Mt Washington

[Robert Chung]

"The Pomeranian" <[email protected]> wrote

> The trouble is that this ends up being a social science because we can't put the subject in a lab
> for extended periods the way we could mice and machines.

Hey, this is why I *like* analysing social science data. The analysis often needs to be more artful
and the reasoning more subtle (though, alas, it rarely seems to be).

> I'm not sure why gradient would be too much of a factor (or any factor?) regarding power v. rpm.
> Maybe it is, but I just don't know why it would be...

Because of force. We all appear to know that given a particular gear, power scales supralinearly
with rpm. What many seem not to know (or haven't internalized as completely) is that while force
also scales supralinearly with rpm on the flat (given a particular gear), as the road tilts up that
relationship changes. Indeed, for very steep grades, force is almost entirely dependent on gear and
almost not at all on rpm.

 

[The Pomeranian]

Tom Kunich wrote:
>
> "The Pomeranian" <[email protected]> wrote in message
> news:[email protected]...
> > The trouble is that this ends up being a social science because we can't put the subject in a
> > lab for extended periods the way we could mice and machines. The bottom line is that good
> > general conclusions would seem to be expensive.
>
> Are they? Do you ride the way you think you should ride or the way that feels natural to you?

The issue isn't about me. The issue referred to is aquiring _general_ and compelling scientific
evidence regarding cadence and power.

 

[Robert Chung]

Arrrrgh. Ooops. Sorry. My bad. I GAVE YOU THE WRONG URL.

The right one is: http://mywebpage.netscape.com/rechung/wattage/cadence/cadence-plot4.png

My apologies. Damn. I also have to apologize for my snide comment about it being funny how some
people can look at the same evidence and come to different conclusions, because I was pointing you
to a different plot. Ugh.

plot4 is just plot2 with the hill-climbing part labeled. I kept referring to hill and altitude
change in the text of my replies and how I couldn't have done this part without the altimeter of the
S710, but the graph I gave you (obviously) didn't have any hill or altitude info on it.

So, let's turn back the clock, if you're willing. What do you see?

Since I ****ed up earlier, I'll show my cards first and tell you what I saw:

A guy who seems to show a preference for rpm in the 90's on the flat seems to prefer a very
different cadence on a hill, and it seems he was producing pretty reasonable power there, too. This
means that the power-cadence relationship isn't straightforward, and that optimal cadence isn't
independent of conditions.

That's it. But you can see why I don't have any argument with your "incentivized preference for
cadence" (well, except that it's a repugnant neologism). I think riders who have been riding for
almost any length of time automagically choose something pretty close to the optimal cadence given
the conditions and constraints facing them. IOW, I tend to think that cadence is a response, not a
factor (which I wrote in response to Tom somewhere else in this thread).

 

[The Pomeranian]

Robert Chung wrote:
>
> Arrrrgh. Ooops. Sorry. My bad. I GAVE YOU THE WRONG URL.
>
> The right one is: http://mywebpage.netscape.com/rechung/wattage/cadence/cadence-plot4.png
>
> My apologies. Damn. I also have to apologize for my snide comment about it being funny how some
> people can look at the same evidence and come to different conclusions, because I was pointing you
> to a different plot. Ugh.

Would I be snide to say that rather than "different people looking at the same evidence and coming
to different conclusions," the same person
(me) looks at different evidence and reach the same or similar conclusion?

Well, don't worry, I don't see the same thing, now I see less.

> plot4 is just plot2 with the hill-climbing part labeled. I kept referring to hill and altitude
> change in the text of my replies and how I couldn't have done this part without the altimeter of
> the S710, but the graph I gave you (obviously) didn't have any hill or altitude info on it.
>
> So, let's turn back the clock, if you're willing. What do you see?

The data points are not sequenced, so it is hard (impossible) to tell. For me this topic isn't what
power someone put out at some specific instant or short time period (2.52 & 5 s), but is rather
roughly that of attaining the most Joules out over a "whole race time period" (for both TTs and Hill
Climb TTs: sustainable power). The lack of sequencing is a problem because it can distort the
results in trying to determine what the sustainable power is for some given cadence. For example, a
rider climbing a hill reaches a short steep switchback for which he/she has inadequately low gears,
and so "stomps on it" for 5 seconds. The "stomping" requires unsustainable power output, but the
sample does show high power there. Immediately after exiting the steeper section, the rider sits
down, "spins fast," and does 10 s of recovery riding. The recovery riding will be lower than what
would normally be sustainable, so the power sample is distorted low, for the higher cadence. The low
cadence is distorted high. How many times has this exact scenario occurred? A lot I'll bet, and it
is due to either habit or lack of low gears.

So I don't believe the difference in powers v. cadence as shown in the plot are yet meaningful as
they stand. Was the hill climbing rider really able to put out 350 sustainable watts at 70 rpm, but
only 250 sustainable watts at 95 rpm (-1.5 dB or -39%).

> A guy who seems to show a preference for rpm in the 90's on the flat seems to prefer a very
> different cadence on a hill, and it seems he was producing pretty reasonable power there, too.
> This means that the power-cadence relationship isn't straightforward, and that optimal cadence
> isn't independent of conditions.

It may not be, but the graph by itself doesn't convince me.

> That's it. But you can see why I don't have any argument with your "incentivized preference for
> cadence" (well, except that it's a repugnant neologism).

Heeeyyy... There are no new words there. You can't complain when you use "automagically" and the
recondite "supralinear." I'm trying to get the explicit meaning. I'm eager for better articulation,
so what do you offer?

> I think riders who have been riding for almost any length of time automagically choose something
> pretty close to the optimal cadence given the conditions and constraints facing them. IOW, I tend
> to think that cadence is a response, not a factor (which I wrote in response to Tom somewhere else
> in this thread).

>> I'm not sure why gradient would be too much of a factor (or any factor?) regarding power v. rpm.
>> Maybe it is, but I just don't know why it would be...
>
> Because of force. We all appear to know that given a particular gear, power scales supralinearly
> with rpm.

We all? I don't presume your wrong (at all), but I don't presume the parameters. Explain.

> What many seem not to know (or haven't internalized as completely) is that while force also scales
> supralinearly with rpm on the flat (given a particular gear), as the road tilts up that
> relationship changes. Indeed, for very steep grades, force is almost entirely dependent on gear
> and almost not at all on rpm.

I don't see how this shows why the so-called "optimum cadence" would change for climb v. flat. On a
10sp 12-25 cassette, the average step size is 8.1%. Not that cadence-plot1.png has a lot of
curvature, but
8.1% "fits into" the seemingly preferred range 88 to 108 rpm quite easily (the power is somewhat
flat in that range). The rider can choose the cadence, within 8%, for some given power output
level. If, on the flat, the required force to increase rpm is getting "too high," they can either
back off or just use an easier gear. I suppose I do suspect the power output is quite flat within
+/-4% of "optimum cadence."

I guess I see it as simply the power is delivered via force and rotation of the pedals. What does it
matter if the energy lifts a weight or gets gas molecules moving? How does the body know if the
energy (power*time) is being transferred to potential energy by lifting a weight, or transferred
into kinetic energy of surrounding gases? The legs are simply pushing on the pedals, at a cadence
selectable within 8%.

Like I said before, I believe bike racers have traditionally been overgeared (for climbing) in the
past, and for a justifiable reason. (Or maybe I should say they simply didn't have low gears as a
reasonable choice, because of the tradeoffs.) For this reason, I'm a little skeptical of the hill
climbing data you have shown. One thing that would interest me is showing hill climbing data that
undeniably showed that the sustainable power for Rider X, while climbing at a "low cadence," was
congruent with the sustainable power that Rider X showed while riding the flat at a higher cadence.
While this would not yet prove any kind of "cadence for conditions" hypothesis, it may at least show
that power delivery v cadence is possibly quite flat.

Riders need to be tested for climbs where they have the gears needed to spin up to about 110 rpm at
any point in the climb, and unprejudicedly do runs focusing on narrow ranges. The same is true for
the flats -- try some low cadences too.

So maybe "optimum cadence" changes according to conditions, I am still uncertain why that would be
true. I am concerned that a tradition of climbing at low cadences, and not having low enough gears
to even fairly test this, could be distorting the results. "Spin to win" prejudice in the flats
could be doing the same, although I am not quite as suspicious of this. I don't care how it comes
out, either way.

 

[Robert Chung]

"The Pomeranian" wrote
> Well, don't worry, I don't see the same thing, now I see less.

That's interesting. In your earlier message, you pointed out that both riders spent most of their
time around 95rpm, and explained it as incentivized preference (I'm more used to the phrase
"revealed preference" (and "automagically" was a typo--though perhaps more a Freudian slip since
I've seen it used and think it, too, a repugnant neologism)). Now, seeing that a different cadence
was used on the hill than on the flat, you reject the theory of incentivized (shudder) preference as
inappropriate. I would classify that as seeing more.

> For me this topic isn't what power someone put out at some specific instant or short time period
> (2.52 & 5 s), but is rather roughly that of attaining the most Joules out over a "whole race time
> period" (for both TTs and Hill Climb TTs: sustainable power).

For me, this topic is whether or not there is such a thing as an optimum cadence and, if so, is it
universal or dependent on conditions (i.e., factor or response). Your original post was that for you
80+ rpm while climbing is optimal. I have no doubt that you know yourself well; I was asking if you
had come to that finding through measurement.

> For example, a rider climbing a hill reaches a short steep switchback for which he/she has
> inadequately low gears, and so "stomps on it" for 5 seconds. The "stomping" requires unsustainable
> power output, but the sample does show high power there. Immediately after exiting the steeper
> section, the rider sits down, "spins fast," and does 10 s of recovery riding. The recovery riding
> will be lower than what would normally be sustainable, so the power sample is distorted low, for
> the higher cadence. The low cadence is distorted high. How many times has this exact scenario
> occurred? A lot I'll bet, and it is due to either habit or lack of low gears.

I'm sure it happens a lot. However, that scenario does not apply to these particular data.

> So I don't believe the difference in powers v. cadence as shown in the plot are yet meaningful as
> they stand.

They may not be. This is not a plot to settle an issue but rather to raise one (and I know how
unusual that is in an rbr post): do varying conditions influence the relationship between
sustainable power and cadence? I'm way short of asking what that relationship might be, or its
magnitude -- I'm still in the plausibility stage. I think these data (and data from other rides I've
seen) support the theory that cadence is a response.

> >> I'm not sure why gradient would be too much of a factor (or any
factor?)
> >> regarding power v. rpm. Maybe it is, but I just don't know why it
would
> >> be...
> >
> > Because of force. We all appear to know that given a particular gear,
power
> > scales supralinearly with rpm.
>
> We all? I don't presume your wrong (at all), but I don't presume the parameters. Explain.

For a given gear speed is linear with rpm, so power scales the same way with rpm as it does
with speed.

> I don't see how this shows why the so-called "optimum cadence" would change for climb v. flat.
> [...] I guess I see it as simply the power is
delivered
> via force and rotation of the pedals. What does it matter if the energy
lifts
> a weight or gets gas molecules moving? How does the body know if the energy (power*time) is being
> transferred to potential energy by lifting a weight, or transferred into kinetic energy of
> surrounding gases? The legs are simply pushing on the pedals, at a cadence selectable within 8%.

I believe it plausible that the body may know for (at least) two different reasons:

1. Because power = force * f(cadence) and the force response is different on a hill vs. on the flat:
on a hill, pedal force is inelastic wrt to rpm while on the flat the opposite is true.

2. Convective cooling.

 

[The Pomeranian]

Robert Chung wrote:
>
> "The Pomeranian" wrote
> > Well, don't worry, I don't see the same thing, now I see less.
>
> That's interesting. In your earlier message, you pointed out that both riders spent most of their
> time around 95rpm, and explained it as incentivized preference (I'm more used to the phrase
> "revealed preference" (and "automagically" was a typo--though perhaps more a Freudian slip since
> I've seen it used and think it, too, a repugnant neologism)). Now, seeing that a different cadence
> was used on the hill than on the flat, you reject the theory of incentivized (shudder) preference
> as inappropriate. I would classify that as seeing more.

It is because the samples are reduced. Note that I wrote _before_ you noted the incorrect graph
"There (in the red line) appears to be higher power output at lower cadences, but the sample numbers
are low and again this may point to unsustainability, and probably does considering the rather
significant power output."

The sample numbers are low in that range (coloring them red didn't change that), and I further
pointed out the sequencing problem, which you've only cleared up just now (and that just in words,
not in an actual sequenced data presentation). I asked the question "Was the hill climbing rider
really able to put out 350 sustainable watts at 70 rpm, but only 250 sustainable watts at 95 rpm
(-1.5 dB or -39%)?" So I'm saying I still have trouble with low sample numbers, a unexplained
disparate power output, and the actual sequencing.

Far from shuddering, I left the whole thing open to more scrutiny:

"I suppose that as a social science, we should ask if the "body has a wisdom" about this. Riders are
incentivized to do as well as possible In seeking the optimum because of the reward incentive, they
"listen to their bodies." The question is are they being fooled by the body or is the body telling
the truth? Are they interpreting the message rightly? Have other social influences come into play
that distort the results? For example, a popularized theme of "spin to win" that may or may not have
been sufficiently scrutinized. Or is the spin-to-win advice generally good but properly vague, and
based on 100 years of bike racing experience?"

I see those question marks as question marks.

> > For me this topic isn't what power someone put out at some specific instant or short time period
> > (2.52 & 5 s), but is rather roughly that of attaining the most Joules out over a "whole race
> > time period" (for both TTs and Hill Climb TTs: sustainable power).
>
> For me, this topic is whether or not there is such a thing as an optimum cadence and, if so, is it
> universal or dependent on conditions (i.e., factor or response). Your original post was that for
> you 80+ rpm while climbing is optimal.

No, I didn't write that. Read it again. You're merging separate sentences. I already explicity asked
you "Where do you think I think it is?" You didn't answer then, and now a number of posts later your
presumption pops out. Do you know why I said "I think it is a decent gearing goal, even if it can't
always be met, to have a gear you can turn at 80 rpm while climbing?" You didn't ask or comment one
way or the other.

> I have no doubt that you know yourself well; I was asking if you had come to that finding through
> measurement.

Actually, I'm opening myself fully to the possibility that maybe I don't know, or maybe I could do
better with a judicious re-evaluation. I'm questioning established prejudices that I, or anyone else
may hold on the matter, and for basic technical analysis. I don't care how it comes out either way.

> > For example, a rider climbing a hill reaches a short steep switchback for which he/she has
> > inadequately low gears, and so "stomps on it" for 5 seconds. The "stomping" requires
> > unsustainable power output, but the sample does show high power there. Immediately after exiting
> > the steeper section, the rider sits down, "spins fast," and does 10 s of recovery riding. The
> > recovery riding will be lower than what would normally be sustainable, so the power sample is
> > distorted low, for the higher cadence. The low cadence is distorted high. How many times has
> > this exact scenario occurred? A lot I'll bet, and it is due to either habit or lack of low
> > gears.
>
> I'm sure it happens a lot. However, that scenario does not apply to these particular data.

Why the disparate power? Can I assume you are saying assuredly that the lower powers (higher
cadences) and higher powers (lower cadences) both occurred with an equal sense of effort by the
rider? You aren't at all concerned by any possible distortions?

> > So I don't believe the difference in powers v. cadence as shown in the plot are yet meaningful
> > as they stand.
>
> They may not be. This is not a plot to settle an issue but rather to raise one (and I know how
> unusual that is in an rbr post): do varying conditions influence the relationship between
> sustainable power and cadence? I'm way short of asking what that relationship might be, or its
> magnitude -- I'm still in the plausibility stage. I think these data (and data from other rides
> I've seen) support the theory that cadence is a response.

I can't argue with that other than to say "response to what?" I raised a few more questions
regarding what I believe needs to be sorted out.

> > >> I'm not sure why gradient would be too much of a factor (or any
> factor?)
> > >> regarding power v. rpm. Maybe it is, but I just don't know why it
> would
> > >> be...
> > >
> > > Because of force. We all appear to know that given a particular gear,
> power
> > > scales supralinearly with rpm.
> >
> > We all? I don't presume your wrong (at all), but I don't presume the parameters. Explain.
>
> For a given gear speed is linear with rpm, so power scales the same way with rpm as it does
> with speed.

Supralinear, as I've always understood it (and had it related to me), is basically a log
scale/response with an axis translation such that the resulting function passes through zero. So for
flat, with the power required varying as the cube of the velocity, I don't see the "supralinear"
aspect. That's why I asked. I assume P(rpm) because that's the way you phrased it.

> > I don't see how this shows why the so-called "optimum cadence" would change for climb v. flat.
> > [...] I guess I see it as simply the power is
> delivered
> > via force and rotation of the pedals. What does it matter if the energy
> lifts
> > a weight or gets gas molecules moving? How does the body know if the energy (power*time) is
> > being transferred to potential energy by lifting a weight, or transferred into kinetic energy of
> > surrounding gases? The legs are simply pushing on the pedals, at a cadence selectable within 8%.
>
> I believe it plausible that the body may know for (at least) two different reasons:
>
> 1. Because power = force * f(cadence) and the force response is different on a hill vs. on the
> flat: on a hill, pedal force is inelastic wrt to rpm while on the flat the opposite is true.

With 8% gear steps, you can be within 4% of optimum, if such a thing as optimum exists. The power is
applied to the pedals and nowhere else in all cases. If the rider doesn't like the force required on
the pedals, they simply change gears. The steps have sufficient resolution. I do hold the
presumption and belief that "optimum cadence" is not sensitive to 4%, and in any case there is
nothing that can be done about it with the current equipment. The resolution is not sufficient to
change tactics during climbing v. flat, as far as I currently understand things.

> 2. Convective cooling.

Consider: EX-1. A rider pedals at 90 rpm in a 53x15, and goes 25.0703 mph. They change the gear to a
53x16, while pedaling at 96 rpm. The speed is unchanged at 25.0703 mph. How did convection cooling
change in any significant way?

EX-2. A rider pedals at 70 rpm in a 39x21, and goes 10.2489 mph. They change the gear to a 39x23,
while pedaling at 76.7 rpm. The speed is unchanged at 10.2489 mph. How did convection cooling change
in any significant way?

Once under a condition, the convection does not change according to rpm, it only changes according
to speed. If there is a baseline energy cost accorded to cadence (which I assume there is, and I
wrote about it under the banner of conservation of energy), then there could be a cooling trade off
in there if pedaling slower has a cooling (efficiency) advantage. That necessarily means that the
power available during climbing is less than that of "flatting." So explain the disparate power of
the climb samples. Why are the climb samples _higher_ in power? They should be lower. Something is
distorted. Either that, or the rider should shift _all pedaling_ to slower comparative rates.

I can't say the "optimum cadence" should not vary according to condition, I'm trying to understand
why it would.

 

[Robert Chung]

"The Pomeranian" <[email protected]> wrote

> It is because the samples are reduced.

Then I suggest you count the observations and think about the statistical principles involved. The
red points represent roughly 24 minutes worth of climbing. In any event, the actual power levels are
a red-herring (though it is slightly interesting that his power on the hill wasn't *lower* than his
power of the flat); the only important thing is that the red points and the black points have
relatively little overlap. Or rather, it's the only important thing to me; it seems you're
interested in a different question, a question that these data may not be able to address. At least,
I think they may not be able to address it; frankly, I've sort of lost the thread of your argument
and I'm not that interested in its recovery. My original question (whether you had measurements to
support your beliefs) has been answered. You don't.

 

[The Pomeranian]

Robert Chung wrote:
>

> My original question (whether you had measurements to support your beliefs) has been answered.
> You don't.

Here is the original extent of "my beliefs:"

"I think it is a decent gearing goal, even if it can't always be met, to have a gear you can turn at
80 rpm while climbing."

The so-called "belief" is actually _pre-measurement_. How can one take measurements without first
having the basic equipment? The extent of my belief is then that one must have the necessary
equipment to make the measurement in the first place. The gears (equipment) come before a power
meter and are the most fundamental piece of machinery. Do you get it now/finally?

 

[Tom Kunich]

Robert, don't you wonder about the actual power curve? It looks to me like a person can output so
much force climbing at a low cadence, upright posture or on a flat TT with an aero position, a much
higher cadence and yet apparently little change in actual power output.

That is, (well trained) climbers don't put out more power on climbs, they are just lighter and hence
at an advantage on the climbs and at a disadvantage on flat TT's.

As you close your chest up you have to breath more shallowly so more rapidly and a higher cadence
helps with that. On climbs you may be a little more efficient at lower cadence but many professional
caliber climbers move so fast that they also have aero problems which forces a lower tighter
position than optimal for efficiency.

It appears from various things I've read and observations I've made that a person can put a great
deal of force into the pedals on a climb and a lower cadence but cannot maintain that same high
force while in an aero position but can increase cadence to achieve the same power output at speed.

All of this suggests that the power output a person can achieve is more closely allied to his
cardio-vascular system than his musclature (note that lifting weights doesn't seem to markedly
increase the ability of a cyclist). Hence I think that cadence in absolute terms is dependent on the
individual's own proportions and the way his limbs and muscles attach.

Since individuals don't really vary all that much in general there is usually a band of cadence in
which most people feel comfortable and tend to ride that way. I think that there are also effects
from the exact body chemistry of the individual (for instance, I have exceptionally large lungs but
my VO2 max is slightly below normal).

The upshot of all this is that each individual has a band of cadence in which he feels comfortable
operating and he probably can't change this by more than 10% or so regardless of the training he
undertakes.

"Robert Chung" <[email protected]> wrote in message
news:[email protected]...
>
> "The Pomeranian" <[email protected]> wrote
>
> > It is because the samples are reduced.
>
> Then I suggest you count the observations and think about the statistical principles involved. The
> red points represent roughly 24 minutes worth of climbing. In any event, the actual power levels
> are a red-herring (though
it
> is slightly interesting that his power on the hill wasn't *lower* than his power of the flat); the
> only important thing is that the red points and
the
> black points have relatively little overlap. Or rather, it's the only important thing to me; it
> seems you're interested in a different question,
a
> question that these data may not be able to address. At least, I think
they
> may not be able to address it; frankly, I've sort of lost the thread of
your
> argument and I'm not that interested in its recovery. My original question (whether you had
> measurements to support your beliefs) has been answered. You don't.

 

[Robert Chung]

"Tom Kunich" <[email protected]> wrote
> Robert, don't you wonder about the actual power curve?

I suppose you mean the power curve as it relates to cadence? I used to, until I started looking at
the data. Now I sort of think of it as much more complicated and dependent on conditions than I
originally thought. This makes it theoretically interesting but not of much practical use. In a
race you don't get to go at your theoretical optimum. Your cadence, and HR, and blood lactate
level, and respiration rate, are going to be determined by how fast the guys around you are going.
It matters little what your "sustainable" power is on a hill because no one goes at that rate.
They're all going into debt, hoping to recover at the top or on the descent. In these kinds of
situations the optimal cadence is the one that, in conjuction with your gearing, gets you across
the finish line first.

At least, I think that would be the optimal cadence. I've never crossed a finish line first. My
cadence must not have been optimal.

 

[Tom Kunich]

"Robert Chung" <[email protected]> wrote in message
news:[email protected]...
>
> At least, I think that would be the optimal cadence. I've never crossed a finish line first. My
> cadence must not have been optimal.

That means your racing wasn't optimal.

 

[Carl Sundquist]

"Tom Kunich" <[email protected]> wrote in message
news:[email protected]...
> "Robert Chung" <[email protected]> wrote in message
> news:[email protected]...
> >
> > At least, I think that would be the optimal cadence. I've never crossed
a
> > finish line first. My cadence must not have been optimal.
>
> That means your racing wasn't optimal.
>

So only one person can have an optimal race in each race?

 

[Tom Kunich]

"Carl Sundquist" <[email protected]> wrote in message
news:<[email protected]>...
> "Tom Kunich" <[email protected]> wrote in message
> news:[email protected]...
> > "Robert Chung" <[email protected]> wrote in message
> > news:[email protected]...
> > >
> > > At least, I think that would be the optimal cadence. I've never crossed
> a
> > > finish line first. My cadence must not have been optimal.
> >
> > That means your racing wasn't optimal.
> >
>
> So only one person can have an optimal race in each race?

"There can be only one."

 

[The Pomeranian]

Robert Chung wrote:
>

> Now I sort of think of it as much more complicated and dependent on conditions than I originally
> thought. This makes it theoretically interesting but not of much practical use. In a race you
> don't get to go at your theoretical optimum. Your cadence, and HR, and blood lactate level, and
> respiration rate, are going to be determined by how fast the guys around you are going.

How can an attack in a mass start race be considered as anything other than a "condition?" What is
"theoretical optimum?"

 

[G.T.]

The Pomeranian wrote:
> Robert Chung wrote:
>
>
>>Now I sort of think of it as much more complicated and dependent on conditions than I originally
>>thought. This makes it theoretically interesting but not of much practical use. In a race you
>>don't get to go at your theoretical optimum. Your cadence, and HR, and blood lactate level, and
>>respiration rate, are going to be determined by how fast the guys around you are going.
>
>
> How can an attack in a mass start race be considered as anything other than a "condition?" What is
> "theoretical optimum?"

theory - 1. A set of statements or principles devised to explain a group of facts or phenomena,
especially one that has been repeatedly tested or is widely accepted and can be used to make
predictions about natural phenomena.

optimum - 1. The point at which the condition, degree, or amount of something is the most favorable.

E.g., the most favorable speed at which can one ride for a given distance as has been learned
through repeated testing. A speed which will not be reached or which will be exceeded at various
points of a mass start race.

HTH, Greg
--
"Destroy your safe and happy lives before it is too late, the battles we fought were long and hard,
just not to be consumed by rock n' roll..." - The Mekons