Durability Of Velocity Aerohead Rims In 20/24 Hole Drillings.

On Nov 8, 2:31*pm, Frank Krygowski wrote:
On Nov 8, 10:52*am, " wrote:





On Nov 7, 11:27*pm, Frank Krygowski wrote:

On Nov 7, 10:05*pm, DirtRoadie wrote:

On Nov 7, 6:05*pm, Frank Krygowski wrote:

*As
with a lot of the issues we talk about, I'm not trying to forbid your
choice. *But I am trying to apply a little science to the discussion.
...
And after you have answered those questions please also tell me what
wheels I need to buy for my bicycle the next time that issue raises..

DR: *There's no need to go into much detail. *It's easy to tell what
wheels you need.

You need the lightest, most aerodynamic wheels you can possibly find.
For you, durability is no concern. *Availability of repair parts (like
proprietary spokes and nipples) is no concern. *Compatibility with any
other part of your bike is no concern. *Actual performance difference
in any given situation is no concern, although you do need to have
numbers to tell your friends. *(Claimed drag reduction ought to
suffice.) *Of course, price is no concern, as long as they're suitably
expensive.

You NEED the wheels with the highest zoot factor, the ones that match
the flashiest advertisements, and that match those used by the teams
with the biggest budgets. *And the following year, when the ads and
the sponsorships change, you'll NEED a new set of wheels.

Hope this helps. *Enjoy!

Wow. What a tirade.

Not a tirade at all! *(I think to qualify as "tirade," a person would
have to be at least frowning while writing. I was far from that!)

My point was just this: *There are people who's enjoyment of cycling
is tied very closely to their perception of their equipment's
sophistication. *It's like the friend I mentioned who bought the ten
pound carbon fiber hood for the sports car he drives to work. *He was
obviously proud of it, and doubtlessly derived pleasure out of driving
a car with a carbon fiber hood.

If a person needs a carbon fiber hood (or a wheel with a spoke count
that's lower than the next guy) to feel good about his ride, what can
I say? *He needs it, so he buys it. *Again, I'm not trying to forbid
any choices.

Now, if we're actually talking about measurable benefits (whether less
time making it home from work, able to stay with buddies on a
recreational ride, consistently better placement in amateur road
races, better chance at making a pro team, measurably better time
trial results, a Tour de France stage win, a new world hour record or
whatever), well it's reasonable to examine numbers on how much any
purported improvement is _really_ worth.

It's my contention that a lot of the touted improvements are actually
negligible. *Many are not worth precisely zero, and not all are
typically negligible, but I think a lot of them are. *In fact, I think
some of the claimed performance gains would be significant only for a
world hour attempt. *Yep, not even a stage win attempt.

Not that I was ever in that universe of athletic performance - but
there have been times I've played with aero improvements to my bike,
back when I tried to go fast. *For time trialing, I'm sure the aero
bars definitely helped. *The rear wheel disk spoke covers probably
helped, although I couldn't really feel it, and I certainly couldn't
find evidence it did. *But things like going from ancient exposed
brake cables to aero hidden cables? *Or an aero water bottle? *Moving
the pump to a more aero position, and other detail efforts? *Just not
enough difference to detect.

To give a further example: *I was on a club ride a week ago that was
supposed to be a fairly well-attended ride, but ended up being tiny,
just me on my touring bike and two guys who were a racer and an ex-
racer, both 15 to 25 years younger than me. *They could have ridden
away from me any time they wanted to.

Now, one guy was on a Cervelo. *Was that why he was faster than me?
Or to put it more practically, if I bought a Cervelo, would I have
been able to keep up with him? *Hell no, not me, not you, and not 99%
of the people who are tempted by performance parts, despite the ads
and claims, and despite "all the racers use them."

Similarly, chewing Dentyne gum isn't _really_ going to cause chicks to
think you're sexy. *That would be true whether or not all the top male
heartthrobs chew Dentyne or not.

- Frank Krygowski

What about the two minutes' advantage, over 40k, for an aero wheel
setup compared to "conventional"? And what about the racing
community-- smart, successful and competitive people who read
equipment comparison tests not directly funded by mfg's? We weren't
talking about lightweight automotive hoods, or chewing gum, or even
bike frames. The subject was wheels, and you went off in an abusive
tirade, ridiculing someone while having very little information about
this person and his bicycling activities, while accusing him of being
a slave of advertising, etc. etc., which is the usual with you.

What's so frustrating to you (and a few others) about people of means
indulging an avocation?
--D-y

On Nov 9, 10:05*am, " wrote:
On Nov 8, 2:31*pm, Frank Krygowski wrote:

Now, one guy was on a Cervelo. *Was that why he was faster than me?
Or to put it more practically, if I bought a Cervelo, would I have
been able to keep up with him? *Hell no, not me, not you, and not 99%
of the people who are tempted by performance parts, despite the ads
and claims, and despite "all the racers use them."

Similarly, chewing Dentyne gum isn't _really_ going to cause chicks to
think you're sexy. *That would be true whether or not all the top male
heartthrobs chew Dentyne or not.

What about the two minutes' advantage, over 40k, for an aero wheel
setup compared to "conventional"?

Of all race types, aerodynamic advantage is likely to be most valuable
in a time trial. It's a maximum effort, completely solo, against
(usually) nothing but the air resistance. That's been known for
probably 100 years.

But even that knowledge can turn into a fetish. I remember a similar
discussion here, where one person was honestly claiming that you could
count on something like a 0.5 second advantage in a 40k TT based on
whether your pinky finger was tucked behind your ring finger or not.
Or was it about clipping your fingernails?

Aero advantage of finger position is an example of something that
never makes it out of the wind tunnel. There are other advantages
(whether aero, or weight, or inertia) that may possibly show up in a
time trial or a match sprint, but get swamped by tactics and random
events in any crit or road race. And only the most extreme advantages
(like going to a recumbent, or losing over five pounds) are going to
be perceptible in non-competitive riding.

Isn't it obvious that _some_ level of theoretical advantage must
disappear into the noise? If not, racers would be shaving their
entire bodies.

And what about the racing
community-- smart, successful and competitive people who read
equipment comparison tests not directly funded by mfg's?

I know, and have known, members of the racing community. As I said, I
was on a ride with two of them not long ago. One was saying "I'm
thinking about trying those ceramic bearings for my crank." Nice
guys, but that's not saying much for their technical judgment.

Of course, here I may be writing to a bunch of guys who think ceramic
bearings will let them surge into the lead!

The subject was wheels, and you went off in an abusive
tirade, ridiculing someone while having very little information about
this person and his bicycling activities, while accusing him of being
a slave of advertising, etc. etc., which is the usual with you.

What's so frustrating to you (and a few others) about people of means
indulging an avocation?

D-y, it wasn't intended to be abusive - any more, I suppose, than your
phrase "which is usual for you."

DirtRoadie has frequently gotten hot with me when I express skepticism
about the wonderful benefits of the latest marketing gimmick. Based
on that, I take him to be a person who (like my sports-car friend) is
really, really into having the latest and greatest. Like the guy
saying "God, I gotta get a carbon frame" at 1:43 in
http://www.youtube.com/watch?v=Vn29DvMITu4

Maybe I'm wrong. But if DR is really so much into high-zoot equipment
that he attacks engineering judgment as heretical, he _needs_ to buy
high-zoot equipment, and I'm not going to try to convince him
otherwise. That was the meaning of my post.

- Frank Krygowski

On Nov 9, 9:01*am, Frank Krygowski
Maybe I'm wrong. *But if DR is really so much into high-zoot equipment
that he attacks engineering judgment as heretical, he _needs_ to buy
high-zoot equipment, and I'm not going to try to convince him
otherwise. *That was the meaning of my post.

Frank-
Let me jump in here. where in hell's name do you get off saying that I
am into high zoot equipment?
Talk about setting up straw men! But at least you left no doubt how
you conduct your analysis by falling hook line and sinker for my
invitation to suggest equipment for me based upon NO INFORMATION
WHATSOEVER. Good job!

The problem I have with you is that you draw a conclusion based upon
YOU and try to generalize to everyone. That's classic religious faith
with nothing remotely scientific about it. Despite haughtily
claiming your "engineering judgment" you are little more than a
religious zealot with little respect for points of view which differ
from yours and that are every bit as legitimate (even using
"engineering" as the touchstone). Even in your faint acknowledgement
of other positions you immediately find it necessary to assert that
YOUR position is better. It isn't BETTER, it's merely YOURS. I don't
care if you are a bleeping engineer (an arrogant one at that), your
opinion for your needs is still ONLY an opinion for YOUR needs.

Now, have you done the homework you promised regarding wheel mass and
power surges?
Remember, that was your offer, not my demand.

DR

On 11/9/2010 10:01 AM, Frank Krygowski wrote:
[...]
DirtRoadie has frequently gotten hot with me when I express skepticism
about the wonderful benefits of the latest marketing gimmick. Based
on that, I take him to be a person who (like my sports-car friend) is
really, really into having the latest and greatest. Like the guy
saying "God, I gotta get a carbon frame" at 1:43 in
http://www.youtube.com/watch?v=Vn29DvMITu4 [...]

If the 4 redheads come with the deal, the price looks much better.

--
Tom Sherman - 42.435731,-83.985007
I am a vehicular cyclist.

On Nov 9, 11:50*am, DirtRoadie wrote:

The problem I have with you is that you draw a conclusion based upon
YOU and try to generalize to everyone. That's classic religious faith
with *nothing remotely scientific about it. *

DR, when I make estimates of the amount of acceleration in a road
race, I'm not basing it on just my experience. We've all watched the
Tour on TV and seen racers cruise along in the pack for mile after
mile.

When I talk about the kinetic energy stored in a rolling wheel, it's
not based on just my wheels. It's easy enough to hit the internet and
determine the mass difference between (say) a wheel typically chosen
for lightness vs. a wheel typically chosen for aero purposes.

And BTW, when Carl goes to his favorite performance calculator
websites and plugs in numbers (or when the owners of those websites
give the results of various equipment choices in various situations)
they are not basing it upon my wheels, my bike or my riding.

I don't drill my brake levers or seatpost. I've known guys that have,
back when that was popular, but I never did. But whether or not I did
it, the practice was abandoned, despite its popularity, because it
didn't make a practical difference. The same thing happened with
aerodynamic rear derailleurs. It's very likely that the same is going
to happen with ceramic bearings, and a lot of the tricks being done to
remove one more spoke from a wheel.

Now about numbers: Trust me, I'm capable of putting numbers on a lot
of what I'm saying. But I'd normally get paid for that sort of work,
because it is indeed work. And I know that the True Believers in this
crowd would not only not pay me, they'd diss the necessary
approximations, or disallow the boundary conditions, or just not
understand what the heck the numbers meant.

Use the numbers Carl pulled up. (And BTW, notice that they confirmed
one of my statements - that aero generally trumps lightness in
competition.)

I know you get very irritated by what I write. Sorry about that. I'm
not trying to slam you, or start flame wars, or slyly ruin anyone's
chances of winning a race. I'm trying to realistically talk about
bicycle technology.

- Frank Krygowski

On Nov 9, 4:01*pm, Frank Krygowski wrote:
On Nov 9, 10:05*am, " wrote:

On Nov 8, 2:31*pm, Frank Krygowski wrote:

Now, one guy was on a Cervelo. *Was that why he was faster than me?
Or to put it more practically, if I bought a Cervelo, would I have
been able to keep up with him? *Hell no, not me, not you, and not 99%
of the people who are tempted by performance parts, despite the ads
and claims, and despite "all the racers use them."

Similarly, chewing Dentyne gum isn't _really_ going to cause chicks to
think you're sexy. *That would be true whether or not all the top male
heartthrobs chew Dentyne or not.

What about the two minutes' advantage, over 40k, for an aero wheel
setup compared to "conventional"?

Of all race types, aerodynamic advantage is likely to be most valuable
in a time trial. *It's a maximum effort, completely solo, against
(usually) nothing but the air resistance. That's been known for
probably 100 years.

But even that knowledge can turn into a fetish. *I remember a similar
discussion here, where one person was honestly claiming that you could
count on something like a 0.5 second advantage in a 40k TT based on
whether your pinky finger was tucked behind your ring finger or not.
Or was it about clipping your fingernails?

Aero advantage of finger position is an example of something that
never makes it out of the wind tunnel. *There are other advantages
(whether aero, or weight, or inertia) that may possibly show up in a
time trial or a match sprint, but get swamped by tactics and random
events in any crit or road race. *And only the most extreme advantages
(like going to a recumbent, or losing over five pounds) are going to
be perceptible in non-competitive riding.

Isn't it obvious that _some_ level of theoretical advantage must
disappear into the noise? *If not, racers would be shaving their
entire bodies.

How do you know they are not, it was practised by ancient Greek
athletes? The advantages of shaving is not necessarily due to removal
of hair but more to the scraping of the skin which should be done with
a rigid blade, not a disposable 'razor'.


And what about the racing
community-- smart, successful and competitive people who read
equipment comparison tests not directly funded by mfg's?

I know, and have known, members of the racing community. *As I said, I
was on a ride with two of them not long ago. *One was saying "I'm
thinking about trying those ceramic bearings for my crank." *Nice
guys, but that's not saying much for their technical judgment.

Of course, here I may be writing to a bunch of guys who think ceramic
bearings will let them surge into the lead!

The subject was wheels, and you went off in an abusive
tirade, ridiculing someone while having very little information about
this person and his bicycling activities, while accusing him of being
a slave of advertising, etc. etc., which is the usual with you.

What's so frustrating to you (and a few others) about people of means
indulging an avocation?

D-y, it wasn't intended to be abusive - any more, I suppose, than your
phrase "which is usual for you."

DirtRoadie has frequently gotten hot with me when I express skepticism
about the wonderful benefits of the latest marketing gimmick. *Based
on that, I take him to be a person who (like my sports-car friend) is
really, really into having the latest and greatest. *Like the guy
saying "God, I gotta get a carbon frame" at 1:43 inhttp://www.youtube.com/watch?v=Vn29DvMITu4

Maybe I'm wrong. *But if DR is really so much into high-zoot equipment
that he attacks engineering judgment as heretical, he _needs_ to buy
high-zoot equipment, and I'm not going to try to convince him
otherwise. *That was the meaning of my post.

- Frank Krygowski

On Nov 9, 2:54*pm, Frank Krygowski wrote:

Now about numbers: *Trust me, I'm capable of putting numbers on a lot
of what I'm saying. *But I'd normally get paid for that sort of work,
because it is indeed work. *And I know that the True Believers in this
crowd would not only not pay me, they'd diss the necessary
approximations, or disallow the boundary conditions, or just not
understand what the heck the numbers meant.

Use the numbers Carl pulled up. *(And BTW, notice that they confirmed
one of my statements - that aero generally trumps lightness in
competition.)

I'll have to look carefully at that because I think there are
underlying assumptions that are not complete ... but on to the
discussion at hand.

...*I'm trying to realistically talk about
bicycle technology.

Yes, let's do that as you offered with regard to wheel mass and
acceleration within the context of power surges in a pedal stroke. I
am particularly interested in the effect on speed.
Now I understand that _energy_ is conserved, but that does not tell
the whole story. Energy is also conserved when doing an up-and-back on
a climb, but average speed nonetheless suffers (even assuming no air
resistance). So starting there, would you like to do some comparing?

DR

On Nov 9, 5:22*pm, DirtRoadie wrote:
On Nov 9, 2:54*pm, Frank Krygowski wrote:


...*I'm trying to realistically talk about
bicycle technology.

Yes, let's do that as you offered with regard to wheel mass and
acceleration within the context of power surges in a pedal stroke. *I
am particularly interested in the effect on speed.
Now I understand that _energy_ *is conserved, but that does not tell
the whole story. Energy is also conserved when doing an up-and-back on
a climb, but average speed nonetheless suffers (even assuming no air
resistance). So starting there, would you like to do some comparing?

OK, if you like.

First, let's note that energy is _not_ actually conserved while riding
a bicycle. If it were, you probably wouldn't get tired. Energy is
dissipated as heat, through various mechanisms. Most of the time (in
racing, anyway) the biggest loss by far is through aerodynamic drag.

Aero losses are higher when the relative air speed (bike through the
air) are higher. That's why the fastest time trials happen in still
air, not on days with winds. You lose more fighting into a headwind
than you gain on the way back. You also lose more energy to wind
resistance when you're speeding down a hill, compared with climbing
it, and the faster you go the more you lose. That's partly why a
breakaway is much more difficult on a long downhill.

So how does this affect level riding with lighter or heavier wheels?
First, we must keep in mind that the differences between light wheels
and heavy wheels are, for any competitive bikes, pretty small. The
percentage differences in total system (bike + rider) inertia are even
smaller. A 153 pound rider on a 17 pound (total weight) bike with
three pound wheels has barely over 2% of his inertia due to the
wheels.

Still: If rider A has lighter, lower inertia wheels than rider B, on
the high power portion of each pedal stroke, both riders are going to
accelerate very slightly, and rider A is going to accelerate
microscopically ahead of rider B.

But on the _low_ power portion of each pedal stroke, both riders are
going to decelerate very slightly ... and here it is: Rider A will
_decelerate_ microscopically more than rider B. Rider B gains during
that phase. Why? Because during the deceleration phase, the wheels
with more inertia will act to keep the bike going, to decelerate
less. It's a flywheel effect.

Practically speaking, it all averages out during ordinary constant
speed level ground pedaling. Rider A may be going 20 mph plus or
minus 0.01 mph (that is, an amplitude of 0.01 mph superimposed on a 20
mph average) while rider B may be going 20 mph plus or minus 0.008
mph, but the practical measurement of each rider's speed is still 20
mph. There's no advantage to lighter wheels in that context.

But there's more. Does it all average out perfectly? No - and the
tiny differences in speed work to the disadvantage of the guy with
lighter wheels! Here's why: The guy with lighter wheels would get to
microscopically higher peak speeds. Remember that aerodynamic power
losses vary with (actually, the cube of) relative speed. During the
portion of the pedal cycle he's at 20.01 mph, he loses more energy
than his side-by-side competitor loses at 20.008 mph. And like the
out-and-back time trialist on a windy day, he doesn't gain it back on
the other half of the cycle. He'll have to be putting out
microscopically more power.

That's the physics. In practice, it's all probably too small to
reliably measure. That (roughly) 2% of inertia in the wheels is not
affected much by the switch to lighter wheels. I mean, how much
lighter? 100 grams total? Then you're playing with maybe a tenth of a
percent of the total inertia. Any effect of that difference will be
wiped out if, say, rider A has to wipe sweat out of his eye. The
slightest vagary of breeze, bumps in the road, drafting a bigger rider
instead of a smaller rider, etc. will wipe out that difference.

"But what if I've trained perfectly, and I've done all I can do and my
training has reached a plateau. Shouldn't I go with the lighter
wheels? (Or maybe the more aero wheels?)

Personally, if it were me, I'd spend the money on other things. A few
sessions on tactics with an excellent coach would probably kill any
wheel advantage you could buy. As they say, knowledge is power.

- Frank Krygowski

On Nov 9, 7:22*pm, Frank Krygowski wrote:
On Nov 9, 5:22*pm, DirtRoadie wrote:

On Nov 9, 2:54*pm, Frank Krygowski wrote:

...*I'm trying to realistically talk about
bicycle technology.

Yes, let's do that as you offered with regard to wheel mass and
acceleration within the context of power surges in a pedal stroke. *I
am particularly interested in the effect on speed.
Now I understand that _energy_ *is conserved, but that does not tell
the whole story. Energy is also conserved when doing an up-and-back on
a climb, but average speed nonetheless suffers (even assuming no air
resistance). So starting there, would you like to do some comparing?

OK, if you like.

First, let's note that energy is _not_ actually conserved while riding
a bicycle. *If it were, you probably wouldn't get tired. *Energy is
dissipated as heat, through various mechanisms. *Most of the time (in
racing, anyway) the biggest loss by far is through aerodynamic drag.

Aero losses are higher when the relative air speed (bike through the
air) are higher. *That's why the fastest time trials happen in still
air, not on days with winds. *You lose more fighting into a headwind
than you gain on the way back. *You also lose more energy to wind
resistance when you're speeding down a hill, compared with climbing
it, and the faster you go the more you lose. *That's partly why a
breakaway is much more difficult on a long downhill.

So how does this affect level riding with lighter or heavier wheels?
First, we must keep in mind that the differences between light wheels
and heavy wheels are, for any competitive bikes, pretty small. *The
percentage differences in total system (bike + rider) inertia are even
smaller. *A 153 pound rider on a 17 pound (total weight) bike with
three pound wheels has barely over 2% of his inertia due to the
wheels.

Still: *If rider A has lighter, lower inertia wheels than rider B, on
the high power portion of each pedal stroke, both riders are going to
accelerate very slightly, and rider A is going to accelerate
microscopically ahead of rider B.

But on the _low_ power portion of each pedal stroke, both riders are
going to decelerate very slightly ... and here it is: *Rider A will
_decelerate_ microscopically more than rider B. *Rider B gains during
that phase. *Why? *Because during the deceleration phase, the wheels
with more inertia will act to keep the bike going, to decelerate
less. *It's a flywheel effect.

Practically speaking, it all averages out during ordinary constant
speed level ground pedaling. *Rider A may be going 20 mph plus or
minus 0.01 mph (that is, an amplitude of 0.01 mph superimposed on a 20
mph average) while rider B may be going 20 mph plus or minus 0.008
mph, but the practical measurement of each rider's speed is still 20
mph. *There's no advantage to lighter wheels in that context.

But there's more. *Does it all average out perfectly? *No - and the
tiny differences in speed work to the disadvantage of the guy with
lighter wheels! *Here's why: *The guy with lighter wheels would get to
microscopically higher peak speeds. *Remember that aerodynamic power
losses vary with (actually, the cube of) relative speed. *During the
portion of the pedal cycle he's at 20.01 mph, he loses more energy
than his side-by-side competitor loses at 20.008 mph. *And like the
out-and-back time trialist on a windy day, he doesn't gain it back on
the other half of the cycle. *He'll have to be putting out
microscopically more power.

That's the physics. *In practice, it's all probably too small to
reliably measure. *That (roughly) 2% of inertia in the wheels is not
affected much by the switch to lighter wheels. *I mean, how much
lighter? *100 grams total? Then you're playing with maybe a tenth of a
percent of the total inertia. *Any effect of that difference will be
wiped out if, say, rider A has to wipe sweat out of his eye. *The
slightest vagary of breeze, bumps in the road, drafting a bigger rider
instead of a smaller rider, etc. will wipe out that difference.

"But what if I've trained perfectly, and I've done all I can do and my
training has reached a plateau. *Shouldn't I go with the lighter
wheels? *(Or maybe the more aero wheels?)

Personally, if it were me, I'd spend the money on other things. *A few
sessions on tactics with an excellent coach would probably kill any
wheel advantage you could buy. *As they say, knowledge is power.

No. Let get right down to it. Skip the aerodynamics (unless you just
want to make that a constant factor). You as always want to expound
on anything and everything. Please SHOW me. Here you have taken your
hypothesis ans simply restated it as a conclusion. That's sloppy and
exactly what you find so offensive when others do it.

Start here. We have two riders CLIMBING at constant speed. EVERTYHING
about them is identical except that one is carrying weight in a water
bottle that is equal to the amount his rims and tires are lighter than
the other rider's (That's to assume we are putting that mass at the
wheel perimeter)
Now taking into account the fluctuation in force/power in their
(identical) pedal strokes, (as exemplified here):
http://www.trainright.com/assets/new...ockdiagram.jpg

Show me just what happens between these two riders with those
fluctuations. In particular, address the microscopically higher
speeds you have noted.

And yes there are some minor glitches in this hypothetical -please
point those out if you see them. But please also try to stay within
the scope of what I have described as much as possible.

Look at this as an opportunity to add the "science" you always refer
to but rarely provide.
Thanks.

DR

PS- Love your consistency in ending "Personally, if it were me, ..."

On Nov 9, 10:31*pm, DirtRoadie wrote:


No. Let get right down to it. Skip the aerodynamics (unless you just
want to make that a constant factor). *You as always want *to expound
on anything and everything. Please *SHOW me. Here you have taken your
hypothesis ans simply restated it as a conclusion. That's sloppy and
exactly what you find *so offensive when others do it.

Start here. We have two riders CLIMBING at constant speed. EVERTYHING
about them is identical except that one is carrying weight in a water
bottle that is equal to the amount his rims and tires are lighter than
the other rider's (That's to assume we are putting that mass at the
wheel perimeter)
Now taking into account the fluctuation in force/power in their
(identical) pedal strokes, (as exemplified here):http://www.trainright.com/assets/new...ockdiagram.jpg

Show me just what happens between these two riders with those
fluctuations. *In particular, address the microscopically higher
speeds you have noted.

And yes there are some minor glitches in this hypothetical -please
point those out if you see them. But please also try to stay within
the scope of what I have described as much as possible.

Look at this as an opportunity to add the "science" you always refer
to but rarely provide.
Thanks.

DR

DR: I _did_ show you, whether or not you understood. Whether riding
on level ground or ascending a hill as you described, the principles
are the same. There are some slight differences in magnitude, but the
effects are the same.

Sure, you can say the aerodynamics are constant, if you want. That's
an approximation which although not perfectly precise, is certainly
close enough to reality, given the tiny fluctuations in velocity. If
we accept that, then the guy on the lighter wheels doesn't actually
lose ground. The two riders would remain exactly side by side. But
the lighter wheels do _not_ provide an advantage.

I don't know what part of the explanation you didn't understand, so I
can't clear up your confusion for you.

Maybe you can dig into one of Carl's favorite calculator sites and
plug in the numbers. Let me know how it comes out.

- Frank Krygowski