Normalized Power -> Optimizing Output for TT's
 

Exactly four months ago, we were debating the effects of watts output going up a hill vs. down a hill.

I asked for some distance vs. altitude data in order to try to optimize power vs. time. Dr. W. responded, but unfortunately, the info/data he gave was from one of the various topo programs; this data was much too rough/incorrect to be useful.

So a few months go by, and I realize I should probably try to get some Garmin data and attempt the same thing. Asmallsol gave me some for a prologue TT we both competed in this past May. Fortunately it had some simple hills in it that would be useful for testing the optimization algorithm.

The algorithm uses Normalized power. My Normalized power isn't exactly the same as Allen and Coggan's, because it's difficult to take a thirty second average when you're in the distance domain; but it uses the same basic concept. The computer, of course, doesn't see a downside to you putting out 100 watts one second and 700 watts the next, so after I got my results back, I applied a simple digital smoothing function to them.

The results are below.

http://i179.photobucket.com/albums/w...untitled-1.jpg

Only three more months of crappy cycling weather.

FYI - One of my frequent riding partners is an artillery officer, and he states that GPS data is unreliable for altitude. You'd be better off using a benchmark calibrated altimeter.

No discussion or conclusions sections?

I would like to see a plot of total energy throughout the test. Use an approximate mass and calculate kinetic, potential and total energy to illustrate how a low speed at the top of a hill is different than a low speed at the bottom and that one could use the potential energy stored to compensate for the reduced power output on the descent... kind of like banking power.

Furthermore, are all watts created equal? ;) One could argue that working hard on the descents is foolish because more of that energy is going into a high drag condition (high speed) instead of using that energy for the lower speed sections like the climbs.

You might enjoy reading these, for hilly time trials uneven power is better.

Variable versus constant power strategies during cycling time-trials: prediction of time savings using an up-to-date mathematical model.
http://www.ncbi.nlm.nih.gov/sites/en...ubmed_RVDocSum
Our findings confirm that time savings are possible in cycling time-trials if the rider varies power in parallel with hill gradient and wind direction.


Acceptability of power variation during a simulated hilly time trial.
http://www.ncbi.nlm.nih.gov/sites/en...ubmed_RVDocSum
finish time for the variable power trial (3670 +/- 589 s) was significantly faster than that for the constant power TT (3758 +/- 645 s), the 95 % confidence interval for the percentage improvement being 0.4 to 4.3 %.

This is true, however it was with my edge 305 which also has a built in pressure based altimeter, and uses that in combination with the GPS signals. The accuracy is questionable, but it does give a rough estimate. The same 30 mile loop normally comes in + or - 50 feet of variance from rides in the past.

I have thought about this a little more and tried to come up with a general equation for pacing. The power at any given time (Pt) is the sum of the power that ideally comes from steady efforts (Ps) and the power that can come from variable efforts (Pv)

Pt = Ps + Pv

Ps is a function of the Cp of the entire event duration (highly FTP dependant)
Pv is a function of Cp of the obstacle duration and intensity (highly AWC dependant)
The actual equations for Ps and Pv could contain many terms to account for everything like aerodynamic effects, slope of road, etc, etc. I won’t even try to suggest those at this time.

On a windless flat there would be no obstacle so

Pt = Ps (which is ideally Cp event duration)

On an uphill the obstacle is positive and you increase power

Pt = Ps + Pv

On the downhill the obstacle is negative (reloading AWC so to speak) so

Pt = Ps – Pv

The model (obviously) already uses Kinetic and Potential energy, so that you can 'bank' the power.


That's the basic premise. In fact, in order to minimize the time used, the model artificially increases the wattage at each point, and then measures the resulting reduction in time. It takes the points that have higher impact and increases those wattages, and takes the points with lower impact and lowers them, so that the normalized power remains constant.


Thanks for the articles, I hadn't seen them.

I've written about the Monod model before and pacing strategy is just another application. The model consists of a critical power, Cp, that can be maintained for a long time, and anaerobic work capacity which is the amount of work that is available above and beyond that from critical power. The simplest treatment to optimize pacing strategy is to take Cp as the minimum power produced over the course of the TT and then add power over Cp up to the limit of AWC so as to minimize time. The next level of complication is to allow a recovery of AWC during periods when power is lower than Cp. To do so however requires some model of the rate of replenishment of AWC as a function of power below Cp and time. I'm currently not familiar with a simple model for this, though.

Garmin 305 dosent rely on GPS for altitude.

ElJ what program did you do this in? If it is excel could I see the file?

Nicely put.

Where have you written about this before? Care to post a link?

As for AWC recovery a good start might be to look at work:recovery ratios done training at different intensities. How much recovery do you need for 20min, 8min, 1min and <30s intervals respectively? It may go from a low of 2:1 work:recovery to 1:10 etc. It certainly wouldn't be simple.. but that's ok.

Search engines are your friend*. I like this as a basic overview, http://www.velo-fit.com/articles/critical-power.pdf but a search of the wattage list should give several more detailed discussions and references.

*I probably could look them up but I think I'm too stupid or lazy.

Here's the first from wattage:

http://groups.google.com/group/watta...3fe204c75dc388

Thanks for the links. I'll try to be less lazy next time.

Physiological effects of constant versus variable power during endurance cycling.
http://www.ncbi.nlm.nih.gov/sites/en...RVAbstractPlus
No differences were found between the CP and VP trials in mean VO2 (CP 3.33 +/- 0.11 L x min(-1), VP 3.26 +/- 0.12 L x min(-1)), mean heart rate (CP 158 +/- 3 min(-1), VP 159 +/- 3 min(-1)), mean blood lactate concentration (CP 4.2 +/- 0.7 mM, VP 4.3 +/- 0.7 mM), or mean RPE (CP 13.9 +/- 0.4, VP 14.1 +/- 0.4). CONCLUSION: Therefore, during a strenuous 1-h effort (78% of VO2max), subjects experienced no additional physiological stress by varying power +/- 5% compared with that during a constant power effort.

Joe Friel wrote about this topic in his blog. Same crap but better written. :)

http://www2.trainingbible.com/joesblog/blog.html

More on Pacing

Since my post last month on negative splits in steady state events such as time trials and triathlons there have been a lot of questions about how the principles described there apply to courses with hills and wind. There have been several scientific studies done on this matter. Here is a brief summary of several of these studies. I'll let you draw your own conclusions.

* Using a mathematical model Swain found that when compared with a constant effort there was a significant time savings in a cycling time trial by slightly increasing power on the uphills and into headwinds and decreasing it slightly on downhills and with tailwinds. (Swain. 1997. A model for optimizing cycling performance by varying power on hills and in wind. Med Sci Sports Exercise 29:1104-1108.)

* This study involved a review of other research such as Swain's above using a mathematical model to predict how hills and wind affect performance in a cycling time trial. The authors then revised the previous models slightly but the results were largely the same as the others: Increasing cycling power on uphills and decreasing it on downhills, and increasing power into the wind and decreasing it when riding with the wind improved time trial times significantly. (Atkinson et al. 2007. Variable versus constant power strategies during cycling time trials: prediction of time savings using an up-to-date mathematical model. J Sports Sci 25(9):1001-1009.)

* Seven male cyclists did a 16.1km (about 10 miles) time trial on a CompuTrainer 3 times each. There was a simulated 8km headwind in the first half of the ride and a simulated 8km tailwind in the second half. The pacing of the 3 rides were: a) self-selected pace, b) constant power and c) variable pacing with 5% higher power into the wind and self-selected and constant with the wind. Times were significantly faster in b and c compared with a. The fastest was c. Variable pacing based on power should be used when there is a headwind. (Atkinson and Brunskill. 2000. Pacing strategies during a cycling time trial with simulated headwinds and tailwinds. Ergonomics 43(10):1449-1460.)

* Seven cyclists did 3 time trials of 800 kilojoules each. A kiloJoule (kJ) is a measure of mechanical energy expended; 1 kcal = 4.184 kJ. Considering that an experienced and fit cyclist is about 23% efficient, this means that they were riding as intensely as they could until they expended roughly 880 kcal. For most such athletes this would take about an hour. The 3 courses and conditions were 1) flat with a self-selected power, 2) hilly with 5% grades ridden at the same constant power as course #1, and 3) same course as #2 but ridden with power varying - 5% greater than #2 on uphills and 5% lower on downills. The overall power was equivalent for all 3 courses and conditions. But the finish time was significantly faster with pacing #3. The results were: #3 - 3670 +/- 589 seconds vs. #2 - 3758 +/- 645 seconds. So varying power by 5% on hills did not significantly change the power output but saved, on average, 88 seconds in a 1-hour time trial. (Atkinson et al. 2006. Acceptability of power variation during a simulated hill time trial. Int J Sports Med 28(2):157-163.)

* So does varying power with hills and wind as suggested in the above studies cause additional physiological stress? That could be quite detrimental for a triathlete who needs to come off the bike and run. But according to Liedl et al this is not a problem. They found that variations of +/- 5% had no negative consequences for the riders' performance when compared with a constant power output. (Liedl et al. 1999. Physiological effects of constant versus variable power during endurance cycling. Med Sci Sports Exercise 31(10):1472-1477.)

* Speaking of triathletes, what is the effect of varying power on the run? A recent Aussie study addressed this issue. Eight triathletes did 2 bike-run workouts. In #1 they they rode steadily for 30 minutes at 90% of their lactate threshold power (another way of identifying FTP). In #2 they alternated +/- 20% (!) of the power they rode at in #1 every 5 minutes for a total of 30 minutes. So they did 5 minutes at FTP + 20%, 5 minutes at FTP - 20%, 5 minutes at FTP + 20%, etc. After each 30-minute ride the triathletes immediately started a run to exhaustion at 16.7 kph (about 6 minute/mile pace). The times for the run to exhaustion improved significantly after the variably paced rides. Following the steady power ride the average time to exhaustion on the run was 10 minutes, 51 seconds (10:51). After the variable-power ride the average run was 15:09 - an imporvement of nearly 50%. That's huge. However, the improvement may well have been because in #2 the last 5 minutes of the ride nefore starting the run was done at 20% below FTP. Coming off of the bike somewhat rested would have been an advantage, especially given that the power for the last 5 minutes was a whopping 20% below FTP. (Suriano et al. 2007. Variable power output during cycling improves subsequent treadmill run time to exhaustion. J Sci Med Sport 10(4):244251.)

I can't read all that.

I assume it mean in a TT over undulating terrain, I'll be faster if I go a bit over FTP on the uphill, and then recover by going a bit under on the downhill?

Correct

Yeah, and the +5%/-5% feels better too. I find the hill climbs feel more natural with a bit more pressure on, the recovery feels nice on the back side, and by the time the next hill comes, I'm feeling guilty about the recovery already :)

I'd think that this model would move around a bit based on drag and weight.

I will buy a pacing strategy from you for $2 per TT. :) I will give you the profile and targeted wattage, you give me the strategy!

Actually, while I do appreciate your work on this, and perhaps it is to do exactly the above (make a little cash) I have to say that knowing my abilities, I doubt I could go so far into the red as your calculations suggest. It would end up costing me too much to recover (of course this is an opinion...maybe we should do some testing? I have an undulating TT in the PA state TT championships and the NYS TT championships that I can send you as well.)

This really seems like a nice application for the Qranium when it comes out. It could tell you your target based on where you are on the course. The research behind that target is in its infancy, but this would be a good tool to start figuring that out.

Actually, the ibike might be an even better head unit with an ANT+ Sport PM because it will actually measure grade, and will have some idea of the relative wind speed. Analysis would have to be done at home, but it could be a good research tool too.

Qranium is supposed to have a barometric altimeter, so I guess that would be good enough to measure grade?

But I think the application with the Qranium would be to plot your TT course out ahead of time using mapping software, then have the Qranium telling you what your power ought to be at any point on the course based on GPS location, rather than sensing the grade in real-time.

WJO, I'd be happy to do some for you au gratis. Consider it karma for sharing your wind tunnel data. But FYI, the altitude data has to be quite smooth. I first tried to do it for mapmyride data or some such, but it isn't good enough. I could filtering it again, but if you had barometric data it would definitely help.

I could relatively easily set it up to 'max' at a certain wattage.

I never thought of charging for the info or the program. My app isn't really set up for wide distribution; I'd have to do a bunch more work to make it user friendly.

I think to do this right, significant testing and course prerides would be required. Certainly not for every race but could be worth the effort finding TSTWKT for a big event.


Sweet food for thought ElJ, this algorithm fascinates me.

I don’t think it’s so much a max power as it is a maximal amount of anaerobic work done. Knowing that you are an engineer I suspect the forces on the rider portion of your algorithm is pretty sweet. However, I feel that power normalization functions will over estimate the available AWC.

Take a look at my little doodle for a proposed solution. The upper plot represents an out of competition test doing a fairly short flat time trail where you instruct the athlete to sprint out the gate and ensure that the TT is strongly positive split. The power output would decay to a constant value. Now we can calculate area A.

The next plot is a race simulation where we allow the optimizer to prescribe any power output –normalizations be damned- up to say CP30s. You also set a rule such that area B minus area C must be less than area A. Everything else can be tweaked to optimize the forces on the rider. ???

IIRC, Monod starts to break down at durations < ~3 minutes. Most TT courses are going to have elevation features that take less than that to traverse, which might present a problem.

Hmm, maybe base it off a rider's current MMP curve, assuring that the pacing strategy's MMP curve stays under it, using AP for the first 5 minutes and NP from 5 minutes +.

Also, ElJ, I think you're going to have to include wind, not just elevation in the algorithm, as it's a pretty serious consideration for optimizing pacing. Have you seen Kraig Willet's article and Ron Ruff's spreadsheet? Might be interesting to you. The only time I've worked out a pacing strategy, I used Ruff's spreadsheet with the addition of an NP calculation.