AEP images

Pool of images for the Aerophysics Exploration Pages

Steve Seibel
www.aeroexperiments.org

This page is still under construction!
This page was last modified on August 29, 2006

 

Sources of images: images on this page that reside on the Aeroexperiments website were created by the author (Steve Seibel) unless otherwise noted. Images on this page that reside on external websites were not created by the author.

 

Views of models and aircraft with dihedral--note that in many of these photos one of the following is true:
1) we can see the bottom surface of the near wing and the top surface of the far wing
2) we can see the bottom surface of the near wing, while we see the far wing an in edge-on manner
3) we can see the top surface of the far wing, while we see the near wing an in edge-on manner
4) we can see the bottom surface of both wings, but the near wing presents us with a larger cross-sectional area, while we see the far wing in a manner that is more nearly edge-on
5) we can see the top surface of both wings, but the far wing presents us with a larger cross-sectional area, while we see the near wing in a manner that is more nearly edge-on.

On some of these aircraft, washout is very evident. For example, when we are viewing the aircraft from the front, sometimes we can see the bottom surface of the inboard part, but not the outboard part, of one or both wings. Alternatively we may be able to see the top surface of the outboard part, but not the inboard part, of one or both wings. When we are viewing the aircraft from the rear, sometimes we can see the top surface of the inboard part, but not the outboard part of one or both wings. Alternatively we may be able to see the bottom surface of the outboard part, but not the inboard part, of one or both wings.

Model of wing with dihedral

The Gentle Lady RC sailplane has a great deal of dihedral, and uses the rudder as the sole means of roll control

More views of aircraft with dihedral: Superfloater. The original version of the Superfloater ultralight sailplane had much more dihedral, and used the rudder as the sole means of roll control.

More views of aircraft with dihedral: MX ultralight. The MX descended from a foot-launched glider that used the rudder as the sole means of roll control. This powered version of the MX has spoilerons on the wing for auxiliary roll control, but there is so much dihedral that the rudder really serves as the primary roll control. The ability to "cross-control" by using the spoilerons to bank the wing to the right (for example) to prevent the aircraft from turning to the left when left rudder is applied is quite limited. Therefore in the presence of a strong crosswind, the MX must be landed in a "crabbed" attitude, with the nose of the aircraft nearly aligned with the flight path through the airmass, rather than with the ground track and runway.

More views of aircraft with dihedral: Ercoupe (oblique view), Ercoupe (nearly head-on), Ercoupe and CGS Hawk Arrow ultralight, Ercoupe Owner's Club website. The Ercoupe has lots of dihedral: note how in many of the photos, we can see the undersurface of the wing nearest the camera, and the top surface of the wing furthest from the camera. However, the Ercoupe is definitely NOT an aircraft that uses the rudder as the primary means of roll control. In fact there are no rudder pedals, and the rudders are coupled to move automatically with the ailerons to compensate for adverse yaw. With no independently controlled rudder, in the presence of a crosswind the Ercoupe must be touched down in a "crabbed" (non-slipping) attitude, with the nose of the aircraft aligned with the flight path through the airmass rather than with the ground track and runway.

More views of aircraft with dihedral: Stinson SR-10 (source: front cover of "Trade-a-Plane" magazine v.69 n. 27 August 2006 credited "courtesy of EAA photographer Mike Steineke"), Schweizer TG-3 (RC model) (source: "Quiet Flyer" magazine v.11 n.8 August 2006 p. 58 "Maiden Flight" by Don Bailey, photo credited Bob Marchi), Turkey Vulture (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003)

Free-flight model airplanes (#1 (source: "Model Aviation" magazine v.32 n.8 August 2006 credited courtesy Royce Childress), #2 (center aircraft in uppermost image)) nearly always have a great deal of dihedral. These aircraft are not controlled by a pilot in any way and so must be inherently stable in roll as well as pitch, i.e. they must be inherently resistant to entering steep diving spirals.

Views of models and aircraft with anhedral--note that in many of these photos one of the following is true:
1) we can see the top surface of the near wing and the bottom surface of the far wing
2) we can see the top surface of the near wing, while we see the far wing an in edge-on manner
3) we can see the bottom surface of the far wing, while we see the near wing an in edge-on manner
4) we can see the bottom surface of both wings, but the far wing presents us with a larger cross-sectional area, while we see the near wing in a manner that is more nearly edge-on
5) we can see the top surface of both wings, but the near wing presents us with a larger cross-sectional area, while we see the far wing in a manner that is more nearly edge-on.

Model of wing with anhedral

Zagi RC glider with anhedral and controllable rudder -- this glider was successfully flown using "wrong-way" rudder inputs as the sole means of roll control.

Planform view of same aircraft (with wings adjusted to a flatter configuration).

This ultralight has a slight amount of anhedral, at least when the wing is not creating lift. How can we tell? If we change our viewing angle slightly, we can see the bottom surface of the outboard part of the far wing (see this zoomed-in close-up of the area around the tie-down fitting near the left wingtip; ignore the lowered aileron and focus instead on the visible part of the lower wing skin) but we can't see the bottom surface of the outboard part of the near wing (see this zoomed-in close-up of the area around the tie-down fitting near the right wingtip). Alternatively, from this angle we can just barely see the "droop" in the leading edges. The leading edges of the wings of this aircraft are unswept and what appears at first glance to be sweep in the photo is actually anhedral. If the anhedral is an intentional feature of the design, it is probably intended to counteract the dihedral-like effect created by the interaction between the slab-sided forward fuselage and the high-mounted wing. Note also that in this view, even though we can't see the bottom surface of the outboard part of the near wing, there is just enough "twist" or "washout" in the wing to allow us to see a bit of the undersurface of the inboard part of the near wing, along with a great deal of the undersurface of the inboard part of the far wing.

Swift ultralight sailplane (Packwood WA)--note that we see the near wing in a manner that is nearly edge-on, while the bottom surface of the far wing is visible. (The far wingtip is resting on the ground. The peculiar black object visible through the "cage" or "fuselage" structure is actually a vortex generator projecting downward from the leading edge of the far wing. The corresponding feature on the near wing is just barely out of the frame of the photo.)

Interestingly, in the above photo the lowered flaps display a dihedral geometry: while the bottom surface of the near flap is visible, a very close look at the photo will reveal that the top surface of the far flap is visible. In other words, the flaps have a dihedral geometry. This illustrates "Seibel's theory of swept hinge lines": when a matched pair of aerodynamic surfaces have aft-swept hinge lines, we create a dihedral geometry when we lower the surfaces and we create an anhedral geometry when we raise the surfaces. When a matched pair of aerodynamic surfaces have forward-swept hinge lines, the opposite is true: we create a dihedral geometry when we raise the surfaces and we create an anhedral geometry when we lower the surfaces. Here's another view of an aircraft that illustrates the "swept hinge line theory": ATOS (Oceanside OR)--the wings have dihedral, but the lowered flaps have much more dihedral than the wings.

A semi-illustrated list of some other "conventional" aircraft with anhedral--note that most of these aircraft have high-mounted wings, and many of them have slab-sided fuselages with a large cross-sectional area, so that the interference between the fuselage and the wing tends to create a strong dihedral-like effect in the presence of a sideways component in the relative wind. Many also have very tall vertical tails, which also create a dihedral-like ("downwind") roll torque in the presence of a sideways component in the relative wind. This effect will be most pronounced when the area of the tail is relatively large in relation to the wing area, and when the vertical height of the tail is relatively large in relation to the half-span of the wings, all of which is true in the case of many of the high-speed aircraft listed here. Most of the aircraft listed here also have swept or delta wings, which also create a dihedral-like ("downwind") roll torque in the presence of a sideways component in the relative wind. In most of these aircraft, the anhedral wing serves to partially counteract these effects, so that the aircraft ends up with a mild dihedral-like effect ("positive coupling between yaw (slip) and roll") overall. Most of these aircraft are military, and/or large transports. LTV A-7, Chance-Vought F-8, #2--note that we see the far wing edge-on, while we see the top surface of the near wing, #3 (see text description), Harrier (various makes and models all have extreme anhedral), #2 (on the uppermost photo we see the top surface of the near wing and the bottom surface of the far wing, and likewise with the anhedral tail surfaces), Lockheed F-104 (extreme anhedral), Dassault-Breguet-Dornier Alpha Jet, MiG-15 (see text description), MiG-17 (see text description), MiG-19, MiG-21, #2 (see text description), Lockheed C-141 (anhedral in flight appears minimal?), Lockheed C-5, Mc Donnell Douglas C-17, Tupolev Tu-16 (see text description), Antonov An-124, Antonov An-225, Illyushin Il-76.

Before we move on to images of aircraft with more complex wing shapes, here's something the reader should be aware of: when an aircraft has a swept wing, simply tilting the aircraft into a nose-up pitch attitude with respect to the viewer's line of sight can create the appearance of anhedral when none is in fact present. For example, see this photo of the B-47 which appears to have a great deal of anhedral but actually only had a slight trace of anhedral or no anhedral, even when at rest on the ground. (Scroll upwards to the photo, then scroll downwards to the 3-view. Note that we an see the undersurface of the wings in the photo.) Likewise, when an aircraft has a swept wing, then simply tilting the aircraft into a nose-down pitch attitude with respect to the viewer's line of sight can create the appearance of dihedral when none is in fact present. For example, a hang glider positioned high over an observer will often appear to have dihedral when it is flying on a heading that is aimed directly away from the observer, even though the glider in fact has anhedral. If we view the aircraft with the wing's mean chord line parallel to our line of sight (e.g. with the wing's mean chord line positioned horizontally, if our eye is positioned at the same height as the wing), this will not be an issue. But more fundamentally, if we assess the wing's anhedral or dihedral by viewing the aircraft from an oblique angle and checking for a difference in the "visual angle-of-attack" at which the left and right wings meet the eye, as described in the many examples above, then the aircraft's pitch attitude will be irrelevant. For example, if we can see the top surface of the near wing and the bottom surface of the far wing, then the aircraft has anhedral, regardless of the pitch attitude of the aircraft. To give another example, if we are viewing the aircraft in an oblique manner and both wings are seen edge-on, or both wings present the same visual "angle-of-attack" to the camera or to the eye, then the wing has no anhedral or dihedral, regardless of whether the wing tips are higher or lower than the wing roots.

Now we'll move on to images of aircraft with more complex wing shapes. Note that in the oblique views, we can continue to see the difference in the visual "angle-of-attack" of each of the matched wing surfaces (e.g. we see the outboard panel of the near wing at a different angle than we see the outboard panel of the far wing), and thus we can tell at once whether that part of the wing (e.g. the outboard portion) has anhedral or dihedral.

Aircraft with anhedral inboard wing panels and dihedral outboard wing panels: Corsair 1 (uppermost image), Corsair 2 (lowermost image), Corsair 3, Corsair 4, Corsair 5, Corsair 6, Corsair 7, Corsair 8

Reiher sailplane with dihedral inboard wing panels and flat outboard wing panels

Aircraft with dihedral inboard wing panels and anhedral outboard wing panels: Osprey (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003), #2 (flapping), Red-shouldered hawk (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003)

Still photos of flex-wing hang gliders illustrating how the combined effects of airframe geometry and sail billow create washout, and also create dihedral on the inboard parts of the wing and anhedral on the outboard parts of the wing:

Photos where we can see the top surface of the tip area of the near wing and the bottom surface of the tip area of the far wing:

#1 (Dog Mountain WA), #2 (Dog Mountain WA), #3 (Packwood WA), #4 (Peterson Butte OR), #5 (Detroit Lake OR), #6 (Peterson Butte OR)

Photos that emphasize how billow creates dihedral in the inboard portion of each wing and anhedral in the outboard portion of each wing:

#1 ("Skysailor" RC trike), #2 (Peterson Butte OR)

Photos that show the above geometries and also emphasize the "washout" angle between the keel tube and the tip tube:

#1 (Peterson Butte OR), #2 (Peterson Butte OR)

Video clips of flex-wing hang gliders illustrating how the combined effects of airframe geometry and sail billow create washout, and also create dihedral on the inboard parts of the wing and anhedral on the outboard parts of the wing:

You tube video of a flex-wing hang glider landing in a wheelbarrow at Fort Funston showing how sail billow creates dihedral in the inboard portions of the wing and anhedral in the outboard portions of the wing. Note also the modest but clearly visible yaw oscillations that take place as the glider launches, and the lack of any apparent strong roll torques arising from these yawing motions.

You tube video of flex-wing hang glider winch-launching --the segment from 0:20 to 0:40 of this short clip gives us a good rear view of the way that sail billow creates washout: as the glider climbs away from us, we can see the top surface of the inboard parts of the wing and the undersurface of the outboard parts of the wing. The same segment also shows how sail billow creates dihedral on the inboard parts of the wings and anhedral on the outboard parts of the wings. Note that when the glider is briefly pointing strongly to the right of our sight line around 0:25, we can see the bottom surface of the outboard part of the far wing but not the bottom surface of the outboard part of the near wing, due to the way that sail billow creates an anhedral geometry in the outboard parts of the wings.

You tube video of flex-wing hang glider launching --skip past the extensive para footage to see the segment between 1:30 and 1:40 of this clip for another rear view of the way that sail billow creates washout: as the glider climbs away from us, we can see the top surface of the inboard parts of the wing and the undersurface of the outboard parts of the wing. The same segment also shows how sail billow creates dihedral on the inboard parts of the wings and anhedral on the outboard parts of the wings.

You tube video of a flex-wing hang glider landing --in this 37-second clip, the segment from 0:11 to 0:17 emphasizes how sail billow creates washout: we can see the undersurface of the inboard parts of the wing but not the outboard parts of the wing. Then the segment from 0:17 to 0:27 emphasizes anhedral: we have an edge-on view of the central and outboard parts of the near wing, and we can see the bottom surface of the central and outboard part of the far wing.

You tube video of a flex-wing hang glider landing --in this 1-minute clip, in the segment from 0:39 to 0:45 we have an edge-on view of the central and outboard parts of the near wing, and we can see the bottom surface of the central and outboard part of the far wing, showing the wing's anhedral geometry.

You tube video of flex-wing hang gliders ridge-soaring --in this 5-minute clip, the segment from 0:50 to 1:10 gives a great view of the top surface of the tip area of the near wing and the bottom surface of the tip area of the far wing. This is primarily due to the way that sail billow creates an anhedral geometry in the outboard parts of the wing, not due to asymmetries in the shape of the left and right wings. Around 0:55, and then again around 1:02, we see the tip area of the near wing in a nearly edge-on manner, and we see the bottom of the tip area of the far wing, again illustrating the anhedral geometry of the outboard parts of the wings. At 1:20 we have a great view of washout on the launching glider--looking at the glider tail-on, we can see the top surface of the inboard part of the wing and the bottom surface of the outboard part of the wing--and then from 1:28 to 1:31 we again see the top surface of the tip area of the near wing and the bottom surface of the tip area of the far wing, due to the way that sail billow creates anhedral in the outboard parts of the wings. Then from 1:55 to 2:05, we are looking at the outboard part of the near wing in a nearly edge-on manner, while we can see the bottom surface of the outboard part of the far wing, again showing the anhedral geometry of the outboard parts of the wings.

You tube video of a landing that didn't come out quite like it was supposed to! Included here to show that the geometry of the trailing edge stays relatively fixed, even as the pilot shifts his weight. The changes in perspective that we are seeing in the above videos are mostly not due to actual changes in the wing shape as the pilot weight-shifts, though this does happen to some extent.

One more clip from you tube: from the Annecy valley in the Rhone-Alpes region of France-- spectacular cliff launches and more. The segment from 2:50 to 3:00 gives a great view of anhedral (we can see the bottom surface of the far wing, while we see the near wing in an edge-on manner). The segment from 3:00 to 3:15 shows how sail billow creates both washout and anhedral (sometimes we can see the bottom surface of the inboard parts of the wings but not the bottom surface of the outboard parts of the wings, and sometimes we can see the bottom surface of the outboard part of the far wing and the top surface of the outboard part of the near wing.)

Perusing the hang-gliding related clips on "You tube" will yield hundreds more segments like these. You are welcome to send me url's of any video clips that better illustrate the points we've been discussing here, or illustrate the same points while being more spectacular, breath-taking, in-focus, brief, etc!

More still photos of flex-wing hang gliders illustrating how the combined effects of airframe geometry and sail billow create washout, and also create dihedral on the inboard parts of the wing and anhedral on the outboard parts of the wing:

Front view of Airborne Blade hang glider, VG on. The glider is inverted so that gravity places a load on the sail and tightens the flying wires. The glider is positioned so that the mid-span chord line is horizontal and parallel to the camera's line of sight. This gives us a view of the wing's overall anhedral geometry that has nothing to do with the height of the wingtips in relation to the line of the keel tube. Note that there is less anhedral than when the VG is off.

Front view of Airborne Blade hang glider, VG off. The glider is inverted so that gravity places a load on the sail and tightens the flying wires. The glider is positioned so that the mid-span chord line is horizontal and parallel to the camera's line of sight. This gives us a view of the wing's overall anhedral geometry that has nothing to do with the height of the wingtips in relation to the line of the keel tube. Note that there is more anhedral than when the VG is on. Note also that the keel tube looks longer than when the VG was on--due to the greater billow, we've had to rotate the glider in a nose-up manner to keep the mid-span chord line horizontal as we loosened the VG, so we are seeing the keel tube in a manner that is less edge-on. This change in pitch attitude can be felt in actual flight--when we fly at trim, the bar moves forward as we loosen the VG and the bar moves aft as we tighten the VG.

Neither of the above photos is meant to be a perfect illustration of the glider's anhedral in a true aerodynamic sense--the idea of keeping the mid-span chord line horizontal is somewhat arbitrary--but less arbitrary than measuring the height of the wingtips in relation to the line defined by the keel tube.

Front view of Wills Wing Spectrum. The glider is inverted so that gravity places a load on the sail and tightens the flying wires. The glider is positioned so that the mid-span chord line is horizontal and parallel to the camera's line of sight. This gives us a view of the wing's overall anhedral geometry that has nothing to do with the height of the wingtips in relation to the line of the keel tube. Note that the anhedral in this photo appears roughly similar to what we see in the photo of the Airborne Blade, VG off.

Side view of Airborne Blade hang glider, VG off. The glider is inverted so that gravity places a load in the sail and tightens the flying wires. The glider is positioned so that the mid-span chord line is horizontal and parallel to the camera's line of sight. Note that a sight-line between the outboard tips of the leading edge tubes passes just under the keel, appearing at first glance to suggest that the glider has only a slight amount of anhedral. This is not really the case--the keel is a poor reference line and due to sail billow, the glider has a significant amount of anhedral, especially in the outboard parts of the wings. We can see this easily in this photo by noting that we can see the top surface of the tip area of the near wing and the undersurface of the tip area of the far wing. With VG on, the outboard tips of the leading edge tubes would ride a few inches lower in relation to the line of the keel tube, but there would be much less billow in the sail, and the glider would therefore have much less anhedral in the outboard parts of the wings.

(To be added: side view of inverted Airborne Blade with VG on. Oblique and side views of Wills Wing Ultrasport during ground-handling in wind, with taut side wires, VG on and VG off.)

Diagrams and graphs illustrating some interesting aspects of the geometry and aerodynamics of flex-wing hang gliders: (note--some of these diagrams pertain to gliders that are thoroughly obsolete, but the geometry is still of interest.)

This diagram shows how sail billow creates washout in the case of a pure Rogallo wing with a conical sail cut and straight leading edges. Note that if we were to view the wing from directly above and slice the wing vertically downward with a blade held parallel to the keel, at various points along the span, the resulting cuts would follow the lines drawn on the surface of the near wing. In other words these lines represent airfoil sections. This is easier to see if the reader also imagines the same lines drawn on the surface of the far wing. With this in mind, note the extreme washout near the tip. Interestingly, if the leading edge is curved so that each wing is defined by a cylinder rather than a cone, this washout vanishes. (Source of diagrams: "The Hang Glider's Bible" by Michael A. Markowski (1977))

These graphs illustrate that sail billow creates washout in the case of a pure Rogallo wing with a conical sail cut and straight leading edges. Note the line representing "aerodynamic twist" versus span in the upper graph. Note that the middle graph shows that the tip area will be creating negative lift when the wing as a whole is at the angle-of-attack that yields the maximum L/D ratio. It's not clear why, according to the bottom graph, no part of the wing develops negative lift when the wing as a whole is at the angle-of-attack that yields the min. sink rate (which corresponds to the maximum value of (Lift cubed)/(Drag squared)), or why there is such a large difference in overall lift coefficient (1.0 versus 0.4) between the min. sink rate angle-of-attack and the best L/D angle-of-attack, since with such a draggy wing, the angle-of-attack difference and airspeed difference between min. sink and best L/D must be small. Perhaps some aspects of these graphs are not completely correct; at any rate the relationship between sail billow and washout is clear. (Source of diagrams: "The Hang Glider's Bible" by Michael A. Markowski (1977))

Here are a few more general rules of thumb about the geometry of twist (washout) and dihedral and anhedral. These rules of thumb are specifically intended to apply to antique and modern flex-wing hang gliders, where the sail shape is influenced by sail billow and whatever battens and sprogs are present. To keep things simple we'll aim these rules of thumb at a simplified aircraft with the following characteristics:

* Swept, linear leading edges, and trailing edges that are unswept or have somewhat less sweep than the leading edges. In other words, a swept or delta planform.

* The leading edges may appear to have some anhedral, some dihedral, or neither, in relation to the wing root chord line or "keel".

* The wing surface is smooth and continuous without abrupt hinge lines. For example, the rules of thumb won't really apply if we've raised or lowered defined wing flaps, regardless of whether or not the flaps run the full span of the wing.

Though these rules of thumb don't take into account details like variations in wing camber etc, they will serve well as a general guide in most instances. These rules of thumb are meant to be applied with the wing's mean chord line in a horizontal position, but in the case of a typical flex-wing hang glider with an appreciable amount of sail billow, the rules of thumb are not extremely sensitive to the glider's pitch attitude. These rules of thumb may or may not be generalizeable to other wing shapes (e.g. unswept wings).

1) Any portion of the wing where the trailing edge rises as it runs from root to tip will have a dihedral geometry.

2) Any portion of the wing where the trailing edge descends as it runs from root to tip will have an anhedral geometry.

3) If the leading edge of the wing has very little sweep, then wherever the trailing edge of the wing rises as it runs from root to tip, the "washout" or negative twist in relation to the wing root will tend to increase, and wherever the trailing edge of the wing descends as it runs from root to tip, the "washout" or negative twist in relation to the wing root will tend to decrease. The extreme case of this geometry would be a wing with constant chord--i.e. with defined tips fully as long as the root chord--in which case the rise and fall of the trailing edge would correspond entirely to the increase and decrease in the washout or negative twist in the wing, in relation to the root chord line.

4) If the leading edge of the wing has a great deal of sweep and the trailing edge does not--i.e. if the wing chord is large at the root and small at the tip--then any "billow" in the sail or wing will tend to create washout or negative twist that steadily increases from root to tip, and the wing will tend to have more washout or negative twist at the tip than anywhere else. We saw this situation in the diagram for the conical Rogallo wing given above.

Because of the geometry expressed in item 3, some modern flex-wing hang gliders may have their greatest amount of washout or negative twist slightly inboard from the wingtips. Regardless of this, for any given part of the wing, if the trailing edge is descending as it runs from root to tip, then that part of the wing will have an anhedral geometry. The washout is really not the cause of the anhedral geometry, rather the downward "fall" in the trailing edge as it runs from root to tip is the cause of the anhedral geometry. Note that if we increase the washout at the wingtip of a flex-wing hang glider by raising the trailing edge of the washout strut or defined tip tube, this will decrease the "fall" in the leading edge as it runs from root to tip in that portion of the wing, which will decrease the anhedral geometry of that part of the wing.

Photos of models to illustrate "Seibel's theory of swept hinge lines". The theory: when a matched pair of aerodynamic surfaces have aft-swept hinge lines, we create a dihedral geometry when we lower the surfaces and we create an anhedral geometry when we raise the surfaces. When a matched pair of aerodynamic surfaces have forward-swept hinge lines, the opposite is true: we create a dihedral geometry when we raise the surfaces and we create an anhedral geometry when we lower the surfaces. In these photos of these models, the relationship of the "leading edge tubes" to the "keel tube" or "fuselage tube" is the same in every picture. The leading edges are swept and in some of the photos the wing panels have been rotated up or down, pivoting around the swept leading edges. Where the trailing edges of the panels have been lowered this has created a dihedral geometry--in an oblique view, we can often see the bottom side of the panel nearest the camera and the top side of the panel furthest from the camera. Where the trailing edges of the panels have been raised this has created an anhedral geometry--in an oblique view, we can see often see the top side surface of the panel nearest the camera and the bottom surface of the panel furthest from the camera.


Wing originally flat, trailing edge lowered, creates a dihedral geometry, mean chord line horizontal, side view
Wing originally flat, trailing edge lowered, creates a dihedral geometry, mean chord line horizontal, head-on view
Wing originally flat, trailing edge raised, creates an anhedral geometry, "keel" horizontal, side view
Wing originally flat, trailing edge raised, creates an anhedral geometry, mean chord line horizontal, side view
Wing originally flat, trailing edge raised, creates an anhedral geometry, mean chord line horizontal, head-on view
Wing originally flat, trailing edge raised, outer panels only, creates an anhedral geometry in outer panels, "keel" horizontal, head-on view
(more photos to be added)

"Seibel's theory of swept hinge lines" applies best to discrete wing panels, but it can also serve as one way to think about how sail billow and wingtip washout affect the dihedral or anhedral geometry of a modern flex-wing hang glider. As the trailing edge of the sail billows upward in the central part of each wing, the sail billow can be thought of as a set of discrete "bends" in the wing surface along a set of defined "hinge lines". (Photo 1).These "hinge lines" are swept forward on the inboard part of wing (so that the billow creates a dihedral geometry on the inboard part of the wing), and these "hinge lines" are swept aft on the outboard part of the wind (so that the billow create an anhedral geometry on the outboard part of the wing). On this model, the "hinge lines" on the wing on the viewer's right are drawn in a way that includes wing-tip washout as well as billow. The lines on wing on the viewer's left only show the effects of billow; the wingtip has not been allowed to wash out. Wingtip washout appears to detract from the aftwards sweep of the "hinge lines" on the outboard parts of the wing, so that the sail billow appears to create less anhedral on the outboard part of the wing than it would if the wing had defined tip struts with zero washout. (We can see the same geometry in this photo: if we pulled the tip struts downward to make them parallel to the keel, eliminating washout, the outboard part of the sail would end up with more anhedral). For a much less complete visualization of the effects of sail billow, we can simply think of sail billow as an upward rotation of the entire left and right wing panels, with the swept leading edge tubes serving as the hinge lines. In other words, sail billow causes the average chord line of each wing to be inclined in a nose-down, tail-up manner in relation to the line of the keel tube. As demonstrated by the above models, this would create an anhedral geometry, even if the leading edge tubes were completely "in plane" with the keel tube.

Diagrams and graphs illustrating some interesting aspects of the geometry and aerodynamics of swept or delta wings:

Illustration of the yaw torque (weathervane effect) generated by a sideways airflow (sideslip) interacting with a swept wing. See the rightmost diagram in the middle of the page. This diagram also shows that when we view the aircraft from above, the leading edge of the "upwind" or "leading" wing meets the relative wind more "squarely" than does the leading edge of the "downwind" or "trailing" wing. In other words, the "upwind" or "leading" wing has less sweep in relation to the relative wind than does the "downwind" or "trailing" wing. This means that the "upwind" or "leading" wing will experience a higher lift coefficient than the "downwind" or "trailing" wing. In other words, the "upwind" or "leading" wing will create more lift than the "downwind" or "trailing" wing. This will create a dihedral-like roll torque in the "downwind" direction--in this diagram, the right wing will tend to rise and the left wing will tend to drop. (Source of diagrams: "Aerodynamics for naval aviators (NAVWEPS 00-80T-80)" by Hugh H. Hurt (1965, Office of the Chief of Naval Operations, Aviation Training Division, for sale by the Supt. of Documents,US Govt. Printing Office))

Illustration of the reduction of lift coefficient due to sweep, and the way that this is most pronounced at high angles-of-attack. See the uppermost diagram. This diagram is the key to understanding why the dihedral-like roll torque created by a swept wing in the presence of a sideways component in the relative wind, is most pronounced when the wing as a whole is flying at a high angle-of-attack. (Source of diagrams: "Aerodynamics for naval aviators (NAVWEPS 00-80T-80)" by Hugh H. Hurt (1965, Office of the Chief of Naval Operations, Aviation Training Division, for sale by the Supt. of Documents,US Govt. Printing Office))

Figure illustrating adverse yaw caused by the "twist" in the relative wind during rolling motions from John S. Denker's superb "See How it Flies" website.

I've added an experimental controllable rudder to these hang gliders: Wills Wing Spectrum, Airborne Blade, Wills Wing Skyhawk, Wills Wing Raven.

I've also used a small drogue chute attached to the wingtip as an alternate way to explore the "coupling between yaw (slip) and roll" of each of the flex-wing hang gliders listed above. The ruler is 18 inches long. Most of the tests used smaller chutes (especially in the initial trials) and this large one was only used at low airspeeds; at high airspeeds (low angles-of-attack) the roll torque (acting to roll the glider toward the wingtip without the drogue chute) due to the glider's "negative coupling between yaw (slip) and roll" was uncomfortably large. The purpose of deploying a drogue chute from the wingtip of a hang glider was to investigate whether the "wrong-way roll torque" observed when flying with the rudder was primarily due to the fact that the rudder was exerting a sideways force on the keel and distorting the airframe, or primarily due to the way that the wing's anhedral geometry was interacting with the sideways airflow component that was created by yawing the nose of the glider to the side (in relation to the actual direction of the flight path and airflow or relative wind). The latter was shown to be the case as similar results were obtained with the wingtip drogue chutes, which would have distorted the airframe in a very different way. #2, #3.

Here are some photos of hang gliders with the wingtip-deployed drogue chutes in place, before flight. This set-up was difficult to photograph, but if you look closely, you can see the wingtip-deployed drogue chutes enclosed in small containers (socks), one or more on each down tube. The pink strings run from the drogue chutes out to to an eyelet on the wingtip (or more precisely, an eyelet at the end of a rod that served as an extension of the most outboard part of the leading-edge tube) and back to the down tube. When a drogue chute was pulled from its container and dropped into the airflow, it ended up trailing behind the wingtip, exerting an aftwards force on the wingtip-mounted eyelet, which created a yaw torque. To jettison the chute, the string was cut or pulled loose at the the point where it was attached to the down tube. Note that the strings are taped to the flying wires to keep them from snagging in brush during launch; it took some experimentation to find a way to do this that would hold firm, yet would release cleanly when I applied some tension to the strings before deploying the drogue chutes. (I always checked that the strings were unentangled and free of foreign debris before I deployed the chutes, or else there would be a risk that the string would not feed cleanly through the eyelet when I was ready to jettison the chutes). On many of these flights I carried 1 or 2 chutes on each side so the amount of yaw torque could be incrementally increased, and also to allow another deployment in case a chute tended "fly" unusually low or high rather than directly behind the wingtip or in case a chute had to be cut away for some other reason before meaningful data could be collected. Please contact the author for more safety-related information before attempting to replicate this experiment! #2, #3, #4, #5, #6

Slip-skid bubbles (analogous to a slip-skid ball, but deflect in the opposite direction) for monitoring aerodynamic sideforces in (hang gliding) flight. This "probe" also includes a centrally-mounted yaw string, which allows a pilot to observe the details of hang glider yaw (slip) dynamics much better than does a "telltale" on one or both of the nose wires. Telltales on the nose wires are impossible to view accurately in flight because of parallax. This probe also inludes reference wires to help the pilot precisely judge the bank angle (by comparing the wires with the horizon). Interested readers are encouraged to make a few flights with a centrally-mounted yaw string (the bubbles and the reference wires aren't necessary for the most interesting observations) and observe the glider's yaw (slip) behavior in response to strong roll and pitch inputs. Side view #1, #2, stowed in tube on front side wire). (Simpler version--this one was kept in place for launching and landing but the elastic-band mounting system allowed the "probe" to move out of place if needed. #2).

Hang glider with "bowspirit" extension to mount forward yawstring for observations of the curvature of the relative wind in turning flight. The "crossbar" near the aft edge of the yaw string is a reference guide to allow the pilot to better judge the angular deflection of the yaw string. #2, #3

Photo of probe on instrumented research sailplane: the "weathervane" device measures yaw (slip) and the "sideways weathervane" device measures angle-of-attack. View of same probe on right wing of sailplane in flight. (Source: "Quiet Flyer" magazine v.11 n.8 August 2006 p. 78 "News from research students: Idaflieg Summer Meeting 2005" by Jochen Ewald, photos uncredited)

This aircraft has an inverted slip-skid ball for use in negative-G flight as well an an upright slip-skid ball for use in positive-G flight. In an aircraft with no prop wash over the nose, a yaw string would work in all flight conditions including 0-G and negative-G flight. (Source: uncredited photo from photo collage in "Flying" magazine v.133 n.7 July 2006 p. 80 "A history of IFR in light airplanes" by Richard L. Collins)

An extreme example of a slip: sustained knife-edge flight by an RC model. The rudder is deflected to the aircraft's right, forcing the nose to point to aircraft's right in relation to the actual direction of the flight path and relative wind. The aircraft is being forced to fly in a yawed (slipping) attitude in relation to the actual direction of the flight path and relative wind. The relative wind is impacting the left side of the fuselage, creating an "aerodynamic sideforce" that acts toward the aircraft's right. This sideforce happens to point in the vertically upward direction in relation to the external world, supporting the aircraft's weight. Since in this particular case the aerodynamic sideforce generated by the impact of the relative wind against the fuselage has no horizontal component acting toward the left or right in relation to the external world, the wing must be kept at the zero-lift angle-of-attack so that no net horizontal force arises to make the flight path curve toward the left or right in relation to the external world. (More normally, i.e. with a less-than-vertical bank angle, to produce a non-turning straight-line slip the wing is kept at a positive angle-of-attack, and is banked in the opposite direction as the nose is yawed.) In the photo, the purely horizontal direction of the flight path and relative wind is revealed by the (faintly visible) smoke trail coming out of the exhaust stack on the aircraft's right side and streaming past the aircraft's right wing. The impact of the airflow against the left side of the fuselage is illustrated by the path of the smoke trail coming out of the exhaust stack on the aircraft's left side. (Source: "3D Flyer" magazine v.3 n.5 September/October 2006 p. 46 "The 2006 Joe Nall event" by John Prescott, photos uncredited).

Another example of sustained knife-edge flight by an RC model. The direction of the flight path and relative wind runs parallel to the top and bottom edges of the photo. See comments above. (Source: "3D Flyer" magazine v.3 n.5 September/October 2006 p. 81 "E-flite Brio 10" by Danny Snyder, photos uncredited).

P-51 Mustang: this view is similar to what we would see if the aircraft were flying directly toward the camera in a straight-line (non-turning) slip, with the pilot applying right rudder and left bank. Note that the left side of the fuselage is visible. (source: "Warbirds digest" magazine n. 9 July/August 2006 p.57 credited to John Lauderback)

Video of sustained straight-line (non-turning) slip from camera mounted on landing gear. Note that the aircraft stayed over the extension of the runway centerline throughout the entire video. The wings-level attitude near the moment of touch-down suggests that there was no significant crosswind. In other words, the actual direction of the flight path through the airmass, as well as the ground track, was aligned with the runway heading throughout the entire video. Note that during the slip, the aircraft is yawed to the right of the actual direction of the flight path and relative wind, and banked to the left, and the flight path is not curving either to the right or to the left.

With no crosswind, the right rudder input and the left bank had to be removed before touchdown.

If there had been a crosswind from the left, the flight path through the airmass would have been aimed to the left of the runway heading in order to keep the aircraft positioned over the extension of the runway centerline. This would have been through throught the video, from the first frame all the way through the landing. The first (strongly slipping) part of the video might have looked about the same, except that the same aircraft heading would have represented a stronger application of right rudder, and more left bank would have been needed to prevent the flight path from curving, and the aircraft's descent rate would have been even higher, because the aircraft would have been flying more "sideways" in relation to the flight path through the airmass. Then at some point before touchdown when the pilot was no longer trying to create extra drag, he would have relaxed the right rudder enough to align the nose with the runway, and would have reduced the left bank enough to preserve the straight-line flight path. At this point nothing has changed in the flight path or ground track--the flight path through the airmass is still aimed to the left of the runway heading and the ground track still coincides with the extension of the runway centerline--but now the wheels are aligned with the ground track so no sideways loads will be imposed on the wheels at the moment of touchdown. The aircraft is still in a steady-state condition and can be flown in this manner indefinitely (except for the fact that it is descending!) At the moment of touchdown, the left wing will still be low, and the rudder will still be deflected to the right, and the nose will still be aligned with the ground track and the runway heading. All this assumes that the pilot is a fan of the "slip" method of crosswind correction rather than the "kick out the crab" method of crosswind correction.

Link to notes on Cessna 190/195/LC-126 with "crosswind landing gear".

A "trike" instructor's website. Since it has no rudder, a "trike" is an example of an aircraft that in the presence of a crosswind, must be landed in a "crabbed" (non-slipping) attitude, with the nose of the aircraft aligned with the flight path through the airmass rather than with the ground track and runway.

A hang gliding instructor's website. Since it has no rudder, a hang glider is an example of an aircraft that in the presence of a crosswind, must be landed in a "crabbed" (non-slipping) attitude, with the nose of the aircraft aligned with the flight path through the airmass rather than with the ground track and runway or "landing line".

A paragliding instructor's website. Since it has no rudder, a paraglider is an example of an aircraft that in the presence of a crosswind, must be landed in a "crabbed" (non-slipping) attitude, with the nose of the aircraft aligned with the flight path through the airmass rather than with the ground track and runway or "landing line".

(More photos and images to be added.)

 

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