cfrp vs. metal

In article ,
"Tom Kunich" cyclintom@yahoo. com wrote:

"Ryan Cousineau" wrote in message
]...

Anyway, if the budget is low, the bike will be steel.

What is really amazing is that the high end steel bikes are SO much better
than the high end anything-else bikes that it isn't funny. Not that there's
anything wrong with a high end carbon bike but the ONLY advantage is that
they're lighter. They probably don't last as long, they don't look any
better, they don't have fancy lug-work etc.

Well, I think I know where you're going with this, in terms of the
craftsmanship, but the durability issue is somewhat debatable, and the
other two are aesthetic judgments akin to saying that a 1958 Chevrolet
Bel Air looks better than a 1992 Chevrolet Beretta.

Aside from the lightness, carbon tubes have been taken into some pretty
clever aero territory, though with bike frames this matters somewhat for
TT bikes, and only a little for a road racer. Steel does not lend itself
to the aero-friendly shapes CFRP frames have assumed.

--
Ryan Cousineau http://www.wiredcola.com/
"In other newsgroups, they killfile trolls."
"In rec.bicycles.racing, we coach them."

On 2009-01-22, Michael Press wrote:
[...]
3) A cube shaped box with the edge length 1 m stands against a wall.
A ladder of length 5 m leans against the wall, and just touches
the box at an edge. How high on the wall is the top of the ladder?

|
|
|\
| \
| \
| \
| \
a \
| \
| \
| \
|___1_____\
| | \
| | \
| 1 \
| | \
|________|__b__\___________

Pythagoras on the big triangle tells us this:

1) (a+1)**2 + (b+1)**2 = 25

There are two smaller triangles. The one formed by a, the top of the box
and the top run of the ladder; and the one formed the right edge
of the box, b, and the lower run.

These two triangles are similar, which means a/1 = 1/b, or, a = 1/b

2) a = 1/b

Substitute (2) into (1) and rearrange and we get the quartic equation:

b**4 + 2*b**3 - 23*b**2 + 2*b + 1 = 0

Now I have been reliably informed that although it is possible to solve
quartics algebraically most people just use a computer these days.

Doing that I get b = 0.2605. a = 1/b, so a = 3.839, so the height up the
wall is 4.839m.

This reminds me of a similar problem, perhaps a bit harder.

An alleyway 5m wide with vertical walls has two ladders in it. One
ladder starts in the bottom left corner and leans against the right
wall. The other ladder starts in the bottom right corner and leans
against the left wall. The first ladder is 20m long, the second 15m
long. How high above the ground is their intersection?

"Michael Press" wrote in message
...
In article ,
"Clive George" wrote:

"Michael Press" wrote in message
...

An engineering type question. Let's have a mathematical solution.

3) A cube shaped box with the edge length 1 m stands against a wall.
A ladder of length 5 m leans against the wall, and just touches
the box at an edge. How high on the wall is the top of the ladder?

About 5m? (though the answer depends on how wide the ladder is)

View this picture with a monospace font.


|
|
|\
| \
| \
| \
| \
| \
| \
| \
| \
|_________\
| | \
| | \
| | \
| | \
|________|_____\___________

Why? Looks nothing like my answer.

Michael Press wrote:
In article
,
Frank Krygowski wrote:

On Jan 21, 6:46 pm, Michael Press wrote:
In article
,
Frank Krygowski wrote:



On Jan 20, 8:23 pm, Tom Sherman
wrote:
The Andre Jute wrote:
I dunno, Chalo. You can save yourself a lot of heartburn if you regard
an engineer an eejit expensively edjicated to tell people with real-
life experience what they cannot do, and when they've done it anyway,
tell them why they shoulda done it some other way.
Mr. Jute's jealousy is showing.
Smart operators learn young that mathematicians, who can work out
anything engineers learn of by heart at college, come cheap,[...]
A mathematician would not have a freaking clue where to start doing what
I do.
Related tale: Many years ago, a very talented mathematician came to a
colleague of mine, because the mathematician had a friend who had just
bought his first CNC mill. The mathematician volunteered to learn to
program it.
My colleague took the time to teach him, and succeeded well. The
mathematician was extraordinarily pleased. His quote: "This is the
first time in my life I've done anything practical!"
Theoretical math is good stuff - in fact, we wouldn't have CNC or much
of engineering without it. CNC programming is good stuff too. But
neither one is engineering. I agree with Tom, a mathematician would
have to start learning engineering at square one.
How does it happen that technically educated people
acquire such low opinions of mathematics? Pick up
a good undergraduate book on algebra, such as
Dummit and Foote, and apply yourself. Or how about
a Primer of Real Functions by Ralph P. Boas or
Real Analysis by Walter Rudin, and really learn
calculus. Or Niven and Zuckerman for number theory.
Mathematicians can do more than you realize,
because mathematics is tough, unforgiving of the
least error, and ultimately rewarding.

I went to an engineering school that emphasized
theory over practice; an unusual approach. Out of
school our graduates were two years behind other
schools's graduates in practice, caught up in
a year, and were way in front after two.

One guy a year ahead of me took his undergraduate
degree in mathematics and landed an extremely high
salary in computers upon graduation.

I don't have a low opinion of mathematics! In fact, the mathematician
in my story is now a friend of mine, and is undeniably brilliant. And
it's certain that if it weren't for a long string of mathematicians
doing math for the pure joy of seeing it work, we would not have tools
like Finite Element Analysis and Solid Modeling, let alone basic
physics.

But it's still true: to learn engineering, that mathematician would
have to start at square one.

Not

I'm sure his knowledge of (for example)
stress and strain,

Differential geometry.

and thermodynamics, are fairly close to zero.

The art of the Legendre transform.
Probability.
Lagrange multipiers.
S = log W.
Why certain quantities are or are not exact differentials.
That is what sinks the phlogiston theory.

You should know by now how shockingly easy
a mathematician finds his way through
applied mathematics. They have done all
the heavy lifting by now.

His
background knowledge of (for example) manufacturing processes and
industrial robotics are close to zero. And that doesn't even get
into the other skills many engineers need to master, like the politics
of dealing with a unionized workforce, writing good specifications,
designing for manufacturability, etc. etc.

He'd probably learn all that quickly, if he cared to - but since he's
in his 50s, he'd never catch up with a good engineering grad in his
30s.

And really, there is some chance he wouldn't be able to learn the
practical stuff. There are very intelligent people who can never work
out which way to turn a wrench!

I am not arguing that experience can be learned through theory.
Constructing mathematical proofs _is_ a transferrable skill.


While I think that both you and Frank make good points, I think that
engineering is subtly different from both science and mathematics. One
could say that mathematics is "pure" and that science employs
mathematics and that engineering employs science, but that is a bit of
an oversimplification. Engineers are typically more pragmatically
minded, but sometimes wind up extending science and/or mathematics in
their quest to solve a particular problem.

My favorite illustrations of this are the work and lives of Oliver
Heaviside -- http://en.wikipedia.org/wiki/Oliver_Heaviside and Nikola
Tesla -- http://en.wikipedia.org/wiki/Nikola_Tesla.

You could argue Heaviside and Tesla were a scientists (physicists) or,
more weakly, mathematicians (Heaviside), but I'd say they were
engineers, perhaps the greatest engineers ever. There are many more
examples like this, including more modern figures.

Frequently, engineers must press on and solve problems in areas with no
formal science or mathematics to support the effort. There are countless
examples. Perhaps the most striking is the very foundation of our
current technological civilization: the digital computer. One could
easily argue that there has been tremendous and transformative
engineering supported by precious little science and mathematics.

This has been my personal experience as an engineer as well. I was
disappointed to discover that the field I became involved in after
formal education, digital system design, was completely divorced from
anything I had studied. That was not a singular experience, either. When
I switched to programming, the situation was similar, and yet again when
I became involved in database applications. In each phase of my career
there was very little formal science and math that I could either apply
or carry over from one discipline to the other.

I agree with Michael that mathematics is a good base for engineering. I
still vividly recall math majors taking our most difficult electrical
engineering courses as easy electives. I counseled my (sophomore ) son
to switch to a math major when he was undecided, arguing that it is
probably the best general basis for a career in science or engineering.
At the same time, I agree with Frank that mathematics is usually not the
larger part of an engineering job. There may be no mathematics at all,
or it may be high school level.

Bicycle material selection strikes me as a classical engineering
problem. In that light, I'd have to say Chalo's arguments are the most
engineer-ish. My conclusion is that because CF is the obvious winner in
specific strength, both in raw and fabricated forms (because of carbon
fiber specific strength and anisotropy/molding, respectively), for
weight-critical applications it's the clear choice. If weight was my
only concern, I'd have CF bikes. Since weight isn't all that important
in my cycling, CF doesn't enter the picture, since, weight aside, it has
little to offer.

A formal engineering approach to material selection would be a weighted
factor analysis, where each characteristic of the material would be
assigned a relative value (for the application). Looking at CF, both as
a frame and component (e.g. fork, seatpost, rim, crank, handlebar, etc.)
material, my informal analysis makes CF out to be a non-optimal choice
in recreational & utility biking, with the additional observation that
many of the popular component applications of the material are
particularly ill suited to its characteristics (seatposts, handlebars
for likelihood of clamping crushing damage; cranks, rims for impact
damage; forks for brittle failure). On the other hand, for the racing
application, CF probably wins in virtually every component.

I don't have any issue with someone making an informed choice to use a
racing bike for recreational or utility cycling, but I do have a problem
with the misrepresentation of a material simply for marketing reasons.
Manufacturers have made an effort to inform buyers of some of the
caveats of CF, but it's pretty much buried in the fine print. Of course
CF is hardly unique in this respect, all bicycle designs that push the
weight limits do so at the expense of safety margins. So I would really
lump my issues with CF into my issues with selling racing bikes to an
often under-informed public. Caveats aside, the risk-reward trade-off is
understated, implicitly or otherwise.

When I was working in the aerospace industry, one of the things I had to
do was a formal failure modes analysis. Simply, you had to consider the
effect of the failure of every single component on the system. While
component failures may not be a leading cause of bicycle crashes, they
do happen. How much you should weigh that in material & design selection
is debatable, but my observations of fellow recreational cyclists and
their equipment choices suggest that it is not given sufficient
consideration. I lay much of the blame for that on the industry.

On Jan 21, 9:14*pm, "Kerry Montgomery" wrote:

Frank,
How does the ladder's thickness obviously matter?
Thanks,
Kerry

Dear Kerry,

Real ladders aren't imaginary lines. For convenient transport and
raising, most of them are extension ladders.

Here's a more realistic diagram, showing a typical extension ladder:

http://upload.wikimedia.org/wikipedi...38/La-main.gif

Imaginary versus real
A B
/ /
/ /
/ //
/ /
/ /
A A

The "width" above would complicate any ridiculously precise
theoretical calculation about where the top of the ladder touches a
wall.

The "top" itself is another problem, since it's likely to be a pair of
rounded end caps, a pair of swivel pads, or even a cross-brace
extending to either side of the "top" of the ladder like this:

http://www.louisvilleladder.com/popup_image.php?pID=134

Hate to try to calculate where the "top" of that ladder touches the
theoretical wall.

In any case, you don't place the bottom of a ladder against a cube at
the base of a wall. Real ladders bow under your weight, so the ladder
would either damage or be damaged by the edge of the cube and would
tend to skip outward when you climbed past the cube.

Cheers,

Carl Fogel

Carl Fogel wrote:

How does the ladder's thickness obviously matter?

Real ladders aren't imaginary lines. For convenient transport and
raising, most of them are extension ladders.

Here's a more realistic diagram, showing a typical extension ladder:

http://upload.wikimedia.org/wikipedi...38/La-main.gif

Imaginary versus real
A B
/ /
/ /
/ //
/ /
/ /
A A

The "width" above would complicate any ridiculously precise
theoretical calculation about where the top of the ladder touches a
wall.

The "top" itself is another problem, since it's likely to be a pair
of rounded end caps, a pair of swivel pads, or even a cross-brace
extending to either side of the "top" of the ladder like this:

http://www.louisvilleladder.com/popup_image.php?pID=134

Hate to try to calculate where the "top" of that ladder touches the
theoretical wall.

In any case, you don't place the bottom of a ladder against a cube
at the base of a wall. Real ladders bow under your weight, so the
ladder would either damage or be damaged by the edge of the cube and
would tend to skip outward when you climbed past the cube.

Let's not get too practical about this classic mathematical problem
that I recall from school where it is taught to develop analysis
methods, useful in various applications, while being phrased in
readily visualized terms. This problem comes to use in applications
for fixed length, mainly linear objects, and how they interact
spatially with objects. The ladder has no thickness in the
mathematical problem, where it is a line of known length, the cube a
square and the floor and wall, horizontal and vertical straight lines.

The problem allows assessing clearance problems with real ladders, if
you like. Too bad the designers of the Modolo Chronos and the
Campagnolo Delta brakes didn't have a feel for how fast the top of the
ladder moves as the foot moves away from the wall. For that matter,
they had no idea about hyperbolic functions or that brakes must be
linear for usefulness. Good engineering takes some mathematics and
practical knowledge of applications.

Jobst Brandt

Carl Fogel wrote:

How does the ladder's thickness obviously matter?

Real ladders aren't imaginary lines. For convenient transport and
raising, most of them are extension ladders.

Here's a more realistic diagram, showing a typical extension ladder:

http://upload.wikimedia.org/wikipedi...38/La-main.gif

Imaginary versus real
A B
/ /
/ /
/ //
/ /
/ /
A A

The "width" above would complicate any ridiculously precise
theoretical calculation about where the top of the ladder touches a
wall.

The "top" itself is another problem, since it's likely to be a pair
of rounded end caps, a pair of swivel pads, or even a cross-brace
extending to either side of the "top" of the ladder like this:

http://www.louisvilleladder.com/popup_image.php?pID=134

Hate to try to calculate where the "top" of that ladder touches the
theoretical wall.

In any case, you don't place the bottom of a ladder against a cube
at the base of a wall. Real ladders bow under your weight, so the
ladder would either damage or be damaged by the edge of the cube and
would tend to skip outward when you climbed past the cube.

wrote:
Let's not get too practical about this classic mathematical problem
that I recall from school where it is taught to develop analysis
methods, useful in various applications, while being phrased in
readily visualized terms. This problem comes to use in applications
for fixed length, mainly linear objects, and how they interact
spatially with objects. The ladder has no thickness in the
mathematical problem, where it is a line of known length, the cube a
square and the floor and wall, horizontal and vertical straight lines.

The problem allows assessing clearance problems with real ladders, if
you like. Too bad the designers of the Modolo Chronos and the
Campagnolo Delta brakes didn't have a feel for how fast the top of the
ladder moves as the foot moves away from the wall. For that matter,
they had no idea about hyperbolic functions or that brakes must be
linear for usefulness. Good engineering takes some mathematics and
practical knowledge of applications.

There's no "K" in Italian, so Modolo's Kronos was named expressly to
appear exotic.

--
Andrew Muzi
www.yellowjersey.org/
Open every day since 1 April, 1971

Andrew Muzi wrote:

How does the ladder's thickness obviously matter?

Real ladders aren't imaginary lines. For convenient transport and
raising, most of them are extension ladders.

Here's a more realistic diagram, showing a typical extension ladder:

http://upload.wikimedia.org/wikipedi...38/La-main.gif

Imaginary versus real
A B
/ /
/ /
/ //
/ /
/ /
A A

The "width" above would complicate any ridiculously precise
theoretical calculation about where the top of the ladder touches
a wall.

The "top" itself is another problem, since it's likely to be a
pair of rounded end caps, a pair of swivel pads, or even a
cross-brace extending to either side of the "top" of the ladder
like this:

http://www.louisvilleladder.com/popup_image.php?pID=134

Hate to try to calculate where the "top" of that ladder touches
the theoretical wall.

In any case, you don't place the bottom of a ladder against a cube
at the base of a wall. Real ladders bow under your weight, so the
ladder would either damage or be damaged by the edge of the cube
and would tend to skip outward when you climbed past the cube.

Let's not get too practical about this classic mathematical problem
that I recall from school where it is taught to develop analysis
methods, useful in various applications, while being phrased in
readily visualized terms. This problem comes to use in
applications for fixed length, mainly linear objects, and how they
interact spatially with objects. The ladder has no thickness in
the mathematical problem, where it is a line of known length, the
cube a square and the floor and wall, horizontal and vertical
straight lines.

The problem allows assessing clearance problems with real ladders,
if you like. Too bad the designers of the Modolo Chronos and the
Campagnolo Delta brakes didn't have a feel for how fast the top of
the ladder moves as the foot moves away from the wall. For that
matter, they had no idea about hyperbolic functions or that brakes
must be linear for usefulness. Good engineering takes some
mathematics and practical knowledge of applications.

There's no "K" in Italian, so Modolo's Kronos was named expressly to
appear exotic.

Thanks, I stumbled onto that just after sending that out to
wreck.bike. You'll notice I got that right in the brake article in
the FAQ. To make up for that the (I) have no "J" either and made my
friend "Jones" into Mr. Inors and they make a tilde with a "gn" as in
Campagnolo.

Jobst Brandt

In article
,
Frank Krygowski wrote:

On Jan 21, 8:16*pm, Michael Press wrote:
In article ,
*"Tom Kunich" cyclintom@yahoo. com wrote:



To be a surpassingly good engineer you need to be a surpassingly good
mathematician for sure. But just being a mathematicians makes you nothing
but a mathematician.

I'll differ with Tom here. To be a surpassingly good engineer, you
need to be a decent mathematician. You certainly don't need as much
research-level theoretical math as the typical professional
mathematician!

Then these two early exercises from the foundations of
the differential and integral calculus will offer no difficulty.

1) There is a rational number between any two distinct real numbers.
Hint: Archimedean property of the real numbers.

2) Every sequence of real numbers has a monotone subsequence.

:-) This is kind of fun.

OK, the proper engineering answer to that is, "Who cares? Those don't
have anything to do with anything practical, and I work to get things
done. Besides, my project deadline is coming up."

See how easy it is to demolish Tom's thesis?

An engineering type question. Let's have a mathematical solution.

3) A cube shaped box with the edge length 1 m stands against a wall.
A ladder of length 5 m leans against the wall, and just touches
the box at an edge. How high on the wall is the top of the ladder?

And the first engineering response is: "Why do you want to know?"
Not to be smart, but to settle the next question: "What's the
tolerance?" Because in the engineering world, there must always be
tolerance, and good enough is perfect.

After that, if the tolerance were less than a few centimeters, the
engineer asks "What are the detail dimensions of the ladder?"
Because, being practical, he knows the ladder's thickness and end
profile obviously matter.

When the questioner says it's really just a theoretical line - that
is, an infinitely thin "ladder," the engineer will say "Oh, this is
just an unimportant little puzzle."

He then may say "The answer is any distance at all between zero and 5
meters." Why? Because you didn't specify _which_ edge of the box the
"ladder" touches, nor which part of the ladder leans against the wall
Considering the bottom and vertical edges of the box, it could be
anywhere from laying on the floor to perfectly vertical. And the
engineer grins.

If the questioner says "No, no, no, I meant the theoretical "ladder"
leans in the usual way against the edge of the cube which is parallel
to the intersection of the wall and floor... and I really want an
answer, please," then the engineer sketches a couple similar triangles
on scratch paper, pops two equations into his equation solving
software, and says:

"4.83850116 meters high, and 1.26052 meters out from the wall. Do you
need it to be more exact than that?"

Your answer is not exact, so the question is meaningless.
I asked for the mathematical solution. Reread, and you will see.

(4.8385011606895490757530113, 1.2605183529032357542752121)

is still not exact; and you did not supply proof of accuracy.

--
Michael Press

The purpose of computation is insight, not numbers.
-- R.W. Hamming

"Michael Press" wrote in message
...
In article
,
Frank Krygowski wrote:

On Jan 21, 8:16 pm, Michael Press wrote:
In article ,
"Tom Kunich" cyclintom@yahoo. com wrote:



To be a surpassingly good engineer you need to be a surpassingly good
mathematician for sure. But just being a mathematicians makes you
nothing
but a mathematician.

I'll differ with Tom here. To be a surpassingly good engineer, you
need to be a decent mathematician. You certainly don't need as much
research-level theoretical math as the typical professional
mathematician!

Then these two early exercises from the foundations of
the differential and integral calculus will offer no difficulty.

1) There is a rational number between any two distinct real numbers.
Hint: Archimedean property of the real numbers.

2) Every sequence of real numbers has a monotone subsequence.

:-) This is kind of fun.

OK, the proper engineering answer to that is, "Who cares? Those don't
have anything to do with anything practical, and I work to get things
done. Besides, my project deadline is coming up."

See how easy it is to demolish Tom's thesis?

Maybe you missed the part where I wrote, "surpassingly good engineer"?