why increasing strength doesn't (automatically) increase power

Shayne, We are not talking about imaginary numbers here. If you prefer
to call it science that we ignore results we don't like or can't
explain so be it. You are not alone in this regards. I don't see why
the higher cadence is necessarily the "unphysical" one. Lots of people
here would argue that higher cadences are better than lower cadences
because they "flush out the lactic acid", even though there is no good
science to back that claim up either.

Frank


"Shayne Wissler" wrote in message news: This conclusion does not follow. There are lots of examples in physics where
you throw out the "unphysical" solution, which is just an artifact of the
method of computation.


Shayne Wissler

"Andy Coggan" wrote in message
ink.net...
"Phil Holman" wrote in message
nk.net...

"Andy Coggan" wrote in message
ink.net...
"Ilan Vardi" wrote in message
om...

How can you not admit that you were completely wrong in
defending
your use
of the term velocity?

Simple: because I wasn't. I specified a direction
("circumferential"),
meaning that what I was speaking about was indeed velocity, not
just
speed.

A nice semantic argument. In this situation we either have
instantaneous
tangential velocity or circumferential speed. As the direction and
pathway is clearly defined at any point on the pedal arc, a simply
stated pedal velocity (taken as instantaneous tangential) is
acceptable.
However, you won't see the combination of terms *circumferential
velocity* used in any of the better physics references even though
it is
regularly (incorrectly) used by physicists. In one dimension,
velocity
is dx/dt and in two dimensions, sqrt(dx^2+dy^2)/dt which, when we
look
at the average pedal velocity for one revolution (in the reference
frame
of the bicycle), is zero. The pedal velocity over any arc length of
the
circle is therefore not the same as the circumferential speed along
that
arc.

I don't follow your argument here - but in any case, I find it telling
that
according to you, circumferential velocity is regularly used by
physicists,
even though you dispute its correctness.

Just as they regularly and incorrectly flip flop speed and velocity.
Just because they do so doesn't mean it's correct. Velocity being a
vector, requires a frame of reference with a coordinate system and there
is no system defined that would explain circumferential velocity in the
way you intended (constant speed).

Phil Holman

"Top Sirloin" wrote in message
...

I like the weight training suggestions in _Performance_Cycling_ by Dan
Morris.
He has you lift for hypertrophy, and then switch to lower weight/higher
speed
lifting and phases in hard low-cadence intervals to create cycling
specific
strength.

I think you mean Dave Morris (another exercise physiologist, BTW). Anyway,
I'd even take one step further: lift for hypertrophy, then go straight to
velocity-specific training on the bike (e.g., if you're a sprinter, practice
sprinting, if you're an off-road racer who needs to be able to grind up
steep pitches, practice grinding up steep pitches, etc.).

Andy Coggan

"Andy Coggan" wrote in message
nk.net...

To put it more simply: non-endurance track racers better be lifting
really
heavy weights, to grow big muscles. For anybody else, weight
training can't
be considered a requirement (or even necessarily useful).

And this is the crux of the entire matter and something that I'd
suspected but for which I hadn't any proof.

So, I ride my road bike up hills peddling as fast as I can and seem to
gain no climbing ability at all. A couple of times a week I ride my
MTB up REALLY steep hills that require me to be in the 24/32 and I'm
barely able to turn the pedals over and keep the bike balanced and my
cadence starts going up everywhere and my speed and stamina increase.

So what the hell is with that?

"Phil Holman" wrote in message
ink.net...

"Andy Coggan" wrote in message
ink.net...
"Phil Holman" wrote in message
nk.net...

"Andy Coggan" wrote in message
ink.net...
"Ilan Vardi" wrote in message
om...

How can you not admit that you were completely wrong in
defending
your use
of the term velocity?

Simple: because I wasn't. I specified a direction
("circumferential"),
meaning that what I was speaking about was indeed velocity, not
just
speed.

A nice semantic argument. In this situation we either have
instantaneous
tangential velocity or circumferential speed. As the direction and
pathway is clearly defined at any point on the pedal arc, a simply
stated pedal velocity (taken as instantaneous tangential) is
acceptable.
However, you won't see the combination of terms *circumferential
velocity* used in any of the better physics references even though
it is
regularly (incorrectly) used by physicists. In one dimension,
velocity
is dx/dt and in two dimensions, sqrt(dx^2+dy^2)/dt which, when we
look
at the average pedal velocity for one revolution (in the reference
frame
of the bicycle), is zero. The pedal velocity over any arc length of
the
circle is therefore not the same as the circumferential speed along
that
arc.

I don't follow your argument here - but in any case, I find it telling
that
according to you, circumferential velocity is regularly used by
physicists,
even though you dispute its correctness.

Just as they regularly and incorrectly flip flop speed and velocity.
Just because they do so doesn't mean it's correct.

There are also physiologists that take exception to the term "eccentric
contraction" - but there's no universal agreement on that, either.

Velocity being a
vector, requires a frame of reference

Around the circumference of the pedal circle.

with a coordinate system and there
is no system defined that would explain circumferential velocity in the
way you intended (constant speed).

I never claimed that the pedal moves at a constant speed.

Andy Coggan

"Andy Coggan" wrote in message
ink.net...
"Phil Holman" wrote in message
ink.net...

"Andy Coggan" wrote in message
ink.net...
"Phil Holman" wrote in message
nk.net...

"Andy Coggan" wrote in message
ink.net...
"Ilan Vardi" wrote in message
om...

How can you not admit that you were completely wrong in
defending
your use
of the term velocity?

Simple: because I wasn't. I specified a direction
("circumferential"),
meaning that what I was speaking about was indeed velocity,
not
just
speed.

A nice semantic argument. In this situation we either have
instantaneous
tangential velocity or circumferential speed. As the direction
and
pathway is clearly defined at any point on the pedal arc, a
simply
stated pedal velocity (taken as instantaneous tangential) is
acceptable.
However, you won't see the combination of terms *circumferential
velocity* used in any of the better physics references even
though
it is
regularly (incorrectly) used by physicists. In one dimension,
velocity
is dx/dt and in two dimensions, sqrt(dx^2+dy^2)/dt which, when
we
look
at the average pedal velocity for one revolution (in the
reference
frame
of the bicycle), is zero. The pedal velocity over any arc length
of
the
circle is therefore not the same as the circumferential speed
along
that
arc.

I don't follow your argument here - but in any case, I find it
telling
that
according to you, circumferential velocity is regularly used by
physicists,
even though you dispute its correctness.

Just as they regularly and incorrectly flip flop speed and velocity.
Just because they do so doesn't mean it's correct.

There are also physiologists that take exception to the term
"eccentric
contraction" - but there's no universal agreement on that, either.

Velocity being a
vector, requires a frame of reference

Around the circumference of the pedal circle.

And the origin is?

with a coordinate system and there
is no system defined that would explain circumferential velocity in
the
way you intended (constant speed).

I never claimed that the pedal moves at a constant speed.

If I pick a circumferential velocity of 2m/s off your chart. I think
your intent is the speed will be constant within the small
accelerations/decelerations due to the variation in pedal force at a
given power output. I take it your term "circumferential velocity" is
meant as the average instantaneous tangential velocity of the pedal at
this power output.

Phil Holman

I was hoping that Ilan's objection was purposefully exemplary -- that is that by illustrating his
objection to the jargonist mouthful "circumferential pedal velocity" with a giant 4D helix he was
showing just how unwieldable -- unspeakable even -- specificities can become in the hands of
sophisticates. Is not "pedal speed" *most* usefully descriptive in this context? One of the most
important things for a teacher to know is what to allow to be simple.

Kirby.

"Ilan Vardi" wrote in message
om...
Benjamin Weiner wrote in message news:3fb5beee$1@darkstar...
Ilan Vardi wrote:

Once again, I use an opportunity to differentiate myself from most
scientists
by admitting when I have made a mistake.

Ilan, you're not a scientist. You are a mathematician.

This is true, but both share the fact that correctness is most important.

-ilan

"Kirby Krieger" h wrote
in message ...
I was hoping that Ilan's objection was purposefully exemplary -- that is
that by illustrating his
objection to the jargonist mouthful "circumferential pedal velocity" with
a giant 4D helix he was
showing just how unwieldable -- unspeakable even -- specificities can
become in the hands of
sophisticates. Is not "pedal speed" *most* usefully descriptive in this
context? One of the most
important things for a teacher to know is what to allow to be simple.

Kirby.

My thoughts exactly. My question is: who is the article written for?
Scientists or cyclists?

I understand what you intended. I simply expanded the analysis in what
I thought was a logical extension and found, what I believed to be an
illogical conclusion. How does your analysis look at strength when
being used submaximally? Would your model predict that strength
training would be beneficial for improving aerobic (submaximal)
performance? How does that analysis work using the model you used? In
your paper you do mention optimum cadence for maximum power so my
bringing up what the model predicts for cadence at submaximal power is
not beyond the pale.

Frank

"Andy Coggan" wrote in message ink.net...
"Frank Day" wrote in message
om...


The analysis has nothing to do with endurance/metabolism, or even with
optimum cadence - it has to do with the role of strength in determining
power output.

Andy Coggan

"GWB" wrote in message
m...

"Kirby Krieger" h wrote
in message ...
I was hoping that Ilan's objection was purposefully exemplary -- that is
that by illustrating his
objection to the jargonist mouthful "circumferential pedal velocity"
with
a giant 4D helix he was
showing just how unwieldable -- unspeakable even -- specificities can
become in the hands of
sophisticates. Is not "pedal speed" *most* usefully descriptive in this
context? One of the most
important things for a teacher to know is what to allow to be simple.

Kirby.

My thoughts exactly. My question is: who is the article written for?
Scientists or cyclists?

A little of both, actually. Hence the adherence to scientific convention re.
the means of data presentation.

Andy Coggan