Aerodynamic question for you engineers

D Ramapriya wrote:
On Jan 26, 5:31 am, Jim Logajan wrote:

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.


Since the CL can be altered by the wing configuration - deployment/
retraction of flaps for a given pitch, e.g., I'm not sure that the CG
and CL need to necessarily coincide for stable flight. Also, for a
body such as an aircraft, I think the CG would theoretically be
somewhere within it while the CL is a point on the fuselage, so their
coincidence may even be an impossibility.

If the total lift vector does not pass through the center of gravity, then
the resulting moment will rotate the aircraft. That is not considered a
stable situation. Here's what I hope is considered an authoritative web
site that discusses this issue:

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

See also any text on flight mechanics and aerodynamics that has sections on
the subject of longitudinal static stability.

"Jim Logajan" wrote in message ...
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.



You are in stable flight when the forces are balanced. You do not want the CG and CP to coincide if you want positive
stability on the airframe. With a conventional aircraft, the CG is forward of the CP and the horiz tail provides a down
force to hold the nose up. The elevator is a wing adjuster and basically sets the AOA. At a high AOA the CP moves
forward and at a low AOA the CP moves back. The rotation still occurs around the CG. This is why the nose pitches down
during a 'stall'. The C/L deteriorates in the stalled condition so it is no longer holding the nose up, and the up force
from the horiz tail pulls it up and the nose rotates down...

When the CG and CL coincide, the elevator forces are very light and the airplane is at best neutrally stable. Because
the CP moves with AOA (therefore C/L) if a gust upsets the aircraft and pitches it up for instance, the CP moves
forward, the plane rotates around the CG as the tail goes down, and there is no self stabilizing force to bring the tail
back up. If left uncorrected the wing will stall. This movement of the CP is just one of the Wright brothers many
insights that allowed them to make an airplane that could be maneuvered.

Now, if you want to be efficient, you load the airplane so the CG is at or just forward of the aft cg limit (and make
sure it will be there as the flight progresses). This way the down force is minimized ands you can fly at a lower AOA,
lower C/L, and therefore drag. I think some of the airliners put fuel in the horiz tail so the CG can be tweaked while
in flight to keep the CG back and maintain higher efficiency.

A canard design is just the opposite. The CG is behind the CP, and when the canard stalls, the nose drops because their
is no longer any lift to hold it up. This is why canards must always stall the front wing first.

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

"Pete Brown" wrote in message ...

If a conventional aircraft is in stable level flight and the stick is
pulled back, all of the texts I have read indicate that the aircraft
pitches up, rotating through the CG.


It rotates around the CG, not through it.


Is this exactly correct or is it a very useful approximation good for
all practical purposes?

Most aircraft have the CG located slightly forward of the center of
pressure ( CP or center of lift) for positive pitch stability. I was
wondering if the actual point of rotation is displaced somewhat aft of
the CG, someplace close to the CG but in fact some small distance
towards the CP.

When the aircraft is subject only to the force of gravity, any
displacement will cause it to rotate around the cg but in flight its
subject to gravity as well as the aerodynamic forces which act through
the CP, suggesting to me that the point of rotation is not quite on the CG.



Thanks

--
Peter D. Brown
http://home.gci.net/~pdb/
http://groups.yahoo.com/group/akmtnsoaring/


Going home after a long day
http://farm2.static.flickr.com/1415/...22928754_b.jpg

The fleet at Summit. Mt. McKinley is about 45nm away at 20,320 msl.
http://farm1.static.flickr.com/187/4...cb8d2482_b.jpg

The 170B at Bold near Eklutna Glacier
http://farm1.static.flickr.com/168/4...a216d7bb75.jpg

There's some great reading here

http://www.av8n.com/how/htm/aoastab.html

It may not answer your exact question, but you'll understand the
areodynamics a bit better.



On Jan 25, 1:22*am, Pete Brown wrote:
If a conventional aircraft is in stable level flight and the stick is
pulled back, all of the texts I have read indicate that the aircraft
pitches up, rotating through *the CG.

Is this exactly correct or is it a very useful approximation good for
all practical purposes?

Most aircraft have the CG located slightly forward of the center of
pressure ( CP or center of lift) for positive pitch stability. I was
wondering if the actual point of rotation is displaced somewhat aft of
the CG, someplace close to the CG but in fact some *small distance
towards the CP.

When the aircraft is subject only to *the force of gravity, any
displacement will cause it to rotate around the cg but in flight its
subject to gravity as well as the aerodynamic forces which act through
the CP, suggesting to me that the point of rotation is not quite on the CG..

Thanks

--
Peter D. Brownhttp://home.gci.net/~pdb/http://groups.yahoo.com/group/akmtnsoaring/

Going home after a long dayhttp://farm2.static.flickr.com/1415/1325102827_f322928754_b.jpg

The fleet at Summit. Mt. McKinley is about 45nm away at 20,320 msl.http://farm1.static.flickr.com/187/4...cb8d2482_b.jpg

The 170B at Bold near Eklutna Glacierhttp://farm1.static.flickr.com/168/437324742_a216d7bb75.jpg

There's a physics issue here called 'frame of reference.'

Think about an external stationary (with respect to the air mass)
observer, and the airplane is made to fly a loop. The center of
rotation to that obsever is the center of the loop.


Or, if the observer tracks the airplane, or even its CG (assume it's
marked on the airplane) he'll see it move laterally at airspeed, then
at the start of the climb will probably see it dip a little bit, then
start assending.

I'm having a hard time imagining a frame of reference where the
airplane would appear to rotate about its CG, where I take 'rotate' to
mean a point about which the tail end goes down and the other end goes
up, because the CG itself will be moving, first down a little (I
think) then up. Down first because the elevator is adusted so it loses
upward lift of increases downward thrust, effectively making the
airplane heavier. As the aoa increases the wings (making a huge number
of assumptions (assume a spherical cow?) increase lift. Note also that
the 'center of lift' of a wing may change with aoa, so even that model
-- all effective lift concentrated at a fixed point -- may fail.

A more minor point, (but why not pick nits?) is that it's unlikely the
CG, center of lift of the wing, and center of lift of the elevator are
all in a straight line. In a high winged airplane the center of lift,
about a third of the way back from the front of the wing, and probably
pretty close to the wing's underside skin, is well above the CG. That
vertical displacement will not affect computing moments for horizontal
flight, but will as directions of flight different from horizontal
take place. Think for a moment or two about a helocopter in horizontal
flight transitioning to a nose up attitude. When I've seen that, it
appears the center of rotation is well above the hellcopter.


I know, there's nothing like adding some mud to the water.








flies a loop
On Jan 25, 1:22*am, Pete Brown wrote:
If a conventional aircraft is in stable level flight and the stick if the texts I have read indicate that the aircraft
pitches up, rotating through *the CG.

Is this exactly correct or is it a very useful approximation good for
all practical purposes?

Most aircraft have the CG located slightly forward of the center of
pressure ( CP or center of lift) for positive pitch stability. I was
wondering if the actual point of rotation is displaced somewhat aft of
the CG, someplace close to the CG but in fact some *small distance
towards the CP.

When the aircraft is subject only to *the force of gravity, any
displacement will cause it to rotate around the cg but in flight its
subject to gravity as well as the aerodynamic forces which act through
the CP, suggesting to me that the point of rotation is not quite on the CG..

Thanks

--
Peter D. Brownhttp://home.gci.net/~pdb/http://groups.yahoo.com/group/akmtnsoaring/

Going home after a long dayhttp://farm2.static.flickr.com/1415/1325102827_f322928754_b.jpg

The fleet at Summit. Mt. McKinley is about 45nm away at 20,320 msl.http://farm1.static.flickr.com/187/4...cb8d2482_b.jpg

The 170B at Bold near Eklutna Glacierhttp://farm1.static.flickr.com/168/437324742_a216d7bb75.jpg