### SINGLE LINE KITE STABILITY, to October 2012.

Contriving an object that, solely by the relationships between its lift, drag, weight and line attachment point, can maintain itself at some elevated station in the centre of a wind stream seems likely to be difficult but maybe not impossible. That it should also be able to do so at every line angle from zero to nearly 90 degrees and in every wind from a whisper to a swirling gale is a hopeless fantasy - except that such things do exist- they're called kites.
Kites are simple, and at the same time complex beyond our understanding. Theory is not of much use.. At best we can know a few things that makes the process of building and flying kites more effective than a random process- but not by much- and making small changes to existing designs is still by far the best development approach.

A way of thinking about the stability of single line kites is to consider what happen in a wind shift. When a kite finds itself off to one side or the other, the line will be at an angle to the new wind direction (when viewed from above or below) and a component of line tension then pulls the nose of the kite towards the centre of the wind, causing the kite to lean over and begin to move back into alignment.
What happens next is crucial; There are kites, that for a particular wind strength and line length, straighten up just enough, soon enough so that they move back exactly to the centre and stay there after being displaced. There are no kites (or at least none I've ever seen) that will do this in all flyable wind strengths and for all line lengths.
More usually, kites go past centre before correcting again.
And if they go past centre by more than the amount of the original displacement, then it's very likely that a series of ever-building lateral oscillations then looping will ensue,.
Or they may fail to straighten up at all and move off inexorably to the other side of the wind until touching the ground.
With so many variables and feedback effects to contend with, the likelihood of there ever being a general predictive theory of single line kite stability is effectively zero.
But that we can't know everything, doesn't mean that we can't know anything:

Some things about single line kites which might be useful - and might even be true:

1. Upward Seeking. For all kites in stable single line flight, the point at which the weight forces act must be below where the lift forces act; so that they are upward-seeking. It is this relationship and this relationship alone which enables kites to sense which direction is up. In a vertical plane transverse to the wind, a kite's centre of gravity (where the weight forces act) can be in front of or behind the acting point of lift forces, but will usually be behind. In the horizontal plane, it must be below.
If other relationships including the line pull angle/position, and dynamic interactions (see 2. Feedback Effects below) are supportive, a tethered object which has both lift and is upward-seeking may be able to fly as a kite. In the absence of either of these characteristics it cannot.
Commentary: An unstated extra condition is, of course, that there must be wind (air movement relative to the kite's tether point in an approximately horizontal plane).
Drag may be more or less than lift but lift must exceed weight.
And because aerodynamic forces increase with the square of the wind speed, while the weight force is constant, for every kite, at some upper wind speed, upward-seeking will fail and the kite will become unstable. By illustration, if a kite can fly in 10km/hr wind, when the wind speed is 100km/hr, the lift force it generates may be as much as 100 times its weight- and the weight force will almost certainly then be 'lost in the noise' as an indicator of where 'up' is.

2. Feedback effects. Only a tiny percentage of tethered aerodynamic objects that have lift and are upward-seeking, are single line stable.
This is because various feedback effects cause them to be dynamically unstable.
Kite stability cannot be considered as the sum of various static effects. A kite's position, direction and velocity at any moment is determined not only by knowable quantities such as weight, centre of gravity, wind speed, lift coefficient, drag coefficient, centre of pressure and line attachment geometry, but also by what it was doing a second ago- which depends on what it was doing the second before that- and so on back to when it launched.
There are many forms of instability; stalls, luffs, spins , and an entire family of misbehaviour that derives from wind induced shape changes but the most common is volatile instability (increasing amplitude over-corrections terminating in looping, 3, below). For kites, this is the definitive destructive feedback effect. Damping is required to tame it. This is provided by aerodynamic drag, often assisted by tail(s)and/or lateral area. Damping effects have to be just enough to prevent lateral oscillations from building, but not so much that the kite can no longer find the centre of the wind.
Commentary: Currently there are no theoretical/analytical approaches which inform single line kite design, and it seems unlikely to me that will be in the foreseeable future, no matter how many numbers are crunched. There are just too many interdependent feedback effects in play for numerical modelling to be useful as a design, or problem solving aid- except perhaps for impracticably reductionist rigid forms- but probably not even for those.

3. Volatile instability, also called hunting/looping instability (lateral oscillations that build through figure eighting into looping) is the most common type of instability and is a function of the kite's drag to lift ratio. For a given kite, any increase in the ratio of drag forces to lift forces will decrease it's tendency to volatile instability.
Volatile instability is initiated when a kite doesn't straighten up quickly enough in responding to lateral displacement by (for example) a wind shift. Sideways movement across the wind window takes it past centre, requiring a further correction to bring it back and so on. If the amplitude of these corrections increases the kite becomes volatile unstable.
The reason that increasing drag forces relative to lift forces decreases volatile instability is because aerodynamic lift forces drive the lateral movement, while the damping of over-corrections is a function (amongst other things) of aerodynamic drag forces (notwithstanding that drag slows response).
Volatile instability can be reduced by either decreasing lift or increasing drag (or by a combination).
Commentary For a given kite, the inclination to volatile stability may not be the same at every line angle, even if the wind strength remains constant. It's not uncommon for kites to be well behaved at high line angles but volatile unstable at low line angles.
That volatile instability is an inverse function of a kite's lift/drag ratio (L/D), which defines the kite's aerodynamic efficiency (line angle) seems counter-intuitive and may surprise some kite fliers- but it seems to be true; not only because of the reasoning offered above but because every kite I've ever built or seen responds this way.
What it also indicates is that while kites with high L/D can be stable and kites with low L/D unstable, high L/D kites will be more inclined to volatile instability than kites with low L/D- and this too is true in my experience.
It isn't an exclusive relationship though; there are ways to combat volatile instability other than by decreasing lift or increasing drag;
For example; by using lateral area (keels or flares), by the use of tails, or by changing the relationship between the kite's centre of gravity and centre of lift.
Or, by moving the drag forces further out from the axis a kite rotates around when it is correcting- which boosts the function that drag has in damping out volatile instability without increasing total drag (so the kite will still fly at the same line angle). An example of this is that volatile unstable parafoils may sometimes be cured by increasing the opening heights of their outer cells while decreasing the opening heights of central cells- which shifts drag forces further from the kite's centre line.

4. Superstability: A tendency to move off inexorably to one side or the other, in extreme cases until the kite sideslips into the ground.
This is a phenomenon that parapents, hangliders and sailplanes experience during tow launching (when they are functioning as kites). That they are often unable to recover, even with extreme pilot action suggests how difficult a problem superstability can be for pilotless single line kites.
Kite superstability can be caused by fabric flares or keels that have floppy leading edges which 'pocket' out to one side causing the kite to lean over.
Or by excessive drag from a tail (best illustrated by how a tail that catches on an obstruction will inevitably cause the kite to fall over to one side or the other. Very long tails have this effect even when they're not caught on anything).
Or by there being too much lateral area ahead of the line attachment point relative to the amount balancing it to the rear. (An arrow will point into the wind if pivoted at its head, but as the pivot point is moved towards the flights, it will hang off to one side or the other).
Geese and crane kites with their long necks are susceptible to this.
And there are other causes as per the commentary below
Commentary: High aspect ratio (defined as span squared /area) like deltas, Genkis and rigid kites (including sailplanes being tow launched), are particularly susceptible to superstability, and I surmise that this is because their aerodynamic efficiency allows them to lean off to one side or the other to such an angle that they no longer generate enough lift in the vertical plane to support their own weight- and sideslip into the ground- sometimes with fatal results. That this reasoning is probably correct is supported by superstability being noticeably more likely as bridle lengths are increased (longer bridles resist recovery from sideslips).
High aspect ratio kites also experience more wind flow over their upper wing than over their lower wing whenever they lean to an extreme extent (because wind speed generally increases significantly with height, especially near the ground). This causes the higher wingtip to generate more lift than their lower wingtip and drives the kite inexorably towards the ground.
Superstability can also be caused by a kite's centre of pressure (where the lift forces act) being too close to its centre of gravity (where its weight acts). This dimension is the length of the pendulum that causes kites to be upward seeking. When this 'pendulum' is very short, it's correcting moment becomes inadequate, and in the time it takes for any lean to correct, the kite will have moved across to one edge of the wind. This dimension also has a profound connection to volatile instability- but it's not a simple relationship. When it is very large in proportion to a kite's size (difficult to achieve without hanging weights off the tail), flight will be stable but often jerky, and at a low line angle. Between the extremes of too short and too long, there is usually a zone when a kite is neither volatile unstable nor superstable, but I don't know of any quantitative method for determining this.

5. The Confusion. The reason why kites don't respond in reliable or predictable ways to changes in their angle of attack (by altering bridle lengths or moving the line attachment points) is that such changes have opposite effects depending on whether a kite is rigged to the lower angle of attack side or the higher angle of attack side of its optimum L/D (lift/drag) ratio (best flying angle) point. And unfortunately, the best angle of flight that any kite can attain will be when it is rigged to this optimum.
For a volatile unstable kite that is rigged to fly at an angle of attack that's steeper than it would be for best L/D, increasing this angle (by shortening the rear bridles for example), will reduce volatility (and make it pull more). For the same kite, decreasing it's angle of attack (by, for example, shortening the front bridles), will increase volatility (and decrease pull). However, if the kite is rigged to an angle of attack less than it would be for maximum L/D (that is, to fly flatter), it will become more volatile unstable (and pull less).
Commentary: That L/D is optimum at some angle of attack (use 10degrees as a first guess) and drops off if the angle of attack is either increased or decreased, is a well known aerodynamic effect, but causes endless trouble for kite fliers- though I expect that very few are even aware of this cause of their difficulties.
During the 70's and '80's , the only way I knew to counter volatile instability (framed kites and soft kites) was to shorten the rear bridles until the kite was nearly stalling- which also made it pull a lot (not ideal for large kites) and to not fly well in lighter winds.
By the middle '90's I'd realised (slow learner) from the above relationship, that an alternative solution would be to bridle kites to fly very flat. This reduced pull and improved light wind flying, but isn't always easy to accomplish because at lower wind speeds a kite's weight determines it's angle of attack (and at a steep angle), and it doesn't decrease to the limit eventually set by bridling until there is sufficient wind. During this angle of attack reduction, at some point the angle of attack will be optimal for L/D and may very well cause the kite to become terminally volatile unstable . Nevertheless, it did prove possible for most designs. From 1995 to 2000, Rays and Gecko's showed this transition most clearly (early maxi Gecko's were the strongest pulling kites for their size I've ever made - they routinely pulled cars around). Alas, I have not yet been able to stabilise Octopussies by this approach (because of their tentacle weight), and still have to use nose stalling - which is annoying because they need to be pulled down and reset whenever the wind increases (or else they go into terrifying loops).

6. Width and length effects. For a kite that has significant width relative to its length, making it wider and shorter for the same lifting area will decrease any tendency to volatile instability. For long narrow kites the effect is opposite.
The further drag forces are from a kite's axis of rotation, the more effectively they dampen volatile instability (as for the effect explained in the commentaries on 3 above).
Commentary: This is a very powerful effect, but often under-appreciated because to utilise it almost always requires making a completely new kite. For parafoils, a change in width to length ratio of even 5% may cure even quite destructive volatile instability.
The higher rotational inertia (flywheel effect) that wide short kites and long narrow kites share (relative to kites that are approximately as long as they are wide) slows response times to angular displacements- which seems to me to be always a bad thing. (The ideal is very rapid response with exact damping so that there is no over-correction; slow responses cause the kite to shift sideways before it recovers, potentially initiating volatile instability or even superstability.) . Rotational inertia effects are quantifiable (see scaling effects below) but to now, I have no certain understanding as to how significant they are for stability- except for knowing that there are wide short kites and long narrow kites and kites everywhere between these extremes that fly well.

7. Scaling Effects: As a kite is made larger, there are changes in three relationships that effect the way it responds to angular and lateral displacement, and that therefore effect stability.
-For rigid, framed, and even soft kites (for which fabric thickness must be increased for very large sizes- even when they have super ripstop reinforcement), area (and therefore lift and drag forces) increase with the square of dimension while structural weights increase at a bit less than the cube of dimension. Big kites are therefore heavier and/or distort more and aren't able to fly in strong winds.
-And, for large kites, the relationship between their rotational inertia (flywheel effect), weight, corrective moment (the length of the upward-seeking pendulum), and aerodynamic forces, cause them to respond more slowly to being knocked askew (by turbulence or wind direction changes for example). As far as I can figure so far, response time is inversely proportional to dimension squared. Large kites therefore respond much more slowly than small kites to lateral and angular displacements- even proportionally. This suggests that large kites should be more inclined to superstability and less inclined to volatile instability than small kites- but from experience, I'm not sure that this is true.
- But what I am sure about, is that this is true for ram air inflated kites- because of disproportionate increases in the mass of air trapped in the cells. A soft kite's area (and weight if the same fabric is used) increases with the square of dimension while the volume of air it contains (at 1.23kg/cu.m) increases with the cube. This causes larger ram air inflated kites to tend towards superstability.
Commentary: When the area of a ram air kite is increased by x 2, the mass of air it contains increases not by a factor of 2 but by 2.83. A negative consequence of this relationship is that every successful ram air inflated single line kite will fly optimally in only one size- make it bigger and it will be inclined to superstability, smaller, towards volatile instability. To counter this effect, the Guinness record size kites we have made use thru cords rather than cells so that most of the internal air mass does not have to rotate with the kite's body.

Forever a work in progress:
Updated to 3 October 2012.
Peter Lynn.