Frank Krygowski wrote:
On 5/28/2017 7:55 PM, Ralph Barone wrote:
Frank Krygowski wrote:
On 5/28/2017 2:58 PM, Ralph Barone wrote:
Frank Krygowski wrote:
On 5/27/2017 12:21 AM, Frank Krygowski wrote:
On Friday, May 26, 2017 at 11:48:13 PM UTC-4, Jeff Liebermann wrote:
On Fri, 26 May 2017 20:36:39 -0700 (PDT), Frank Krygowski wrote:

Bicycle riddle:
http://www.popularmechanics.com/scie...icycle-killer/
- Frank Krygowski

When you're done with that bicycle riddle, try this bicycle mechanical
problem:
http://www.popularmechanics.com/science/math/a26070/riddle-of-the-week-24/
(I guessed wrong, as usual).

I got it, but by a very different mental process than what they used.

I'll hold off discussing until others have had a chance to work on it.

- Frank Krygowski

So little interest in the riddle that was actually technical!


It was relatively obvious (by virtue of the fact that it was posed as a
riddle, there had to be some non-intuitiveness to the answer) and I deduced
the right answer. There just wasn't much left to talk about afterwards.

Just curious: How did you deduce the right answer?

I can see one very detailed way, requiring some simple math, and one
sort of shortcut way, no numbers required. I used the shortcut.


If you look at the system, the "gain" in torque
from pedals to wheels is less than one (for almost all bikes), therefore
the mechanical advantage is greater than one in the other direction. If you
had locked the drivetrain and pulled on the pedal with a string, there
would be equal and opposite forces on the pedal and the tire. Putting it
all together, if you apply some force to the tire and an equal force to the
pedal, the force applied to the tire will "win" and the bike will move
forwards.

Except you got it wrong!

For the pedal position shown (crank vertical, string pulling
horizontally backwards on the bottom pedal, and a bike with common
gearing) the bike moves _backwards_ when the string tries to rotate the
cranks in their normal direction.

See
http://www.popularmechanics.com/scie...f-the-week-24/

So the new question is: Why?

Or if people want to get more mathematical, we could ask under what
conditions would the bike move forward instead.


Yeah, that too... I actually did get it right, then botched it during the
explanation (and you can choose to believe that it or not, as you see fit).

I alluded to one possible situation where the bike would go forward, and
that was ultra low geared bikes. If the combination of long cranks, small
front chainring, large rear sprocket and small rear wheel combined to make
the bike move less than 2•pi•crank length for each rotation of the crank,
then the bike will move forwards (at first, at least).