Re: Bicycle physics question

On Wed, 19 Jun 2024 22:39:07 -0000 (UTC), <bp@www.zefox.net> wrote:

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?

Oops.  It should be "can't".  Unfortunately, it's also 1/2 wrong.  One
CAN use potential energy to do work, but the work isn't done until
after things start to move.  This article sorta fumbles through the
concept:
"Is potential energy and "work done" the same thing?"
<https://physics.stackexchange.com/questions/94077/is-potential-energy-and-work-done-the-same-thing>

Potential energy can certainly do work, think of a trebuchet.

Notice the word "can".  Yes, potential energy can do work, but no work
is done until the trebuchet starts to move.  For an exercise in
frustration, try calculating the amount of work done by an object that
isn't moving.  Work = force * distance_traveled.  If the distance
traveled is zero, no work is done.

Potential energy is lost in leaning.

True.  None of that potential energy goes into moving the bicycle
forward (or backwards).  Easy enough to test:
Dismount from your bicycle.  Jam the wheels against something that
keeps the bicycle from moving sideways.  Grab the top tube.  When you
lower or raise the top tube, do you feel any force the might move the
bicycle forward or backwards?  You shouldn't.  Therefore don't expect
leaning the bicycle over to gainfully contribute to forward or
backward movement.

Tom thinks it's going into tire friction,

"Tom thinks" is an oxymoron.

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..

Before the discovery of quantum theory, it was axiomatic that if it
can't be detected or observed, it doesn't exist.  Fortunately, nobody
has invented a quantum bicycle.

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

Tom is certainly politically to the right. 

When you turn the motorcycle handlebars on a twisty road, you feel
quite a bit of resistance to turning.  The motorcycle wants to
continue going forward in the direction of travel and your turning the
front wheel tries to convince it to go not in a different direction.
The resistance to the turning force causes the tires move slightly
sideways.  Going sideways is highly abrasive and causes tire wear
through friction.  A side effect of the tire wear is heat or energy
loss.

"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...

Apology accepted.  I've been trying to keep the math at a very simple
level or totally avoid the math by using gedankenexperiment (thought
experiments) and analogies.  When I start using anything more complex
than basic arithmetic, I instantly lose half my audience.

Thanks for writing,

You're welcome.

bob prohaska

--
Jeff Liebermann                 jeffl@cruzio.com
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