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From: Frank Krygowski <frkrygow@sbcglobal.net>
Newsgroups: rec.bicycles.tech
Subject: Re: Bicycle physics question
Date: Wed, 19 Jun 2024 20:46:41 -0400
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On 6/19/2024 6:39 PM, 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?
> 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..

I haven't thought deeply about this, but I suspect there's no practical 
change in potential energy due to the lean. But I'll admit my thinking 
on this is both somewhat fuzzy and esoteric. Here goes:

The leaning of the bike+rider occurs only when the bike is turning - 
that is, undergoing a lateral acceleration. The amount of lean is 
precisely what's necessary to balance the vector sum of gravity (or its 
acceleration) and the lateral acceleration.

One of the concepts that kick-started Einstein toward relativity was the 
fact that gravity (or its acceleration) and linear acceleration are 
indistinguishable. Specifically, he realized that no measurement done 
inside an isolated elevator can tell whether it's gravitational force or 
upward acceleration that causes a passenger to stay in contact with the 
floor.

So it's logical to treat as identical sorts of vectors both the upward 
force on a cyclist (fighting gravity) and the lateral force on a turning 
cyclist (pushing him into a curve). It's the resultant of those two 
forces against which potential energy is determined. And again, the 
cyclist's angle is always what's necessary to exactly balance that 
resultant.

So in that reference frame, there is no reduction in potential energy. 
The bike+rider's CG is always the same distance above the tire. No 
change in PE, no resulting change in KE.

Again, a bit fuzzy. I haven't bothered to work out all the details. But 
for now, that's my bet.

-- 
- Frank Krygowski