Feb 08, 2013, 07:01 AM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,299 Posts the problem in a nutshell (accidental duplicate post)
Feb 08, 2013, 07:03 AM
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the problem in a nutshell

Quote:
 Originally Posted by vespa Lateral lift creates the sideslip.
The fundamental problem here is that we are equating a force with a velocity. That is an Aristotelian concept that cannot square with modern Galilean /Newtonian physics.

That's the problem in a nutshell. That's why those vector diagrams have no explanatory power to say anything about the cause of the sideslip.

Especially when the sideslip velocity is constant, not increasing.

http://csep10.phys.utk.edu/astr161/l..._dynamics.html

A force causes an acceleration, not a velocity. If that acceleration is purely centripetal in nature, then that acceleration will not drive the aircraft sideways through the airmass.

It's a bit of a sticky problem, because in curving flight, the aircraft isn't a valid inertial reference frame. Nonetheless, the point remains that a centripetal acceleration, in and of itself, cannot make the yaw string blow sideways. Any more than the pull of the sun's gravity on the earth results in a decrease in the distance between the earth and the sun. The instantaneous velocity of the earth is strictly perpendicular to the direction of the pull of the sun's gravity. (Taking, of course, the simplified case of a perfectly circular orbit.)

You and I both agree that in the real-world case of banked, turning flight, you can't have a steady centripetal acceleration without a yaw rotation.

We also agree that if you are banked, but failing to rotate in yaw, you are going to end up slipping.

Yet there are some differences in our viewpoints that are not trivial. A careful reading of previous posts will reveal some significant differences of opinion in some instances, regarding the role of aerodynamic sideforce generated by the sideways flow across the fuselage, etc..

I say that if you bank without a yaw input, you initially do indeed have a centripetal acceleration and the flight path does start to curve. However, as the flight path starts to curve, this sets up a sideways flow across the aircraft. The resulting sideforce slows the turn rate and would eventually drop the turn rate to zero if the aircraft heading did not begin changing. Simultaneously, the sideways flow across the aircraft interacts with the aircraft's "directional stability" or "weathervane" stability to generate a temporary yaw torque to overcome yaw rotational inertia and initiate the required yaw rotation.

Note that if the bank angle is decreasing, not increasing, then yaw rotational inertia tends to drive a skid rather than a slip. To the extent that yaw rotational inertia plays any significant role at all, it tends to keep swinging the nose around at a rate that was appropriate to the earlier, steeper bank angle. This will tend to swing the nose too far toward the inside or low side of the turn-- this is a skid. To understand why we tend to see some slip, and some resulting rolling-out torque from dihedral, even as an aircraft is slowly rolling back toward wings-level after an upset (imagine an aircraft with lots of dihedral and ample hands-off roll stability, i.e. ample tendency to return to wings-level flight), we have to look to other causes of sideslip. Such as the effects generated by the curvature of the relative wind across the various dimensions of the aircraft, in turning flight.

Those simple vector diagrams equating sideslip with some net horizontal force on a banked aircraft, give us no insight into any of this. They just confuse us with outdated Aristotelian notions.

Steve
Last edited by aeronaut999; Feb 08, 2013 at 10:00 AM.
Feb 08, 2013, 07:28 AM
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response

I don't want to steal the thunder of my previous post #92, which really said everything that need be said. But to respond to some specifics--

Quote:
 Originally Posted by vespa Yes, that is exactly the point I was making. I was showing you the meaning of the vector diagrams, lateral lift component, and pure sideslip. This comes first. You need to understand the cause of the slip before examining the yaw that results. No. Absolutely not. Lateral lift creates the sideslip. That's all. That's first. All the subtleties of wingtips and curved flow etc. come later. Lateral lift -> side slip.
Well, it's pretty clear that you and I have a fundamental disagreement! Because I don't agree with any of the above. Unless you are only talking about the slip due to yaw rotational inertia, which we seem to agree is usually minor, and sometimes even acts to produce a skid rather than a slip. (Consider again the case of the aircraft with lots of dihedral slowly rolling toward wings-level, as explained in a bit more detail in my previous post #92. Yaw rotational inertia cannot cause a slip here. Only effects related to the curving relative wind can create a slip here.)

Quote:
 Originally Posted by vespa No. Absolutely not. Lift is perpendicular to the free stream and the span. It has nothing to do with the path. That's not up for discussion, it's the actual definition. If you want something else you'll have to come up with a new word.
First let me note that you were quoting something I posted about "lift acting tangent to the flight path" or something like that. That was an error that has since been fixed: I meant to say that lift acts perpendicular to the flight path, not tangent to the flight path. Which I assume you would still want to disagree with, so here is my response--

In non-curving motion, the situation is simple-- the flight path and the relative wind (free stream) are equal and opposite. (I hope it's clear enough from the context, that I am strictly speaking of the flight path through the airmass, not the flight path over the ground!) In curving flight, the aircraft has a pitch rotation and a yaw rotation and different parts of the aircraft are moving in different directions. It is extremely useful to recognize that the relative wind is curved as a result-- different parts of the aircraft feel different relative wind directions. This is a genuine curvature in the free stream. We can measure it with a telltale or yaw string, as long as we don't put the telltale or yaw string in a place where it is affected by the physical disturbance of the flow by the aircraft. I.e. as long as it is really in the free stream. (Obviously it's a bit of a thought experiment, as it is impossible to truly be in the free stream when we are near the aircraft. But it is a useful thought experiment.) The situation is not that different from the situation in rolling flight, where we have a "twist" in the free stream that "twists" the orientation of the local lift and drag vectors, creating an adverse yaw torque. As illustrated here http://www.av8n.com/how/htm/yaw.html#sec-adverse-yaw

If we wish to define all the lift and drag vectors strictly in relation to the direction of the free stream at the CG of the aircraft, we can do that too, but it is less useful.

For more, please take a moment to read the full text associated with the diagram in the above link.

Either way, let's not divert this into an argument about terminology. That is not really the source of our deeper disagreement here.

Also please note that this concept of the relative wind following the curve of the flight path, only really applies to situations where the slip angle is constant (and other variables such as angle-of-attack are constant.) If the slip angle is changing, the yaw rotation rate is not synchronized to the turn rate, and the yaw rotation rate will induce local changes in the relative wind that will not be mirrored in the flight path. For example imagine an instant in time where an aircraft is travelling in a straight line, but is in the midst of a yaw oscillation, with zero slip as measured at the CG at that instant in time, or maybe better yet with zero slip as measured at the center of lateral area of the aircraft at that instant in time, but with a non-zero yaw rotation rate. In other words the aircraft heading is swinging from left to right and at this moment in time, happens to be precisely aligned with the direction of the flight path as measured at the CG of the aircraft. Due to the non-zero yaw rotation rate, yaw strings at the nose and tail will be deflected in opposite directions-- there is a curvature in the relative wind that is not mirrored in the flight path. The relative wind perfectly follows the curve of the flight path ONLY when variables such as sideslip angle are constant. Nonetheless as long as this limitation is appreciated, the concept of the relative wind or free stream curving to follow the curving flight path is an extremely useful tool for thinking about the dynamics of turning flight.

Quote:
 Originally Posted by vespa You won't find any loopholes. If you're turning and there is no difference in drag between wingtips it is because you are holding open the drag rudder on the inside wingtip. There's really no other way to have the drag be equal at different speeds.
This is something that you need to take up with ShoeDLG. He seems to be suggesting otherwise. That the drag between the two wings may be equal, or the inboard wing may be generating more drag than the outboard wing. I haven't yet given his detailed posts the careful reading and thought that they deserve. Also there are some outside sources that I want to re-read, such as (now quoting) a 2-part series of articles called "Spiral Stability and the Bowl Effect" by Blaine Beron-Rawdon that appeared in Model Aviation in September and October 1990, and also a series of articles entitled simply "Dihedral, a 4-part series" by the same author in the same magazine in August through November of 1988. These articles provide an excellent introduction to the way that "airflow curvature" affects the spiral stability and control of a slow-flying, long-spanned aircraft. These articles discuss "airflow curvature" in relation to stability and efficiency in rudder-controlled model sailplanes, but the ideas within apply to all aircraft. (end quote). (By the way I think it is better to talk about the curvature in the relative wind, not the curvature in the airflow, to make it clearer that we are really talking about the free stream, not anything related to the disturbance of the air by the aircraft.) Also I want to re-check some of my own (video) data I've collected in the past re the deflection of yaw strings at the aft end of slow-flying long-spanned aircraft.

Steve
Last edited by aeronaut999; Feb 08, 2013 at 03:52 PM.
Feb 08, 2013, 10:37 AM
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More details

Quote:
 Originally Posted by vespa So this curved wind is really just another factor resisting the yaw rate, and thus you need even more slip or rudder input to overcome it and maintain a continuous turn. In other words, curved relative wind does not cause a slip, it resists a yaw rate.
As far as yaw rate goes, I think it's clear by now that the curving relative wind is generating both proverse and adverse yaw torques, especially in the case of a turn with no rudder deflection. Net yaw torque is zero. There is no basis for saying that the curved relative wind resists yaw rate, or that it causes yaw rate. There is no need for yaw rate to have a "cause". Only a change in yaw rate needs to have a "cause". We're getting back to Aristotle vs Newton again.

Throughout this thread I keeping getting vibes from some of your posts, that you feel that something must be acting to drive a yaw rotation rate in a steady turn. Maybe it is just a difference in the way we are looking at yaw damping. The "curving relative wind / tangent point" approach does take full consideration of all the adverse yaw torques or anti-turn yaw torques, which are the same thing as the yaw damping torques, at least in the case of a steady-state turn with a constant slip angle. (More generally, adverse yaw isn't the same thing as yaw damping, but the labels seem equivalent in the case of a steady-state turn with constant slip angle.)

In some ways my viewpoint is closer to yours than you probably think, as it is still my intuitive feel that usually the outboard wingtip makes more drag than the inboard wingtip, so the whole aircraft must indeed fly at some non-zero slip angle to equalize the yaw torques. I.e. the tangent point between the fuselage centerline and the curving flight path lies aft of the vertical fin. But after reading ShoeDLG's comments to the contrary, I am not yet ready to make a forceful argument that this is always the case.

Quote:
 Originally Posted by vespa We define a coordinated turn as the wing being perpendicular to the airflow.
That is a matter for debate. We could define a coordinated turn as a turn with the slip-skid ball centered. No net sideforce. Depending on how the lateral area of the aircraft is distributed along the fuselage, there might be sideways flow over the wing. Of course we also would have to consider the side force from a deflected rudder, which is not trivial. It is not unreasonable to define a coordinated turn as one with no sideways airflow over the wing, but it is not the only possible definition. It could be a rather useful definition for talking about some aspects of aerodynamics, I don't have any problem with that.

Quote:
 Originally Posted by vespa So it should be clear that to turn we need to continuously generate both a lateral force and a yaw moment. This is why planes do not perform coordinated turns by themselves. Even if you had zero roll stability such that the plane could maintain a bank angle, it still could not make a coordinated turn without something asymmetric (rudder, aileron, etc.) creating a constant yaw moment. It can however, slip, weathervane, and thus perform an uncoordinated turn.
I think that in the real world, the dynamics do usually work out such that there is usually going to be some net sideforce toward the outside of the turn in a no-rudder turn, so that a slip-skid ball falls to the inside of the turn. I also think that in the real world the dynamics do usually work out in such a way that there is a slipping airflow over the wing in a no-rudder turn.

Remember though, I detailed the case of the hang glider that performed a wings-level turn against the direction of the deflected rudder several posts ago. Post # 47. That seemed to be a stumbling block to your way of analyzing things. Perhaps you have improved the analysis so that is no longer a problem? At the end of the day I think we would end up agreeing on what is the source of the centripetal (turning) force in this case. But it is a very counter-intuitive example at any rate.

Steve
Last edited by aeronaut999; Feb 08, 2013 at 02:42 PM.
 Feb 08, 2013, 12:26 PM Registered User Germany, BW, Stuttgart Joined Mar 2012 1,049 Posts There's another small consideration that I think applies to the the differential drag/lift between the inboard/outboard wings of a plane in a steady, level turn. If the plane is at non-zero angle of attack, then the lift direction is not aligned with the aircraft z-axis. This means that: 1. Any differential lift will result in a yawing moment 2. Any differential drag will result in a rolling moment Because AOAs are typically small, we might expect the "differential lift-yawing moment coupling" to be small. However, local C_l's may be 10's of times greater than local C_d's. If you deflect an aileron to oppose the rolling moment due to the lift/drag differential between the inboard/outboard wings, this will introduce yet another yawing moment. So if you look at the sideslip angle at the vertical fin, that sideslip has contributions from: 1. Yawing moment due to drag differential 2. Yawing moment due to lift differential 3. Yawing moment due to aileron deflection (to counter rolling moment due to lift differential) 4. Yawing moment due to aileon deflection (to counter rolling moment due to drag differential) All of these are likely small in comparison to the yawing moment due to sideslip of the vertical tail. This just further complicates any effort to isolate the yawing moment due to drag differential.
 Feb 08, 2013, 12:33 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,299 Posts The big picture I just thought of a nuance that needs to be brought out, that I might be accused of blurring over. Remember, it is only valid to think of the relative wind as curving to follow the curving flight path, when the slip angle is constant (more details on this in post #93). When turning without using the rudder, immediately after banking, the aircraft heading is initially constant. (For simplicity, we're ignoring adverse yaw torques due to rolling, and just looking at yaw rotational inertia.) The banked wing is initially creating a curve in the flight path, but there is no yaw rotation (aircraft heading is constant), so the slip angle is increasing, not constant. The relative wind or free stream is uniform in direction all over the aircraft. The direction of the relative wind or free stream is such that it will interact with the vertical fin or equivalent surfaces to generate a "weathervane" yaw torque. As the yaw rotation begins, the relative wind starts to be non-uniform across the various surfaces of the aircraft. Once the slip angle has stabilized, the yaw rate is in synch with the turn rate and now the relative wind truly does curve to precisely follow the curvature of the flight path. So as the turn first begins, the sideslip must be driven entirely by yaw rotational inertia. Only later, as the yaw rotation ramps up, do effects related to the curving relative wind begin to kick in. At first glance, this observation could be construed as a validation of the simple vector diagram "explanation" of sideslip. I.e. the "Aristotelian" explanation (see post #92). The point I would emphasize is that this vector diagram "explanation" is only valid for the instantaneous moment at the start of the turn where the yaw rotation rate is zero. Holding this up as a general "explanation" of sideslip leads us far astray. Most particularly, we are misled as to why there should be any sideslip when the bank angle is slowly decreasing, rather than increasing. Consider again the case of a very stable airplane, perhaps a free-flight model airplane, with a great deal of dihedral, slowly rolling to wings-level after a disturbance, with no pilot input. Something is creating a roll torque to overcome roll damping and sustain a non-zero roll rate. That something is the interaction between sideslip and dihedral. But since the bank angle is decreasing, and the required yaw rotation rate is decreasing, yaw rotational inertia actually tends to swing the nose too far into the turn, creating a skid rather than a slip. Only when we understand that the relative wind is curved in turning flight, so that different parts of the aircraft experience different relative wind directions and speeds, can we understand why there is actually some sideslip in this instance. That's the big picture. Anything less leads to endless chicken-and-egg arguments, or teleological statements that this or that effect is "causing" a motion, when in fact, a constant motion is not in need of a cause. Last edited by aeronaut999; Feb 08, 2013 at 02:51 PM.
Feb 08, 2013, 12:39 PM
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Quote:
 Originally Posted by ShoeDLG So if you look at the sideslip angle at the vertical fin, that sideslip has contributions from: 1. Yawing moment due to drag differential 2. Yawing moment due to lift differential 3. Yawing moment due to aileron deflection (to counter rolling moment due to lift differential) 4. Yawing moment due to aileon deflection (to counter rolling moment due to drag differential) All of these are likely small in comparison to the yawing moment due to sideslip of the vertical tail. This just further complicates any effort to isolate the yawing moment due to drag differential.
Thanks for keeping on the problem... there's a lot to digest--

For starters though, I would be interested to see whether or not I can observe whether the airflow is striking one side of the vertical tail or the other, in a constant-banked no-rudder turn. That would be a satisfying observation regardless of the various possible causes...

Steve
Last edited by aeronaut999; Feb 08, 2013 at 12:45 PM.
Feb 14, 2013, 05:01 PM
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I finally got around to making some changes to the Vortex Lattice Code I've been using/developing. I analyzed a rectangular wing with no twist, no dihedral and no tail (a true plank) in a level 30 degree bank left turn at different speeds. The parameters I used were:

Weight 1.0 lb.
Span 5.0 feet
Chord 0.5 feet
Airfoil: NACA 63-009
Bank Angle: 30 degrees
Aileron Span: full
Aileron Hinge Line: unswept at 80% Chord

I set conditions for a steady level turn for a couple of different speeds on either side of L/D_max (adjusted AOA for level flight equilibrium and aileron deflection for zero rolling moment). The first chart below shows the rolling moment coefficient, C_N, as a function of airspeed. A positive value of C_N (within the chosen coordinate system) means the airplane wants to yaw with its nose into the turn (skid). A negative value means it wants to yaw with its nose out of the turn (slip). You can see that somewhere around the speed for L_D_max, the yawing moment coefficient changes sign. This means that differential drag on the wings will cause a yaw into the turn at some speeds and a yaw out of the turn at others.

To give a sense for how the lift and drag components are distributed along the span:

-The second plot shows the lift distribution at 20 fps
-The third plot shows the induced drag distribution at 20 fps
-The fourth plot shows the total drag distribution at 20 fps
-The left wing is on the inside of the turn

The aileron deflection starts out at about 3 degrees at 20 fps, is less than a degree at 30 fps and goes down to 0.1 degree at 50 fps.

C_N has a minimum value of about -0.00005 at about 40 fps (it's not surprising |C_N| gets smaller at higher speeds because the turn rate is going down as you go faster in a level, constant-bank turn).

It's worth noting that this is not a purely drag-related effect. You would expect aileron deflection (inboard-downward/outboard-upward) to increase the drag on the inboard wing and decrease the drag on the outboard wing. It does, but the resulting lift differential makes the the wing want to yaw nose out of the turn. At higher speeds, aileron deflection creates a nose-out yawing moment, at lower speeds a nose-in moment. I didn't expect that.

I'd be interested to see how close these results are to what AVL would predict.

# Images

Last edited by ShoeDLG; Feb 16, 2013 at 09:40 AM.
Feb 19, 2013, 10:46 AM
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?

Quote:
 Originally Posted by ShoeDLG It's worth noting that this is not a purely drag-related effect. You would expect aileron deflection (inboard-downward/outboard-upward) to increase the drag on the inboard wing and decrease the drag on the outboard wing. It does, but the resulting lift differential makes the the wing want to yaw nose out of the turn.
Shoe can you help me understand what you mean by the last sentence above?

Why is there a lift differential? Aren't we assuming ailerons are deflected as needed to hold bank angle constant?

Also, how does a lift differential make an outboard yaw, if not via a difference in drag?

Are the lift vectors of the left and right wings acting in different directions, because the aircraft is rolling?

Is the aircraft rolling? I.e. is the aircraft descending? Or are you assuming a constant-altitude turn, relative to the airmass?

Or is the effect you are talking about arising from the fact that since angle-of-attack is non-zero, lift acts in a direction that is not precisely aligned with the vertical axis of the aircraft (like you said in post #95)? But even so, I'm not clear on why there is a difference in lift, if we are holding bank angle constant.

Thanks, I would like to understand better.

Steve
Last edited by aeronaut999; Feb 19, 2013 at 11:04 AM.
Feb 19, 2013, 12:25 PM
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Quote:
 Originally Posted by aeronaut999 Why is there a lift differential? Aren't we assuming ailerons are deflected as needed to hold bank angle constant?
By "lift differential" I was trying to refer to the difference in lift distribution between the case where the elevons are undeflected and the case where they are deflected to achieve zero rolling moment. I think it's intuitive that deflecting the inboard aileron downward (and the outboard aileron upward) will generally increase the drag on the inboard wing and reduce the drag on the outboard wing (the resulting drag difference should contribute to a skid). This is what I observed. However, this aileron deflection caused an overall change to the yawing moment that was nose-out-of turn (slip). This was due to the change in lift distribution.

Keep in mind that the condition for roll equilibrium is not quite equality between the lift on the inboard and outboard wings. Because the centroid of the lift distribution on the inboard wing is shifted toward the "fuselage" (and away from the fuselage on the outboard wing), the inboard wing will have to carry slightly more lift in order for the rolling moments to cancel.

Quote:
 Originally Posted by aeronaut999 Also, how does a lift differential make an outboard yaw, if not via a difference in drag?
Through the component of the lift direction perpendicular to the airplane z axis (due to AOA)

Quote:
 Originally Posted by aeronaut999 Are the lift vectors of the left and right wings acting in different directions, because the aircraft is rolling? Is the aircraft rolling? I.e. is the aircraft descending? Or are you assuming a constant-altitude turn, relative to the airmass?
The aircraft has a very small, but non-zero roll rate. Because the AOA is positive, the wing has a small pitch attitude. The magnitude of the body-axis roll rate at zero pitch attitude rate and zero bank angle rate is equal to the sine of the pitch attitude times the heading rate. This is accounted for in my analysis, but it's a very small effect . I assumed a constant-altitude turn.
Last edited by ShoeDLG; Feb 19, 2013 at 05:21 PM.