputs at 3 durations). It also allows you to see a variable power pacing proposition based on the optimisation approach outlined above. If the course is varied, then this should demonstrate some time savings against the constant power approach. And that is the point of all this: free time savings that result from an intelligent use of your fitness.

Inputs: Environmental Variables

• Temprature (Deg C). Input a temperature in degrees Celcius (e.g. 20)

• Pressure (Millibars). Input the ambient air pressure in Millibars (e.g. 1013). You can get this number from any good weather forecast.

• Relative Humidity (%). Input the ambient air humidity in percent (e.g. 20). Again you can get this number from a weather forecast.

• Wind Direction. Select the applicable wind direction as a heading (e.g. NW) or else input a wind bearing between 0 and 255 degrees. This is the direction the wind is blowing from, not to.

• Wind Speed (KPH). Input the wind speed in Kilometes per hour (e.g. 5).
  
  

Inputs: The Rider & Bike

• Rider + Bike Weight (Kilos). Input total weight in kilos (e.g. 80).

• CdA. This is the metric of aerodynamic drag (Coefficient of drag x frontal Area) applicable to the rider and bike combined. The figure is expressed in metres squared. Typical cycling values are in the range .20 to .30

• Tyre Radius. Input the radius of your wheels (including tyres) or simply use the dropdown to select one of the popular values.

• Wheel Intertia. This is a hard to measure coefficient. It is suggested to retain the default of 12.

• CRR (Rolling Resistance). Select the coefficient of rolling resistance applicable to the course. The dropdown is a handy way to select typical values.

• Inputs: Rider Critical Power

Observations of "best" sustainable power (Mean Maximal Power) at 2 or 3 of the selectable durations. For more details of the theory behind Mean Maximal and Critical Power modelling see the Monod (Critical Power) Calculator.

Quote Power At / Drivetrain Efficiency

Power meters such as the SRM, Quarq & Ergomo measure wattage at the cranks.  The actual wattage delivered to the hub, where a PowerTap would measure it, is a little bit lower due to drivetrain inefficiencies. Specify drivetrain efficiency in percent (eg 97.5, which would be a good estimate). The significance of this parameter is that, if the model is set up to calculate the power required to achive a particular time on a particular course,  the power required of the cyclist will be a little higher if quoted at the crank. ie 97.5 watts required at the road = 97.5 watts at the at the hub = 100 watts at the crank, when drivetrain efficiency is 97.5%.

Intensity Scaled Power As

Select a preferred intensity scaling methodology.

• Normalised Power. Corresponds to the method outlined in the "Cost of Power" introduction above.
  
  

Course Sectors

• Direction. Select the applicable direction as heading (e.g. NW) or else input a bearing between 0 and 255 degrees. This relates the riders direction to the wind, so a ride direction of "S" (180 degrees) is an unmitigated headwind when the wind direction is "N" (0 degrees).

• Distance (KM). Input the ride distance in kilometres (e.g. 40).

• Average Grade (%). Input a gradient in percent (e.g. 3 is 3 percent, -2 is -3 percent).

• Power (Watts). If specifying some manuakl adjustments input the sector power in watts.

• If you have loaded a predefined course (public or attached to your profile) then mousing over the sector number (e.g. "Sector 1") will display the sector name.
  
  
  

Outputs

• Average power over the course.

• Intensity Scaled (e.g. Normalised) power over the course.

• Midpoint. The time to mid distance which may be of interest to time triallists contemplating split times, especially on out and back courses.

• Joules. Rider energy consumption over the course, assuming 25% mechanical efficiency.

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Outputs: Best Constant Power

Here you will see the "rider best" constant power applicable for the course, and total time.

Outputs: My Adjustments

Here you will see alternative intensity scaled power and time numbers accounting for any of your adjustments to sector specific powers, if applicable.

Outputs: Optimised Variable Power

If the model has been able to suggest a variable power pacing plan that will reduce and minimise the course time within the limits of the riders duration specific power limitations then the intensity scaled power and time numbers will display here. The proposed specific powers will appear in the respective sectors.

Outputs: Sector Group Intensity Scaled Powers

These somewhat numerous outputs are important. It was said above that the riders performance is constrained by his duration specific power limitations. These outputs form a check of sector or sector group specific intensity scaled powers through all combinations of sectors. None of these numbers should appear in red. Red numbers indicate that the riders performance limitations have been exceeded and you should watch these especially carefully if running the model with your own power adjustments.


Power Benchmarks

Where am I on the spectrum of cycling ability and where do I want to be? All competitive bike riders ask themselves these questions and all coaches are trained to think about their clients in a similar way. Both of these questions amount to performance “benchmarking” and the adoption of power in cycling has progressed the discipline of benchmarking like never before. We provide the following tools:

Time Trial & Triathlon (Bike Leg) Benchmarks

Use this resource to cross reference finishing times and average power outputs applicable to performance in standard distance time trials and triathlon bike legs. We simplify matters by assuming a flat course and windless conditions but you can adjust the figures for applicable rider weight and riding position.

Ascent Benchmarks

Evaluate the wattage per kilo implied by the weight and ascent time of any rider on a range of significant mountain ascents. Benchmark pro riders watts per kilo, "VAM", or estimate your own or an another specific riders time given a weight and wattage assumption.

CPL Users Power Data

The beauty of power data, interpreted relative to rider weight or aerodynamic drag, is that it entirely defines performance potential in cycling. We collect power data, anonymously, from our registered users and present some views of the summary data for benchmarking applications.