More Math Problem Thoughts.

Dug up this post from the BTR forum the other day, when someone sent me an email about "math problems". There's a pretty vocal contingent out there that likes to think they've got it all "figured out" when it comes to riding a bike in a triathlon. In my experience, models aren't necessary in this case, and only serve to distract efforts and energy from things that truly matter when it comes to performance.

This stuff isn't rocket science.

Something to consider at least!

Here's the first two posts in a thread from one of the guys who is vocal about the efficacy of his conclusions and methodology. Note the date...

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Ashburn

Posted: 14 Sep 2005 09:14 am Post subject: Modelling violations

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I got some good feedback and suggestions from Kraig on the "windy day pacing model." Whilst the model certainly illustrates that one cannot use time-weighted average power as a constraint, the normalized power algorithm (AKA "gizmo power algorithm" - kraig) can also be shown to produce fatal mis-hits as well.

Constructing a rectangular or circular course, where there will be short-ish high-head-wind segments, results in the model asking me to ride significantly harder than possible for the segment duration. More particularly, a course that is short enough will result in those high-power segments being acceptably short. Double the size of the course, and the power prescription (as a % of the global constraint) is the same, but the segment duration is now too long -- even if we reduce the global constraint to reflect the longer overall race duration.

As with the AP-constrained model, this version also demands a constraint based on an athlete's actual power-duration curve, as derived from long, variable effort rides. I.e., a segment lasting 20 minutes cannot be constrained to the rider's max power over 20 minutes, but rather to a lower figure that reflects that this is but one segment of a longer event. What is that figure? I think only experience can decide.

All in all, it still boils down to manual tweaking.

It's an interesting exercise, but as somebody on the other thread mentioned, models have their limits.

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post #2
Ashburn
BTR - Pro


Joined: 24 Sep 2004
Posts: 544
Location: San Diego
Posted: 14 Sep 2005 09:18 am Post subject: Re: Modelling violations

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Ashburn wrote:

All in all, it still boils down to manual tweaking.



And, to close the loop on my earlier analogy to using optimizers in the investment field, Markowitz (father of optimization) once closed an essay on the use of optimizers this way:

In the end, good investment management comes down to the judgment of reasonable men.

True of many endeavors, I suspect.

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And here's another thread that talks about how I view this modeling stuff (in Feb of 2006), especially for IM or HIM efforts. IMHO, this modeling exercise, and trying to "pin a single number on the whole deal" (as Kirk likes to say!) while interesting and whatnot, doesn't really add any practical value to individuals seeking to perform as well as they can in their next event.

Note the practical recommendations I make - nothing complicated, or original, but they are what they are. It's also interesting to note another thing that I always like to keep in mind - simply the perspective that there are many paths to the same result. Another thing to consider is that the illusion of knowledge and understanding does not do a service to anyone.

Anyway, here's a couple of my favorite posts from the thread linked to above:

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kraig wrote:

FWIW, I don't think bike racing and triathlon racing is a math problem, and therefore, I find this math exercise to be of little practical use. It's intellectually challenging, sure, but in the end it doesn't add value. I came to this way of thinking after doing the exercise on many, many diverse courses using lots of different assumptions for constraints - in the end, the most robust approach was the simplest one (one that is KJ based - edit kraig). Furthermore, inexperienced folks would probably get the most benefit by simply adopting a constant power strategy at the appropriate average power.

What's the appropriate average power - well, that's what practice is for, right?

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Ashburn wrote:

If it was linear, then pacing wouldn't matter.

Kraig wrote:

It's not that pacing doesn't matter - it's just that the excruciating details don't matter that much when compared to doing the basics well... e.g - doing as kirk suggests earlier - or as you have yourself suggested - don't be "stupid".

Most folks will benefit (who are doing the Oside 70.3 HIM for the first time or are relatively inexperienced with endurance athletics) the most from honestly assessing their fitness (i.e, doing only what they know they can do in training) and striving for a globally oriented constant power effort - let the super dial it up/down a bit when it thinks it needs to as terrain varies and use the PM to keep things in check from a global perspective.

On race day, I think one has to keep it simple - ya gots to run what you brung - and let the super make adjustments as needed.

That and have fun with the whole process...

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The Fiber Profile Column

Whoa, big "whoop-de-doo" over on the BTR forum for the past few weeks where lots of undies got up in a bundle. Ahhh, geeeeeezzzzz, it's just a web forum about bike crap - glad I got the chance to open the johari window for myself a bit in that thread.

Refreshing, in fact, to state some of my values, my ideas on changing behaviors, and having the opportunity to represent what I believe (ya know, bike racing isn't a math problem!) despite being continually attacked by a select few.

Anyway, during the sharing of ideas, I linked to a great thread that took place a long time ago, where Kirk made some good observations back in January of 2006. Here's a particularly relevant post in that thread:

http://biketechreview.com/phpBB2/viewtopic.php?t=504&postdays=0&postorder=asc&highlight=fiber+column&start=48

Here's the relevant bits of that post for those averse to clinking on links and whatnot:

"For a given cadence, changes in power (force) are the result of changes in the motor-units recruited. More force, more power, more motor-units. Fatigue can also result in the recruitment of additional motor-units. When motor-units normally recruited at a certain power begin to fatigue (produce less force when they fire), additional motor-units are recruited to take up the slack in order to maintain the power (force). Because of the progressive, sequential nature of motor-unit recruitment with the needed force, increasing power (force) generally requires additional recruitment.

I look at an entire muscle as a column, a column roughly divided up into power levels I call fiber-profiles. At max power (say a 5s sprint), most of the column fires. At low power, only the bottom section associated with that power is used. As fatigue at a given power sets in, the fiber-profile "creeps up” the column, as additional motor-units are recruited to maintain force (added to the top). So, the fiber profile associated with a given power as fatigue sets in includes more motor-units than when fresh.

So, take the example of cruising along at 250w (let’s say that’s a tempo intensity), a certain fiber-profile (composed of individual motor-units) is used to generate the force required to produce 250w. Over time, fatigue will set in within that fiber profile. That fatigue manifests as reduced force. In order to maintain that 250w (force), additional motor-units, ones normally recruited at higher powers, are then brought into that power’s fiber-profile.

So, it terms of recruitment associated with 20MP (or any power), as long as the power is at that level or higher, I know that AT LEAST the smallest potential fiber-profile associated with that power is recruited…and as fatigue sets in…that fiber-profile only grows larger (more motor-units recruited…added to the top) to make up for the drop in force production in the fatigued motor-units. The fatigued motor-units are still recruited, their force production just drops. So, that 250w *may* eventually recruit some of the motor-units normally within the >95% of 20MP profile with sufficient fatigue, but it is unknown to me exactly when this happens. When I train at intensities > a given power, say 95% of 20MP, I know that a given fiber-profile is recruited, and as fatigue sets in, this profile creeps up the column.

So, I think that at least a minimal level of recruitment can be associated with a given power, and that by acknowleding this minimal profile, I can quantify the amount of stimulus seen by that minimal profile (although it may grow to include more motor-units) via my choice of 60s chunks which include that profile (bins or time in zone are similar). I’d love to hear of ways that recruitment order and force production can commonly get tossed out of whack so that limitations to this way of thinking can be identified. If these issues do exist, it may also influence the use of powermeter data in general, because if non-sequential recruitment of motor-units occurs, a given power number has less meaning (at least to me). There is always more to be learned!

Kirk"

Yeah, visualizing things in terms of a column of fiber recruitment makes sense to this caveman, especially considering that when one uses gears, cadence is confined to a relatively small range (outside of the transition to/from coasting).

Good stuff to think about, anyway.

Oh yeah, I've disabled comments on this entry, so, if you'd like to engage others on the topic, feel free to sign up and post your thoughts on the BTR forum:

http://biketechreview.com/phpBB2/index.php

keep it real out there, folks.