REFLECTOR: Statics & Dynamics - Center of Gravity

[Al Gietzen]

Distribution of mass

Polar moment of inertia

Angular momentum

Angular acceleration

"Quasi-static" situation

          

What the heck happened to "Radius of Gyration"?  That must be in there
somewhere:-)

 

Ah-h-h; poetry..

 

Al

 

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 <mailto:tmartino at troubleshooter.com>  Martino 

To: 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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