Why Kites Don’t Fly
by Peter Lynn
(Found in Kiting Magazine 2011 Vol 33 Issue 2)
Thoughts on Single Line Kite Stability For a kite to fly on a single line, it must, as the most basic condition, have some way to detect which way is up. All single line kites that aren’t under some sort of remote control do this by having their centre of lift position (CL, where lift forces act) above their centre of gravity (CG, where weight forces act). The pendulum effect that this creates causes such kites to point upwards, and upwards they will fly, until they get to a line angle at which wind-generated lift exactly matches the kite’s weight (when the kite is said to be at its apex) disregarding dynamic effects of course.
But unfortunately, we can’t disregard dynamic effects because they very often prevent kites from flying stably at their apex. And, at some upper wind speed, they will always prevent kites from doing so. This is because, while the lift (and drag) forces that drive dynamic instabilities increase with the square of wind speed, the weight force (from which the kite derives its upward seeking tendency) is constant. At some wind speed therefore, the pendulum effect will be overwhelmed by aerodynamic forces and the kite will crash — if it doesn’t break first.
Dynamic instabilities derive from apparent wind effects; changes to the air speed experienced by a kite that are caused by its own movements. Of particular significance for dynamic instability is the relationship by which, when a kite is turning, the lift on the faster wing will increase by more than the lift on the slower wing decreases.
It’s useful to consider two main failure modes for single line kites. One, over correction, is when a kite reacts too aggressively while re-aligning itself with the wind and triggers dynamic effects. The other, under correction, is when it reacts too slowly. An example of over-correction is when recovery from some directional displacement (a change in wind direction for example) initiates a series of increasing amplitude lateral oscillations that build until the kite starts to loop uncontrollably. An example of under correction is when a kite takes so long to recover from a directional displacement that while doing so it traverses completely to one side or other of its wind window and collapses.
In addition to the relative magnitude of a kite’s pendulum Why Kites Don’t Fly by Peter Lynn effect, the four main elements that influence over correction/under correction are tail drag (tails, trailing drogues etc), laterally disposed drag (drag sources to each side), lateral area (keels, flares, dihedral, anhedral), and longitudinal dihedral (often called reflex).
Tails are clever because they don’t begin to apply any corrective force to a kite until there is substantial angular displacement (tail drag increases with the sine of the angle of displacement, so by 10°, say, are providing 17% of the maximum corrective effect they are capable of). The beneficial effect of this is that tail drag allows a kite to adapt quickly to minor wind direction changes (quickly enough so that the kite will not shift too much laterally while doing so) but comes in with rapidly increasing corrective force if for some reason the kite gets seriously tipped. Tails will therefore rarely if ever make a kite’s response so slow as to cause under correction, unless their end catches in a tree or they are REALLY long. The bad bit about tails is that they cost lift to drag ratio (L/D). (L/ D is a general measure of aerodynamic efficiency. For gliders it defines how many metres they fly forward for every metre of sink. For traction kiting it measures how well you can go upwind. For single line kites, it determines line angle; in fact the tangent of the angle, relative to the horizontal, of the flying line at the kite, is exactly the kite’s L/D).
Laterally disposed drag — that is, having sources of drag out to each side of the kite — also has a clever effect; because drag rises with the square of wind speed, when a single line kite with substantial outboard drag gets into a destructive turn, the drag on the faster side will increase by more than the drag on the slower side decreases, providing active damping. Such drag elements will also decrease L/D of course, except if they are an intrinsic and essential part of the kite anyway. The insight being offered here, and it’s a major one, is that aspect ratio (AR, effectively width to length ratio) is the most powerful ‘costless’ (by L/D) dynamic instability cure available to kite designers. A way to make this understandable is to consider a square kite, 1m on each side, lifting area 1m2 (aspect ratio 1.0). If such a kite is built and is found to be inclined to over correct and go into destructive looping, then if it’s rebuilt to 1.25m span x 0.8m long (still 1m2 but now AR 1.56), it will have much less tendency to over correct, and may even be inclined to undercorrect. This is because the drag associated with the wingtips, while still having similar cost with respect to L/D, is further out from the kite’s centre of lift, so will be more effective in resisting any rotations (in the plane of its lifting surfaces) that the kite becomes subject to (that is, it slows turns). Adjusting a kite’s aspect ratio is therefore a way to get correction that’s neither too fast (loops out of control) nor too slow (flies off to one side or the other and crashes or stalls). Wingtip drag isn’t referenced in any way to up/down, all it can do is slow down turns — and of course this can be a bad thing when it slows a desirable recovery — but on balance it is hugely beneficial because it slows down all the movements which energize dynamic instability, unplugs their power source so as to speak.
The third main useful stabilizing element, lateral area (flares, keels, dihedral, anhedral, etc), is also relatively costless by L/D, and can be very effective at damping out any incipient over correction but has to be of appropriate magnitude and carefully positioned. If a kite with substantial lateral area (as a proportion of its lifting area) is subject to an angular disturbance (that is, the longitudinal axis of the kite gets out of alignment with the wind direction), the aero forces acting on this lateral area can cause the kite to move a long way sideways across the wind window before the pendulum effect gets it back in line — that is, excessive lateral area can promote under correction. Clearly, the longitudinal placement of lateral area will have an effect also. If disposed mainly behind the kite’s CG, it can promote rapid re-alignment but may also exacerbate dynamic effects (over correction). If in front of the kite’s CG, it will tend to cause under correction and make it very difficult for the kite to fly centrally (that is, directly downwind of the line tether point). Although dihedral (upward angled wings) and anhedral (downward angled wings) have some different effects on how single line kites react, they are primarily both just ways to get lateral area. There is a mistaken belief that dihedral is ‘stable’ while anhedral is ‘unstable’ but this comes from aeroplane experience and doesn’t generally apply to kites. When an aeroplane rotates around its longitudinal axis, if the downside wing loses projected area at a faster rate than the upside wing gains projected area then the rotation will become self-promoting. Aeroplanes are made with dihedral so that they are auto-stable in rotation about their longitudinal axis. For kites, bridles generally prevent this sort of rotation anyway. Kites with centre line bridling (most diamond kites for example), require dihedral for the same reason that aeroplanes do, but kites with laterally disposed bridles (like sleds for example) don’t.
Longitudinal dihedral, or reflex, the fourth and last major single line kite stabilizing element has the obviously beneficial effect of reducing or eliminating luffing tendencies, but its underlying influence is more profound. Because aerodynamic lift forces drive instability (of both the over correction and under correction types), anything that decreases lift without changing other things too much will generally improve a kite’s stability. “More longitudinal dihedral” is just another way of saying “less camber,” and having less camber will cause less lift to be generated, (a generally applicable aerodynamic effect). Introducing longitudinal dihedral therefore deals directly to over correction, but it’s a rather ugly solution, a last resort (usually taken when graphics considerations don’t permit other more efficient form changes), because it also directly reduces L/D, and by a lot if it’s to be effective. It’s influence on under correction is equivocal: reducing lift does reduce the driving force that makes a kite traverse off to the side before it’s pendulum effect can straighten it up (less lift means that it won’t get as far before correction occurs). But, longitudinal dihedral also shifts the kite’s CL rearward (nearer to its CG), which reduces the effective pendulum length and therefore its corrective effect (while adding to its usefulness against over correction).
More Reasons Why Kites (Often) Don’t Fly
There are a large number of effects that influence kite stability (or more usually the lack of). I’ve described some fundamental ones. Here are some more. The approach in the first section was to consider effects from the perspective of how a kite responds when its axis becomes misaligned with the wind direction. Optimally, kites should neither undercorrect nor overcorrect. This perspective is not only fundamental to kite stability but usefully leads to explanations as to why particular kites behave (and misbehave) the ways they do. Even more usefully, it leads to predictions as to the effect on stability that possible changes will have. Someday, these may even be quantifiable to some extent.
It is the angle of the line relative to wind direction that matters, not line length in the absolute sense, but this angle is a function of the line’s length (and the kite’s size) so it’s usually called the “line length effect” to avoid using “line angle”, which has multiple associations with stability influences. When a kite is laterally displaced from its proper position directly downwind from the tether point, its line will then have some angle to the wind when viewed from above, and the shorter the line’s length, the greater this angle will be. There will then be a component of line tension acting to pull the kite back towards its central position equal to the sine of this angle times the line’s projected length. The magnitude of this centralizing force is therefore directly proportional to line length for any given lateral displacement of the kite. This will tend to exacerbate any over correction tendency and mitigate under correction. A more rigorous description requires consideration of the line’s angle in the vertical plane also, but the effect is more easily understood in the first instance by considering horizontal angles only. An often experienced practical demonstration of this is when large Cody type box kites (which tend to over correct because they have so much lateral area to rearward, though this is masked in normal flying by their high lateral area to lifting area ratio), are being pulled in. By the last few meters of line they are often over correcting so violently as to be completely uncontrollable. An opposite example is that kites which are virtually un-flyable because of severe under correction can be usable when tethered directly off their bridles; that is, flown on a VERY short line.
Kites don’t scale That is, as they are made bigger, their behavior changes. Aerodynamic forces increase with the square of the wind speed, but to retain the same margin of strength in proportion to its size as a kite is made bigger, its weight will need to increase with the cube of dimension. So, larger kites will generally be heavier in proportion to their area, and this affects their flying — most obviously in light winds but also in their under correction/over correction balance. Kites that tend to over correct will do this even more so as their weight/area ratio increases. Kites that tend to under correct will do this less as their weight/area ratio increases. However, in practice, this can be masked by other effects. A practical demonstration of this is the way that kite behavior changes in rain; extra weight pushes them toward over correction, although this can be masked by fabric stretch effects.
For framed kites, builders very often don’t increase the strength and rigidity of the structure proportionally when they make bigger versions. A result of this is that such kites tend to distort more in stronger winds, and the extra drag that this generates may damp out the additional over correction that comes from the increasing weight/area ratio. Of course, such kites will also deform so severely as to become un-flyable in wind speeds that their smaller scale version was happy in (or they’ll break). For ram air kites (often called soft kites) up to sizes of even a few hundred square meters (that is, VERY large kites by most standards) weight/area doesn’t tend to change at all. This is because available fabrics are much stronger than necessary for smaller soft kites. However, the mass of air inside such kites increases with the cube of dimension while their area increases with the square. Mass is not the same as weight in this context. The internal air mass is neutrally buoyant, doesn’t make any contribution to the kite’s pendulum effect at all, but by Newton’s approximation of Einstein’s theories, it has inertia, so requires the application of a force to get it to move or to stop moving. For ram air inflated single line kites, the inertia of this air mass proportionally slows the rate of recovery from any misalignment as the kite is scaled up, causing very large ram air inflated kites to tend, often terminally, towards under correction. A partial solution to this is to use thru-cords rather than ribs by the principle that the internal air mass is then able to rotate (or not rotate) independently to some extent. The kite’s weight pendulum when acting to correct a misalignment isn’t then resisted by the inertia of all the internal air mass, but just of those bits trapped in corners. Octopus and Ray kites that were originally rib and skin construction did seem to have less inclination to under correction in larger sizes when re-designed using thru cords instead.
Why do stable framed kites seem to be much easier to build than stable soft kites? Perhaps it’s that there are thousands of years of experience behind framed kites and only 50 or so for soft kites, but there are two other reasons (at least). The first is that closed soft kites tend to have smooth curved upper surfaces in their leading edge areas, which promotes attached flow over the kite’s upper surface, significantly increasing the aerodynamic lift that such kites will have. Because the force driving instability for kites is aerodynamic lift, more lift equals less stability (of both the under correction and over correction type), other things being equal. In contrast, most framed kites have sharp edged leading edges which cause flow to immediately separate and ensures that they will rarely if ever have attached flow over their upper surfaces. This reduces lift and therefore improves stability. By this theory, open leading edge soft kites should tend to be more stable than closed styles (many Parafoils have open leading edges that encourage flow to separate over the top surfaces rather than remain attached) and they do generally seem to behave better. Why don’t we always design soft kites with open leading edges then? There are reasons, like appearance, for more lift (if there’s stability to spare), to retain internal inflation in turbulence, and to pressurize against water ingress when flying off boats. The other soft kite effect is that their rigidity keeps pace exactly with aerodynamic forces as wind speed increases (to the limit of fabric impermeability anyway). However, their weight pendulum effect does not increase at all, so will eventually be overwhelmed by these aerodynamic forces. In contrast, framed kite structures deflect progressively more as wind increases, offsetting at least some of the increase in lift forces as the wind speed increases. Framed kites are therefore more likely to remain stable through to higher wind speeds than soft kites.
Von Karman Effects
These are airflow-driven rhythmic oscillations that, in our case, causes cylindrical form kites to oscillate in some wind speeds. The most easily recognizable every day von Karman effect is the “vortex street” visible downstream of a post sticking out of a stream. When encountering the post, flow splits evenly, half going around each side. However, because of inevitable asymmetries in the post, the flow, and the universe, the split streams don’t arrive back at the downstream side at quite the same moment. The flow stream that arrives first then continues to be sucked around the post until it is, from an observer’s perspective, moving upstream against the main current. At some point it then finds this situation unsustainable, separates from the pole surface and is carried off downstream, turbulently. The opposite side stream then has its turn and repeats the process. The observer will see this as a succession of alternating turbulent eddies drifting off downstream and gradually re-merging with the stream’s flow. An effect of this is that the pole (in this case) will be subject to oscillating sideways forces as each vortex separates. Industrial chimneys have spiral flow interrupters on their upper reaches to prevent this rhythmic effect becoming destructive. I think that many large ram air inflated kites are subject to von Karman effects, Dolphin and Gecko styles in particular. Any kite for which airflow passes around some even approximately cylindrical form is likely to be. I should test this by using smoke trails, but haven’t as yet. I expect it is right though, because another characteristic of von Karman oscillations is clearly observable on these kites. This is that as wind speed increases, the lateral oscillations decrease and eventually cease completely, probably because at higher wind speeds, flow separates chaotically rather than periodically and also because the flow period gets out of synch with the kite’s mass. When oscillations are being caused by some dynamic effect of over correction, they tend to continue to increase with wind speed until the kite loops out. A way to eliminate von Karman effects is to have some feature that causes separation, like long fins for a fish kite. For themed kites, unfortunately, anatomical requirements often make such features unacceptable.
Speed Sensitive Aerodynamic Damping.
There is a diverse group of aerodynamic features that can act to damp out dynamic effects. Because they don’t kick in until one of the kite’s wings is travelling significantly faster than the other, they don’t change the kite’s fundamental over correction/under correction balance. Rather, they do allow kites with significant over correction responses to resist the build up of destructive dynamic figure-eighting that would otherwise occur. Because having a fast response to misalignment is desirable in a kite providing that dynamic effects don’t then get away, these are very useful tools for kite designers to have available. Delta kites have a version. When a Delta style kite starts to figure eight with increasing amplitude, the faster moving wing tip will have more load on it than the opposite slower one. This asymmetry of load distorts the kite’s form, causing the faster wing tip to twist off more, generate less lift and proportionally more drag. The slower wing tip will respond oppositely, generating more lift and less drag. This reduces the speed difference between the tips, damping out a dynamic build up that could otherwise become destructive. Rokkaku kites have a similar mechanism. When one side of a Rokkaku experiences higher apparent wind speed than the other side, asymmetry of aerodynamic forces causes the faster side to increase its camber and the slower side to flatten off. This increases the drag and decreases the lift on the faster side and decreases the drag and increases the lift on the slower side, which, as with the Delta mechanism, acts to prevent destructive dynamic effect building up. Many framed kite styles have this type of automatic built in dynamic damping, but soft kites don’t, except that most closed soft kites get some dynamic damping from internal pressure not holding inflation as well against external pressure on their faster wing’s leading edge as on the slower side. Differential speed sensitive air brakes could be fitted to the wings of soft kites to damp dynamic effects in the same way that the relationship between structures and skin do for Deltas and Rokakus. I’ve tried a few ideas for these and will do more work in this area when I get time (like by not going to so many kite festivals, yeah right!). Potentially differential air brakes should be able to offset a lot of the stability deficit that closed soft kites often seem to exhibit by comparison to open leading edge soft kites, and even to framed kites.
The Main Reason Single Line Kites (Often) Don’t Fly
It’s because kite stability is sensitive to angle of attack, the angle at which wind strikes a kite’s surface(s), and angle of attack (called A of A from now on) varies widely with line angle and wind strength. Specifically: A of A is high — close to 90 even — when line angle is low (while launching for example) and also when there’s barely enough wind to keep a kite up. A of A is low when a kite is flying at high line angle and in stronger winds.
The reason that kite stability is sensitive to A of A is because the point at which aerodynamic forces act on a kite (the centre of pressure, C of P) is a function of A of A and the distance between the kites C of P and it’s centre of gravity, (C of G, where the weight forces act) is THE most critical determinant of stability.
“A of A”, “C of P”, “C of G”. . . getting confused by all this jargon yet? These three are unavoidable, but figure 1 explains them visually, which always helps, and I promise there’ll be no more.
It’s a required characteristic for single line kites that the point at which a kite’s weight forces act (it’s C of G) must be below where it’s lift forces act (it’s C of P). This creates a sort of pendulum which points the kite upwards, without which, it will more likely try to fly under the ground than above it. And, as explained earlier, the length of this pendulum (relative to the size of the kite and other features it may have such as lateral area of course) determines whether it will under correct or over correct. A very short pendulum makes a kite tend towards under correction, a longer one to over correction (and there will be a range in between where it might be stable). (But just in case you were thinking how simple this all is, there’s an exception; VERY long pendulums can also be stable.)
It’s obvious from symmetry, that for a rectangular plate at an A of A of 90°, the C of P will be at half chord (figure 2). That this point moves towards the leading edge as the A of A decreases (figure 3) is not so obvious, and the reasons for it weren’t really understood until mathematical fluid dynamics developed sufficiently in the 19th century, but it is so. Most kites aren’t flat plates, but it’s still generally true that their C of P moves towards the leading edge as A of A decreases. (Or at least it does so until the A of A approaches zero, when it becomes very dependent on the particular airfoil shape and can go a little weird, but this needn’t concern us here).
Changes in A of A as wind speed and line angle vary cause the C of P to move along the kite’s axis, which changes the effective length of the pendulum, and can move it out of the range where stable flying occurs. In particular, they can cause the corrective effect exerted by a kite’s weight to be inadequate when the kite is flying at a high A of A. And, this is exacerbated by the reflexive or “nose-up” shape of almost all soft kites and many framed kites (including rokkaku’s, Indian fighters, and delta’s). “Nose -up” shape is used to prevent luffing (when the angle of attack becoming negative) and also to reduce the extent to which the C of P will move so far forward of the kite’s centre of gravity as to cause over correction when the kite is flying at low A of A. Unfortunately, as can be seen from figure 4, it also makes under correction more likely at high A of A.
There are many observed kite behaviors that are explained by A of A effects, and the one that is particularly annoying me just now is the repetitive swaying behavior of tubular soft kites (that is, fish shapes and similar). With aspect ratios generally much less than 0.5, tubular form kites are not very effective at generating lift (L/D’s generally less than 1.0). To develop enough lift to offset even their own weight, especially in light winds, they fly at high A of A (30° to 45° or even more) at which the C of P is likely to be not much above the C of G, and might sometimes even be below it for short periods (but not for any sustained period or else they won’t be flying. See figure 5). That the characteristic misbehavior of this style of kite is caused by their C of G being too close to their C of P is supported by various observations:
- Movement amplitude decreases when weight is added to the rear of the kite (providing the effect isn’t masked by the increase in A of A that this can cause)
- Movement decreases at higher wind speed, because A of A decreases (but over correction may then begin to occur).
- Flattening the kite’s front and narrowing the rear (shifting the C of P forward), without changing weight disposition generally reduces swaying.
- Adding drag (by way of drogues, etc.) to the rear helps a bit but doesn’t have as much effect as expected.
- Flying on a very short line helps, which is characteristic of kites that tend to under correction. The swaying that Ray (especially the smooth tail style) and Octopus type soft kites can get into when launching — sometimes even spinning — is also an A of A effect. It ceases when the kite gets to 30° flying angle or so and the supporting observations that apply to tubular form kites are also seen with these styles.
However, A of A effects are not confined to soft kites: The way that Indian and other bow-framed fighter kites spin rapidly when line is released (which allows bow pre-tension to pull the kite flat) is also an A of A effect. Of course it’s also partly due to their not having any lateral area (which has a directional effect) when there is no line tension, but mainly it’s because when flying at an A of A approaching 90°, the C of P moves so close to the C of G that the kite loses its sense of direction and spins around.
A of A effects also help explain why tails are more effective than drogues or other trailing drag devices for stabilizing errant kites. The difference comes from tails having weight as well as providing drag. The above shows why, at high A of A, kites tend to under correction, and at low A of A, to under correction. Drogues provide extra drag but have negligible weight. They slow the kite’s responses, so reduce over correction but don’t help with under correction. In light winds, a tail’s weight pulls the kite’s centre of gravity rearward to reduce under correction. In stronger winds when the kite will be flying at higher line angle (low A of A), tails generate enough lift to be largely self supporting. In this state, their weight doesn’t shift the kite’s original C of G down much so won’t exacerbate over correction. However, their longitudinal drag still acts to combat over correction and perhaps their resistance to sideways displacement helps damp movements as well.
This is a brief description of a complex and indeterminate field. Like all things that are subject to turbulent flow (the weather, for example), single line kites will never be fully predictable. But there are some things that are both true and useful that can be established, which is what I’ve tried to do. I’ve tested the above against the kites I see flying, and don’t think I’ve seen anything that falsifies any of it. However, there are so many overlapping effects and other influences that it’s sometimes difficult to see through all this fog to the fundamental relationships. No doubt I’ve made errors in at least some respects. I’ll modify and correct when these come to light. Back in 1973 I reckoned I’d have this done by my 30th birthday (1976), but it’s taken a bit longer.
You can find more of Peter Lynn’s insights at www.peterlynnhimself.com and www.peterlynnkites.com.