(The question is why single line kites (don't) fly- as always.)
Not being an Einstein, it's taken a LONG time for me to come to something that's both understandable (like general relativity, yeah right) and simple (like E =MC2 ). AAGH Indeed
The first law of (single line) kites is well established now, and VERY simple in it's meaning, even if sometimes a bit obtuse when put into words. Basically it's that kites point up (rather than down or sideways) because their weight (by the dead hand of gravity) acts at a point below where their lift (from wind forces) pushes them up. If the lift forces act at a point below an object's centre of gravity then it quickly turns upside down and dives groundward- and isn't a kite by any definition.
But this first law is a 'necessary condition', not a definition of what is, and is not, a kite. Not everything with it's centre of gravity below it's centre of lift will fly as a kite - in fact most things won't. This is because of various instabilities - feedback effects- that can easily overwhelm the upward-pointing mechanism of the first law.
Of all the various forms of instabilities that kites are subject to, one looms largest;
And that is what I generally call 'volatile instability'; left to right movements of ever increasing amplitude that morph into looping and usually end in a crash.
Following is a useful theory as to why and how volatile instability relates to a very basic characteristic of every kite.
The 'second law' of (single line) kites:
I can be very precise about this, and will be if you insist, but the essence is that (volatile) instability is driven by lift and damped by drag.
And I would guess that most if not all kitefliers know half of this already, at least intuitively .
Just about everyone who has ever flown a kite knows to add tail (which is pure drag) to stop diving and looping.
The not quite so intuitive other half is that anything that reduces lift has the same stabilising effect.
It's then a simple step to understanding volatile instability as a function of lift/drag ratio.
Which is just a succinct way of saying that anything that increases drag relative to lift will make a kite less susceptible to volatile instability.
A statement of the second law is therefore:
Instability is a function of lift/drag ratio.
Which can also be stated as Stability is a function of drag/lift ratio- but seeing as lift /drag (L/D) is the usual and recognised ratio for just about everything that flies, it's appropriate to state it in the first form.
Drag is the aerodynamic force pulling the kite downwind.
Lift is the aerodynamic force lifting the kite- at 90 degrees to the drag force.
About now I should list exceptions and conditions, and if you want to be pedantic, there are some; Angle of Attack
Except that firstly for those that are (pedants that is), I would first direct you to what I haven't said; and I haven't said that this law is exclusive. I am saying that it always applies, but I'm not saying that other things don't apply as well.
Nor am I saying that all kites are equal; in the sense that some kites can fly stably at a much higher line angle (the tangent of which is an exact measure of a kites L/D) than other kites. The second law states only that for each of these kites any increase in their L/D (more lift or less drag) will make volatile instability more likely- and cause it's onset to occur at a lower wind speed.
But when it comes to making changes to improve stability, it does matter where drag is removed from and where lift is added to. If, for example, drag forces can be caused to act further out from the axis the kite rotates around when it becomes unstable, and/or the lift forces can be moved nearer to this rotational centre then stability will be improved without any net change in lift or drag.
But even after this cavil, it's all so very simple, so why isn't this second law already basic knowledge for kite fliers?
The reason, I think, is to do with the way our brains are organised. Our intuitive understanding of relationships between connected things allows for proportional increases and decreases, even at changing rates, (which is how come we can ride bicycles) but doesn't do that well when relationships between cause and effect are very complex. Kite L/D varies with angle of attack and wind speed in ways that may be beyond our intuitive grasp - they are for me anyway. Even though I know intellectually what is actually happening, I still find myself having to consciously reject intuitive- and wrong- explanations.
Firstly, a kite's L/D is not constant over the wind range. Kite L/D Versus Wind Speed
In light winds, L/D is low (line angle decreases as the wind drops). And in stronger winds, fabric and structure distortion eventually cause kites to become less aerodynamically efficient - reducing their L/D (see graph; kite L/D versus wind speed).
From this, and applying the second law, it becomes clear why almost all kites are stable in light winds, why most become volatile unstable at some middle wind strength (as their L/D increases to the point where it exceeds their stability limit) , and why a few will make it 'over the hump' (as their L/D drops off again) and maintain stability until they break rather than crash.
Secondly, and most perversely, kite L/D has a "difficult" relationship with it's angle of attack. (see graph; Kite L/D versus angle of attack.)
When a kite is first launched, it's angle of attack will be nearly 90 degree's- and it's L/D will consequently be so low that stability won't generally be an issue. As it climbs and it's angle of attack decreases, L/D increases, pretty much proportionally , and stability might - or might not- become problematical (depends on the specifics of the kite).
This far is clear and intuitive.
But when it's angle of attack reduces to less than 5 degrees or so (10 degrees for some kites, 3 degrees for others) then it's L/D stops increasing and begins to decrease. Kite L/D Versus Angle Of Attack
The effect of this is to confuse nearly every kite flier as to cause and effect, because (for example), this will mean that sometimes shortening the kite's rear bridle(s) will improve it's stability and sometimes lengthening it's rear bridle(s) will. In response to this level of confusion, most of us just withdraw into faith based beliefs - while some give up completely and become artists.
And to make things even worse, this tip-over point, at which the relationship between L/D and angle of attack reverses is exactly where most kite makers will be tuning their kites to- because it's the setting at which they achieve their highest flying angle.
The "stability limit" line in the Kite L/D versus wind speed graph is the fundamental prediction that this 'second law' makes.
Apart from when the natural period of a kite functioning as a pendulum coincides harmonically with aerodynamic effects, I can't as yet see any good reason why the 'stability limit' shouldn't be a straight line.
So there it is; finally, a life's work in just two pages- with apologies for having sometimes said I wouldn't publish until I could get it down to just one.
BUT WHAT IF IT'S WRONG?- Aagh!
PETER LYNN, ASHBURTON NZ, JULY 1 '13
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