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 Fifty Plus (50+) Share the victories, challenges, successes and special concerns of bicyclists 50 and older. Especially useful for those entering or reentering bicycling.

 07-13-12, 04:43 PM #2 cyclinfool gone ride'n     Join Date: Aug 2007 Location: Upstate NY Bikes: Simoncini, Gary Fisher, Specialized Tarmac Posts: 4,051 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) a mile
 07-13-12, 04:46 PM #3 contango  2 Fat 2 Furious     Join Date: Nov 2010 Location: England Bikes: 2009 Specialized Rockhopper Comp Disc, 2009 Specialized Tricross Sport RIP Posts: 3,997 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 3 Post(s) Crankarm length of 175mm means your pedals would describe a circle of diameter of just about 1100mm, or 43.3", or 3.61 feet 78rpm equals 4680 rotations per hour. So for 4680 rotations to take you 17.3 miles each rotation would take you 19.52 feet I'm going to take a bit of a leap of faith and speculate that the distance the shoe travels per rotation is the same whether you pedal for the full rotation normally, or you were in a theoretical situation where you lifted the back wheel, rotated the pedals once while stationary, and then rolled forward 19.52 feet with the pedals stationary. That may not be entirely accurate but given you probably aren't doing the same cadence the entire time, the same speed the entire time, or necessarily even in the same gear the entire time, it's probably a fair enough approximation (that said it's late, so maths geeks feel free to tell me I'm wrong) That would make the distance the pedals travelled per rotation 19.52 + 3.61 = 23.13 feet. So over the course of your 17.3 miles in an hour those 4680 rotations would have the pedals moving 23.13 x 4680 = 108,248 feet, so over the course of one mile they would travel 108248/17.3 = 6257 feet. So the pedals are moving 18.5% further than the bottom bracket. __________________ "For a list of ways technology has failed to improve quality of life, press three"
 07-13-12, 04:51 PM #4 locolobo13  Senior Member     Join Date: Oct 2011 Location: Phx, AZ Bikes: Trek Mtn Bike Posts: 1,384 Mentioned: 3 Post(s) Tagged: 0 Thread(s) Quoted: 78 Post(s) I was thinking more cycloid like. Or a "Curtate Cycloid"? http://en.wikipedia.org/wiki/Cycloid Have no idea how to calculate distance.
 07-13-12, 05:44 PM #5 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Tom - But the shoe is moving up and down in addition to forward, so it's distance will be greater than a mile, won't it? The bike as a whole goes one mile, but the circular motion of the pedals, just like the circular motion of the wheels, means those parts travel farther. Put simply, the wheel hub goes one mile, but a point on the tire moves more than a mile, just like the shoes.
07-13-12, 05:57 PM   #6
TomD77
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 Originally Posted by Kurt Erlenbach Tom - But the shoe is moving up and down in addition to forward, so it's distance will be greater than a mile, won't it? The bike as a whole goes one mile, but the circular motion of the pedals, just like the circular motion of the wheels, means those parts travel farther. Put simply, the wheel hub goes one mile, but a point on the tire moves more than a mile, just like the shoes.
I thought about it more after the post and deleted the post to think more. I've come to the conclusion that there is no correlation of pedal distance to forward distance. Say you have a bike with an infinite gear ratio, then any given pedal speed can have from a zero forward velocity to infinite forward velocity. Therefore the answer changes relative to the crank distance, gear ratio and wheel size.

Last edited by TomD77; 07-13-12 at 06:07 PM.

 07-13-12, 06:03 PM #7 cyclinfool gone ride'n     Join Date: Aug 2007 Location: Upstate NY Bikes: Simoncini, Gary Fisher, Specialized Tarmac Posts: 4,051 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) I stick with my original answer, that is unless you tell me the exact direction of travel, the date and time of travel and your longitude and lattitude because we all know that we are spinning through space on a rotating ball in a moving universe - and that poor little shoe is traveling with us...
 07-13-12, 06:07 PM #8 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Tom - OK, assume a 700 x 25 tire. The gear inches ratio could be calculated from that with the speed and cadence number.
 07-13-12, 06:25 PM #9 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Here's my answer. Assume you're on a trainer. The bike moves a distance of zero, but the pedals and shoes move pi(crank length) * # of revs. Using that formula, going 17.3 mph means 1522.4 ft/min = 3.4682 min per mile. 78 rpm cadence thus = 270.5 revs per mile. pi(175 mm) * 270.5 revs = 148,715.49 mm per mile. 148,715.49 mm = 487.912 feet. The answer thus, I think, is 5280 + 487.9 = 5767.9 feet. But after reading the wikipedia article lobolobo links above, I think the correct answer requires calculus that this lawyer, who barely passed Calculus for Babies in college, no longer knows. Am I right or wrong?
 07-13-12, 06:44 PM #10 Dudelsack  A might bewildered...     Join Date: Oct 2011 Location: Loovul Bikes: Bacchetta Giro ATT 26; Lemond Buenos Aires Posts: 6,351 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 4 Post(s) N+1. The answer always seems to work with cycling related questions. __________________ Signature line for rent.
 07-13-12, 07:05 PM #11 DnvrFox Banned.     Join Date: Aug 2001 Bikes: Posts: 20,917 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Err . . Does this change your calculations any?
 07-13-12, 07:13 PM #12 Bearhawker Member   Join Date: Apr 2012 Location: Prince Edward Island, Canada Bikes: '12 Motobecane Turino, '12 Trek 3700 Disc Posts: 38 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Another wrinkle... if the outer edge of the tire goes around faster than the hub does, does the center of the hub actually move?
 07-13-12, 07:35 PM #13 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) My answer is wrong because the distance the shoe travels on a trainer is pi(2 * 175 mm), not pi(175mm).
07-13-12, 07:36 PM   #14
Kurt Erlenbach
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 Originally Posted by Bearhawker Another wrinkle... if the outer edge of the tire goes around faster than the hub does, does the center of the hub actually move?
On a trainer, the answer is no. In my problem, the hub moves exactly one mile.

 07-13-12, 07:42 PM #15 Retro Grouch  Senior Member     Join Date: Feb 2004 Location: St Peters, Missouri Bikes: Catrike 559 I own some others but they don't get ridden very much. Posts: 27,916 Mentioned: 5 Post(s) Tagged: 0 Thread(s) Quoted: 633 Post(s) When you're out on a morning ride, you need to focus more on what you're doing.
 07-13-12, 08:25 PM #16 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) OK, here's an new part of the answer. The length of the arc of a cycloid is 8r. But the movement of shoes on a bike describe a curtate cycloid, not a cycloid. The movement of a point on the outside of the tire describes a cycloid. The radius of the tire is about 340 miilimeters, or 13.39 inches, making the tire circumference 2* 3.1416 * 340 = 2,136 millimeters = 7 feet, or 753.3 revolutions per mile. The distance a point on the tire moves thus is 8r(753.4) or 8* 13.39 * 753.3 = 6733 feet. So the valve stem goes 6733 feet (or a little less, because it's not on the outside) when the bike goes a mile. Now I need the find the formula for calculating the arc of a curtate cycloid, which would describe the distance the shoes move. I learned something tonight.
 07-13-12, 08:26 PM #17 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) And R-Grouch, you are completely right.
 07-13-12, 08:53 PM #18 zonatandem Senior Member     Join Date: Dec 2003 Location: Tucson, AZ Bikes: Custom Zona c/f tandem + Scott Plasma single Posts: 10,985 Mentioned: 2 Post(s) Tagged: 1 Thread(s) Quoted: 61 Post(s) The shoe does not tragel anywhere.
 07-13-12, 10:06 PM #19 TomD77 Senior Member     Join Date: Jul 2010 Location: Florida Panhandle Bikes: Posts: 572 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) It's not that hard. Say you are in a 50:18 gear and (for simplicity) your wheel circumference is exactly 6.5 feet and your crank length is exactly 7 inches. Each rotation of the crank (1.82 feet) will yield 18 feet of forward movement for a ratio of very close to 10:1 of crank distance to forward distance. So the answer is 528 feet per mile. If you're asking about the more complicated case of pedal movement relative to a stationary reference, it is additive. Look at your watch as you are in a car at 60 mph, how far does the second hand travel in one minute if it is perpendicular to the direction of travel? One mile plus the circumference of the dial. Last edited by TomD77; 07-13-12 at 10:32 PM.
07-13-12, 10:38 PM   #20
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 Originally Posted by Retro Grouch When you're out on a morning ride, you need to focus more on what you're doing.
Dunno about that. My best rides are when I have some thought train going and I'll temporarily surface and wonder where the last 5 miles got off to.

07-14-12, 04:30 AM   #21
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 Originally Posted by Kurt Erlenbach Tom - But the shoe is moving up and down in addition to forward, so it's distance will be greater than a mile, won't it? The bike as a whole goes one mile, but the circular motion of the pedals, just like the circular motion of the wheels, means those parts travel farther. Put simply, the wheel hub goes one mile, but a point on the tire moves more than a mile, just like the shoes.
If you have a cadence counting computer take the distance traveled in miles by the bike and compare it to the distance derived from the circumference the shoe travels and the total pedal strokes. No matter how you visualize the "sine" wave or other foot motion, all it does is travel around a circle x number of times for y minutes. I believe that all the other perceived motions cancle out.

As a quick example, assume a gear ratio that results in the foot going forward relative to the ground at twice bike speed at the top of the pedal circle. That would also result in a foot speed relative to the ground of 0 at the bottom of the circle. I contend that the overall result is that your shoes don't know the difference between riding a stationary bike and riding down the trail. They only know the cicle distance and the time.

That could be completely wrong, but it's my intuitive "guess".
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Last edited by maddmaxx; 07-14-12 at 04:38 AM.

07-14-12, 05:05 AM   #22
BeastRider
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REALLY??.....That's what you are concerned about??......

 07-14-12, 05:45 AM #23 Garfield Cat Senior Member     Join Date: Oct 2004 Location: Huntington Beach, CA Bikes: Cervelo Prodigy Posts: 6,411 Mentioned: 2 Post(s) Tagged: 0 Thread(s) Quoted: 148 Post(s) The shoes only travel when you get off the bike and walk around in them. The rest is meaningless. Take a look at your heel cushion and the scuff marks.
 07-14-12, 06:47 AM #24 Kurt Erlenbach Senior Member Thread Starter     Join Date: Jul 2007 Location: Space Coast, Florida Bikes: Posts: 2,423 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) The path of the shoe is not a curtate cycloid because the chain and gearing intervene. The path a shoe traces on a child's tricycle is a curtate cycloid, when the pedal is connected directly to the drive wheel. Knowing the tire radius is 340 mm allows calculation of the gain ratio - 270.5 turns of the crank = 270.5(2pi(175mm)) =297,431 mm = 975.8 feet. So to move a point on the outside of the wheel 6733 feet, which is what's required to roll a wheel of r=340 mm one mile, requires turning the crank a distance of 975.8 feet. Somewhere in the ratio of those numbers, about 6.9 to 1, is an important fact.
07-14-12, 07:23 AM   #25
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 Originally Posted by Kurt Erlenbach My answer is wrong because the distance the shoe travels on a trainer is pi(2 * 175 mm), not pi(175mm).
Someone always drags pi into threads on this forum.
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