BMW: CG, CM, and moments of inertia
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Date: Sat, 31 May 1997 06:55:24 -0700 (PDT)
To: Dan Arnold <arnold@owt.com>
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: bmwmc@world.std.com

At 1:47 PM 5/31/97, Dan Arnold wrote:
>
>I was standing next to Jodi at Chief Joe last summer at a lecture by an
>expert on the finer points of riding, lines, etc. when he gave 'lowering
>the CG' as a reason for standing on the pegs.  Where do they get this
>nonsense?

This is a very common misconception. I was once at a workshop given by the
great Keith Code and I heard him make the same claim.  I guess some people
believe once you become a great rider it automatically makes you an expert
in physics -- nevermind that you have to bend some universal laws of
physics to make your point.  :-)

Regards,
Roozbeh
__________________________________________________________________________

Date: Sat, 31 May 1997 16:19:38 -0700
To: bmwmc@world.std.com
From: Mark Ketchum <mketchum@hooked.net>
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: roozbeh@wco.com

Roozbeh Chubak wrote:
>
>This is a very common misconception. I was once at a workshop given by the
>great Keith Code and I heard him make the same claim.  I guess some people
>believe once you become a great rider it automatically makes you an expert
>in physics -- nevermind that you have to bend some universal laws of
>physics to make your point.  :-)
>
Rambling on (and on . . . )

Rooz, you know you're right that the center of mass (CG) doesn't change
when one simply compresses one's leg(s) against the footpeg(s). Butt it
appears that you (or others, it's hard to keep these threads straight) are
claiming that those who say they corner better by loading the footpegs are
FOS from a physics standpoint. And that's wrong; they aren't changing the
CG but they are changing the system dynamics.

The machine and rider are not a single degree of freedom (SDOF) system,
with a single mass at the CG. It's really a multi degree of freedom (MDOF)
system, with the rider (1/4 - 1/3 of the total mass?) linked to the machine
with "springs" and "dampers" that are their arms, legs, thighs, knees, and
butt. You can change the spring and damping values of those "links" using
your muscles. This can influence the vehicle dynamics.

If you "stand" a centimeter above the seat, or even if you just take some
weight off your butt, your body mass is kinda "base isolated" from the
machine. You probably know that from railroad track experience. Coupling
between the masses is weak this way. Put yer cheeks down, though and
dynamic coupling goes up. This changes the forces in both your body and the
machine. Making things different on the two sides of the bike can change
things too.

So it is theoretically possible to influence cornering dynamics by pushing
with various body parts.

It may also be true that the "best" way to steer might depend on the rider.
If you are large in mass, with loose springs and lots of damping, then the
best technique might be different than if you are small in mass or more
"solidly" built.

So there may be physics explanations why different strokes for different
folks. No need for anyone to be FOS. Just don't pretend that m/c physics is
simple or easy. I've barely touched on the complexity here.
_____________________________________
Mark A. Ketchum <mketchum@hooked.net>
__________________________________________________________________________

Date: Sat, 31 May 1997 17:26:10 -0700 (PDT)
To: Mark Ketchum <mketchum@hooked.net>, bmwmc@world.std.com
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia

At 11:19 PM 5/31/97, Mark Ketchum wrote:
>
>Roozbeh Chubak wrote:
>>
>>This is a very common misconception. I was once at a workshop given by the
>>great Keith Code and I heard him make the same claim.  I guess some people
>>believe once you become a great rider it automatically makes you an expert
>>in physics -- nevermind that you have to bend some universal laws of
>>physics to make your point.  :-)
>>
>Rambling on (and on . . . )
>
>Rooz, you know you're right that the center of mass (CG) doesn't change
>when one simply compresses one's leg(s) against the footpeg(s). Butt it
>appears that you (or others, it's hard to keep these threads straight) are
>claiming that those who say they corner better by loading the footpegs are
>FOS from a physics standpoint. And that's wrong; they aren't changing the
>CG but they are changing the system dynamics.

You must be confusing me with someone else.  I have never claimed you can't
corner better by loading the footpegs.  (However it is true that I assert
you do not *need* to put weight on pegs to be able to turn the bike -- and
I went out and tried that out for myself -- but I have never said that that
is the best way of making turns.)  In fact, in an earlier post of mine I
mentioned that when I ride a bike standing fully upright, I use *only* the
pegs for steering the bike through turns.

This discussion got really hot and produced two camps only when we got to
"putting weight on the footpegs lowers the center of gravity" part.  There
are some excellent riders on the list who take turns beautifully by
weighing their pegs.  So far so good.  But then they go on to "explain" the
"science" behind what it is that they do so well and then...  we we get
into moto-fizix. :-)

Regards,
Roozbeh
__________________________________________________________________________

Date: Sun, 01 Jun 1997 11:36:08 -0700
To: bmwmc@world.std.com
From: Mark Ketchum <mketchum@hooked.net>
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: roozbeh@wco.com (Roozbeh Chubak)

Roozbeh Chubak wrote:
>
>This discussion got really hot and produced two camps only when we got to
>"putting weight on the footpegs lowers the center of gravity" part.  There
>are some excellent riders on the list who take turns beautifully by
>weighing their pegs.  So far so good.  But then they go on to "explain" the
>"science" behind what it is that they do so well and then...  we we get
>into moto-fizix. :-)

Rooz, I think you are both over simplifying and taking things too
literally. Stick with me here and I'll explain an alternative view.

The significance of the center of gravity (CG) is that it describes the
average point of application of the inertia (F=MA) forces. For the rigid
(SDOF) systems of college physics classes, this happens to coincide with
the center of mass. For a flexible (MDOF) system, the center of application
of inertia forces changes with time and with the frequency of excitation,
and does not always correspond to the center of mass. In a MDOF system, you
can change the centroid of application of inertia forces by introducing
springs and dampers between the masses. This is one of the principles of
seismic base isolation - you put springs and dampers under the building to
reduce its effective mass and lower its "effective" or "dynamic" CG.

<digress>
By the way, you have to be careful about what you learned in high school
and college physics. Even the classical (low speed) stuff can be
misleading. Rocks and feathers do *not* fall at the same speed when dropped
from a tower, the Tacoma Narrows bridge did *not* fail due to resonance
(see http://www.hooked.net/~mketchum/wind.html ), and the center of mass is
*not* always the effective center of gravity.
</digress>

So, when a rider puts arm-and-leg springs and dampers between the machine
mass and the rider mass, it's obvious that the center of mass hasn't moved,
as you have so consistently maintained. But the frequency-dependent
effective centroid of application of inertia forces may well have moved
right-left or up-down. And since "center of gravity" is the shorthand term
everyone uses for "effective centroid of application of inertia forces"
whadawe get? Folks claim the CG moves, because from the viewpoint of what
the rider cares about, *it has*.

When a previous skeptic heard this view, he said "Do the analysis and show
me." I said back, "Do the analysis, my ass!" and as a matter of fact, my
ass has done the analysis. This is the seat-of-the-pants stuff that becomes
clear to some shade-tree types but gets confusing to the Jr bookawitz who
knows some physics but not enough. The jargon makes it even more confusing,
particularly when it is used loosely and interpreted literally. =8^)
_____________________________________
Mark A. Ketchum <mketchum@hooked.net>
__________________________________________________________________________

Date: Sun, 01 Jun 1997 21:44:23 -0700
To: mketchum@hooked.net
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia

At 6:36 PM 6/1/97, Mark Ketchum wrote:
>Roozbeh Chubak wrote:
>>
>>This discussion got really hot and produced two camps only when we got to
>>"putting weight on the footpegs lowers the center of gravity" part.  There
>>are some excellent riders on the list who take turns beautifully by
>>weighing their pegs.  So far so good.  But then they go on to "explain" the
>>"science" behind what it is that they do so well and then...  we we get
>>into moto-fizix. :-)
>
>Rooz, I think you are both over simplifying and taking things too
>literally. Stick with me here and I'll explain an alternative view.
>
>The significance of the center of gravity (CG) is that it describes the
>average point of application of the inertia (F=MA) forces. For the rigid
>(SDOF) systems of college physics classes, this happens to coincide with
>the center of mass. For a flexible (MDOF) system, the center of application
>of inertia forces changes with time and with the frequency of excitation,
>and does not always correspond to the center of mass. In a MDOF system, you
>can change the centroid of application of inertia forces by introducing
>springs and dampers between the masses. This is one of the principles of
>seismic base isolation - you put springs and dampers under the building to
>reduce its effective mass and lower its "effective" or "dynamic" CG.

Mark, I think everybody knows this. Why are you wasting bandwidth on the
obvious?

< S N I P >

>And since "center of gravity" is the shorthand term
>everyone uses for "effective centroid of application of inertia forces"

No, not everyone uses it that way -- *I* certainly don't : I use it
interchangably with center of mass -- but I'll let you have the last word
on the subject.  ;-)

Regards,
Roozbeh
__________________________________________________________________________

Date: Sun, 01 Jun 1997 22:07:55 -0700
To: bmwmc@world.std.com
From: Mark Ketchum <mketchum@hooked.net>
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: roozbeh@wco.com

I (Mark Ketchum) contributed to a very drawn-out thread:

>>The significance of the center of gravity (CG) is that it describes the
>>average point of application of the inertia (F=MA) forces. For the rigid
>>(SDOF) systems of college physics classes, this happens to coincide with
>>the center of mass. For a flexible (MDOF) system, the center of application
>>of inertia forces changes with time and with the frequency of excitation,
>>and does not always correspond to the center of mass. In a MDOF system, you
>>can change the centroid of application of inertia forces by introducing
>>springs and dampers between the masses. This is one of the principles of
>>seismic base isolation - you put springs and dampers under the building to
>>reduce its effective mass and lower its "effective" or "dynamic" CG.
>
Roozbeh Chubak responded:
>
>Mark, I think everybody knows this. Why are you wasting bandwidth on the
>obvious?

Rooz, I am relieved that you find it obvious that putting springs and
dampers under an object can lower its effective or dynamic center of
gravity. Many folks don't understand this. All along, I thought you were
arguing the opposite. I guess I *am* wasting bandwidth.
________________________________
Mark Ketchum <ketchum@wenet.net>
__________________________________________________________________________

Date: Sun, 1 Jun 1997 22:21:06 -0700 (PDT)
To: Mark Ketchum <mketchum@hooked.net>, bmwmc@world.std.com
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia

At 5:07 AM 6/2/97, Mark Ketchum wrote:
>
>I (Mark Ketchum) contributed to a very drawn-out thread:
>
>>>The significance of the center of gravity (CG) is that it describes the
>>>average point of application of the inertia (F=MA) forces. For the rigid
>>>(SDOF) systems of college physics classes, this happens to coincide with
>>>the center of mass. For a flexible (MDOF) system, the center of application
>>>of inertia forces changes with time and with the frequency of excitation,
>>>and does not always correspond to the center of mass. In a MDOF system, you
>>>can change the centroid of application of inertia forces by introducing
>>>springs and dampers between the masses. This is one of the principles of
>>>seismic base isolation - you put springs and dampers under the building to
>>>reduce its effective mass and lower its "effective" or "dynamic" CG.
>>
>Roozbeh Chubak responded:
>>
>>Mark, I think everybody knows this. Why are you wasting bandwidth on the
>>obvious?
>
>Rooz, I am relieved that you find it obvious that putting springs and
>dampers under an object can lower its effective or dynamic center of
>gravity. Many folks don't understand this. All along, I thought you were
>arguing the opposite. I guess I *am* wasting bandwidth.

But it was all worth it, Mark.

Yes, it is true that in my ignorance I used to believe that you could not
change the center of mass by putting weight on the pegs (as long as there
was no change in position of the body/bike). Silly me.  But you have been
very persuasive in your arguements -- and you did not even have to resort
to using Greek letters or integrals signs to make your point.  I am happy
to report that you have succeeded in convincing me that the bigger the
springs one places under the footpegs, the lower the  center of mass gets.

First thing tomorrow I am off to the hardware store to get me a couple of
garage door type springs and attach them to my footpegs.  Then I am gonna
yo-yo me and my bike in the backroads of Berkeley Hills, happy in the
knowledge that with the help of my friend Dokta Ketchum I have harnessed
the power of seismic base isolation and I am gonna just float around those
tight turns.

;-)

Regards,
Roozbeh
__________________________________________________________________________

Date: Mon, 02 Jun 1997 07:57:12 -0700
To: bmwmc@world.std.com
From: Mark Ketchum <mketchum@hooked.net>
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: roozbeh@wco.com (Roozbeh Chubak)

Roozbeh Chubak wrote:
< s n i p >
> . . .  I am happy
>to report that you have succeeded in convincing me that the bigger the
>springs one places under the footpegs, the lower the  center of mass gets.

Actually, you probably want small (flexible) springs and big dampers.
Pretty much like yer legs! . . . to lower the effective CG. And remember,
the center of mass doesn't actually move.

Jeez, am I gonna hafta explain this again? =8^)

BTW, Rooz, I'm glad you still describe me as "my friend Dokta Ketchum". I
was worried there for a while after I re-read a couple of my posts. My
apologies to you and anyone in the audience about what sounded alot like
name-calling.
_____________________________________
Mark A. Ketchum <mketchum@hooked.net>
__________________________________________________________________________

Date: Mon, 2 Jun 1997 08:41:04 -0800
To: Mark Ketchum <mketchum@hooked.net>, bmwmc@world.std.com
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia

At 6:57 AM 6/2/97, Mark Ketchum wrote:

>BTW, Rooz, I'm glad you still describe me as "my friend Dokta Ketchum". I
>was worried there for a while after I re-read a couple of my posts. My
>apologies to you and anyone in the audience about what sounded alot like
>name-calling.

I am not aware of anything you said that calls for an apology.  :-)

But I would welcome an explanation -- in layman terms please. When you say:
".... to lower the effective CG. And remember,the center of mass doesn't
actually move."  are you saying that there are circumstances under which in
a stationary object the center of mass and the center of gravity do not
coincide?  Mark, this is not a trick question, nor is it bait: I really do
want to know the answer and then we can let this thread R.I.P.  :-)

Regards,
Roozbeh
__________________________________________________________________________

Date: Mon, 02 Jun 1997 10:37:09 -0700
To: bmwmc@world.std.com
From: Mark Ketchum <mketchum@hooked.net>
Subject: Re: BMW: CG, CM, and moments of inertia
Cc: roozbeh@wco.com (Roozbeh Chubak)

Roozbeh Chubak wrote:

>But I would welcome an explanation -- in layman terms please. When you say:
>".... to lower the effective CG. And remember,the center of mass doesn't
>actually move."  are you saying that there are circumstances under which in
>a stationary object the center of mass and the center of gravity do not
>coincide?  Mark, this is not a trick question, nor is it bait: I really do
>want to know the answer and then we can let this thread R.I.P.  :-)

In layman terms? I'm not sure this fits that requirement, but here goes:

To answer your narrow question: No, for a *stationary* object, there are no
circumstances that I can think of under which the center of mass and the
center of gravity do not coincide. But you and your cycle are not
stationary objects when you are cornering. Therefore, I find myself
compelled to continue:

For any body at rest, or a rigid body in motion, the center of mass and the
center of gravity coincide. Remember that the center of gravity is defined
as the center of application of inertia (or gravity) forces, and since in
simple cases they coincide, they are commonly (but incorrectly?) used
synonymously. "Center of Gravity" is really short for "Center of Gravity
Forces" where the mass is accelerated by gravity or other arbitrary
influences. So the center of mass is a property of the body only, while the
center of gravity is also a function of the acceleration field acting on
the body. Under a uniform acceleration field, they coincide.

For a flexible body in motion, the center of mass and the center of inertia
forces (aka center of gravity) do not always coincide when the body is
subjected to an acceleration field that varies in space. So if various
parts of the body are accelerating differently (which is almost always true
on a cornering motorcycle), then the two centers won't necessarily coincide.

That's about as lay as I can get right off hand. To go farther, I'd have to
resort to body integrals, d'Alambert's Principle (a mass develops an
inertia force proportional to its acceleration and opposing it), Hamilton's
Principle (the variation of the kinetic and potential energy plus the
variation of the work done by the nonconservative forces considered during
any time interval must equal zero), and the principle of virtual work. I
don't think that's what you had in mind. Was this? =8^)
_____________________________________
Mark A. Ketchum <mketchum@hooked.net>
__________________________________________________________________________

Date: Mon, 2 Jun 1997 10:46:06 -0800
To: Mark Ketchum <mketchum@hooked.net>, bmwmc@world.std.com
From: roozbeh@wco.com (Roozbeh Chubak)
Subject: Re: BMW: CG, CM, and moments of inertia

At 9:37 AM 6/2/97, Mark Ketchum wrote:

>For any body at rest, or a rigid body in motion, the center of mass and the
>center of gravity coincide. Remember that the center of gravity is defined
>as the center of application of inertia (or gravity) forces, and since in
>simple cases they coincide, they are commonly (but incorrectly?) used
>synonymously. "Center of Gravity" is really short for "Center of Gravity
>Forces" where the mass is accelerated by gravity or other arbitrary
>influences. So the center of mass is a property of the body only, while the
>center of gravity is also a function of the acceleration field acting on
>the body. Under a uniform acceleration field, they coincide.
>
>For a flexible body in motion, the center of mass and the center of inertia
>forces (aka center of gravity) do not always coincide when the body is
>subjected to an acceleration field that varies in space. So if various
>parts of the body are accelerating differently (which is almost always true
>on a cornering motorcycle), then the two centers won't necessarily coincide.

Dear Mark:

Very clear explanation, one which makes it quite understandable!
Especially the last sentence that now clarifies the effects of springs and
dampners you were referring to in an earlier post.

Regards,
Roozbeh
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