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Old Feb 08, 2013, 08:01 AM
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the problem in a nutshell

(accidental duplicate post)
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Old Feb 08, 2013, 08:03 AM
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the problem in a nutshell

Quote:
Originally Posted by vespa View Post
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
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Old Feb 08, 2013, 08:28 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 View Post
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 View Post
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 View Post
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
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Old Feb 08, 2013, 11:37 AM
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More details

Quote:
Originally Posted by vespa View Post

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 View Post
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 View Post
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
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Old Feb 08, 2013, 01:26 PM
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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.
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Old Feb 08, 2013, 01:33 PM
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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.
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Old Feb 08, 2013, 01:39 PM
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Quote:
Originally Posted by ShoeDLG View Post

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
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Old Feb 12, 2013, 08:01 AM
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Aristotelian fallacy, yaw damping, curving relative wind

I've been thinking about this a bit more- I still say that the common vector "explanation" of why a bank causes a sideslip, is an example of Aristotelian logic. In reality, a steady force doesn't imply a steady velocity in the direction of that force. A force creates an acceleration, not a velocity. Again to return to the example of the earth orbiting the sun (and considering the simplified case of a perfectly circular orbit)-- the earth is constantly accelerating toward the sun, but the earth's instantaneous velocity toward the sun is always zero. Because the acceleration is always exactly perpendicular to the trajectory. Just as lift acts perpendicular to the flight path and relative wind or free stream airflow.

So, just because we can express the weight vector, or the vector sum of the weight vector and the lift vector, in a form that contains a spanwise component, doesn't explain why a banked aircraft tends to slip sideways through the air in the absence of rudder input. Rather, the fact that the lift vector, or the vector sum of lift and weight, contains a horizontal component, explains why the flight path tends to curve (turn), as viewed from above. Along the same lines, any net vertical force- i.e. any imbalance between weight and the vertical component of lift- will make the flight path curve upward or downward. Since an aircraft is free to "weathervane" in the yaw axis to align itself with the relative wind, looking at these force vectors really offers no insight into why these horizontal and vertical curvatures of the flight path should involve any sideslip.

In situations where the turn rate and/or the the rate of downward curvature in the flight path is increasing rather than constant, creating a demand for an increased yaw rotation rate, yaw rotational inertia will have some tendency to cause sideslip. However, if the bank angle is constant or decreasing, not increasing, then yaw rotational inertia cannot cause a slip. If the bank angle is decreasing, yaw rotational inertia actually tends to cause a skid. So this cannot explain why an aircraft with a great deal of dihedral tends to return to wings-level after an upset.

(Nonetheless, yaw rotational inertia is not trivial. For example, by aggressively pumping alternating left and right rudder inputs, we can "pump up" a yaw oscillation that involves a much greater slip angle than we could obtain simply by holding full rudder in one direction. The dynamic is not unlike a child "pumping" a swing. Taken to extremes, this can put a dangerous sideload on the vertical fin! Similarly, even on an aircraft with no rudder, we can use adverse yaw from the ailerons to "pump up" a large yaw oscillation. With the right timing, we can make the aircraft "fishtail" dramatically from side to side, with relatively little roll. )

I do agree that aerodynamic damping of yaw is a cause of sideslip whenever an aircraft is banked and turning. To generate the yaw torque needed to overcome yaw damping, some significant part of the rear portion of the aircraft must experience a sideways flow.

The most common way to view an aircraft's motion is to consider the motion as including a linear component, and a rotation about the cg, and a sideslip angle as measured at the cg. Since the rotation affects the direction of the local relative wind, it is possible for parts of an aircraft to experience zero sideways flow, even if the slip angle at the cg is not zero.

An unusual case exists in the idealized case of a slender fuselage of negligible surface area, and no difference in drag between left and right wings. If we yaw this aircraft around the cg, the vertical fin will create a yaw damping torque. Yet in curving flight, the vertical fin can perfectly streamliine itself to the airflow. Since the cg is ahead of the fin, there will be some slip at the cg. A yaw string at the cg will blow sideways. The slip can be viewed as being caused by yaw damping, yet the vertical fin is not actually being dragged sideways through the air. The deflection of the airflow over the vertical fin caused by yawing the aircraft around the cg, is exactly equal and opposite to the slip angle of the aircraft as a whole (as measured at the cg), so there is no sideways airflow over the vertical fin.

Another way to view an aircraft's motion is to recognize that in a steady-state turn, when variables such as sideslip angle and angle-of-attack are constant, the aircraft's pitch, yaw, and roll rotations are synchronized to the curving flight path in such a way that the relative wind curves to precisely follow the path of the flight path. This has been called the "bowl effect". At any given moment, different portions of the aircraft are moving through the air in different directions, and so experience different directions in the relative wind or free-stream airflow. As long as slip angle, angle-of-attack, etc are constant, the resulting curvature in the relative wind precisely conforms to the curvature of the flight path.

(Here is an example of a case where the slip angle is not constant and the relative wind does not curve to follow the curving flight path: an aircraft is flying on heading of 0 degrees, and the pilot lowers the right wing and curves the flight path to a trajectory of 010 degrees, while applying left rudder to hold a heading of 0 degrees. The flight path curved (turned) 10 degrees, but at any instant during that turn or curve, a snapshot of the aircraft would show that yaw strings at nose, cg, and tail were all streaming parallel to each other. With no yaw rotation, there was no curvature in the relative wind.)

(Conversely, if we use aggressive alternating rudder inputs to "fishtail" back and forth in yaw, we will see yaw strings at the nose and tail will be slightly deflected, in opposite directions, each time the nose is swinging back through our original heading. Now the yawing motion is causing what we might call a "shear" in the relative wind vectors. Yet there may be very little curvature in the flight path, particularly in the case of an aircraft with minimal cross-sectional area as seen in side view.)

Returning to the case of a normal, steady turn with a constant slip angle:

The centerline of the fuselage can only be tangent to the curving flight path at a single point. All portions of the aircraft that lie aft of the tangent point feel a skidding airflow (yaw string blows to inside). All portions of the aircraft that lie forward of the tangent point feel a slipping airflow (yaw string blows to outside). If the tangent point lies forward of the nose, the entire aircraft feels a skidding airflow. If the tangent point lies aft of the tail, the entire aircraft feels a slipping airflow.

In our idealized case of an aircraft with a slender fuselage of negligible surface area, and no difference in drag between the left and right wings, the tangent point was exactly at the vertical fin. The vertical fin is perfectly streamlined to the flow.

In a sense, one could argue that there is really no yaw damping going on here. But it is more accurate to say that the curving-relative-wind approach doesn't really "see" yaw damping as a discrete phenomenon. Rather, the yaw damping torques-- the yawing-out torque generated by any elements of the aircraft forward of the cg that may be feeling a "slipping" airflow (yaw string blowing to outside), and the yawing-out torque generated by any elements of the aircraft aft of the cg that may be feeling a skidding airflow (yaw string to blowing to inside), and the yawing-out torque generated by any surplus of drag of the outboard wing, compared to the inboard wing-- are all included in the concept of a curving airflow that curves to follow the flight path, and also moves at a faster velocity over the outboard wingtip than the inboard wingtip. The effects that could be viewed as a result of yaw damping, can also be viewed as a result of the curving nature of the relative wind in turning flight. And changing the sideslip angle as measured at the CG, is the same as making a forward or aft shift in the tangent point between the fuselage centerline and the curving relative wind. So the "curving relative wind" approach incorporates the aircraft's linear motion, and the aircraft's slip angle as measured at the CG, and the aircraft's rotation about the pitch, yaw, and roll axes.

Since the rearmost parts of an aircraft have the greatest tendency to "weathervane" or streamline themselves with the curving flow, in any aircraft with positive directional stability or yaw stability, the tangent point in a steady-state no-rudder turn will lie aft of the CG.

When we add surface area (as seen in side view) to the aircraft at some specific point along the fuselage, the tangent point between the fuselage centerline and the curving relative wind migrates closer to the region of added surface area, as long as the added surface area is aft of the cg. Because the added surface area means that that particular region along the fuselage has a greater tendency to streamline itself with the curving flow. Adding surface area aft of the cg and ahead of the tangent point makes the tangent point migrate forward, reducing the slip angle as measured at the cg. Adding surface area aft of the cg and behind the tangent point makes the tangent point migrate aft, increasing the slip angle as measured at the cg.

(Adding surface area ahead of the cg always makes the tangent point migrate aft, increasing slip angle as measured at the cg.)

(Adding surface area to the aircraft can also change the radius of curvature of the flight path, by contributing a sideforce component in the presence of a sideways flow. In particular, surface area added near the cg or ahead of the cg will always generate a sideforce that opens up the turn to a larger radius. The effect of adding surface area far aft is a bit harder to predict-- see below.)

If we enlarge the vertical fin, the tangent point migrates closer to the vertical fin. In other words the enlarged vertical fin has a greater tendency to "weathervane" or streamline itself with the curving flow. If the tangent point was originally forward of the vertical fin, enlarging the vertical fin will move the tangent point aft toward the fin and increase the slip angle as measured at the cg. This would seem to be most likely in an aircraft with a long slab-sided fuselage, minimal fuselage area ahead of the cg, and a short wingspan. If the tangent point was originally aft of the fin, enlarging the fin will move the tangent point forward toward the fin, decreasing the slip angle as measured at the cg. This would seem to be most likely in an aircraft with a slender streamlined fuselage, a relatively short tail moment-arm, and a long wingspan.

Isn't it generally the case that enlarging the vertical fin decreases the slip angle as measured at the cg, so that any dihedral in the wing geometry generates less rolling-out torque, and the pilot must therefore give more rolling-out torque (or less rolling-in torque) to hold the bank angle constant, in a no-rudder turn? If so, this indicates that the entire aircraft is feeling a slipping flow, meaning that the tangent point lies aft of the vertical fin. This indicates that the outboard wing is in fact generating more drag than the inboard wing. Don't most aircraft follow this pattern?

Doesn't the fact that the wingtips tend to operate at a lower L / D ratio than the wing roots, mean that any aircraft can be viewed as having little airbrakes open at each wingtip, so that the faster-moving outboard wingtip is always generating more drag than the slower-moving inboard wingtip, no matter what aileron inputs the pilot may be making to hold the bank angle constant?

Isn't it a well-known principle of spiral stability that increasing the size of the vertical fin can lead to a spiral dive, because the slip angle at the cg is reduced, so wing dihedral now generates less rolling-out torque? This suggests to me that in the absence of rudder deflection, a banked aircraft normally feels a slipping flow over the entire aircraft, meaning that the tangent point lies aft of the vertical fin, and suggesting that the outboard wingtip is creating more drag than the inboard wingtip. Granted, we need to use some caution in applying the curving relative wind / tangent point concept to a dynamic situation like a spiral dive where the slip angle may be increasing rather than constant; only when the slip angle is constant does the curve of the relative wind precisely follow the curve of the flight path. Also, as an aircraft is rolling into a spiral dive, bank angle is not constant. Without the constraint of constant bank angle, we don't have the yawing-in (anti-slip, pro-skid) torque that would be generated if the pilot applied a rolling-out aileron input to hold the bank angle constant. Still, it seems to me that the observed effects of increasing the size of the vertical fin, suggest that most aircraft experience a slipping flow over the entire aircraft and tail, in constant-banked turning flight with no rudder input. Which in turn, suggests that the outboard wingtip is making more drag than the inboard wingtip, even if the pilot is holding a rolling-out aileron input to keep the bank angle from increasing.

I'll post some observations of tail-mounted yaw strings in the future.
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Old Feb 14, 2013, 06:01 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.
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Old Feb 19, 2013, 02:36 AM
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That is very interesting Shoe. Now, what if there is zero aileron deflection, and roll torque is zero because there is some sideslip and some dihedral? Then which wing makes the most drag? And, will the airflow strike the inside/low side, or the outside/ high side, of the vertical fin?

I would suppose that the effect of dihedral (with sideslip) is very similar to the effect of ailerons.

I have been re-reading Blaine Beron-Rawdon's articles in "Model Aviation" magazine entitled "Dihedral" (4 parts, Aug-Nov 1988), and "Spiral Stability and the Bowl Effect" (2 parts, Sept-Oct 1990)..

(These articles may be easily viewed on-line at the AMA website; apparently you don't even need to be a current AMA member to view back issues of Model Aviation, as the site never asked me for my member number).

The author is dealing with rudder/ elevator sailplanes with no ailerons. In the case where the rudder is centered, it seems that the author starts with the assumption that the vertical fin will be 100% streamlined to the local flow. But then on p. 177 of the Oct 1988 article, we read "My best guess would be that for typical RC sailplanes you can count on the plane yawing outboard about 2 or 3 degrees more than a very large vertical stabilizer would allow." I.e. author suggests that the yaw angle may be 2-3 degrees greater than would be required to perfectly streamline the vertical fin. Which to me suggests that the outboard wing is making more drag than the inboard wing.

The author's analysis has many limitations-- he certainly doesn't go into a detailed analysis of the difference in drag between the left and right wings that is induced by their different angles-of-attack due to slip and dihedral, or the difference in drag between the left and right wings induced by their different airspeeds. In fact in several places in the series he states that his formulae ignore any difference in drag between the left and right wings. Essentially he assumes that the slip angle is completely determined by the length of the tail boom, and that the vertical fin is completely streamlined to the flow. Then he works out how much dihedral is needed to achieve equal lift on both wings, comparing various distributions of dihedral ( such as simple V-dihedral, polyhedral, and parabolic wing shape). Then he comments that some free-flight aircraft achieve roll stability with a much shorter tail boom than would be predicted, by using a small vertical fin, that allows the higher drag of the outboard wing to yaw the plane out to a higher slip angle than would be predicted if the vertical fin were completely streamlined.

Still, it is a starting point.

I recently was flying my Spyder 2-meter sailplane, with a transmitter programmed with an "aileron kill switch". On some flights the aileron kill switch would drop the aileron rate to a very low value, and on other flights the aileron kill switch would drop the aileron rate all the way to zero. The idea was to let the glider stabilize in a left or right bank with no aileron input, so that it would settle into the "natural" bank angle for the dihedral geometry, tail boom length, and airspeed. I was videoing a yaw string on the tail to see if any deflection was visible. But I haven't yet analyzed the results. Any guesses as to direction of yaw string deflection in a low-airspeed 30-to-40-degree banked turn in this situation?

Would washing out the tips (or reflexing both ailerons upward) increase or decrease the "natural" bank angle associated with low-speed flight with no aileron input? Also, would washing out the tips cause there to be a stronger sideways (slipping, yaw string blowing to inside) flow at the tail, when the glider was stabilized at the "natural" bank angle associated with low-airspeed flight with no aileron input? I would think so, because the washed-out tips are not lifting much, they are just being dragged through the air and generating a yaw torque toward the faster-moving, outboard wingtip, it seems to me. Again I have some video but haven't had a chance to analyze it . It will take some time, as I have to compare the headband-mounted GoPro camera that captured my spoken notes, with the keychain video camera on board the glider...

In hindsight, re-reading the articles mentioned, above I'm starting to think that I may have needed to freeze the elevator in a fixed position, as well as centering the ailerons, to get the tail yaw string to settle down in a constant position. The last article in the series talks about how changes in lift coefficient change the spiral stability. For a given elevator position, circle radius affects lift coefficient, because the way that the curving airflow affects the angle-of-attack of the tail, which then affects the angle-of-attack of the wing. (We could also call this "pitch damping".) So you end up with a relationship where a given model with a given tail boom length and dihedral angle and elevator position will settle into a constant-banked turn at one particular bank angle, but changing any of these variables will change the "stable" bank angle. Any change in bank angle, even a slight rolling motion followed by a return rolling motion the other way, is going to disturb the yaw strings due to adverse yaw from rolling. So maybe my experiments had too many pitch inputs for good data, we'll see.

I'm noticing that another limitation of the series of articles is that the author doesn't consider the variations in lift and drag caused by roll damping. A circle that is descending (relative to the airmass) always involves a rolling-in motion, which increases the angle-of-attack of the inboard wing. Another way to say this is to note that both wings have the same sink rate but the inboard wing is flying at a lower airspeed, so it ends up with a higher angle-of-attack. In one of the articles the author notes that he considers this effect to be minor for typical thermalling circles at modest bank angles.



Steve
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Old Feb 19, 2013, 11:46 AM
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?

Quote:
Originally Posted by ShoeDLG View Post

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
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Old Feb 19, 2013, 01:25 PM
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Quote:
Originally Posted by aeronaut999 View Post
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 View Post
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 View Post
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.
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