Coordinated turns without rudder, and autopilots

Andrew Sarangan wrote:
On May 29, 7:16 am, Matt Whiting wrote:
Ron Natalie wrote:
Matt Whiting wrote:
Not true. The vertical fin can only provide a weather-vane affect
when a slip or skid has been induced.
You have no clue what you are talking about. The skid and slip are the
result of the airplane NOT weather vaning into the wind. There are
a number of reasons for this. The primary one in turns is the "adverse
yaw" due to the differing drag caused by the displaced ailerons. Many
designs do a lot of things to mitigate this. Still it takes a lot of
aileron displacement to overcome the natural desire for the airplane
to track into the wind (due to the vertical stab).
In coordinated flight there is no slip or skid and hence the fin
provides no lateral force.
This is the definition of coordinated flight, not cause and affect.
The rudder isn't there to help the vertical stab do its job, it is
there to do a job that the vertical stab can't do.
Sorry. The incorrect. You need the vertical stab to even fly
coordinated when you are not turning. If it is two small the
airplane will tend to yaw on it's own (the more bulbous your
fuselage, the more this is a probelm...there was a design Piper
tried that used an almost helicopter like bubble on the front...
without the slab sides to help the vertical stab, the plane
just would as well fly slipping as nromal).
The vertical stab is nearly always set up to get the aircraft
to fly coordinated in normal cruise level flight. It is frequently
slightly offset to correct for other aerodynamic unbalances.
The rudder is just at trim to handle other flight regimes.
It's mostly there for the high AOA regimes of Take-off and
landing.
I don't know where you got your engineering degree, but you better
demand a refund. A vertical stabilizer does not provide any lateral
force unless there is some degree of slip or skid. In coordinated
flight, it is just along for the ride. Many airplanes will oscillate
slight in the yaw axis for this reason. It takes a very large vertical
stab to keep the excursions small enough to not be detectable,
especially in a longer fuselage airplane. The rudder can provide a side
force in anticipation of a slip or skid and thus maintain coordinated
flight and never allow the slip or skid to develop in the first place.

Matt- Hide quoted text -


You are assuming that the primary role of the rudder is to fly co-
ordinated. I would argue the opposite. The primary role of the rudder
is to fly un-coordinated, such as in a cross-wind landing, forward
slip, spin etc.. An airplane that always flies perfectly co-ordinated
(with or without rudder) would be of little use.

I'm not assuming that at all nor did I ever say that. The rudder has
many roles. Coordinating turns is just one of the roles. My point was
simply that the vertical stabilizer alone will not provide a coordinated
turn with an airplane whose ailerons generate any adverse yaw at all.


Nevertheless, I don't believe your analysis is correct, even from an
engineering control system point of view. The vertical stab and yaw
can be thought of as a closed loop system. Yaw is the error signal.
The vertical stab creates a lateral force that minimizes the error
signal by providing a negative feedback. One could argue that a
vertical stab serves no purpose if there is no yaw. But no airplane
flies perfectly co-ordinated. They continuously slip and skid as they
fly, and it is the vertical stab that kicks in the feedback to
stabilize the system. Since the effect of the vertical stab is highly
dependent on the airspeed, at lower airspeed one would need a bigger
vertical stab. In other words, you would need an adaptive feedback.
Since it is clearly not practical to enlarge the vertical stab during
flight, the next best thing you can do is to rotate it, and this what
the rudder does. Simply put, a rudder provides the means to enhance
the effect of the vertical stab during flight.

That is precisely what I said. As a controls engineer, I'm quite
familiar with the operation of control systems. My point was that you
must have an error (yaw) in order for the fin to provide any stabilizing
force. This means that you have to enter uncoordinated flight before it
does anything. The rudder can be used similar to feed-forward control
or model predictive control. When a turn is planned, the rudder can be
applied in coordination with the ailerons to exactly offset the adverse
yaw force and maintain coordination throughout the turn entry. With a
fin alone, the airplane will be uncoordinated during the turn entry and
will only enter coordinated flight again once the transient has been
damped. That is the entire point and is in contrast with Ron's earlier
comment about a rudder not being needed to provide coordinated flight
and only being needed for "outlying" conditions. I guess if you
consider turning the airplane to be an outlying condition, then Ron is
correct.


The original statement that the rudder simply assists the vertical
stab at the outlying regions is correct. If a vertical stab could be
designed such that its effectiveness is independent of airspeed, then
a rudder won't be necessary to fly co-ordinated. But for reasons I
stated earlier, such an airplane would still not be very useful.

No, that statement is not correct. The rudder doesn't just assist the
vertical stab, it does things it can't do. The stab can't prevent
unbalanced forces from the ailerons from causing adverse yaw. It will
provide a restoring force once the adverse yaw exists, but it won't
return the airplane to coordinated flight until the unbalanced aileron
forces cease. The rudder CAN prevent adverse yaw by countering the
unbalanced aileron forces BEFORE coordinated flight has departed.

This is a simple concept. Is it really that hard to understand?

It is like the difference between controlling your speed manually in
hilly country vs. using cruise control. If I want to invest the
concentration, I can hold speed much more precisely on hills than can my
car's cruise control. The reason is that I can anticipate the hill and
start feeding in throttle before the car slows down. The cruise
control, OTOH, is like the vertical stab and can't do diddly until after
the car has already begun to slow down as it needs an error signal to
work with. I don't need an error signal and can thus control the speed
more tightly. Same when going over the crest of the hill. I can
anticipate this and back off the throttle before the car beings to gain
speed. Most cruise controls will overshoot at least 2-3 MPH going over
a hill as they need an error in order to start responding and the
natural lag in the system will cause overshoot.


Matt