For simplicity, let's assume one axle and a flat deck trailer. My
experience has been the sway is dependent on the relationship of the
Center of Mass (CM) to the axle, in other words, if the CM is in front
or behind the axle.

Hitch - CM - Axle = stable
Hitch - Axle - CM = unstable

Trailers are self-correcting in terms of steering, like a caster on a
piece of furniture. If the wheel "steers" to the left like this \ , the
back and the front of the wheel touching the ground get resistance from
the ground. But the resistance on the back has more leverage in
relationship to the pivot, so the force is translated into a clockwise
turning moment about the pivot. This turning moment corrects the
orientation of the caster until it is pointed parallel to the direction
for travel, like this |.

So front-heavy trailers correct themselves regarding steering like the
caster, but the corrections are small. In tail-heavy trailers, the
steering corrections are large and they may even yank at the tow
vehicle.

I still don't understand it; I'm just restating the problem.

Smart weight???  Where would one acquire such weight?  I am sure I would
prefer it to dumb weight.

Thinking about it a little more one could have a really long trailer that is
very heavily loaded in the rear and you could pull it at very high speeds,
with a short wheelbase vehicle, without any trouble.  But only as long as
there is no wind, no bumps or anything else to get it into a sway condition.
But god help you if it begins to swing!!

Nothing more frightening than having the trailer begin to do the steering.

This is true and just about all trailer sway issue start with tow
vehicle stabilty issues. (tires and suspension not up to the extra load
on them)

That happens.  Ever see a small trailer "wagging" all over the road when
being pulled by a big truck?

I still think the problem with real amplification comes when the tow vehicle
gets into the act as well.  Now we have the tail wagging the dog.   It can
add even more energy, to the point where it causes them to roll.

If it were only due to the trailer 5th wheels and those using Hensley
hitches would not be almost immune to the problem.

As I said I have had it happen to me. Going perhaps too fast down a steep
grade when a gust of wind out of a canyon hit us.   The trailer started to
take control of the steering.  A quick flip of the brake control manual
lever pulled it right out.

Sheesh this has been beaten to death - Real easy to imagine and try out. Go
to your grocery store and get a cart.  Stand on the front of the cart and
start riding it like a scooter pushing it backwards in a straight line and
tell me what happens....(yes, the front wheels under and to the front of
your feet do pivot, but that only helps to accelerate the fact that your
cart is attempting to put your a.s out in the front)

Scott

One problem is that the tow hitch is not stationary.  When the trailer
sways the tow vehicle also sways.  The lighter the tow vehicle the
larger the sway.

You got that just right.  It is difficult to visualize but basically the
center of gravity will always try to get in front of the one wheel pivot
that you describe - I like that description - it's a little easier than
mine was I think...

So let's just try to take this a little farther!

If the C.G. (center of gravity) of the trailer is offset by a small
distance from the single wheel, the amount of force will be less than if
the C.G. is farther from that single wheel.  So if we take an out of
balance/rear C.G. situation and go from say 2 feet behind the exle to 4
feet behind the axle, things will happen much more rapidly as far as the
trailer geting out of control.  Likewise, if we have a C.G. ahead of the
axle at two feet it will stabilize less quickly than if the C.G. were four
feet ahead of the axle.  (This is really a description of why there is
tongue weight on any trailer.)

IMPORTANT NOTE:  The longer a trailer is, it will usually have what
engineers call a larger "radius of gyration."  Simply put, it is like
having a bigger flywheel that once it starts rotating is harder to stop.
If heavier weaight is distributed closer to the axles, even a larger
trailer will be easier to handle. That is why larger trailers on any TV
will want/need all of the steering
dampers and what not whereas a shorter trailer will not require those
neccessarily. By integrating the two vehicles a bit more, they can both
fight disturbances from straight and "normal" a little bit better.  It
begins to matter that the capacities of the TV are at this point. It also
starts to involve the attachment point (TT vs 5R.)

Note that aerodynamic forces will play a very large role for crosswinds
and attachment points.  This also includes the TV into the equation.  Note
that most RVs have the axle placement around 60-65% rearword (or more.)
That solves the C.G. problem but the aerodynamic and harmonic issues will
vary from combination to combination of vehicles.

Harmonics is difficult to explain and harder yet to analyze but my guess
is most folks here have had the situation where a vehicle combination
"just didn't tow right" at a certain speed but was fine at higher and/or
lower speeds.  That is the dynamic/harmonic of that particular combination.

Uff Da!  That's a lot.  I actually know it helped me to think a lot about
trailer dynamics although I haven't had any problems yet...

That's what I think makes all the difference. *but* these thought
experiments never work on the actual dynamic problem. It's too complicated.