Re: Bicycle physics question

Jeff Liebermann <jeffl@cruzio.com> wrote:

On Tue, 18 Jun 2024 00:16:01 -0000 (UTC), <bp@www.zefox.net> wrote:
 

While out for a motorcycle ride this morning a question
applicable to both bicycles and motorcycles came to mind:
>
When a bike/cycle is leaned into a turn, its center of gravity
is lowered.

 
Gravity doesn't move.  However, your center of mass does move and is
lowered.
<https://en.wikipedia.org/wiki/Center_of_mass>
 

That would seem to remove some potential energy.

 
True, but it's a tiny amount of energy.
 
Potential_energy = mass * gravity * height
or
joules = kg * 9.8 meters/sec^2 * meters
 
Notice that it's the same change in potential energy whether you're
moving of standing still.  You could be riding furiously or at a
traffic light, and the change in potential energy would be the same.
Your forward motion is also not involved in the potential energy
calculation, because it is perpendicular to force vector (gravity).
 
If you were to lean the bicycle over 1/2 meter and you and your
bicycle weigh 80 kg (176 lbs), the change in potential energy would
be:
Potential_Energy(change) = 80 * 9.8 * 0.5 = 392 joules or 392
watt-seconds
>
<https://www.omnicalculator.com/physics/potential-energy>
I like calculators that allow me to mix metric and imperialist units.
 

To undo the lean, the wheels have to be steered back under
the CG, which requires pedal effort on the bicycle and extra
throttle on the motorcycle.

 
Correct.  Assuming 100% efficiency (most of which is lost in
compressing the tires), in the above example, you will need to supply
392 joules of energy to return to an upright position.  Note that the
energy is supplied only in the upright direction (perpendicular to the
ground) and does not involve anything in the forward direction. 
 
There are some interesting comments in this discussion:
<https://www.bikeforums.net/advocacy-safety/288303-what-makes-bike-turn.html>
 

But, leaning a bike/motorcycle doesn't seem to make it go
perceptibly faster, so if it takes work to stand it back up,
where did the energy of leaning over go?

 
It didn't go anywhere.  It's all POTENTIAL energy, not kinetic energy.
You can use potential energy to do work.  Only kinetic energy can do work.

       ^
     can't <-typo?
Potential energy can certainly do work, think of a trebuchet. Potential
energy is lost in leaning. Tom thinks it's going into tire friction,
we all seem to agree the amount is smallish compared to the KE of
the bike and dissipation caused by air drag making it hard to detect..

Maybe Tom's right. Front tires on motorcycle certainly wear faster
on twisty roads, even at low (35 mph) speeds.

"The epitome of futility is the analysis of velocipedes with z
wheels, where z is a complex number..."

 
That's true only on a rough road, where the velocipede can move in the
Z direction (up and down) going over the bumps.  The z axis is also
involved in making a turn, where z component of the centripetal force
keeps the rider and bicycle from falling over.

In the context of the original joke z=x+iy, where i is the
square root of minus one. Apologies for the obscurity...

Thanks for writing,

bob prohaska