The effect of VG on anhedral: why the net geometric anhedral decreases as a VG is applied

August 31 2005 edition
Steve Seibel
www.aeroexperiments.org
steve at aeroexperiments.org

 

NOTE August 2006: all the content in this section has now received a fresher treatment in the "Semi- Unconventional Aerophysics Tutorial" pages. Many items that are not yet covered in the main text pages of the SUAT section are covered briefly on the page entitled "Pool of images for Semi-Unconventional Aerophysics Tutorial Pages." This older material is still accurate to the best of my knowledge except for one point: I now feel that the suggestion that increasing wingtip washout (as opposed to increasing sail billow) will tend to create an anhedral geometry was unwarranted.

 

This topic is addressed in much more detail in the article entitled "How billow and washout increase the net geometric anhedral of a swept wing, and other related topics". Here we'll try to confine ourselves to a very few of the most important points. For more, see the entire text of the longer article...

The passages marked "*" are excerpts from this article and the passages marked "**" are additional notes.

Note August 2005: many of the ideas in this article are now contained in the photos and text that can be accessed from the related page on this website entitled Photos of hang gliders and models to illustrate how billow contributes to the net geometric anhedral of a swept wing.

 

*In the case of a swept wing with washout and/or billow, things get extremely interesting. For example, at first glance many hang glider wings appear to be fairly flat, i.e. they appear not to have very much anhedral, especially if we are talking about single-surface wings, and especially the old Rogallo models. But look at these photographs and notice how washout and billow are very clearly adding to the wing's net geometric anhedral. Note how we can often see the top surface of the outboard portion of the wing that is closest to the camera. And note how we can often see the undersurface of the outboard portion of the wing that is farthest from the camera. Recall how we've already seen that this will create a roll torque when there is a sideways component in the airflow. And bear in mind that the outboard areas of the wing are more important than the inboard areas of the wing, when it comes to the balance of roll torques. As we look at the wing from the side, when we can see the top surface of the outboard portion of the near wing and the bottom surface of the outboard surface of the far wing, we are seeing net geometric anhedral. (Photo 3: pilot landing at Packwood WA) (Photo 4: Dwayne Hyatt launching at Peterson Butte OR) (Photo 5: Dwayne Hyatt flying at Peterson Butte OR) (More photos illustrating how washout and billow contribute to the net geometric anhedral of a swept wing)

*It's very clear from these photos that washout and billow can greatly increase the net geometric anhedral of a swept wing.

*Think about the shape of a wing will change as a VG is applied. If the VG is of the older "pulley" type (as opposed to the "cam" type), will the slight lowering of the tips, by a few inches, in relation to the keel, be enough to compensate for the lost billow and twist? Will the wing end up with less, or more, net geometric anhedral when the VG is applied?

*The in-flight experiments to look at coupling between yaw and roll that we'll describe elsewhere on this website, as well as rough measurements of geometry when the glider is on the ground, both show that a typical flex-wing hang glider ends up with much less net geometric anhedral when the VG is applied than when the VG is loose, even with a conventional "pulley" VG system, and more so with a "cam" VG system. More on this below.

*Some specific aerodynamic observations--such that the fact that a wing typically needs more high-siding when the VG is applied--initially appear to suggest that the net aerodynamic anhedral decreases as the VG is applied. However, there are other possible explanations for this. In a stabilized constant-bank turn, there is only a slight amount of sideslip anyway, so even a large amount of anhedral will only generate a small roll torque. (Remember, it's a misconception that anhedral or dihedral will generate a roll torque whenever the one wing is "more horizontal" and the other wing is "less horizontal". Anhedral or dihedral will only generate a roll torque when there is a sideways component in the airflow over the wing, i.e. a sideslip or skid). Here's one possible explanation for the increased amount of high-siding that is typically required when the VG is tight: tightening the VG removes washout and makes the tips "work" much harder than they do when the VG is loose. This is much like an increase in wingspan. This means that the rolling-in torque that is created by the fact that the outboard wingtip is moving faster than the inboard wingtip becomes much larger when the VG is tight. Many other subtle effects related to the flexible geometry of the entire wing may also come into play here.

*Of course, the increased sail tension when the VG is tight obviously means that the wing will respond much more slowly to a pilot's roll inputs. We aren't including this effect in our concept of "effective aerodynamic anhedral". We'll touch on the relationship between sail tension and aerodynamic damping in the roll axis in more detail elsewhere on this website. However, the decrease in net geometric anhedral that takes place when the VG is tight is another reason that a modern flex-wing hang glider becomes less responsive in the roll axis when the VG is tight.

*In this photograph we have only raised the outboard trailing edges of each wing, by rotating the outer panels around the aft-swept hinge line formed by the leading-edge tubes. This has increased the wing's net geometric anhedral (Photo 12). A good side view of this model will be included in a future edition of this article--from the right angle, we can see the top surface of outboard portion of the near wing and the bottom surface of the outboard portion of the far wing, making it obvious that the wing will generate a strong roll torque toward the camera if the wing is sliding sideways toward the camera, i.e. if the airflow (relative wind) is blowing from the camera toward the wing. This particular model is really the key to understanding how billow and washout contribute to the net geometric anhedral of a swept wing. At first glance, an observer might be tempted to think that by raising a portion of the outboard areas of each wing, we must be creating dihedral, not anhedral. This would be a misconception--the three-dimensional geometry of this swept wing is such that we are clearly increasing the wing's net geometric anhedral.

*Why is this glider on its top (photo 16)? We're returning to our earlier idea of positioning the glider in a pitch attitude where the chord line at mid-span is horizontal. Note how the undersurface becomes invisible exactly at the mid-span point in the head-on view (photo 17)--the glider has been positioned so that an imaginary fore-and-aft chord line connecting the trailing edge to the leading edge runs horizontally (parallel to the ground) exactly at the mid-span point. The glider is inverted so that the flying wires are tight and the top wires are loose, and also so that gravity will pull the sail down into a shape that very, very loosely approximates the in-flight shape. With the glider in this orientation, we can measure the vertical distance between the quarter-chord point at the wing root and the quarter-chord point at the wing tips. (We've specified the quarter-chord point because for any given airfoil-shaped slice of the wing, the aerodynamic center is generally near the quarter-chord point, and also simply because we need to pick a fixed reference point one way or another). We can take this vertical distance figure to be a quantitative measure that is very loosely related to the wing's net geometric anhedral. Then we can tighten the VG. This removes some of the billow in the sail, lowering (in the glider's own reference frame) the trailing edge at mid-span. In the head-on view, the point where the trailing edge becomes invisible will migrate outboard on each wing, so that the wing as a whole will appear to be "flying" at a higher angle-of-attack in the glider's own reference frame. In order to return the mid-span chord line to an alignment that is parallel to the horizon, so that the trailing edge again disappears exactly at the mid-span point, we'll need to rotate the nose down (in the glider's own reference frame). This will raise the tips upward (in the glider's own reference frame), due to the sweep in the wings. On the other hand, the tips will have a tendency to lower a few inches (in the glider's own reference frame) as we tighten the VG, because this glider has a conventional "pulley" VG system, so the flying wires will tend to tighten. After we've tightened the VG, and lowered the nose of the glider (in the glider's reference frame) to return the mid-span chord line to a horizontal attitude, we can re-measure the vertical distance between the tips and the root as described above. When we actually make the measurement we find that the total vertical distance between the wingtips and wing root is now less, so our quantitative estimate of the wing's net geometric anhedral is now smaller. The upward displacement of the tips as we rotated the entire glider in a nose-down manner (in the glider's own reference frame) to keep the center-section chord line horizontal has been more significant than the downward movement of the tips (in the glider's own reference frame) due to the tightening of the side wires due to the conventional "pulley" VG system.

*By the way this "downward rotation of the nose" that we keep mentioning in the above paragraph is obvious in actual flight when we pull the VG on--the bar moves aft.

*The reader may object that the glider's pitch attitude in space, or the glider's angle-of-attack, shouldn't affect our estimate of the wing's net geometrical anhedral. This is true. And we're really not thinking about the pitch attitude or angle-of-attack per se--for example we haven't paid any attention to the fact that the wing as a whole needs to fly at a higher angle-of-attack when the VG is loose, because the highly twisted, billowed wing is less efficient aerodynamically. We're just thinking about the actual, physical chord line of various parts of the wing, and how they change when the VG is loosened or tightened. The orientation of the wing's mean chord line does have an effect on the wing's net geometrical anhedral, as we've already seen with the models. Certainly the mean chord line is a much more valid reference line than the keel tube--the keel tube has no aerodynamic or geometric significance at all. There's no reason whatsoever to assume that anhedral should be measured with the keel in a horizontal position, when washout and billow mean that most of the wing is oriented at an angle of incidence that is completely different than the line defined by the keel. The common idea that "applying the VG creates more anhedral" commits exactly this error--it takes the keel as a fixed reference line and ignores the radical changes in the 3-dimensional shape of the wing that occur as the VG is applied.

Note August 2005: for more photos relating to the idea of placing a glider in a pitch attitude where the chord line at the mid-span point of each wing is horizontal, see this page.

*Now let's end our attempt to put the wing in a specific, defined pitch attitude, and put away our measuring tape, and simply eyeball the wing with the VG loose and with the VG tight, while the glider is inverted in order to load up the flying wires and allow the sail to billow in the normal direction. If the VG is loose, when we look at the wing in a side view, we can see a great deal of the top surface area of the outer wing panel on the wing nearest the observer, and we can see a great deal of the undersurface of the outer wing panel on the wing furthest from the observer. This is due to washout and billow. When we tighten the VG, we see much less of the top surface of the wing nearest the observer, and much less of the bottom surface of the wing farthest from the observer, especially if we concentrate our attention on the outboard portions of the wing, which are farthest from the CG and therefore most important as far as the total balance of roll torques is concerned. As we eyeball the wing from a side view, it becomes very clear that the wing has much less net geometric anhedral with the VG tight than with the VG loose. (More photos of all this will be added in the future). Again, it's clear that when we apply the VG, the decrease in washout and billow is affecting the overall three-dimensional geometry of the wing in a way that is much more important than the slight lowering of the wingtips due to the way that the conventional "pulley" VG system tends to tighten the flying wires. Also, eyeballing different gliders in this manner readily reveals that the Wills Wing Spectrum, which has very little droop in the leading edge tubes as compared to the line of the keel tube, and a very small keel pocket, and at first glance appears to have very little anhedral, actually has enough billow and washout that it ends up with more net aerodynamic anhedral than does the Airborne Blade with the VG on. The three-dimensional geometry of a swept, billowed, washed out, flexible wing is complex enough that we can really learn more from an educated "eyeballing" of the wing from a side view, than we can learn by trying to measure the vertical distance between the wing root and the wingtips while holding the wing in some specified pitch attitude.

*Let's think a bit about the effects of a "cam" VG system versus a "pulley" VG system. With either system the wing ends up with less net geometric anhedral (as we've defined it above) as the VG is tightened, but this effect is more pronounced with a "cam" VG system, because the geometry is such that the wing tips do not get pulled downward in relation to the keel as the VG is applied. At first glance this doesn't seem like such a great idea--after all, anhedral helps provide better roll response on a rudderless aircraft, and roll response becomes slower as sail tension increases, so why should we want to take away even more of the net aerodynamic anhedral when the VG is tight by using a "cam" VG system? Of course, it is nice to have the side wires tight on launch when the VG is loose. And if we take the viewpoint that the glider's characteristics with the VG full on should include the maximum possible aerodynamic efficiency, regardless of the cost in terms of the roll response rate, then the choice of a "cam" VG system makes perfect sense. Also, the more we can reduce the net geometric anhedral, the less the glider will tend to enter into yaw-roll oscillations during flight at high airspeeds (low angles-of-attack).

*Added notes April 2005: this material will undergo some revision in the near future. One item that is currently lacking is a photograph of a 3-dimensional, continuous model--not made up of discrete surfaces--of a "conventional", rigid, swept wing with an exaggerated amount of washout. Photographs of such a model would convincingly demonstrate that in any case where the washout can be modeled as a rotation or twisting of the wing surface about an aft-swept axis, the washout will increase the wing's "net geometric anhedral". On the other hand, if the wing has such a very modest amount of sweep that the washout can be modelled as a rotation or twisting of the wing surface about a non-swept or forward-swept axis, then the washout will have no effect on the wing's "net geometric anhedral", or in the latter case, will actually decrease the wing's "net geometric anhedral". Again, 3-dimensional models are needed to convincingly illustrate these ideas.

*Added notes April 2005 continued: in the case of a flexible hang glider wing with both sail billow and washout, it appears that the geometry is such that increasing the washout at the wingtips can actually end up diminishing the very pronounced net geometric anhedral that would otherwise be created by the sail billow in the mid-span area of the trailing edge of each wing. This relationship is apparent in some of the photos used in this article. So in the case of a flexible hang glider wing, the increased sail billow, not the increased wingtip washout, is the key factor that increases the wing's "net geometric anhedral" when the VG is loose, and decreases the wing's "net geometric anhedral" when the VG is tight. These relationships will be explored more rigorously in a future edition of this article.

 

 

For more photos illustrating that billow contributes to anhedral, and illustrating that a hang glider has more "net geometric anhedral" when the VG is loose than when the VG is tight, see the related page on this website entitled "Photos of hang gliders and models to illustrate how billow contributes to the net geometric anhedral of a swept wing".