The NAMCv3 and Polar Moment of Inertia

I have been living large lately through Scott's design modifications, builds and flight reports.  Lately RC has had to take a back seat to my runaway freight train life these days.  Thanks to Scott and this page, I still get to daydream and think about aerodynamics and flight characteristics as I plan my next build.

Scott really hit on a basic concept of physics that we partially addressed in the past.  In our early days of the RPCv3s, we both we not happy with weather vaning and the EPPE (elevon polar pitch effect).  We fixed that by redesigning the elevons by decreasing their overall size to that more of a scale type craft.  In a natural progression, we both felt that the Mig was too long.  Scott has built and modified the FRC Su and vastly improved it as well by NAMCifying it as well.  Scott has posted his mods as well as as comparison of the length ratios as compared to the Mig.  Somewhere between the short Su and the stretched Mig was the sweet spot.  Scott found it in NAMCv3.

In addition to shortening the "wheelbase' of the Mig, Scott also brought the controllable mass of the airplane closer the center of mass and the Cg.  The center of mass is actually the integral of mass density. Meanwhile, Cg is the integral of force of gravity.  For my brain, center of mass is a static measurement while Cg is dynamic, i.e. plane at rest vs is the air.  By shortening the plane it, there is less plane to rotate around the Cg therefore the plane requires less energy to move in the roll, pitch or yaw axis.  This energy to rotate an object and overcome its inertia is referred to as torque.  The ability of an object to resist torsion is referred to it polar moment of inertia.  This is commonly abbreviated to a descriptor as an objects polar moment.  Basically, how is easy is to accelerate/decelerate an object.  I found a great example at http://www.avcanada.ca/forums2/viewtopic.php?f=3&t=94865.  I included his entire post:



As a pilot, you are taught to respect W&B. They
are tremendously important, and must be within
limits. Terrible things will happen if they are not,
you are told.

But then you hear about people flying over-gross
without incident (eg transatlantic ferry flights) and
the baby gets thrown out with the bathwater, and
people start disregarding W&B.

Despite what you have heard, weight is probably
the least important of the three topics of this thread.

You can increase the max gross of a 40-flap 172 by
150 lbs if you jigger the microswitch on the selector
so that you can't get more than 30 flaps. There's
even an STC for it.

I have flown airplanes that IMHO flew like they were
well over their max gross, they climbed so badly. A
fully loaded M20J on a hot day comes to mind, as does
a C150, which is frequently flown over max gross.

As I mentioned in the Accidents forum, an aircraft with
a forward C of G is going to be gentle and docile. It's
going to fly nicely and recover well from stalls and spins.

It is easy to develop contempt towards such an aircraft,
but beware that at the same weight, if you try to fly with
an aft C of G, like college girls on spring break, it's going
to behave badly. It's going to be sensitive in pitch, and
it's going to be a handful in stalls and spins. Might not be
recoverable at all.

tl;dr C of G is what matters, not weight. Weight just makes
your airplane climb like a pig, and a runway hog, which is
immediately obvious. A bad C of G, like your girlfriend off
drunk at Daytona on spring break, is not so obvious.


Now onto Polar Moment of Inertia (PMI) which is a measurement
of how the mass is located.

The best way to understand this is to take an egg carton with
four eggs in the center, close it, and spin it back and forth on
a shiny countertop, holding it from above in the center. See
how easy it is, to start and stop it spinning, with all the mass
in the center?

Now, open the egg carton and put two eggs in each end
and close it. Same weight, same balance, but a wildly
increased PMI. Now repeat the experiment, spinning it back
and forth, holding it at the center. See how much more torque
is required to start and stop it spinning?

This is why you want to centralize mass, which is actually
really hard on the wing spars, a subject for another time (ZFW).

So why did Scott notice such a hugh difference with the NAMCv3 vs prior Migs?
1. Overall shorter length
2. Most importantly, he put all of his eggs in one basket by centralizing the moveable mass of the plane (motor moved forward, centered the servos, battery, ESC)

Hope I didn't scramble (I know, corny attempt at humor) your brain!

Next it will be interesting to see how the NAMCv3 handles with the NTM and a markedly increased polar moment with a bigger battery as well.  The answer will be better the v2 with the same setup.  Why, because the fundamental law of gravity shall not be denied!

Stephan