Coordinated turns without rudder, and autopilots

Andrew Sarangan wrote:


Your analogy with driving tells me a little about your line of
thinking. In that case, why does the car to slow down when it hits a
steep hill? It is due to the inability of the engine to respond fast
enough for the sudden demand in power.

No, it is because there is always a lag in a real world feedback control
system or it goes into oscillation.

The lag is due to what is called the margin of stability.

It is possible to design a control system that is virtually instantaneous.

This is called a critically damped system.

The problem with that is that if anything changes, like linkages wear,
the system can easily go underdamped and it goes into oscillation.

You don't want to be in a vehicle at 65 MPH with the cruise control
going into oscillation.

So for safety, cruise control systems are over damped, i.e. have a
large margin of stability.

For a fair explanation of control systems and stability, see
http://en.wikipedia.org/wiki/Control_theory

snip rest

--
Jim Pennino

Remove .spam.sux to reply.

Andrew Sarangan wrote:

Your analogy with driving tells me a little about your line of
thinking. In that case, why does the car to slow down when it hits a
steep hill? It is due to the inability of the engine to respond fast
enough for the sudden demand in power. Obviously, the cruise control
does a pretty good job over small hills otherwise we would not be
using them at all. If the engine were powerful enough and had a quick
response, it should be able to maintain a constant speed over a steep
hill. When you manually apply some extra throttle in anticipation of
the approaching the hill, you are in fact 'helping' the cruise control
do its job better. You are not doing something the cruise control is
inherently incapable of doing. You are simply reducing the transient
period. If left to its own device, the cruise control should
eventually reach the set cruise speed over the hill, unless the engine
is too small for the hill.

No, it still isn't the same. No matter how large the engine, or how
fast it responds, the end result is that a control system takes no
action until an error is present. So at least SOME loss or gain in
speed is required for the cruise to work, that is inherent in any
feedback control system. Sure, if you can measure the error with
greater resolution, and have a very large actuator with very fast
response, you can make the amount of divergence from set point ever
smaller, but you can't take it to zero.


Consider an imaginary airplane with an infinitely large vertical fin.
Would it need rudder to fly co-ordinated? I hope you would agree that
the answer is no. The infinitely sized fin will generate an infinite
restoring force, which really means the airplane will never deviate
from co-ordinated flight. Now reduce the fin size to something smaller
and practical. The restoring force will also scale down. In this case,
the force may not be large enough to restore co-ordinated flight in
all possible scenarios, such as slow flight and steep turns. In some
cases it may experience a longer transient, and in some cases it may
not reach co-ordinated flight at all. It all depends on how large the
fin is, and how much air is flowing around it. In such cases where the
fin can't do its job satisfactorily, the rudder is used to help it
along.

Same here. An infinitely large fin has infinite drag and thus the
airplane would not fly so stability would not be an issue. :-)
However, for any practical airplane with any adverse yaw forces during a
turn, a fin alone will not maintain coordinated flight. A larger fin on
a longer tail will get closer to be sure, but at least SOME yaw
divergence is required for the fin to work. It is inherent in the way
it works. There simply is not way to eliminate that fact. A rudder
works differently since it gets its ability to act from other than
aerodynamic forces (the pilot pushing on the rudder provides the
actuation force). The rudder than thus provide yaw forces independent
of any yaw displacement. The fin simply can't do this.


So I still do not see your line of thinking.

Well, I've given it my best shot, so I'll sign off now. I can't think
of any other way to explain it.


Matt

On May 30, 5:57 am, Matt Whiting wrote:
Andrew Sarangan wrote:
Your analogy with driving tells me a little about your line of
thinking. In that case, why does the car to slow down when it hits a
steep hill? It is due to the inability of the engine to respond fast
enough for the sudden demand in power. Obviously, the cruise control
does a pretty good job over small hills otherwise we would not be
using them at all. If the engine were powerful enough and had a quick
response, it should be able to maintain a constant speed over a steep
hill. When you manually apply some extra throttle in anticipation of
the approaching the hill, you are in fact 'helping' the cruise control
do its job better. You are not doing something the cruise control is
inherently incapable of doing. You are simply reducing the transient
period. If left to its own device, the cruise control should
eventually reach the set cruise speed over the hill, unless the engine
is too small for the hill.

No, it still isn't the same. No matter how large the engine, or how
fast it responds, the end result is that a control system takes no
action until an error is present. So at least SOME loss or gain in
speed is required for the cruise to work, that is inherent in any
feedback control system. Sure, if you can measure the error with
greater resolution, and have a very large actuator with very fast
response, you can make the amount of divergence from set point ever
smaller, but you can't take it to zero.

Consider an imaginary airplane with an infinitely large vertical fin.
Would it need rudder to fly co-ordinated? I hope you would agree that
the answer is no. The infinitely sized fin will generate an infinite
restoring force, which really means the airplane will never deviate
from co-ordinated flight. Now reduce the fin size to something smaller
and practical. The restoring force will also scale down. In this case,
the force may not be large enough to restore co-ordinated flight in
all possible scenarios, such as slow flight and steep turns. In some
cases it may experience a longer transient, and in some cases it may
not reach co-ordinated flight at all. It all depends on how large the
fin is, and how much air is flowing around it. In such cases where the
fin can't do its job satisfactorily, the rudder is used to help it
along.

Same here. An infinitely large fin has infinite drag and thus the
airplane would not fly so stability would not be an issue. :-)
However, for any practical airplane with any adverse yaw forces during a
turn, a fin alone will not maintain coordinated flight. A larger fin on
a longer tail will get closer to be sure, but at least SOME yaw
divergence is required for the fin to work. It is inherent in the way
it works. There simply is not way to eliminate that fact. A rudder
works differently since it gets its ability to act from other than
aerodynamic forces (the pilot pushing on the rudder provides the
actuation force). The rudder than thus provide yaw forces independent
of any yaw displacement. The fin simply can't do this.

So I still do not see your line of thinking.

Well, I've given it my best shot, so I'll sign off now. I can't think
of any other way to explain it.

Matt

Matt.

Consistently excellent explanations. It is amazing to me how people
tend to view (in its simplist form) that a fixed torque can overcome
consistently a variable one under "all" circumstances.

Nice job.

Robert