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Elliptical Chainrings
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#53
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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) |
#54
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Elliptical Chainrings
atriage wrote:
On 23/07/2013 03:35, Steve Freides wrote: 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. Did you go to any kind of school at all? http://www.thefreedictionary.com/torque Several, in fact. -S- |
#55
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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
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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
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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
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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
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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
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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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