That damn wind

In article ,
"Gennaro" wrote:

"Jobst Brandt" wrote...

I think it was all the miles I have ridden with and against wind
that inspired me to analyze the not obvious effects of wind on a
rider. I hope it is understandable:

http://www.sheldonbrown.com/brandt/wind.html

As pointed up in the past, that "analysis" is flawed in some points
and the results are actually downright obvious.

Rather than throwing aspersions, how about explaining what you find
incorrect and what the correct analysis is. This article has been
reviewed by various aerodynamics people and not found wanting in
accuracy. This sounds a lot like the pro-helmet arguments. How about
clarifying?

As a matter of fact, and as stated, already in the past I enquired about
some points, but you chose not to clarify them, so this time I just opted
for a faster reply.
Ok, I'll try again! Unfortunately I am in a hurry and won't have much
time for a couple of days, but I can quickly point up main problems.

(1) You claim that D = W^2. That's simply not true. In fact
drag is just *proportional* to the square of the air speed!
You got rid of all the coefficients with your process of
normalization.

(2) Your figure 4 is not clear at all. Does it referr to an
"out-and-back" time trial? What happens in for alpha90?

(3) You chose an extremely convoluted way to show two results
which are quite obvious:
(a) The stronger the adverse "inline component" of the
crosswind, the more power you need to keep constant speed.
-- This is self-evident! Do you really need three graphs to make
this point?
(b) in an out-and-back time trial, a tailwind does not makes up
for time lost riding into a headwind of the same speed
-- This is hardly surprising, given that the relationship between power
and speed is not linear but exponential.

It may be. Analysis based on the kinetic theory of
gases concludes that power is polynomial in speed. What
is the basis of your thesis "the relationship between
power and speed is not linear but exponential"?

On 2010-03-17, Jobst Brandt wrote:
Michael Press wrote:
[...]
-- This is hardly surprising, given that the relationship between
power and speed is not linear but exponential.

It may be. Analysis based on the kinetic theory of gases concludes
that power is polynomial in speed. What is the basis of your thesis
"the relationship between power and speed is not linear but
exponential"?

It is in the article.

The analysis is based on equations from a gas dynamics text and the
curves make numerical results more understandable than tables of
numbers would. The disagreement some readers have with this article
stand alone in their position and have never offered what they feel is
the "correct" solution, only that the current one is all wrong. This
routine is getting tiresome and is the same as critiques of the book
"the Bicycle Wheel" that plenty of capable engineers have reviewed
with a positive assessment.

I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).

But that isn't an exponential relationship, as he correctly points out.

f(x) = x^3 is polynomial
f(x) = e^x is exponential

There's nothing exponential about wind resistance.

On 17 Mar, 08:52, Ben C wrote:
I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).
But that isn't an exponential relationship, as he correctly points out.
f(x) = x^3 is polynomial
f(x) = e^x is exponential
There's nothing exponential about wind resistance.

Neither there is anything strictly polynomial about it (except, of
course, if you make a model you believe in). I would put it this way
and I would save both thesis, in fact.

Linear laws (which are polynomials, by the way) are nothing but
approximations in the small. So are (higher order) polynomials, which
are, of course, a little better the higher the order.
Then, why should one resist and refuse to make a best fit with
exponentials?

Olynomials and exponentials are all legitimate, each with its own
merits and shortcomings. None can be trusted outside its range of
adequacy.
None is the truth, if there is such a thing.

So, there is nothing to argue about.

Sergio
Pisa

In article
,
sergio wrote:

On 17 Mar, 08:52, Ben C wrote:
I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).
But that isn't an exponential relationship, as he correctly points out.
f(x) = x^3 is polynomial
f(x) = e^x is exponential
There's nothing exponential about wind resistance.

Neither there is anything strictly polynomial about it (except, of
course, if you make a model you believe in). I would put it this way
and I would save both thesis, in fact.

Linear laws (which are polynomials, by the way)

Depends on what you mean by linear.

y"(t) = y(t)

is a linear differential equation. Is the solution

y(t) = exp(t)

linear?

Definition:
The function f is linear if and only if

f(x+y) = f(x) + f(y)..

The function f: R - R, y(x) = x^2 is not linear using
the definition, because
f(x+y) = xx + 2.x.y + yy != xx + yy.

Sometimes f: R-R, f(x) = a.x + b is called linear, but
the more careful call it affine.

are nothing but
approximations in the small. So are (higher order) polynomials, which
are, of course, a little better the higher the order.
Then, why should one resist and refuse to make a best fit with
exponentials?

Olynomials and exponentials are all legitimate, each with its own
merits and shortcomings. None can be trusted outside its range of
adequacy.
None is the truth, if there is such a thing.

I was careful to state the basis of the analysis: the
kinetic theory of gases. On that basis it is true that
wind resistance increases as the third power of speed.

So, there is nothing to argue about.

Yes, there is, since you contest what I wrote.

I nominate Michael Press for RBT Hairsplitter of the Year.

Andre Jute
The IPCC -- longest hand job in the history of mass hysteria -- has
now lasted almost twice as long as the Third Reich


On Mar 17, 1:28*pm, Michael Press wrote:
In article
,

*sergio wrote:
On 17 Mar, 08:52, Ben C wrote:
I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).
But that isn't an exponential relationship, as he correctly points out.

Ben C wrote:
On 2010-03-17, Jobst Brandt wrote:
Michael Press wrote:
[...]
-- This is hardly surprising, given that the relationship between
power and speed is not linear but exponential.
It may be. Analysis based on the kinetic theory of gases concludes
that power is polynomial in speed. What is the basis of your thesis
"the relationship between power and speed is not linear but
exponential"?
It is in the article.

The analysis is based on equations from a gas dynamics text and the
curves make numerical results more understandable than tables of
numbers would. The disagreement some readers have with this article
stand alone in their position and have never offered what they feel is
the "correct" solution, only that the current one is all wrong. This
routine is getting tiresome and is the same as critiques of the book
"the Bicycle Wheel" that plenty of capable engineers have reviewed
with a positive assessment.

I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).

But that isn't an exponential relationship, as he correctly points out.

f(x) = x^3 is polynomial
f(x) = e^x is exponential

There's nothing exponential about wind resistance.

If you've got the time, I've got some pepper I need de-fly****ted.

On Mar 17, 7:52*am, Ben C wrote:
On 2010-03-17, Jobst Brandt wrote:





Michael Press wrote:
[...]
-- This is hardly surprising, given that the relationship between
power and speed is not linear but exponential.

It may be. *Analysis based on the kinetic theory of gases concludes
that power is polynomial in speed. *What is the basis of your thesis
"the relationship between power and speed is not linear but
exponential"?

It is in the article.

The analysis is based on equations from a gas dynamics text and the
curves make numerical results more understandable than tables of
numbers would. *The disagreement some readers have with this article
stand alone in their position and have never offered what they feel is
the "correct" solution, only that the current one is all wrong. *This
routine is getting tiresome and is the same as critiques of the book
"the Bicycle Wheel" that plenty of capable engineers have reviewed
with a positive assessment.

I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).

But that isn't an exponential relationship, as he correctly points out.

* * f(x) = x^3 is polynomial
* * f(x) = e^x is exponential

There's nothing exponential about wind resistance.

Michael's point, as always, hangs on some weasel words, in this case:
"Analysis based on the kinetic theory of gases concludes that power is
polynomial in speed." If there's a disagreement here, it is about
angels dancing on the head of pin.

You have it already, as demonstrated in your parenthetical aside,
"(the real power is probably not exactly 3, but close to it)". This is
one of those examples that abound in the applied sciences where a
known element is multiplied by itself to represent more or less
approximately an element not otherwise conveniently open to
quantification. (And some precise examples too, for instance in
electronics you can measure the voltage -- even if the Michael Presses
of this world will quibble about whether you measured peak, average,
RMS, etc.)

I imagine Michael had his education beaten into him in school run by
Jesuits. He's the only one who doesn't yet grasp that he is too old
for such childish games. Don't encourage him.

Andre Jute
Relentless rigour -- Gaius Germanicus Caesar
But not hairsplitting! -- Andre Jute

On 2010-03-17, Andre Jute wrote:
On Mar 17, 7:52*am, Ben C wrote:
On 2010-03-17, Jobst Brandt wrote:





Michael Press wrote:
[...]
-- This is hardly surprising, given that the relationship between
power and speed is not linear but exponential.

It may be. *Analysis based on the kinetic theory of gases concludes
that power is polynomial in speed. *What is the basis of your thesis
"the relationship between power and speed is not linear but
exponential"?

It is in the article.

The analysis is based on equations from a gas dynamics text and the
curves make numerical results more understandable than tables of
numbers would. *The disagreement some readers have with this article
stand alone in their position and have never offered what they feel is
the "correct" solution, only that the current one is all wrong. *This
routine is getting tiresome and is the same as critiques of the book
"the Bicycle Wheel" that plenty of capable engineers have reviewed
with a positive assessment.

I think you're misunderstanding Michael's point. You probably both agree
that the power of wind resistance is proportional to speed cubed, or
thereabouts (the real power is probably not exactly 3, but close to it).

But that isn't an exponential relationship, as he correctly points out.

* * f(x) = x^3 is polynomial
* * f(x) = e^x is exponential

There's nothing exponential about wind resistance.

Michael's point, as always, hangs on some weasel words, in this case:
"Analysis based on the kinetic theory of gases concludes that power is
polynomial in speed." If there's a disagreement here, it is about
angels dancing on the head of pin.

The difference between a polynomial and an exponential function is not
hairsplitting or counting angels on pins.

It's a legitimate quibble. My only regret is I spoilt the fun by
explaining to Jobst what was going on but I suspect he disregards my
posts anyway so it's probably nothing to worry about.

The last time this came up Gennaro and Press provided some explanation
about how that third power (second power for force) is a theoretical
result that you can derive fairly easily. That was very interesting and
something I didn't know before, always believing this to be just a rough
empirical result.

As if quibbling on RBT needed justification anyway. sergio's
repudiation, which was apparently based on General Skepticism, was far
more bogus.

In article
,
Andre Jute wrote:

I nominate Michael Press for RBT Hairsplitter of the Year.

I would be happy to discuss this with you if you had the tools.

On Mar 19, 1:09*pm, * Still Just Me *
wrote:
On Fri, 19 Mar 2010 12:48:53 -0500, Michael Press
wrote:

In article
,
Andre Jute wrote:

I nominate Michael Press for RBT Hairsplitter of the Year.

I would be happy to discuss this with you if you had the tools.

He's trying to buy the tools from Jay Beattie right now.

I have hair-splitting tools, but they are for reverse follicle, small
diameter French hair. -- Jay Beattie.