Aerodynamic question for you engineers

On Jan 25, 7:31*pm, Jim Logajan wrote:
Phil J wrote:
Imagine
that you had a couple of tall jack stands that you could place under
the wings to elevate the airplane a foot or so off the ground. *Let's
say you place the stands under the wings just back from the CG such
that you have to press down on the tail to keep the nosewheel off the
ground. *This is similar to the condition of flight since the center
of lift is aft of the center of gravity. *Now if you push down on the
tail, the airplane will rotate about the center of lift. *Wouldn't it
work the same way in the air?

They aren't equivalent situations, mechanically speaking.

As I understand it, the force of the tail plane's elevators typically moves
the center of lift forward and backward along the airplane's axis as the
elevators are moved up and down (as well as changing the lift magnitude a
little - though that is secondary). One presumably enters stable flight
when the center of lift is moved to coincide with the center of gravity.

Actually as I understand it in stable flight the CL is aft of the CG.
The airplane remains level not because these two are in line, but
because the tail is pressing down to counterbalance the offset of the
CL.

After thinking about this question some more, it strikes me that this
situation is equivalent to a lever and fulcrum. The lever doesn't
rotate around it's CG, it rotates around the fulcrum point. In an
airplane, this point is the center of lift.

Regarding the CL moving around, I think even given that complication
the airplane would still rotate around the CL.

Phil

Phil J wrote:
Actually as I understand it in stable flight the CL is aft of the CG.
The airplane remains level not because these two are in line, but
because the tail is pressing down to counterbalance the offset of the
CL.

I should have used the term "total lift" so as to avoid confusion with the
lift generated only by the main wings. What you state above appears
internally consistent and correct with the definitions you are using.

After thinking about this question some more, it strikes me that this
situation is equivalent to a lever and fulcrum. The lever doesn't
rotate around it's CG, it rotates around the fulcrum point. In an
airplane, this point is the center of lift.

Whether you are talking about center of total lift (that generated by the
main wings, tail or canards, and fuselage) or center of lift of the main
wings, what you state above is _incorrect_.

I know that what you wrote sounds plausible, but the problem is that the
main wings are no more a fulcrum than the tail wings. Suppose the main wing
and the tail wing are very nearly the same size and produce nearly the same
lift and all have elevator controls? Which line is the fulcrum point now
about which the airplane rotates?

Regarding the CL moving around, I think even given that complication
the airplane would still rotate around the CL.

Here's a NASA web link that explains where the rotation point is:

http://www.grc.nasa.gov/WWW/K-12/airplane/acg.html

Try to find some books on flight mechanics and look for the chapters or
sections that appear to discuss longitudinal static stability of aircraft.
They should all say that the aircraft rotates about the center of gravity.

On Jan 26, 1:50*pm, Jim Logajan wrote:
Phil J wrote:
Actually as I understand it in stable flight the CL is aft of the CG.
The airplane remains level not because these two are in line, but
because the tail is pressing down to counterbalance the offset of the
CL.

I should have used the term "total lift" so as to avoid confusion with the
lift generated only by the main wings. What you state above appears
internally consistent and correct with the definitions you are using.

After thinking about this question some more, it strikes me that this
situation is equivalent to a lever and fulcrum. *The lever doesn't
rotate around it's CG, it rotates around the fulcrum point. *In an
airplane, this point is the center of lift.

Whether you are talking about center of total lift (that generated by the
main wings, tail or canards, and fuselage) or center of lift of the main
wings, what you state above is _incorrect_.

I know that what you wrote sounds plausible, but the problem is that the
main wings are no more a fulcrum than the tail wings. Suppose the main wing
and the tail wing are very nearly the same size and produce nearly the same
lift and all have elevator controls? Which line is the fulcrum point now
about which the airplane rotates?

Regarding the CL moving around, I think even given that complication
the airplane would still rotate around the CL.

Here's a NASA web link that explains where the rotation point is:

http://www.grc.nasa.gov/WWW/K-12/airplane/acg.html

Try to find some books on flight mechanics and look for the chapters or
sections that appear to discuss longitudinal static stability of aircraft.
They should all say that the aircraft rotates about the center of gravity.

Ok, I think it see it. There is a difference between the center of
lift and the location of the total lift vector (I guess you could call
this the net lift). In a non-canard airplane, the main wing is
pushing upward and that is the center of lift we have been
discussing. But the stabilizer is pushing downward. The net effect
of these two forces is to move the location of the total lift vector
forward to the CG location, and that results in stable flight. So a
rotational force will rotate the airplane around that point just like
a lever rotates on a fulcrum. The same thing would happen in a
canard, except that the location of the total lift vector would be
between the two wings since they both push upward.

Phil

On Jan 26, 9:52 am, Phil J wrote:
After thinking about this question some more, it strikes me that this
situation is equivalent to a lever and fulcrum. The lever doesn't
rotate around it's CG, it rotates around the fulcrum point. In an
airplane, this point is the center of lift.

Regarding the CL moving around, I think even given that complication
the airplane would still rotate around the CL.


This might hold if the CL (or CG as some would argue) is
rigidly fixed. But in flight, we're in a rather elastic medium, and
things move around, even leaving out forward motion.
Imagine, for example, two kids on a seesaw or teeter-totter or
whatever name by which you know that playground thing. Two kids, same
distance from the pivot, same weight. The board rotates around the
pivot. The CG is at the pivot. No argument there. But suppose we had a
different mounting for that pivot, one where the pivot was suspended
by a couple of springs. Same kids, same weight, board level and kids
motionless. (Yeah, right: motionless kids.) Now I walk up to one kid
and shove down on him; where will the board *really* pivot? As i push
down, the pivot point will move down some, too, because of the mass
and inertia of the kid at the other end. Now the real point of
rotation is somewhere along the board between the pivot and the far
kid, and it'll move back toward the pivot as that kid starts to move
upward. At any instant in this process it's somewhere besides the
original CG.
We could complicate things: A heavier kid near the pivot, a light
kid at the other end, but this light kid is a little too light, so we
have a small spring pulling down under his seat, just enough to keep
the seesaw level. Just like the engine in our airplane (big kid near
the pivot), the mass of the airplane behind the CG (light kid) and the
elevator's downforce (little spring). The main pivot, still on big
springs (wing in the air) will still move downward at the instant I
shove down on the light kid and the real rotational point will be
somewhere on the big kid's side of the pivot.
Rotation about the CG works if we ignore all the other
variables. Trouble is, those variables are with us every time we fly.
We can watch an aerobatic airplane twisting around in the air,
appearing to rotate around its CG, but is it really? Can we see the
small displacement of that point (do we even know exactly where it is
just by looking at the airplane?) at the instant of any change in tail
forces or flight path?
Like I said earlier, CG is probably good enough for our puddle-
jumper purposes, but I think the guys who study advanced aerodynamics
would have something to add to it. I don't think it's really all that
simple.

Dan

wrote in message ...
On Jan 26, 9:52 am, Phil J wrote:
After thinking about this question some more, it strikes me that this
situation is equivalent to a lever and fulcrum. The lever doesn't
rotate around it's CG, it rotates around the fulcrum point. In an
airplane, this point is the center of lift.

Regarding the CL moving around, I think even given that complication
the airplane would still rotate around the CL.


This might hold if the CL (or CG as some would argue) is
rigidly fixed. But in flight, we're in a rather elastic medium, and
things move around, even leaving out forward motion.
Imagine, for example, two kids on a seesaw or teeter-totter or
whatever name by which you know that playground thing. Two kids, same
distance from the pivot, same weight. The board rotates around the
pivot. The CG is at the pivot. No argument there. But suppose we had a
different mounting for that pivot, one where the pivot was suspended
by a couple of springs. Same kids, same weight, board level and kids
motionless. (Yeah, right: motionless kids.) Now I walk up to one kid
and shove down on him; where will the board *really* pivot? As i push
down, the pivot point will move down some, too, because of the mass
and inertia of the kid at the other end. Now the real point of
rotation is somewhere along the board between the pivot and the far
kid, and it'll move back toward the pivot as that kid starts to move
upward. At any instant in this process it's somewhere besides the
original CG.
We could complicate things: A heavier kid near the pivot, a light
kid at the other end, but this light kid is a little too light, so we
have a small spring pulling down under his seat, just enough to keep
the seesaw level. Just like the engine in our airplane (big kid near
the pivot), the mass of the airplane behind the CG (light kid) and the
elevator's downforce (little spring). The main pivot, still on big
springs (wing in the air) will still move downward at the instant I
shove down on the light kid and the real rotational point will be
somewhere on the big kid's side of the pivot.
Rotation about the CG works if we ignore all the other
variables. Trouble is, those variables are with us every time we fly.
We can watch an aerobatic airplane twisting around in the air,
appearing to rotate around its CG, but is it really? Can we see the
small displacement of that point (do we even know exactly where it is
just by looking at the airplane?) at the instant of any change in tail
forces or flight path?
Like I said earlier, CG is probably good enough for our puddle-
jumper purposes, but I think the guys who study advanced aerodynamics
would have something to add to it. I don't think it's really all that
simple.

Dan



In a sense it is that simple. The CG does move due to accelerations of the aircraft in flight (your spring analogy is
close), but the aircraft still rotates around the center of mass at any given moment (no pun intended!).

Dan also...d²