Polar Moment of Inertia (and other non-linearities)

[Colonel]

This is something that I touched on in the spin discussion, but it's important
enough to warrant it's own topic.

Most pilots think they are doing a first class job if they calculate a weight &
balance.  While W&B is nice, it's a long way from the whole story.

Weight is easy to understand.  If you put the airplane on a bunch of scales
in hangar with the doors closed, and add up the readings on all the scales,
you get the total weight of the aircraft.  While various paper pushers will tell
you that the maximum certified gross weight of an aircraft is written in stone,
that's actually not the case.  People fly over max gross all the time, sometimes
with paper, sometimes without.  If you are heavy, your stall speed goes up
and your required runway length increases, and your climb rate and maximum
altitude decreases.  At least until you burn some fuel off.

Balance is far more important.  Regardless of weight, you will not enjoy flying
an aircraft with the C of G too far forward or aft.  And if you enter a spin with
an aft C of G, it may not be easily recoverable.

So, you've calculated W&B and it's good.  End of story, right?

Wrong.  I could show you two seemingly identical aircraft sitting next to each
other on the ramp, with the same W&B but with very different spin characteristics.

The difference is not in the rigging, but in the distribution of mass.  This is easy
to understand.  Take a carton of eggs, with four eggs in the center spots, and
hold it in the center on your shiny kitchen counter.  Rotate it back and forth.  See
how easy it is, to start and stop moving, with the eggs in the center?

Now open the carton, move the four eggs to the outermost ends.  Close the top,
and it sure looks the same, and it has the same W&B as the first configuration.

But if you do the same test, holding in the center from above, and rotating it on
a shiny surface, you will see that it's much harder to start and stop rotating.

This is called polar moment of inertia, and is calculated as the integral of
radius SQUARED dm.  That's all jibber-jabber except for the squared function.
You double the radius with the same mass, PMI is now FOUR TIMES what
it was originally.

Human beings tend to think everything is linear.  You might remember

Y = mX + b

but if you don't, that's ok.  Many things in aviation are NOT linear, like
lift, for example, which is a function of velocity SQUARED.

Kinetic energy - which you have to dissipate after landing - is also a
function of velocity SQUARED and it will determine if you run off the
end of the runway, or not.

Drag is decidedly non-linear as well.  It increases dramatically with
small decreases in airspeed, on the back side of the power curve.

If the above doesn't convince you of the importance of precise airspeed
control on final, I don't know what will.  An experienced, skilled pilot knows
what his airspeed should be on final, and he nails it.

Note that it is a fiction of the paper pushers that you should establish an
airspeed at the start of a 5 mile final and drag it in at that speed.  BS.

I like 180 mph in my biplane at 5 miles, decreasing to 160 mph, then 140 mph,
then 120 mph then 100 mph over the runway threshold.  Safe and efficient.

If you can only fly final at [i]one[/i] airspeed, you need more training.  Like large
patterns, that's fine for student pilots but once you acquire some experience
and skill, you should be able to fly a decreasing speed final.  If you don't believe
me, fly a 172 into Pearson sometime, and set up a prim and proper 70 mph on
5 mile straight-in final and drag it in, and get back to me on how popular you are.

Clearly student pilots should not fly 172's into busy airports.  But a reasonably
skilled pilot can, without enraging ATC.  It does not hurt the airplane to do so.

Try hard, to have more knowledge and skill, than a student pilot.  Try really hard,
because there is more to aviation than just the virtuous signaling of egalitarianism.