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Elliptical Chainrings



 
 
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  #51  
Old July 23rd 13, 02:35 AM posted to rec.bicycles.racing
Steve Freides[_2_]
external usenet poster
 
Posts: 665
Default Elliptical Chainrings

wrote:

A lot of times when trying to loosen a tight nut or bolt, if you
place the handle of the wrench lower than 12 o'clock you can exert
more pressure onto the handle but *NOTHING* else has changed. That's
what the eliptical chainring does. It allows more force to be applied
at the former deadzones of TDC and BDC. The gear size (effective
diameter of a direct drive wheel) doesn't change nor does the length
of tthe lever - just the amount of force that can be applied to that
lever.


We need to send you back to science class. How does the shape of the
chainring allow you to apply a different amount of force.

-S-


Ads
  #53  
Old July 23rd 13, 11:15 AM posted to rec.bicycles.racing
none
external usenet poster
 
Posts: 13
Default Elliptical Chainrings

In article ,
Steve Freides wrote:
Mower Man wrote:

Wrong. It does. And it's so obvious as to beggar belief. The slack in
the chain is utterly irrelevant, too.


Let us consider what's happening at a point in the rotation of the
chainrings where it's clearly not round. Are you suggesting there is a
different amount of pedal travel in order to advance the chain at the
rear wheel by one link? That's the crux of the issue - you are arguing,
I believe, that the amount of pedal travel varies throughout a pedaling
circle as the shape of the chainring changes - because if it doesn't,
then there is no difference.


The pedal still travel over a perfect circle but not the chain.
So for a given travel of the pedal, the chain travel a different
amount or if you prefer, to achieve a given amount of travel of the
chain, the amount of travel needed by the pedals varies.

What really could make a difference is if the shape of the chainring
effectively changed the gear ratio during a single pedal revolution. If
that happened, then we'd be talking about something tangible, the
reduction of force required by a lower gear at the point the rider's
legs were weakest. Now that sounds like it could be truly useful.


We are talking about definite physical, mechanical differences. This
is a hard fact.

OK, last try at explaining this:

The precise maths for the elipse of ovoid require inifite series and
usenet is maybe not the ideal place to go there so please allow me to
try to simplify by using a square.

1- chain, teeth, strap, pulley, gear, etc

Some peoples have been focusing in teeth too much.

Can we all agree that any of the following is equivalent:

Front = 40 teeth Rear = 20 teeth
Front = 400 teeth Rear = 200 teeth
Front = 4000 teeth Rear = 2000 teeth
Front = 4 million teeth Rear = 2 millions teeth
Front = 4 billion teeth Rear = 2 billion teeth

There's no difference in the gearing for any of the above.

So for the sake of simplicity, I'll continue this with a case of a
front rig with 8000 teeth with each teeth being 0.1mm.

2- The pedal move along a circle.

I think we all agree with this.

3- The chain rig is solidly attach to the pedal. Rotating the pedal
10 degrees rotate the chain rig 10 degrees around its point of
rotation regardless of the shape.

4- The chain is always in contact with the front part of the rig so it
will follow the perimeter of the rig.

5- Circular chain rig:
my 8000 teeth chain rig is 800.0 mm in circumference, it has a radius
of 127.3mm and a diameter of 254.6 mm (i.e. 800.0/Pi)

If you rotate the pedal 1/16th of a rotation (22.5 degree), the rig
will rotate 22.5 degree and the chain will be pulled by the length of
an arc of 22.5 degree with a radius of 127.3mm which is 50.0mm. As
this is a perfect circle, this is also 1/16th of the total
circumference. This will pull 500 teeth on the chain.

Since this is a perfect circle, all possible segments of 22.5 degree
are identical to any other segment.

6- Square chain rig

Now let's replace our circle chain rig with a square one.
This is a square with each side 200.0mm long.

(bad ascii art for orientation reference:
___
| . |
|___|

The perimeter of the square is 4*200.0mm = 800.0mm. This is the same
perimeter as our circular chain rig. This square also has 8000
teeth and a full 360 deg rotation with pull 8000 teeth on the chain.

If you draw a vertical or horizontal line from the center of the
square to the edge, it will be 100.0mm

If you draw a diagonal line to the corner, it will be 141.4mm
(i.e. ( 1/sin(45) ) * 100.0mm )

The pedal however are still going around in a circle. So what happens
if we compute the length of a partial rotation of the square. The
simplest way to compute this is to draw right-angle triangle and use
trigonometry.

Let's try 45 degrees: We can draw that this will go from the
horizontal to the 45 deg angle and visually we can se that this will
be 100.0mm. Trigonometry also shows that this is 100.0mm
(tan(45)*100.0mm) as expected.

What about 22.5 degree: From 0 to 22.5 degree, the length of the
perimeter section is tan(22.5) * 100.0 = 41.4mm.

The length of the section from 22.5 to 45 degree is:
(tan(45)*100.0mm) - (tan(22.5)*100.0mm) = 58.6mm

22.5 degree rotation centered over the center of the flat bit:
The length of the section from -11.25 to +11.25 is:
(tan(-11.25)*100.0mm)+(tan(11.25)*100.0mm)= 39.8mm

22.5 degree rotation centered over the corner:
The length of the section from 33.75 to 56.25 is:
((tan(45)*100.0)-(tan(33.75)*100.0)) * 2 = 66.36mm

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections result
in more mm. There's still exactly 2000 teeth per 90 degree rotation and
8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but the
speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)




  #55  
Old July 23rd 13, 04:21 PM posted to rec.bicycles.racing
Steve Freides[_2_]
external usenet poster
 
Posts: 665
Default Elliptical Chainrings

none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)


This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?

-S-


  #56  
Old July 23rd 13, 04:46 PM posted to rec.bicycles.racing
none
external usenet poster
 
Posts: 13
Default Elliptical Chainrings

In article ,
Steve Freides wrote:
none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)


This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.


Yes

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?


Yes
(depending on the specific shape of the rig and the specific
alignment.)


  #57  
Old July 24th 13, 12:03 AM posted to rec.bicycles.racing
Sir Gregory Hall, Esq·
external usenet poster
 
Posts: 98
Default Elliptical Chainrings

"none (Yannick Tremblay)" yatremblay@bel1lin202. wrote in message
...
In article ,
Steve Freides wrote:
none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)


This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.


Yes

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?


Yes
(depending on the specific shape of the rig and the specific
alignment.)




It sounds good in theory but the theory cannot be proven
because it's wrong. The ONLY thing that determines
gearing in number of teeth. Not changing the number
of teeth (as in upshifting and downshifting to change
the number of teeth) will cause the gear ratio to remain
the same. Any illusion that an elliptical chainring pulling
more or less chain teeth at any given time is an illusion.
It's not the diameter of the chainring at the ingress
or egress of the chain from the chainring time that matters
but rather the number of teeth that will maintain the
same gear ratio no matter the shape.

An ellipse with 53 teeth is no different than a circle with
53 teeth when it comes to gear ratio. There is no way
to get some increased or reduced gear ratio without
changing the number of teeth.


  #58  
Old July 24th 13, 12:18 AM posted to rec.bicycles.racing
atriage[_7_]
external usenet poster
 
Posts: 78
Default Elliptical Chainrings

On 24/07/2013 01:03, Sir Gregory Hall, Esq· wrote:
"none (Yannick Tremblay)" yatremblay@bel1lin202. wrote in message
...
In article ,
Steve Freides wrote:
none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)

This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.


Yes

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?


Yes
(depending on the specific shape of the rig and the specific
alignment.)




It sounds good in theory but the theory cannot be proven
because it's wrong. The ONLY thing that determines
gearing in number of teeth. Not changing the number
of teeth (as in upshifting and downshifting to change
the number of teeth) will cause the gear ratio to remain
the same. Any illusion that an elliptical chainring pulling
more or less chain teeth at any given time is an illusion.
It's not the diameter of the chainring at the ingress
or egress of the chain from the chainring time that matters
but rather the number of teeth that will maintain the
same gear ratio no matter the shape.

An ellipse with 53 teeth is no different than a circle with
53 teeth when it comes to gear ratio. There is no way
to get some increased or reduced gear ratio without
changing the number of teeth.


My God you're stupid.
  #59  
Old July 24th 13, 12:33 AM posted to rec.bicycles.racing
Sir Gregory Hall, Esq·
external usenet poster
 
Posts: 98
Default Elliptical Chainrings

"atriage" wrote in message
eb.com...
On 24/07/2013 01:03, Sir Gregory Hall, Esq· wrote:
"none (Yannick Tremblay)" yatremblay@bel1lin202. wrote in message
...
In article ,
Steve Freides wrote:
none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)

This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.

Yes

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?

Yes
(depending on the specific shape of the rig and the specific
alignment.)




It sounds good in theory but the theory cannot be proven
because it's wrong. The ONLY thing that determines
gearing in number of teeth. Not changing the number
of teeth (as in upshifting and downshifting to change
the number of teeth) will cause the gear ratio to remain
the same. Any illusion that an elliptical chainring pulling
more or less chain teeth at any given time is an illusion.
It's not the diameter of the chainring at the ingress
or egress of the chain from the chainring time that matters
but rather the number of teeth that will maintain the
same gear ratio no matter the shape.

An ellipse with 53 teeth is no different than a circle with
53 teeth when it comes to gear ratio. There is no way
to get some increased or reduced gear ratio without
changing the number of teeth.


My God you're stupid.



I bet this *stupid* guy can kick your ass on a bike.

--
Sir Gregory


  #60  
Old July 24th 13, 07:58 AM posted to rec.bicycles.racing
atriage[_7_]
external usenet poster
 
Posts: 78
Default Elliptical Chainrings

On 24/07/2013 01:33, Sir Gregory Hall, Esq· wrote:
"atriage" wrote in message
eb.com...
On 24/07/2013 01:03, Sir Gregory Hall, Esq· wrote:
"none (Yannick Tremblay)" yatremblay@bel1lin202. wrote in message
...
In article ,
Steve Freides wrote:
none (Yannick Tremblay) wrote:

So basically, if we turn the pedals 22.5 degree (along the circular
movement of the pedal), the amount the chain will be pulled depends on
the position of the square.

0 to 22.5 deg = 41.4mm =~ 414 teeth
22.5 to 45 deg = 58.6mm =~ 586 teeth
45 to 67.5 = 58.6mm =~ 586 teeth
67.5 to 90 = 41.4mm =~ 414 teeth

-11.25 to 11.25 deg = 39.8mm =~ 398 teeth
11.25 to 33.75 deg = 46.9mm =~ 469 teeth
33.75 to 56.25 = 66.4mm =~ 664 teeth
56.25 to 78.75 = 46.9mm =~ 469 teeth

There is still exactly 200.0mm per 90 degree but some subsections
result in more mm. There's still exactly 2000 teeth per 90 degree
rotation and 8000 teeth per 360 degree.

7: elipse, ovoid or any other shape:

The same principle applies. The maths just become a bit more
complicated and you may need infinite series to get the exact result.
Visually, it is noticeable looking at:
http://en.wikipedia.org/wiki/File:Pa...ic_ellipse.gif
that the speed of travel of the point on the circle is constant but
the speed of travel of the point on the elipse varies, sometime being
faster and sometimes slower. This is also what happens would happen
to a chain on an elipse.

If you want more details, you could look at papers such as:
http://www.noncircularchainring.be/p...elease%202.pdf
The purely mechanical section of this paper is irrefutable. They
compute the angular velocity of various chainrig using AutoCAD and
MATLAB. The biomechanical section where they produce an equation to
model the human is where there is room for interpretation.

Some manufacturers also have literature on their site on the subject.

Yannick
(sorry about the long message but this is not pantomine, this is
science and facts)

This makes some sense to me. What you are saying is that a non-round
chainring will pull more, or fewer, chain links/teeth through a
particular section of the pedalling circle, effectively changing the
gearing during the time - more chain pulled is the same as having a
stiffer, bigger gear, and less chain pulled is the same as having a
smaller gear.

Yes

So the net effect, you're saying, is to give an easier to pedal, smaller
gear where we we are weakest in the pedalling cicle, and a stiffer gear
where we have more strength - is that what you're saying?

Yes
(depending on the specific shape of the rig and the specific
alignment.)



It sounds good in theory but the theory cannot be proven
because it's wrong. The ONLY thing that determines
gearing in number of teeth. Not changing the number
of teeth (as in upshifting and downshifting to change
the number of teeth) will cause the gear ratio to remain
the same. Any illusion that an elliptical chainring pulling
more or less chain teeth at any given time is an illusion.
It's not the diameter of the chainring at the ingress
or egress of the chain from the chainring time that matters
but rather the number of teeth that will maintain the
same gear ratio no matter the shape.

An ellipse with 53 teeth is no different than a circle with
53 teeth when it comes to gear ratio. There is no way
to get some increased or reduced gear ratio without
changing the number of teeth.


My God you're stupid.



I bet this *stupid* guy can kick your ass on a bike.

You sure could if you're as good as you *imagine* you are. What you
really are however is an aging deluded ****.
 




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