REFLECTOR: Re: Statics & Dynamics - Center of Gravity

Tue Jan 4 20:18:29 CST 2005

Jorge,

I'm a little uncomfortable with the term "more stable", because what we are
talking about isn't really a stability issue.  For two items of the same
total mass, the one that has the most "mass particles" the farthest from the
center of mass will have the highest "polar moment of inertia".  The higher
the polar moment of inertia, the more "moment" (force x distance) must be
applied to the object to produce a given angular acceleration.

This is analogous to the case where we are considering linear motion, rather
than rotation.  There the mass of the object is significant, rather than the
polar moment, and it's force that produces an acceleration, rather than a
moment producing an angular acceleration.

Whether this is "better" or not depends on what you want.  Aerobatic
airplanes have smaller polar moments, so that they have rapid angular
accelerations from the moments provided by their control surface.  On the
other hand, a B-747, in addition to having a very large mass, also has a
very large polar moment of inertia, so the pilot is well advised to keep
rotation speed "small" so as not to hit the tail on the runway when taking
off!

Keith Hallsten

----- Original Message ----- 
From: "Jorge Bujanda" <jbujanda at dslextreme.com>
To: "Velocity Aircraft Owners and Builders list" <reflector at tvbf.org>
Sent: Tuesday, January 04, 2005 5:43 PM
Subject: Re: REFLECTOR: Re: Statics & Dynamics - Center of Gravity

> Keith/Tom
>
> Excuse my ignorance but I have much to learn about airplanes and
> aerodynamics. For those like me who only were exposed to physics in high
> school, I want to try to have this one clear in terms I can understand.
> Is the following a true statement based on your comments?
>
> When abruptly disturbed, the structure formed by two olives in the
> middle of a skewer hanging by a thread from the center of gravity is
> more stable, or more prone to be returned to its original position, than
> the structure of the same two olives (same mass) located one at each end
> of the skewer, for any given disturbing force? In other words, mass
> closer to the CG is better than distant from the CG?
> Please clarify. Thanks
>
> Regards,
> Jorge Bujanda
> XL FG
> Palmdale, CA
>
> "Make your best case... not the best case."
> "Spare the noise... convince through silence."
>
>
>
>
> KeithHallsten wrote:
>
> > Center of mass and center of gravity are two names for the same thing.
> > However, the distribution of mass can give a different polar moment of
> > inertia even if the overall mass and the center of gravity is the
> > same. This will result in more angular momentum at a given rate of
> > rotation when the mass is distributed farther from the center of mass.
> > Therefore, the potential for over-rotating is more significant when
> > you have a heavy engine balanced by, say, a heavy battery tucked into
> > the nose.
> > As long as you fly real smooth, with low angular accelerations, you
> > have a "quasi-static" situation, in which the current forces are most
> > significant. However, as angular accelerations increase, the dynamic
> > effects become more pronounced and statics alone cannot explain the
> > behavior.
> > Keith Hallsten, Mechanical Engineer & Civil Engineer
> >
> >     ----- Original Message -----
> >     From: Tom Martino <mailto:tmartino at troubleshooter.com>
> >     To: reflector at tvbf.org <mailto:reflector at tvbf.org>
> >     Sent: Tuesday, January 04, 2005 11:38 AM
> >     Subject: REFLECTOR: MODIFICATIONS
> >
> >     I don’t profess to be a genius, but I do have extensive education
> >     in physics and related sciences ... and what I am reading on this
> >     forum about “Center of Gravity” (CG) and “Center of Mass” (CM) is
> >     not accurate.
> >
> >     The following statement is inaccurate: “When the center of mass
> >     gets too far away from the center of gravity, it makes the object
> >     unstable”.
> >
> >     I think what people mean to say is: “When the CM gets too far
> >     astray from the CG envelope, the object become unstable”.
> >
> >     Physics dictates that the CG must be the same as CM when weights
> >     and moments are factored by their distances from a common
> >     reference point. They are one and the same ... also referred to as
> >     the “Centroid”.
> >
> >     A CG Envelope is determined by the Mean Aerodynamic Cord (which is
> >     the average distance from the leading and trailing edge of the air
> >     foil). The middle of this is the center of lift.
> >
> >     If you picture the plane being lifted on a string at its center of
> >     lift ... the CG takes on simple meaning. If forward ... the object
> >     will lean forward, if aft, it will lean aft.
> >
> >     Heavy weight on one end or the other has nothing to do with it, so
> >     long as the CG has been calculated properly and falls within the
> >     safe envelope. That is why it is called “Center of Gravity”.
> >
> >     Sudden, jerky movements can disrupt the stability but does not
> >     make it inherently unstable. However, when you are close to the
> >     ground, you may need more time to recover than the ground will
allow!
> >
> >     In other words ... as you get farther away from the center of the
> >     envelope, the recovery becomes more difficult but it is almost
> >     never dangerous unless close to the ground or “out of balance”.
> >
> >     As far as ground handling, the center of rotation is the only
> >     thing that matters at lower speeds. As speed increases you shift
> >     over to center of lift and ascend. When the CG is aft in the
> >     envelope, the transition could cause a prop strike if not rotated
> >     properly.
> >
>
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