Last week I posted an article that showed the optimal power pacing strategy for a 40 km cycling time trial where there is a headwind for the first half and a tailwind for the return leg. In that article, I used CCAP as the power metric to constrain the power output for the cyclist in the time trial. In this post, we will take a second look at the optimization performed for the situation where the overall power is constrained to 250 watts and the wind speed is 5 m/s. The difference in this second look is that we will perform the optimization using “normalized power” (general mean) instead. We will do it for standard normalized power with a 30 second rolling average and a 4th order exponent as well as normalized power with exponential smoothing instead.

Race Course for the Pacing Optimization

For all the optimizations and plots shown in this article, you download them here: HeadTailWindR1.zip. To run the simulations yourself, you will need Optimal Cycling V0.9.1 or greater. Note that in the optimizations done here, we are using 428 points to represent the course and that acceleration effects are taken into account.

Optimized Power Using CCAP

From the previous article, here is the optimized power plot obtained using the CCAP power metric:

Plot #1: Optimized Power Using CCAP, 250 Watts, 5 m/s Wind

In Plot #1, the suggested power output in the first half of the course with the headwind is about 274 watts. The suggested power for the return leg with the tailwind is about 204 watts. Also, notice that it is recommended to have a short spike in power at the start of approximately 300 watts and to decrease your power when close to the finish.

Optimized Power Using Standard Normalized Power

Now, we take a look at the optimized power obtained by using a standard normalized power of the 4th order using a 30 second rolling average:

Plot #2: Optimized Power Using Standard Normalized Power, 250 Watts, 5 m/s Wind

Plot #3: Optimized Power Using Standard Normalized Power, 250 Watts, 5 m/s Wind (Start)

Plot #4: Optimized Power Using Standard Normalized Power, 250 Watts, 5 m/s Wind (Zoomed Middle)

Plot #5: Optimized Power Using Standard Normalized Power, 250 Watts, 5 m/s Wind (Finish)

The optimized power pacing strategy obtained using standard normalized power gives power plots that exhibit some unusual characteristics because of the use of a rolling average in the power metric. Plot #2 shows the overall view of the power plot and the very large spike in power at the start makes the graph difficult to see clearly.

Plot #3 shows just the start of the optimized power and we can see that using standard normalized power results in a suggestion of starting out at about 1200 watts! The suggested power for the start could have been even higher if the simulation didn’t cap the power output for the cyclist to a maximum value of 1200 watts. After this huge effort, the suggested strategy is to bring the power output down 0 watts and then bring it back up to race pace.

Why does standard normalized power give this seemingly illogical suggestion? The answer is because standard normalized power utilizes a 30 second rolling average that requires us to average the power output for the first 30 seconds of a race before calculating actual normalized power values. This averaging results in overly optimistic starting powers and then a characteristic large dip because it is beneficial to bring your speed up quickly from zero.

In Plot #4, we see the zoomed in plot of the middle portion of the race. The suggested power riding into the headwind is about 261 watts and the suggested power for the return leg with the tailwind is about 228 watts. Note that there are a couple of power spikes in the transition between these two states caused by the use of the rolling average. In Plot #5 at the end of the race, the rolling average once again causes problems with the suggested power output as seen by the greatly varying power.

What can be done about these power spikes caused by the use of a rolling average in standard normalized power? The answer is that we can remedy it to an extent using a different form of averaging as we will see in the following section.

Optimized Power Using Exponentially Smoothed Normalized Power

Now, we are going to take a look at the optimized power obtained using normalized power with exponential smoothing:

Plot #6: Optimized Power Using Exponentially Smoothed Normalized Power, 250 Watts, 5 m/s Wind

Plot #7: Optimized Power Using Exponentially Smoothed Normalized Power, 250 Watts, 5 m/s Wind (Start)

Plot #8: Optimized Power Using Exponentially Smoothed Normalized Power, 250 Watts, 5 m/s Wind (Zoomed Middle)

Plot #9: Optimized Power Using Exponentially Smoothed Normalized Power, 250 Watts, 5 m/s Wind (Finish)

Comparing Plots #6-9 with those of Plots #2-5, we can see that using normalized power with exponential smoothing provides more sensible results due to fewer large power spikes. Looking at Plot #7, we can see that we still have the unusual suggestion that we start the race at the maximum power of 1200 watts but we don’t have the dip to zero power anymore caused by the use of a rolling average.

In Plot #8, the suggested power output riding into the headwind is about 261 watts and the suggested power output for the return leg with the tailwind is about 228 watts. These suggested numbers are essentially the same as what we obtained in the middle portion of the race using standard normalized power. Also note that the transition of the power between these two states is much cleaner in Plot #8 compared to Plot #4.

In Plot #9 for the end of the race, we can see that we don’t have the same wild power spikes that standard normalized power produced in Plot #5. There is still a bit of noise, but is much cleaner.

Discussion

What can we take away from this comparison? The answer is that one must be careful in using averages as part of a power metric because it can lead to unintended power spikes if you use it to solve for the optimal power pacing for a given race course. Standard normalized power is not suitable for use in solving for the optimal power pacing because of the problems shown above where we do detailed simulations that take into account acceleration. Modifying standard normalized power to use exponential smoothing instead of a rolling average gives more realistic results but there is still the problem of abnormally high suggested power outputs for the start of a race.

CCAP gives more sensible results for the start and finish of the race as seen in Plot #1. However, there is a problem of extended power output above functional threshold power (FTP) that affects both types of power metrics. As noted before, CCAP gives a suggestion of 274 watts riding into the headwind and 204 watts riding with the tailwind. By comparison, the power out suggested by each of the normalized power optimizations gave 261 watts for the headwind and 228 watts for the tailwind. It may not be possible for a cyclist to ride at 274 watts or even 261 watts for the extended time needed to cover 20 km going into a 5 m/s headwind if his FTP is 250 watts.

This means that I will be improving CCAP in the future in order to provide a solution that gives both stable power values as well as take into account the duration a cyclist spends above certain power levels. In particular, I will be looking at and coding energy flow models to see what is viable.