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  • bicycle puzzle

    Here is a puzzle which I've seen confound some of my rocket scientist friends, even those who ride bicycles to work. It's been around for years, so I'm sure some of you have seen it. But I don't think it is widely known.

    The experiment involves a bicycle with its pedals in the vertical position as shown. Assume the bicycle is balanced (by side forces only) so that it doesn't fall over.

    Tie a string to the lower pedal (14), and standing behind the bicycle, pull backward on the string. Which direction does the bicycle move?

    Allan Ostling

    Phoenix, Arizona

  • #2
    bicycle puzzle

    If the bike is balanced side to side and no other forces involved I would guess it would move backwards. However if there were a small drag goin rearward it would tend to propel forward. This is just a dummy guess, ha ha.

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    • #3
      My first thought was that the bike would move forward, but I just tried it, and the bike went backward. But I think it will depend on the gear ratio, and that if you had a ratio (measured in inches, the traditional method over here) that was less than the diameter of the driven wheel, the bike would move forward.

      The bike in the picture appears to have a ratio of about 65 to 75 inches, so it will go backward.

      Someone with a mountain or touring bike handy, try this, assuming your low gear is less than 26 inches.

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      • #4
        The bike will move backward even faster than the string pulling it because the peddle, driven by the rear wheel and chain coupling to the sprocket, will move in the opposite direction (away from the string tugger).

        Edit: clarification - the pedal moves forward relative to the bike, not the string tugger.
        Last edited by dp; 09-18-2007, 02:02 AM.

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        • #5

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          • #6
            Originally posted by john hobdeclipe
            My first thought was that the bike would move forward, but I just tried it, and the bike went backward. But I think it will depend on the gear ratio, and that if you had a ratio (measured in inches, the traditional method over here) that was less than the diameter of the driven wheel, the bike would move forward.

            The bike in the picture appears to have a ratio of about 65 to 75 inches, so it will go backward.

            Someone with a mountain or touring bike handy, try this, assuming your low gear is less than 26 inches.


            I believe you are correct, to me it makes sense that its all up to the gearing, I cant imagine a bike still moving backwards with extreme gearing ----
            think for a second on those wierd ass wind sculptures that someone posted, some of them walked directy into the wind -- they did this by means of gearing, the fan blades that were powered were at an extreme ratio and over rode the rest of the winds force on not only the blades themselfs but all the rest of the sculpture,,, the bike experiment is no different, My Mt. bike in high gear (48/11) gets pulled imediatly backwards BUT, in low gear (24/32) it grid locks, im a thinnin it would go forward with a 22/34 but realize as soon as the crank arc is a fair degree beyond BDC then the advantage would start to get taken away until gridlock is achieved once again.....

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            • #7
              I may not understand this, but I would think it would move forward ( chain drive action) until the pedals were parallel to the ground. Then you are pulling on a fixed point, against a coaster brake.

              Coasts, so it would come to the pulling force.

              You put forward force on the pedal, you engage the clutches, it goes forward.

              Cheers,

              George

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              • #8
                The bike goes nowhere unless you pull hard enough to make it skid backward. It can't move forward because you are pulling it back. The pedal can't move backward farther than the bike moves forward since the driving sprocket is larger than the driven sprocket.
                Free software for calculating bolt circles and similar: Click Here

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                • #9
                  "The bike goes nowhere unless you pull hard enough to make it skid backward. It can't move forward because you are pulling it back. The pedal can't move backward farther than the bike moves forward since the driving sprocket is larger than the driven sprocket."





                  Nope --- the bike moves imediatly backwards with no skidding what-so ever, while doing it the pedal actually moves foreward whilst being tugged on in the reverse direction, but thats only with the illustration given,

                  Like J.H. stated, with the proper gearing the bike moves imediatly foreward and the pedal is drawn to the back and like I stated with a no advantage no dis-advantage gearing the bike will grid lock its drive system, Now and only now will you skid the rear tire to draw it backwards... EDIT: the picture of the bike in the illustration is in no way to be confused with gearing that could even aproach a gridlocked drivetrain as the front sprocket would have to be smaller than the rear...
                  Last edited by A.K. Boomer; 09-18-2007, 12:51 AM.

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                  • #10
                    Evan has it, the bike doesn't move.
                    I seldom do anything within the scope of logical reason and calculated cost/benefit, etc- I'm following my passion-

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                    • #11
                      Originally posted by darryl
                      Evan has it, the bike doesn't move.

                      wrong answer dude, Hint --- listen to the mechanic!


                      That bike in the illustration gets pulled imediatly backwards without dragging its tire...
                      Last edited by A.K. Boomer; 09-18-2007, 12:48 AM.

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                      • #12
                        Oops, you might be right. Evan's answer seemed right to me, but let me think this out again (without resorting to getting the bicycle out)

                        Ok, if you were actually pedalling, even though the bottom of the crank is moving backwards relative to the bicycle, it's actually always moving forward. Therefore it will actually move backwards if the bicycle is moved backwards, even though it would then be moving forwards relative to the bicycle itself. If you pull it backwards with the string, the force you apply is resisted only by the torque imparted to the tire against the ground. Because of the drive ratio, there will be less torque applied to the ground than that applied to the pedal. Right you are, Boomer, the bicycle moves backwards.

                        I'm going to post this bit of logic before I try it with the bicycle.
                        Last edited by darryl; 09-18-2007, 01:08 AM.
                        I seldom do anything within the scope of logical reason and calculated cost/benefit, etc- I'm following my passion-

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                        • #13
                          I got my bike out to prove I had enough of a low gear to propell in foreward motion, i dont but I know im still right about this, like I stated, its the exact same principle on how that guy got his mechanical wind machines to walk against the wind...

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                          • #14
                            Originally posted by A.K. Boomer
                            wrong answer dude, Hint --- listen to the mechanic!


                            That bike in the illustration gets pulled imediatly backwards without dragging its tire...
                            Yep - the mechanical advantage belongs to that big tire turning that tiny sprocket against that big sprocket. That tire and gearing ration will counter turn the sprocket which causes the lower pedal to move forward (counter clockwise).

                            Just to help clarify, imagine the rear tire is a gear in a rack and can't skid.

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                            • #15
                              I think we have a little problem here with the thought experiment. My concept of pulling it backward doesn't allow for the rope to move forward, only the bike. I am considering the problem as if the backward pull is applied by a rope taken up by a winch fixed in place.
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