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THE LAWS AND THE COMMENTARIES.

Everything I know about single line kites (which is less than I thought I did).
Tversky and Kahneman's groundbreaking empirical studies of human behaviour (see August 2012 Newsletter) convincingly show that experts in complex fields (like the stock market and weather forecasting), may not only be worse at predicting future trends than the ordinary informed person, but remain erroneously convinced of their special competence even after being presented with irrefutable evidence to the contrary.
Knowing so much about their subject, they frame everything within that knowledge set, and therefore fail to give enough weight to randomness and external influences.
This is called the framing effect.
And, their persistent overconfidence comes from being subject, as all of us are, to what can be called the self belief bias, best illustrated by how, when things go well we take personal credit- but when things go wrong, blame bad luck or someone else.

These revelatory insights made me think again about how well I understand the behaviour of single line kites (a very complex field).
Unfortunately, after considering this as dispassionately as I could, the answer was; not very well at all, not nearly as well as I had thought I did.
Fortunately this has immediately led to a better success rate in dealing with recalcitrant kites. By the simple expedient of trying not only the changes indicated by whatever theories I'm currently in thrall to, but their opposites as well, I'm now getting problems fixed at nearly twice the rate.
Seems I'd been far too confident that I knew which amongst many effects was the dominating influence in particular circumstances.
Nearly twice the success rate, but not quite- and the difference, small though it is, represents those few things that were actually true amongst all the things I thought I knew.
And here they are:

1.
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, the weight force can be in front of or behind the acting point of lift forces, but will usually be behind.
Commentaries on 1:
If other relationships including the line pull angle/position, and dynamic interactions are supportive, an 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.
Drag may be more or less than lift but lift must exceed weight.
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, then when the wind is 100km/hr, the lift force it generates may be as much as 100 times its weigh- which then gets 'lost in the noise' as an indicator of where 'up' is.
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).

2.
Basic stability 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 and increase its tendency to superstability. Volatile instability , also called hunting/looping instability, is lateral oscillation that build through figure eighting into looping. Superstability is an inclination to lean over and move off inexorably to one side or the other, in extreme cases until the kite is against the ground.

Commentaries on 2:
For a given kite, basic stability will not be the same at every line angle, even if the wind strength remains constant- it's not uncommon for kites to be volatile unstable at low line angles (while climbing for example) but superstable once they get to their apex.
Also, it matters where the drag forces act relative to the axis a kite rotates around when it becomes unstable. For example, a parafoil that is volatile unstable may sometimes be cured by increasing the opening heights of the outer cells while decreasing the opening height of central cells. Moving drag forces further from the kite's centre line improves their capacity to damp out volatile instability without increasing total drag at all (so they still fly at the same line angle).

3.
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 and increase its tendency to superstability. For long narrow kites the effect is opposite.
This is for two reasons;
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).
And, moving mass further from the axis of rotation increases it's rotational inertia (like a flywheel) which slows responses to perturbations.
Commentary on 3: This is a very powerful effect, but often underappreciated because to use this to shift the balance between volatile and superstability, it's almost always necessary to make a completely new kite. For parafoils, a change in width to length ratio of even 5% can tip a particular design from volatile instability into superstability.

4.
Soft kite scaling: As ram air inflated kites are made larger, the inertia of the mass of air trapped in the cells disproportionately slows their response to being knocked askew (by turbulence or whatever). This is because the 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. Large ram air inflated kites are therefore inclined to superstability.
Commentaries on 4: 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. Framed kites are also subject to similar scaling disproportionalities- but to a lesser extent.

Forever a work in progress, but increasingly useful for me- and I hope for you.

This newsletter will also appear under the suitably pretentious "Laws and Commentaries" title on the peterlynnhimself website, and in this location will be corrected and extended from time to time. How much of it is truth will no doubt be resolved in the fullness of time!


Peter Lynn, Chengdu, China, October 1 , 2012

PS. Hopefully Robert (van Weers), who runs this website, can be persuaded to do pretty pictures to make visualisations easier- these will be added as they become available.




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