Feb 03, 2013, 01:06 PM
War is over (if you want it)
Thousand Oaks, CA
Joined Mar 2004
2,662 Posts
Quote:
 there's a net force that acts horizontally... the aircraft tends to be dragged sideways... There's no causal link
I don't even know where to go from here. I tried to explain physics, flight dynamics, etc. to you but you insist of creating your own reality in opposition to the "smoke and mirrors" textbook explanation. Did you really just claim that there's no causal link between F and ma?

And yes of course "my line of reasoning", Newton's, and every textbook explains the issue of "the net yaw torque is not zero in a steady turn". In a coordinated turn the rudder provides a yaw moment. Without rudder or sufficient aileron drag, slip occurs and the fin provides a weathervane moment. Either way, the plane must produce a moment throughout the turn but of course the net is zero in a steady turn because aerodynamic damping/drag is always there resisting any yaw rate.
Last edited by vespa; Feb 03, 2013 at 03:02 PM.
Feb 05, 2013, 10:14 AM
Registered User
The Willamette Valley, Oregon
Joined Dec 2008
1,234 Posts
Causes of sideslip

Quote:
 Originally Posted by vespa I don't even know where to go from here. I tried to explain physics, flight dynamics, etc. to you but you insist of creating your own reality in opposition to the "smoke and mirrors" textbook explanation. Did you really just claim that there's no causal link between F and ma? And yes of course "my line of reasoning", Newton's, and every textbook explains the issue of "the net yaw torque is not zero in a steady turn". In a coordinated turn the rudder provides a yaw moment. Without rudder or sufficient aileron drag, slip occurs and the fin provides a weathervane moment. Either way, the plane must produce a moment throughout the turn but of course the net is zero in a steady turn because aerodynamic damping/drag is always there resisting any yaw rate.
Vespa I think you are taking a static viewpoint, not a dynamic one.

Of course F=ma, and there is a centripetal acceleration (that's the "a") in curving flight. Since an aircraft is free to "weathervane" in yaw, as the flight path curves (accelerates) the aircraft can adopt an attitude where it is facing nose-on into the flow, and there is no requirement that there be a sideways flow over the aircraft. If the aircraft is facing nose-on into the flow, there is no yaw torque from "weathervaning". Which is no surprise-- we know that net yaw torque must be zero in a steady-state turn.

The above describes a steady-state turn where yaw rotational inertia is not a consideration. When we are talking about changes in bank angle, turn rate, and yaw rotation rate, things are more complex and yaw rotational inertia comes into the picture. I discussed this in posts 73.

Also, all the above is a first approximation. One issue that is not addressed by the ideas above is the fact that the flight path and relative wind/ airflow are curving in a turn, and therefore it is impossible for the entire length of the fuselage and vertical fin to be parallel to the flight path and airflow/ relative wind. Rather the line of the fuselage is tangent to the curving flight path and relative wind only at one single point along the fuselage-- or at a point that may lie somewhere aft of the tail (entire aircraft feels slipping flow) or forward of the nose (entire aircraft feels skidding flow) of the projected line of the fuselage. Another way to say this is to note that the yaw rotation of the aircraft induces changes in the direction of the relative wind from nose to tail. Just as a rolling motion induces changes in direction of the relative wind across the wingspan. Also the yaw rotation induces a differences in airspeed across the wingspan-- as we noted in earlier posts, the inboard wingtip is moving faster than the outboard wingtip.

But this whole business of the curving nature of the flight path and relative wind is an unnecessary complication if we are not even clear on the basic physics of moving bodies. If we assume that the radius of curvature of turn is large enough that there is no significant difference in the direction and speed of the flight path and relative wind across the various dimensions of the aircraft (length, span), and if we look at a steady-state turn where yaw rotational inertia is not a factor, then there is no requirement at all that the horizontal lift from the wing drag the aircraft sideways through the air in a manner that induces a sideways (slipping) flow over the aircraft. Rather, the yaw rotation of the aircraft is synchronized with the curving flight path in such a way that the horizontal force from the banked wing always points toward the center of the turn. I.e. it is a centripetal force. Creating a centripetal acceleration. F=m/a and Fc= 1/2 m v^2 / r. With no requirement for sideslip.

You mention a requirement for rudder deflection. It is only the curving nature of the flight path and relative wind, and the resulting differences in drag between the inboard and outboard tips, and the resulting difference in relative wind direction between nose and tail, that ends up requiring we deflect a rudder if a yaw string somewhere near the middle of the aircraft is to be centered. If the radius of curvature of the flight path is large enough that the curvature in flight path across the various dimensions of the aircraft is neglible, then there is no requirement for rudder deflection.

You mention aerodynamic damping resisting yaw rate. Aerodynamic damping in the yaw axis is another manifestation of the curving nature of the flight path/ relative wind. The whole aircraft cannot be parallel to the flight path and relative wind at the same time. If the fin is not parallel to the flight path and relative wind, then it generates a yaw torque. Another way to say the same thing is break the aircraft's motion into a linear component and a rotational component. If the center of rotation is not at the vertical fin, but rather somewhere ahead of the fin, then the vertical fin will create a yaw damping torque. I can't emphasis strongly enough, that these are two different ways to say the exact same thing. You can ask where the line of the fuselage is tangent to the curving flow, or you can break the motion into a linear component and a rotational component, and ask where is the center of rotation. It's the same thing. The center of rotation need not be at the CG. You can treat it as if at is at the CG, but then you will need to make another adjustment for the slip angle of the whole aircraft, to correctly predict the angle of all the yaw strings from nose to tail. Just as you can initially assume that the point where the line of the fuselage lies tangent to the curving flight path is at the aircraft CG. But then to correctly predict the deflection of all the yaw strings between nose and tail, you will need to make another adjustment for the slip angle of the whole aircraft, which is really just another way of recognizing that the tangent point of the fuselage to the curving flow may lie well forward or aft of the CG and may in fact be well aft of the tail.

So yes, we can have aerodynamic damping in yaw, but that is a nuance arriving from the curving nature of the flight path and relative wind. If we are looking at a scale where the physical dimensions of the aircraft are negligible compared to the radius of curvature of the flight path, then we have no aerodynamic damping in yaw. Aerodynamic damping in yaw is a secondary effect generated by the curving nature of the flight path and relative wind, not something that arises from the basic Newtonian mechanics of curving motion. If you were thinking of the need for a yaw torque to overcome yaw damping, that could explain some of the difference in our points of view.

And bearing all that in mind, I stand completely by my critique of the cause in sideslip as explained in various aerodynamics textbooks, as noted in post 73. The cause of the slip is NOT an "uncompensated component of the weight vector", or "the horizontal component of the lift vector", or anything like that. If we say that the cause of the slip is yaw damping, i.e. the fact that the fin is tending to meet the flow at a non-zero slip angle, then isn't this really due to the increased drag experienced by the outboard, faster-moving wingtip? So it seems to me. At any rate, you certainly can't talk about yaw damping without talking about the fact that the flight path has significant curvature across the various dimensions of the aircraft. Which leads directly to the effects I was talking about in posts 57, 68, 70, and 73.

In essence my point is that the basic Newtonian mechanics of curving flight don't predict any sideslip any a constant-banked turn, until we take our analysis to the level of detail where we are considering the fact that the flight path and relative wind has significant curvature from nose to tail of the aircraft, and has significant change in magnitude (speed) from wingtip to wingtip. "Damping" is one way to talk about the effects arising from the curving nature of the flight path. Yes I agree that these effects are crucial to understanding why we see some sideslip in a steady turn.

Just as roll damping arises from the changes in direction of the flight path and relative wind between on wingtip and the other wingtip, when an aircraft is rolling. Different points along the span are following different "flight paths", i.e. moving through space in different directions, as the aircraft rolls.

If you are saying that yaw damping, i.e. effects arising from the curvature in the relative wind between nose and tail, is key to understanding why we tend to see some sideslip in a steady turn, then I agree. That's not what I was getting out of the explanations offered in the various sources I linked to post 73, and I still say that those explanations and force vector diagrams are incomplete and misleading. Specifically, you could divide these sources into at least 3 different categories. Some give the reader the impression that the slip is caused by the fact that the weight vector has a spanwise component during banked flight. Some give the reader the impression that the key is that some of the weight is "uncompensated" during an uncommanded turn where the G-load (lift force) may be initially near 1 G, and it's the spanwise component of this "uncompensated" portion of the weight vector that drives the slip. Which leaves the reader with the impression that there will be no more slip if the G-load (lift force) is allowed to increase as needed to bring the forces back into balance. And some give the impression that it's the horizontal component of the lift vector that drives the slip-- which is really bizarre, since the complete lift vector always acts perpendicular to the span. I still say it's all a "smoke and mirrors" trick, if an unintentional one, and we can't understand anything about why an aircraft tends to slip during turning flight, until we start looking into the nuances of the curving nature of the flight path and relative wind, and the resulting differences in airflow direction and speed from nose to tail and wingtip to wingtip. If these differences are negligible, then slip will be negligible.

The next step in this line of exploration will likely need to be closer look at yaw damping. Which is kind of where I was already going with ShoeDLG. What precisely is the balance of yaw torques in a constant-banked turn? What precisely is the yaw orientation of the aircraft, relative to the curving line of the flight path and relative wind? If the pilot gives no rudder input, is the airflow tending to strike the outboard side of the vertical fin, or the inboard side? If the inboard side, then the fin is contributing no "yaw damping" or adverse yaw torque, rather the fin is contributing a proverse yaw torque. Does this sometimes happen? What is the contribution of the difference in drag, if any, between the inboard and outboard wingtips?

Steve
Last edited by aeronaut999; Feb 05, 2013 at 11:17 AM.
 Feb 05, 2013, 01:08 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,234 Posts Another spin on the above, is to point out that you can't argue that the vertical fin is simultaneously making a weathervane (proverse) yaw torque and a yaw damping effect (adverse yaw torque). If the tangent point between the fuse and the curving flight path lies forward of the fin but aft of the cg, then the fin is making a slight damping (adverse) yaw torque to offset the weathervane (proverse) yaw torque of the middle parts of the fuse that lay between the tangent point and the cg. Meanwhile the portion of the fuse that lies ahead of the cg is also contributing a damping (adverse) yaw torque. On the other hand if the drag of the outboard wingtip is dominating, then the nose may be yawed out so far that the tangent point between the centerline of the fuselage and the curving flight path lies well aft of the fin, in which case the entire fuse and fin is feeling a "slipping" airflow. In this case the fin, and all the portions of the fuselage that lie aft of the cg, are contributing a weathervane (proverse) yaw torque. Only the portions of the fuse that lie forward of the cg are contributing a damping (adverse) yaw torque. I suspect that this is often the case. In all cases, net yaw torque is zero. We could do some actual observations of tail-mounted yaw strings to see which of these scenarios is the case in a typical constant-bank turn with no rudder input. Steve
 Feb 05, 2013, 04:03 PM War is over (if you want it) Thousand Oaks, CA Joined Mar 2004 2,662 Posts What you're not seeing aero is the fact that a yaw rate requires a yaw moment to overcome any yaw-rate related drag *at all times*. If you balance the aiplane on the tip of your finger and spin it like a basketball it will quickly slow to a stop. A continuous turning flight path is the same thing so the plane must be generating some yaw force to overcome this resistance - either rudder, wingtip drag, or slip-induced weathervaning. So yes, the sum of all yaw moments is zero but only if you ackowledge *all* forces, including drag/damping. The curving relative wind also causes the plane to weathervane out of a turn (slip) but you're putting the egg before the chicken. The plane has to be yawing first (or accerating slip) in order for the relative wind to be curved. 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. To address your scenario of a fin producing either adverse or proverse yaw moments dependent purely on it's location in the curved wind, this is simply a case of definition. We define a coordinated turn as the wing being perpendicular to the airflow, therefore a fin will always produce an adverse yaw force due to the curved flow. If the flow is tangent to the fuselage at some point other than the wing location, then by definition you are either slipping or skidding. 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.
 Feb 05, 2013, 05:09 PM Registered User Germany, BW, Stuttgart Joined Mar 2012 864 Posts Steve, For the case of a rectangular planform wing, you can easily estimate the yawing torque due the additional profile drag of the outer wingtip moving faster than the inboard wingtip. If you assume that the wing section profile drag coefficient, C_d, is constant (this simplification will over-predict the magnitude of the torque because the inboard wing will have to operate at higher C_l's in order to maintain roll equilibrium), then you can show that the yawing moment coefficient due to the difference in tip speed is about: C_N_tip = (C_d / 6) * (span / turn_radius) How does this compare to the yawing moment coefficient due to a vertical tail that experiences a sideslip angle due to flow curvature? The yawing moment coefficient of a vertical tail that is a distance d aft of the CG (with zero sideslip at the CG) is about: C_N_fin = C_L_alpha_fin * V_v * (d/ turn_radius) where V_v is the vertical tail volume coefficient. The ratio is: C_N_tip / C_N_fin = C_d * span/ (6 * C_L_alpha_fin * V_v *d) For a draggy, close-coupled airplane with a small, low aspect ratio vertical tail (C_d = 0.015, C_L_alpha_fin * V_v = 0.04, d/span = 0.25), C_N_drag / C_N_fin is about 0.25. In other words, even for a configuration that strongly exaggerates the effect, the torque due to the profile drag difference is only about a quarter of the torque due to the vertical tail sideslip. Under more typical conditions it's less than 1%. I don't think you could accurately measure this with a yaw string at the tail. This analysis also ignores the induced drag. I was able to show using a vortex lattice code that the torque due to the induced drag difference between the inboard/outboard wings acts in the opposite direction from the torque due to the profile drag difference (with the magnitude getting bigger at lower speeds). Below a certain speed the torque due to induced drag difference does become bigger than the torque due to profile drag, and the inboard wing makes more total drag. Bottom line: The yawing moment due to the difference in wingtip drag is: 1) small compared to the "flow curvature torque" due to even a small, closely-coupled vertical tail, and 2) of different sign below a certain airspeed. I don't think the drag difference due to the inboard/outboard wings makes as big a contribution (or even a contribution in the same direction) as you suggest. I will try to tighten up my vortex lattice analysis, but it would be interesting to see if someone else gets the same result using AVL. Last edited by ShoeDLG; Feb 06, 2013 at 05:14 AM. Reason: equation fix
 Feb 06, 2013, 06:51 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,234 Posts Vespa-- Imagine a space craft in a universe devoid of all other bodies (no gravitational pull). Imagine that the spacecraft has a thruster nozzle at the cg, pointing out the left side and steadily firing. Imagine that the spacecraft has some forward velocity. As the thruster nozzle fires, the flight path will curve. If we have initiated the proper yaw rotation rate such that the nose of the spacecraft always points "forward", i.e. parallel to the flight path, then the force from the thruster serves as a centripetal force and the flight path will describe a perfect circle. No yaw torque is needed except for an initial yaw torque to initiate the required yaw rotation. That is a first approximation of a banked turn in winged flight. It is a better approximation for high-airspeed flight than for low-airspeed flight, because at low airspeed the turn radius is smaller, and so all these effects arising from the curvature in the flight path and relative wind across the physical dimensions of the aircraft become more significant. Such as the yaw damping effect, and the resulting sideslip tendency. The spacecraft analogy shows perfectly why a simple diagram showing a banked aircraft with some net horizontal (or spanwise) force component acting on it, offers no explanatory insight at all as to the cause of sideslip in turning flight. When we do start including the curving nature of the relative wind in our analysis, the details of the yaw torque/ weathervane / damping / tangent point/ wingtip drag discussion become quite interesting. I'll post some diagrams later. Steve Last edited by aeronaut999; Feb 06, 2013 at 07:12 PM.
 Feb 06, 2013, 07:15 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,234 Posts Shoe thanks for the detailed post; haven't yet had time to start digesting it. Or to do any actual experimental observations... Steve Last edited by aeronaut999; Feb 07, 2013 at 12:51 PM.
 Feb 06, 2013, 07:47 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,234 Posts (Accidental duplicate post) Last edited by aeronaut999; Feb 07, 2013 at 04:29 PM.
 Feb 06, 2013, 07:49 PM Registered User The Willamette Valley, Oregon Joined Dec 2008 1,234 Posts Shoe, it seems to me that in an idealized case where the fuselage is just a slender stick of neglible cross section, then if there is no difference in drag between wingtips, the vertical fin will streamline itself perfectly to the flow, generating neither proverse ("weathervane") nor adverse ("damping") yaw torque. In other words the line of the fuse will be tangent to the curving flight path exactly at the fin. In this ideal case, even a tiny increase in drag of the outboard tip will yaw the nose further outboard, causing the flow to strike the inboard side of the fin. The tangent point has moved aft, to some point behind the fin. On the other hand, even a tiny increase in drag of the inboard wing tip would yaw the nose inboard so that the flow would strike the outboard side of the vertical fin. Now the tangent point has moved forward of the fin. I'll sketch out some diagrams of some less idealized cases later... Steve
 Feb 06, 2013, 10:33 PM War is over (if you want it) Thousand Oaks, CA Joined Mar 2004 2,662 Posts I'll try one more analogy for you: Roll a marble across a table, now tilt the table. This is your banked airplane -- now sideslipping and veering, but not "turning" per say. This is how the wing produces a slip, just as the table pushes perpendicular to the marble, the wing always lifts perpendicular to the span and an unbalanced component of this lift produces a horizontal acceleration. You can draw the vectors out intuitively, or you can draw them with senseless "lateral gravity components" like some of those texts you posted, it doesn't matter as long as you add them correctly. There's no smoke and mirrors here. This is why airplanes slip when banked. Now the marble doesn't weathervane but an airplane would. This weathervaning -- as a result of slip -- is what allows a plane to turn with only a bank input, albeit uncoordinated. Hopefully this helps you understand the textbook vector diagrams as well as the source of, and requirement for a yaw rate in aileron turns. And again, since we're talking about air, not space, the yaw rate must be maintained by some continually applied force, such as the weathervane moment, aileron drag, or rudder input. So if you're turning without applying a yaw input, you're slipping.
Feb 07, 2013, 03:43 AM
Registered User
Germany, BW, Stuttgart
Joined Mar 2012
864 Posts
Quote:
 Originally Posted by aeronaut999 Shoe, it seems to me that in an idealized case where the fuselage is just a slender stick of neglible cross section, then if there is no difference in drag between wingtips, the vertical fin will streamline itself perfectly to the flow, generating neither proverse ("weathervane") nor adverse ("damping") yaw torque. In other words the line of the fuse will be tangent to the curving flight path exactly at the fin. In this ideal case, even a tiny increase in drag of the outboard tip will yaw the nose further outboard, causing the flow to strike the inboard side of the fin. The tangent point has moved aft, to some point behind the fin. On the other hand, even a tiny increase in drag of the inboard wing tip would yaw the nose inboard so that the flow would strike the outboard side of the vertical fin. Now the tangent point has moved forward of the fin.
I agree, and you can estimate the equilibrium sideslip angle at the tail for the experiment you have suggested. The yawing moment coefficient due to the difference in tip speed (considering only profile drag) is:

C_N = C_d * span * cos( bank_angle) / (6 * turn_radius)

the yawing moment coefficient due to the vertical tail is:

C_N_tail = V_v * C_L_beta_tail * beta_tail

In equilibrium, C_N = C_N_tail. Setting C_N = C_N_tail and solving for beta_tail gives:

beta_tail = C_d * span * cos( bank_angle) / (6 * V_v * C_L_beta_tail * turn_radius)

With flight conditions and a configuration that REALLY amplify this effect:

C_d = 0.02
V_v = 0.01
C_L_beta_tail = 2.0
bank_angle = 30 deg

beta_tail < 5 degrees

Under more typical conditions:

C_d = 0.01
V_v = 0.03
C_L_beta_tail = 3.0
bank angle = 30 degrees

beta_tail < 0.5 degrees

Once again, the assumptions that go into this analysis (constant C_d and no induced drag) result in an overestimate of the magnitude of the tip speed effect. I'm not suggesting the effect doesn't exist, I'm suggesting that a yaw string on the tail is not going to allow you to resolve an equilibrium sideslip angle of a degree or two. I suspect it won't even allow you to determine the sign of the effect (you'd definitely want to do this with a rudderless airplane, otherwise any non-centering tendency would dominate the result).
Feb 07, 2013, 11:56 AM
Registered User
The Willamette Valley, Oregon
Joined Dec 2008
1,234 Posts
2 approaches to looking at yaw rotation

Quote:
 Originally Posted by vespa What you're not seeing aero is the fact that a yaw rate requires a yaw moment to overcome any yaw-rate related drag *at all times*. If you balance the aiplane on the tip of your finger and spin it like a basketball it will quickly slow to a stop.
I guess I would hope that one insight that comes out of all these words, is that we can treat the aircraft's motion as a linear motion plus a spinning or rotatational motion, or alternatively we can draw the curving line of the flight path and relative wind and draw the aircraft, to scale, on that line, and explore what point on the fuselage centerline is tangent to the curving line of the flight path and relative wind.

Either approach takes into account the aircraft's rotational motion and resulting damping or anti-damping effects.

The basic principles of yaw stability suggest that the tangent point will generally lie aft of the CG. Because the rearmost parts of the aircraft have the greatest tendency to "streamline" themselves with the curving flow, if there is not a large difference in drag between the wingtips.

All parts of the aircraft forward of the tangent point feel a "slipping" flow (yaw string streams to outside) and all parts of the aircraft aft of the tangent point feel a "skidding" flow (yaw string streams to inside).

The tangent point may lie aft of the tail or forward of the nose. But let's take a case where it lies between the CG and the vertical fin. All the fuselage surface area ahead of the CG feels a "slipping" flow (yaw string to outside) and so generates an adverse yaw torque. Here is your yaw damping effect.

On the other hand, all the fuselage surface aft of the CG and forward of the tangent point feels also feels "slipping" flow (yaw string to outside), but this now generates a proverse (nose to inside) yaw torque. Here is your "weathervane" effect.

Interestingly, in this case the vertical fin, being aft of the tangent point, feels a "skidding" flow (yaw string to inside). This also generates an adverse yaw torque, contributing to yaw damping. So both the nose and the fin are contributing a yaw damping torque, while much of the fuselage between the CG and the fin is contributing a proverse or anti-damping or "weathervane" yaw torque.

We would have to take a much more circuitous route to get the same insights, if we simply tried to think of yaw damping by envisioning the aircraft as spinning around the CG. At first glance, if we imagine the aircraft is simply spinning around the CG, we tend conclude that the fin is also contributing an adverse yaw torque or a damping yaw torque. This would be a wrong conclusion.

In a sense, it is more valid to treat the tangent point as the center of rotation, than to treat the CG as the center of rotation. And it makes a difference-- if we move the point we are treating as the center of rotation, we change the adverse or proverse yaw contributions of the various parts of the fuselage and fin. If the outboard wingtip is making lots of drag, and the tangent point lies aft of the vertical fin, then the entire fuselage and fin are feeling a "slipping" flow (yaw string to outside). In this case the entire aft fuselage and fin are contibuting a proverse yaw torque, and only part of the fuselage that lies forward of the CG is contributing an adverse (damping) yaw torque.

Again, we would have to take a much more convuluted path to reach the same insights if we just envisioned the aircraft as spinning around the CG.

Or take the idealized case of an aircraft with a very slender fuselage of neglible surface area. Assume also that the left and right wings are generating exactly the same amount of drag. In this case the vertical fin will tend to streamline itself with the flow, so the tangent point will be right at the vertical fin. The vertical fin will generate neither a proverse (anti-damping) nor adverse (damping) yaw torque. In this idealized case there is NO YAW DAMPING AT ALL. If we analyze yaw damping by imagining this aircraft as simply spinning around the CG, we will come to a DIFFERENT conclusion-- we will imagine that yaw strings at the nose are streaming inboard and yaw strings at the tail are streaming outboard, and so we will predict that the fin contributes a yaw damping effect. This will be a wrong conclusion.

Is an example of failure of the conventional theory? Not necessarily-- as long as we recognize that we aren't finished yet. We need to factor in some more terms that take into account the slip angle of the entire aircraft as measured at the CG. Then we'll end up with a proverse yaw torque generated by this slipping airflow over the fin, which will add to the damping yaw torque from the fin to give a net yaw torque of zero. Or to put it another way, to correctly predict the yaw string deflection at the fin, we'll need to add the (slipping) yaw string deflection of the aircraft as a whole, as measured at the CG, to the (skidding) yaw string deflection induced at the fin by the aircraft's rotation around the CG, to correctly predict a net yaw string deflection at the fin of zero.

So we can treat the aircraft's motion as a rotation around the CG, plus a slip or skid angle at the CG, plus a linear motion.

But isn't it a much more holistic approach to recognize that we actually have a curving flight path and a curving relative wind, and that there is a single tangent point between the centerline of the fuselage and this curving flight path? The yaw string deflection at any point on the aircraft depends solely on where that part of the aircraft lies in relation to the tangent point.

Anyway, either approach is valid. I don't agree that my approach fails to adequately and accurately consider all yaw damping effects that may be at play. And one nice thing about my approach, what we might call the tangent-point approach, is that it really underlines the fact that yaw damping arises entirely from the fact that the whole aircraft cannot be tangent to the curving flight path and the curving relative wind. In other words the undisturbed streamlines are not straight, they have a curvature to them. We can come to the same conclusion by visualizing the aircraft as moving in a linear manner plus rotating about the CG, plus a slip/ skid angle for the whole aircraft as measured at the CG, but it is a less intuitive connection.

Steve
Last edited by aeronaut999; Feb 07, 2013 at 12:44 PM.
Feb 07, 2013, 12:23 PM
Registered User
The Willamette Valley, Oregon
Joined Dec 2008
1,234 Posts
force vectors on a turning aircraft

Quote:
 Originally Posted by vespa I'll try one more analogy for you: Roll a marble across a table, now tilt the table. This is your banked airplane -- now sideslipping and veering, but not "turning" per say. This is how the wing produces a slip, just as the table pushes perpendicular to the marble, the wing always lifts perpendicular to the span and an unbalanced component of this lift produces a horizontal acceleration. You can draw the vectors out intuitively, or you can draw them with senseless "lateral gravity components" like some of those texts you posted, it doesn't matter as long as you add them correctly. There's no smoke and mirrors here. This is why airplanes slip when banked. Now the marble doesn't weathervane but an airplane would. This weathervaning -- as a result of slip -- is what allows a plane to turn with only a bank input, albeit uncoordinated. Hopefully this helps you understand the textbook vector diagrams as well as the source of, and requirement for a yaw rate in aileron turns. And again, since we're talking about air, not space, the yaw rate must be maintained by some continually applied force, such as the weathervane moment, aileron drag, or rudder input. So if you're turning without applying a yaw input, you're slipping.
Vespa, there is a substantive problem with the marble analogy. As the marble's flight path curves, the direction of the gravity force that is inducing the curve remains fixed. Therefore what starts as a centripetal force inducing a curving trajectory, ends up as a purely thurst force, accelerating the marble to roll faster down the sloping table in a straight line.

On the other hands, a wing's lift force always acts perpendicular to the flight path. As the flight curves, the direction of the lift force changes, so it remains a centripetal force. (Or more accurately, the horizontal part of the lift force remains a centripetal force.)

You could argue that this is true even if the aircraft fails to rotate at all in yaw. Strictly speaking, it is not the yaw rotation that re-directs the lift force so that it continues to point toward the center of the turn. Rather, it is the very nature of lift, to always act perpendicular to the flight path regardless of any slipping or skidding or yaw rotation or lack thereof.

Of course, if the slip angle gets too extreme, because the flight path has curved and the aircraft heading has not changed, the airfoil shape as presented to the relative wind is not what the designer intended and there may be no more lift!

Also, at outrageously extreme slip angles, the whole concept of "banking" starts to become meaningless. If we are banked 30 degrees and then we curve the flight path 90 degrees with no heading change, so that we have a 90 degree slip angle, we are no longer banked in any meaningful way that will have any tendency to generate a horizontal lift component acting perpendicular to the flight path and drive a turn.

Of course now we are touching on the absurd...

More to the point in the real world, we know full well that if the fuselage fails to rotate as the flight path begins to curve, the sideways flow over the fuselage will set up a sideforce that has an anti-centripetal component and resists the turn. (Now we're back to talking about sideforce! The turn will be more hindered by the lack of yawing, if the fuselage has big slab sides, than if it is slender and streamlined!) At some slip angle the sideforce would completely stop the turn and there will be no more curvature in the flight path.

However we'll never see such an extreme slip angle as to stop the turn completely, just due to yaw rotational inertia alone. That is impossible. Some other factor like the drag from a lowered aileron on the inboard wing would have to be at play, to allow an aircraft to slip so much that it is banked but not turning at all.

In the absence of an aggravating factor like that, directional stability will always generate a yaw torque that initiates the required yaw rotation, sooner or later. All aircraft have directional stability, so you aren't going to ever have the case where the flight path has curved through a quarter or a half of a circle and the nose hasn't changed heading at all. The directional stability will generate the momentary yaw torque required to initate a yaw rotation. That's what brings the discussion out of the realm of the absurd and back into the realm of common sense.

So-- I still say, that a vector diagram showing some horizontal force component, or some spanwise force component, acting on a banked aircraft, gives absolutely no insight whatsoever as to why that aircraft might tend to sideslip sideways through the air. You have to take the analysis to a deeper level to begin to have any insight into that.

Also Vespa your yourself said something about "banked but not turning". You seem to be saying that a lack of turning, is somehow contributing to the cause of the sideslip. I say it's just the opposite-- it's the curving flight path-- the turning-- that sets up the differences in direction and magnitude of relative wind across the various dimensions of the aircraft, and creates the tendency for sideslip. (You can have a sideslip in non-turning flight but that is due to factors that we aren't really discussing at the moment-- like the fact that the lowered aileron may be making more drag than the raised aileron-- as occured in my comments re the Challenger ultralight or Ka6 sailplane in earlier posts on this thread.) (Also you can have a situation where the bank angle has just recently increased, or is still increasing, and yaw rotational inertia is promoting a temporary sideslip, but we seem to be coming to agreement that this is generally not the major cause of sideslip in most situations.)

At the end of the day I keep coming back to the view that the horizontal force vector acting at the CG of a turning aircraft is simply the cause of the turn, plain and simple. It cannot be viewed as a fundamental cause of sideslip. Changes in the direction of the airflow experienced by various parts of the aircraft during the turn, are the cause of the sideslip. The tail feels a different airflow direction than the nose, etc, so the whole aircraft cannot be perfectly streamlined to the flow.

Quote:
 Originally Posted by vespa This weathervaning -- as a result of slip -- is what allows a plane to turn with only a bank input, albeit uncoordinated.
I agree that some slip must occur to create a weathervane yaw torque. However consider the ideal case of the aircraft with the slender fuselage of neglible surface area, and no difference in drag between wingtips. The fin will tend to streamline itself perfectly with the curving flow. In a constant-banked turn with no rudder input, yes there will be some slip as measured at the CG of the aircraft, or at the nose, but net "weathervane" yaw torque is zero. A brief initial yaw torque did arise to inititate the yaw rotation as the aircraft banked, but that was only momentary. Once the aircraft settles into the turn, the fin is streamlined and creates no yaw torque in this particular idealized case. There is no yaw damping at all. See my previous post (# 87) for quite a bit more on this particular situation. Also, nothing is generating any sideforce, so a slip-skid ball will be centered. (For this last condition, perhaps we also need to stipulate zero dihedral/ anhedral, so that the wing's projected side area is negligible.)

Steve
Last edited by aeronaut999; Feb 07, 2013 at 06:14 PM.
Feb 07, 2013, 02:18 PM
Registered User
The Willamette Valley, Oregon
Joined Dec 2008
1,234 Posts
marbles and bobsleds

Quote:
 Originally Posted by vespa I'll try one more analogy for you: Roll a marble across a table, now tilt the table. This is your banked airplane -- now sideslipping and veering, but not "turning" per say. This is how the wing produces a slip, just as the table pushes perpendicular to the marble, the wing always lifts perpendicular to the span and an unbalanced component of this lift produces a horizontal acceleration. You can draw the vectors out intuitively, or you can draw them with senseless "lateral gravity components" like some of those texts you posted, it doesn't matter as long as you add them correctly. There's no smoke and mirrors here. This is why airplanes slip when banked. Now the marble doesn't weathervane but an airplane would. This weathervaning -- as a result of slip -- is what allows a plane to turn with only a bank input, albeit uncoordinated.

Nonetheless there is one sector of aviation that is completely sold on this line of argument and believes that any turn where the nose is dropping and the airspeed is rising, i.e. any turn where lift is temporarily too small for the bank angle, is a slipping turn. Not so.

Steve
Last edited by aeronaut999; Feb 08, 2013 at 07:40 AM.
Feb 07, 2013, 06:02 PM
War is over (if you want it)
Thousand Oaks, CA
Joined Mar 2004
2,662 Posts
Quote:
 there is a substantive problem with the marble analogy.
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.

Quote:
 You seem to be saying that a lack of turning, is somehow contributing to the cause of the sideslip.
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. Again, please try to understand the marble analogy. Or the frozen lake, or the asteroid, or the spaceship or... we're going in circles here. The lateral lift is the cause of the sideslip. There's a reason every single textbook states this. Because it's true.

Quote:
 a wing's lift force always acts tangent to the flight path
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.

Quote:
 I still say, that a vector diagram showing some horizontal force (F) component, or some spanwise force component, acting (=) on a banked aircraft, (m) gives absolutely no insight whatsoever as to why that aircraft might tend to sideslip sideways(a) through the air.
Uh.

Quote:
 ideal case of the aircraft with the slender fuselage of neglible surface area, and no difference in drag between wingtips. The fin will tend to streamline itself... and creates no yaw torque
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.