Mounting a turn coordinator on the tail?

On 1 Aug 2006 13:50:21 -0700, wrote:

Didn't anybody read "Stick and Rudder"?

To make an object travel on a curved path, you need a "centripetal"
force. This isn't a "centrifugal force", which is a made-up construct
that helps to understand what it feels like to be in a vehicle that's
moving you in a circle, a centripetal force is a real force that's
acting upon an object that pulls it towards the center of a circle.
Now, if you're traveling in a circle, the force that's pulling you
toward the center of the circle acts in a direction perpendicular to
your direction of motion, and since your direction of motion is always
changing (you're going around a circle, after all), the direction of
that centripetal force is necessarily continually changing as well.

If you bank the wings to the left, the lift vector will start dragging
you to the left. You'll begin "slipping", drifting sideways through the
air. If this was the end of it, you'd never end up traveling in a
circle, you'd just keep drifting slightly sideways, you nose would keep
pointing where it was pointing before, and your track over the ground
would still be a straight line, but just slightly "diagonal", at an
angle to what it was before.
Well, no, actually, if this was the end of it and the "horizontal
component of lift" was the ONLY horizontal force acting on the plane
(no drag of any kind, no thrust from the engine, etc) the plane as a
whole would end up travelling in the same direction it was originally
going, but spinning around a vertical axis passing though the plane's
centre of gravity. What's more, because the horizontal force is
acting through a point behind the CG, the plane would spin in the
opposite direction to the force.
The plane would spin, rather than drift, because the horizontal force
changes direction as the plane rotates.
It's not easy to imagine this, but think of the space shuttle
stationary in space, then having a sideways horizontal force applied
behind the CG,


But when you slip, there's now a net component of drag acting sideways
against the side of the plane. Since most of our surface area is behind
the CG, when you blow really hard against the side of a plane, it tends
to yaw into the wind. As the plane yaws to the left, the wings also
turn to the left, and the direction that the lift vector is pointed in
turns as well. Bingo, now you've got a real "centripetal force", one
that continually changes direction to point at a 90 degree angle to
your curving path. Now your ground track can form a circular path.

Well, no, actually, if you're introducing wind resistance, you need to
also consider the increased drag from the outer wing being raised as
the plane is banked. The turning force from this is often
substantially greater than the weather-vaning effect, and is why many
planes demonstrate adverse yaw when they're initially banked.

You need that yaw to turn the wings to continually update the direction
of lift, to create circular motion. Now you're a little closer to that
rock on a string model.

Alternately, if you're intentionally doing a slip, like if you're
landing in a cross-wind, you could always apply opposite rudder. This
acts counter to the "weather-vaning" moment, and prevents the plane
from yawing, which prevents the wings from "rotating", preventing the
lift vector from changing direction. By stopping the nose from changing
direction, you stop the plane from moving in a circular path, and you
just "slip" sideways up against the wind (possibly just to resist a
cross-wind and maintain a straight path along the ground).
-harry

... What's more, because the horizontal force is
acting through a point behind the CG, the plane would spin in the
opposite direction to the force.

And when the plane is flying straight and level, since the wing is
behind the CG, shouldn't the wing, similarly, be continually pulling
the tail up over the nose, leading the plane to tumble through space?
Why doesn't it? Because while the wing is aft of the CG, the tail
provides a downward force to balance it. Since the tail is so much
further away from the CG than the wing is, it can leverage a relatively
smaller force to balance out the torque, while allowing the much larger
force at the wing to provide a net upwards force to support the plane's
weight.

When the plane is in a bank, yes, the wing is providing a horizontal
force from behind the CG again. But nothing has changed from the
straight and level case, there's still an upside-down wing back there
at the tail, and it's still balancing out the torque produced by the
wing being behind the CG. When the wing is banked, the tail is banked
too.

It's not easy to imagine this, but think of the space shuttle
stationary in space, then having a sideways horizontal force applied
behind the CG

But imagine another sideways horizontal force applied in the opposite
direction at the tail, exactly strong enough to balance the "torque".
If your left force is applied aft of the CG, but fairly close to it
(like where the wings are), and your counter-balancing right force is
applied at the tail, much further from the CG, then a relatively small
force at the tail will be enough to counter the much larger force at
the wing, due to leverage.

So our torques are equal, preventing any rotation, but there's still a
net force to the left (the force up near the wing is much larger), so
there will be a net translational force to the left. Your space ship
will accellerate to the left without rotating.
-harry

This makes sense. Thanks.

On 1 Aug 2006 19:16:28 -0700, wrote:

... What's more, because the horizontal force is
acting through a point behind the CG, the plane would spin in the
opposite direction to the force.

And when the plane is flying straight and level, since the wing is
behind the CG, shouldn't the wing, similarly, be continually pulling
the tail up over the nose, leading the plane to tumble through space?
Why doesn't it? Because while the wing is aft of the CG, the tail
provides a downward force to balance it. Since the tail is so much
further away from the CG than the wing is, it can leverage a relatively
smaller force to balance out the torque, while allowing the much larger
force at the wing to provide a net upwards force to support the plane's
weight.

When the plane is in a bank, yes, the wing is providing a horizontal
force from behind the CG again. But nothing has changed from the
straight and level case, there's still an upside-down wing back there
at the tail, and it's still balancing out the torque produced by the
wing being behind the CG. When the wing is banked, the tail is banked
too.

It's not easy to imagine this, but think of the space shuttle
stationary in space, then having a sideways horizontal force applied
behind the CG

But imagine another sideways horizontal force applied in the opposite
direction at the tail, exactly strong enough to balance the "torque".
If your left force is applied aft of the CG, but fairly close to it
(like where the wings are), and your counter-balancing right force is
applied at the tail, much further from the CG, then a relatively small
force at the tail will be enough to counter the much larger force at
the wing, due to leverage.

So our torques are equal, preventing any rotation, but there's still a
net force to the left (the force up near the wing is much larger), so
there will be a net translational force to the left. Your space ship
will accellerate to the left without rotating.
-harry