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Starting with a blank sheet of paper and a pencil, the quest begins. The first task is to perfect the basic delta, the pure triangular shaped kite with the simplest geometry: an isosceles triangle. For this the mathematics are equally uncomlicated. It's not even necessary to calculate the wing's area. It's not necessary to go beyond the basic delta, either, for the performance and handling of a perfected standard delta is beyond reproach and definitely worth striving for. The process starts with a light wind prototype, or test kite, with fairly long, bendy wing spars - in other words a light frame. After a series of test flights in as wide a range of winds as possible, make a smaller one, scaled down about 2%. Follow with smaller and smaller versions, in stronger and stronger winds, until they're unflyable. Usually the previous version (about 2% larger) is the best all round flyer. An earlier version may become a favorite light wind kite as well.
Note how smooth the 13 footer in the photo is. There's little or no wrinkling. Taping the wings has controlled stretch, and the frame is ideally suited to the wings. The kite flies very well without excessive flexing.
After learning the process of perfecting a design, the next step might be to look for small ways to improve on the basic delta, or at least try something different. It is possible to improve on one or another aspect of the basic delta's flying qualities by clipping the wingtips, extending the wing at the spine, and scalloping the trailing edges.
Scalloped trailing edges reduce drag and lead to steeper flying angles, but they also reduce stability and require a high level of precision in both design and execution. The wing spars are thinner and lighter because there is lower load from drag for them to handle.
Clipped wingtips add a flap of fabric on the trailing edges that increases stability over a better wind range at the expense of a few degrees of flying angle. Their wing spars need to be stronger, and therefore heavier, thanks to the extra mass of flapping fabric and the associated drag. As a result, they are usually good over the widest wind range of all deltas.
Extending the center spine achieves the same wing as clipping the tips, but with subtle differences. The spars would be a different length and the spreader pockets located differently. One only needs this way of looking at a delta, as distinct from the clipped wing tip version, if the materials at hand require it. That is, if it didn't fly the first time.
Whether doing a scale drawing of a new design on paper or a full-sized kite on fabric, I begin by marking it out along the centerline, starting from the nose. Working on one wing half, I mark the end of the centerline, and then measure perpendicularly to the wing tip along a baseline using a pair of sufficiently long straight-edges and a large set square. The baseline is at a right angle to the end of the centerline. This defines the "standard delta" wing (with straight trailing edge, a true delta wing), and the fin is based on a few simple proportions. The spreader attachment point is measured up from the wing tip along the leading edge. It is based on spar length, which is a proportion of the leading edge. Using proportions enables easy scaling.
Between the end of the spine and the wing tip the fabric can be cut in a straight line, but it could also be scalloped or have extra material as a flap or apron (as they're sometimes called). Thus a standard delta with a scallop is still a standard delta - the end of the spine and the wing tips are on the baseline. The towing points are trickier to calculate for scalloped trailing edges, but, in general, trailing edges don't present any major problems. For example, imagine a series of kites, all the same design with identical frame proportions, but each one is a different size. They might have fringed, flapped, straight and scalloped trailing edges, depending on their size - the smaller the kite, the more they need trailing edge drag and vice-versa.
What if the center spine is extended beyond the baseline, or the wing tip is raised a short distance above it? That is, bits are either tacked on or chopped off the true delta wing. It's no longer a standard delta wing, no longer a single isosceles triangle, no longer standard, and to relate experimental non-standard designs to other known designs meaningfully, the towing points must be expressed in such a way that they can be compared and duplicated. They need to be based on wing area; simple proportions will not do. But that's not the problem.
The problem is that the wing spar length and spreader position depend on whether the proposed new wing is considered to have an extended keel or clipped wing tips. It's more than just semantics. For a standard wing with a keel extension the spars and spreader position are the same as on a standard delta. However, if one considers that the wing below the raised wing tip has been removed, or "clipped," the spars will then be shorter and the spreader attachment point different (this will be shown below). The value of this approach is that sometimes one way works while the other doesn't.
So, although two non-standard wings might be identical in shape and size, there can be several ways to look at them, resulting in different fins (but identical towing points), different wing spar lengths and different spreader positions - hence a different balance. And that's the reason for this page. It isn't complexity for the sake of complication; it's a rule-of-thumb for simplifying the design of non-standard delta kites. If anything, this approach is too simplistic, but it serves to limit the number of variables one might have to change over the course of developing a design. The alternative would be to develop each and every kite from scratch.
Although at first glance splitting delta kite wing shapes into separate categories looks like over-complicating an essentially simple structure, the purpose is to simplify designing. Identifying different wing types is useful to experimenters who want to apply their own specific set of design parameters, whatever they may be, to wing shapes other than single isosceles triangles, while retaining similar flying qualities. Without these classifications it would be impossible to calculate equivalent towing points when making experimental changes to wing geometry.
Scaling up or down or changing the nose angle on a standard delta would not change the proportional towing point position, but a change from a simple standard delta to a trapezoidal shape, where each wing is a separate non-right triangle, will. A standard delta's wings are based on right triangles. If the wings are anything other than right triangles, they are usually either extended at the keel, or clipped at the wing tips.
This is shown in greater detail below
The illustration at right shows how the same basic geometry can yield three different-looking versions of the same kite simply by choosing different trailing edge treatments. 1 is a straight trailing edge, 2 is a scalloped trailing edge, and 3 is a trailing edge flap. The fin's towing point will be the same for 1 and 3, but different for 2.Problems arise when attempting to carry over a given set of properties from one wing shape to another. An example would be designing a new kite with a shape like this one, based on known wing spars from, say, a standard delta. The goal would be that the new design performs and behaves at least as well as the original, but when so doing it becomes evident that there may be more than one way to look at the new layout, mainly affecting the length of wing spars and position of the spreader, and hence the balance and stiffness of the new design. The towing point position has to be re-calculated anyway, but in order to get the same lift, stability and feel as the original, one has to be able to calculate a towing point equivalent to the original. Handling qualities, lift and wind range all depend on the towing point, and since I like to use one particular optimum position for most of my light wind kites, whenever doing a new design I want the new towing point to be at that same optimum position.
At this stage it doesn't matter if the trailing edges are scalloped, straight, flapped or aproned - we're still on paper here. The terminology applies to the figure outlined by the three points used to lay a wing half out: the nose, tail and wing tip. Starting from the nose point, the wingtip point is defined by the tangent of half the nose angle, but expressed in the actual dimensions used. The tail point may be further along at the end of an extended spine.
Sound complicated? It isn't - it's really simple. Using two straight edges and a square, you mark out the wing tip. The tangent of half the nose angle might be, say, 40/36, which means you go down 36 inches from the nose, and then across 40 inches at a right angle to mark the wing tip. For a standard delta, that's all there is to it. If it's a clipwing or extended keel delta, then the length of the spine is more than 36 and the tail point gets marked accordingly.
When I began experimenting with wing geometries other than the straight single-triangle of the true delta, I found I could no longer define the towing point in terms of a simple percentage or fraction which would be the same for all cases. Instead, each design had its own unique towing point, and so there was no way to compare different experimental designs. I realized that the same design could be seen, for instance, as having either an extended keel or clipped wing tips. Which one it actually was determined the length of the wing spars and the position of the spreader strut.
On the surface these distinctions in wing geometry look trivial, but each type of delta has its own distinct advantages and flying characteristics. Since I wanted to try as many as I could think of, I needed to distinguish between types in order to design the fins for any given layout. To be useful to everybody, technical and non-technical people alike, it had to be a simple rule-of-thumb sort of idea - not too complex.
My non-rigorous solution involved finding the basic, standard "delta within." It is a geometrical template; a way to locate the various other dimensions. The drawings below show what I mean.
The three kites are lined up along a baseline through the wing tips of the "standard delta" on the left. The wing spar lengths and the spreader strut locations are set by a standard set of proportions.
Within each of the kites lies a basic delta, shown in red. The middle kite is an "extended keel delta," where the wing root chord is extended aft. Note how the geometry of the "delta within" determines the length of the wing spars and the position of the spreader. The right hand kite is a "clipped wing delta" - the hidden delta is partly outside on this design. Some of the wing area is removed, or "clipped," from the wing tips, but the fronts of the wing spars and the position of the spreader are still determined by the virtual delta within. Notice the difference between the last two frames above; the clipped wing delta on the right has relatively short wing spars. The two kites look different here, but check out how they look side-by-side when scaled to the same length.
They look the same! But the spar lengths, spreader positions and fin lengths are different. Yet both kites share the same towing point position.
So, if the kite flies, what does it matter? Well, let's look at an example: my Wildcard is a popular and useful kite; it is used by British falconers in breezy areas. It was originally designed in and for the winter winds here in this corner of Wales. It was supposed to be an R6 with a scallop, a clipped wing design fitting in between the R5 Rustler and the R8. Well, it flew brilliantly, but I found I'd made a mistake on it as I was laying it out. I had actually made it as an extended keel delta, rather than the clipped wing one I'd intended. Naturally I corrected the mistake, but, unfortunately, it didn't fly any more! It became impossible to control. There was just a bit too little wing spar left between the spreader pockets and the wing tips, effectively making the wings too stiff. The only solution was to convert the prototype back to the geometry that worked: in this case an extended keel delta. These differences may seem insignificant, but the result certainly wasn't. One customer said he thought the Wildcard was the my crowning achievement. Well, now you know; it came about by mistake, or, as Professor Harold Alexander might have put it, serendipitously.
This simplified approach works best for extensions or clips of up to about 11%, on kites with fairly standard nose angles. There is also a fourth type, which I call hybrid deltas - they're a blend of types, and serve to show that simple rules-of-thumb have their limitations.
There is another completely different approach to designing deltas: by eyeball. After all, the hidden delta idea depends on the standard delta geometry you begin with. I have seen Takeshi Nishibayashi lay out a large delta completely by eyeball. Anybody can do it, of course. On big deltas there is a wide range of workable towing point positions. But such designs are by definition not repeatable, nor can one learn much from doing them, other than perhaps if it's a lucky day or not.
There is another possible type that may have already crossed the mind. Why not extend the wing spars at the wing tips (or chop off the trailing edges) for another interesting delta shape, as shown here?
Yes, it is possible, and I made a couple of these back in the mid '70s. They can be designed using the same principles as the kites above. But, the design is flawed. Whether there is a scallop or not, or whether there are battens or strings (as shown above) to the trailing edge, the air just goes over such wings in the wrong direction. In practice the whole of the wing suffers from serious fluttering and provides precious little lift to boot. I liked the shapes I could make, on paper, but the kites were disappointing in the air.
Taking a closer look, it becomes clear that there is a lot of extra spar mass on relatively little wing surface area. Remember, too, these are not rigid structures. These longer, wobbly wing spars have a longer than normal region of flex - from the spreader pockets all the way to the extended wing tips. This area has no tension, and relies on smooth air flow for a nice, clean shape. This doesn't happen; instead, the wing tips ride in severe, shearing turbulence at all times. What I gleaned from this was that the slightly clipped wing, in stark contrast, providing as it does a clean air flow at the tips, must therefore be better. I have always worked to make my wing fabric as smooth as possible using just the ambient wind, not additional stiffeners.
When air flows past a kite, the air underneath tends to flow out towards the wing tips, while that on top tends to go over the leading edges and curl back and in towards the middle. The two motions together create a swirl, or vortex, at the wing tips. The lack of fabric tension at the tips as the spars flex allows the fabric to flap between these two opposing flows (and at an angle where pressure is equal) but the air on both surfaces becomes turbulent, with the air underneath is almost pushing against the trailing edge, and all you get is a mess.
The conclusion is that it is better to design delta wings with a standard, clipped, or only moderately extended wing plan. They have shorter spars, more working surface area, and the flow at the tips is smoother. The "working" part of delta wings can be considered to be the area within the relatively flat central diamond visible in many of the photos. Outboard of this fairly rigid area where the fabric is suspended by the freely flexing spars, the panels take a conical shape. This is where any fluttering is concentrated. The fluttering gives stability. Many commercial deltas rely on excessive fluttering to mask construction faults, but a controlled amount is advantageous. Even scalloped deltas' outer wing panels flutter when the wings flex; the more they flex, the more the wings flutter; the more wind there is, the more stabilizing drag is automatically laid on. This may be a key factor for all deltas. Problems occur if, for instance, one wing tip begins to flutter before the other, which can drag a delta into a dive to one side. And beyond a certain amount, excessive flexing leads to excessive drag. The kite's inherently stable shape is lost, too much lift is lost, and the kite gets dragged down, possibly sustaining permanent damage as a result.
As shown above, different wing types are identified and defined so that standardized or personal design geometry - whatever it may be - can be used to maintain performance consistency across a range of different wing shapes.
This naming convention allows one to calculate virtually identical, or equivalent towing points across the range of different delta types. But there's more to fin geometry than just towing points. Unfortunately, when it comes to fins the rules aren't so cut-and-dried. While the conventions can be strictly applied to fins, it's also possible to interpret them in more ways than one for the sake of, say, appearance or convenience. These are, after all, rules-of-thumb, not immutable physical laws.
My standard delta layout defines fins using the towing point position, the length across the top, and depth. The length is a percentage of the spine, and the depth is a fraction of the half-span. When the wings are clipped or the keel is extended, there can be more than one way to interpret the fin's parameters. Length of fin based on the hidden delta might be just the starting point. For example, the rule for an extended-keel delta might suggest that the fin ought to start at the back edge of the hidden delta, some distance up from the end of the spine, but you may want it to extend all the way back to the end of the spine. Although the rule can define the front point of the fin, if there's an extension aft beyond the hidden delta, the front may well need some extension to avoid weathercocking (that's where there's so much fin aft of the center of rotation that when a kite starts to dive, the fin actually helps guide it deeper into the dive, rather than acting to correct it).
At another stage of designing, I came to like the looks of fins extended rearward beyond the trailing edge. It was when I started using higher nose angles, and I discovered that extending the center spines rearward beyond the back edge of the wing redressed an inherent imbalance that otherwise prevented the kites from flying properly. Running the fin to the end of such extended spines just seemed to look good. Only later did I realize I would need to extend the fins proportionally forward as well, to push the nose back up to get out of dives.
Against my own rules, I still extend the fins on my extended-keel deltas right to the end of the spine, rather than cutting them off at the hidden delta's virtual trailing edge. This can necessitate extending the front end of the keel as well. (If the fin extends too far to the front, the kite will constantly "hunt" from side-to-side in climbs as well as at station.)
I prefer lightweight (thin) center spines on light-wind kites - all they have to do is stretch the skin out at the middle. Some of my earliest deltas in the mid-1970s had tiny fins only 8% of the wing area in size - isosceles triangles a quarter of the half-span in depth. They wouldn't fit into my current "standard delta" set of dimensions, but they worked just the same, at least on smallish deltas up to 6 or 7 foot span (bigger than that requires deeper fins or else there may be some pitch instability). The short fins gave the spine a nice camber by allowing the rear portion of the wing to flex up, conveniently spilling wind in gusts. Those small fins were very light at a time when the AKA was recommending double thickness fins to lower the center-of-gravity. I wouldn't argue against such small fins today; I only drifted away from them because I wanted to reduce the fluttering of the wing fabric. The fluttering wasn't necessarily a bad thing - the kites were very stable and rode out gusts; I just wanted to see if I could "clean up" the wings. Full length fins minimized the tendency of the spine to flex and reduced the fluttering. I also liked the handling of deltas with full-length fins. As I only flew in light winds and thermals, there was little need for fins that allowed wind spillage. Who knows, I may end up going back to those short fins one day.
Nowadays I also use heavier center spines than absolutely necessary on some kites. This is only for increased durability, though some writers in the past have recommended heavier spines on deltas to lower the center-of-gravity. Anyone who wants to know what that actually means in terms of a kite's flying characteristics is urged to try one for himself.Commercial kites sometimes have an extra grommet on either side of the point of the fin.
Although there's no apparent need to calculate towing points when bridles are used, it helps if the designer knows the fore-and-aft limits of the range of adjustment, in addition to the fin's length and (approximate) depth. Adjustable bridles are used on tunnel-keels, Delta-Conynes (or delta-pilots), single fins with small bridles (like my Shifter Fins), and on kites with two fins in tandem. Fins with two or more towing points and even two separate fins are other possibilities.
Remember, as kites get smaller, the range of possible towing point positions shrinks to practically nothing, and vice-versa - big deltas have a generous range approaching a fifth of the length of the spine. I am not at liberty to say exactly how I calculate towing points, having promised Harold Alexander and John Loy I wouldn't, but suffice to say that for any given delta design the exact limits may have to be determined by experimentation anyway. Clue: If you see a published drawing of a "Dan Leigh" delta, if the key dimensions aren't as I have drawn them for the standard delta on this site, then it's not mine. If the drawing shows a scallop that's not dimensioned with an exact radius (or two tangential radii), then it definitely is not mine. It is not possible to work out towing points unless the exact wing area is known, precisely, taking into account every bit trimmed off or turned under.
Delta-Conynes, or delta-pilots as we used to call them at the Round Pond, can be very fine flyers. They have a big hole in the middle that relieves excess pressure in gusty or windy weather; they seem to do everything well if you zero in on a good one. I recommend keeping the nose angles between 90° and 95 or 96° to keep the spreaders short.
I never liked the job of fitting the center sticks, though. To keep the front and rear V-cells flat, the center sticks have to be just right. I also found that (on some delta-pilots and tunnel-keels at least) the two spines have to be thinner than a single one would be, to keep the weight down. Then, the two sides bend out. To prevent such bending, and to simplify construction and give a clean, wrinkle-free cell, I prefer the tunnel-keel, a single cell running the length of a normal fin, or full-length with the front angling back from the nose to the center stick at about 45°.
For Shifter Fins and tandem fins the aim is to design them so that wherever the towing ring is set, neither edge of the fin can go slack (rendering it relatively useless). Don't just make the bridle longer; if it doesn't twist up it can get hooked on a wingtip. Tandem fins should maintain the same sidewise center of area as a single fin - don't make the back one too big, and, again, make sure the rear fin is kept tensioned at both extremes of the towing ring setting. (These are probably fairly simple to design but I've never done it - I balked at having to work out the relative sizes of the two fins and their geometry, conscious of weathercocking and the potential for a stress concentration on the spine where the two fins meet.)
Thinking back to those old-style short, shallow fins (above), I tried a kite with a bridle like the one with two fins, but without the rear fin, running the bridle from the towing point of the fin to the tail end of the spine. The fin's towing point was at about 18% (equivalent), but I didn't like it and replaced the test fin and bridle with a normal fin.
The middle picture above is a guess based on a kite seen only with binoculars from Parliament Hill (Hampstead Heath, London) in the late '70s. It seemed to be flying from Primrose Hill, roughly a mile and a quarter distant. The appeal of this arrangement for me is that, although from the side it looks like a delta-pilot, it doesn't have the extra center panel requiring two spines and an extra-long spreader. A 25 or 30% longer spreader has to be either thicker (and therefore heavier), or made from a stiffer material (i.e. changing from wood to carbon tube), or given extra support.
The right-hand picture shows a fin using exactly the two extremes of towing point, fore-and-aft, for light and fresh winds. I add extra taping from the front ring to the tail end to carry the load across the bias of the fabric, which would otherwise stretch, and sometimes there's an extra stick on the front edge of the fin to keep it from flapping about when the line's attached to the fresh wind position. Some people string a bridle between these two rings. The extra stick can be removable, or else folded parallel to the spine for rolling the kite up. I found making the sleeves and pockets for those extra sticks too fiddly, what with the towing rings on their thick tapes plus the fin edge reinforcing, and so started using Shifter Fins instead - they're easy to roll up with the kite. Of course, one could also simply make two fins, with different towing points, and either roll one up or stick it to one wing with velcro or something.
For any such deltas with bridles or fins that allow adjustment for different winds, one also needs wings that work within the extremes of the range of adjustment. Stiff, heavy wings for strong winds won't perform in light winds, and light-wind wings with long thin spars will just fold up in strong winds.
So there can be several approaches: stiff and heavy, light and bendy, or somewhere in between. Deltas with stiff and/or heavy frames are almost impossible to get to fly anyway, but once a working combination is found, it can be done. In the end I tend to collect an assortment of lightweight frame parts for such kites. Lightwind wings are no problem in the flying department, and, ideally, if just the right scale factor is found, the reduced pull as the towing point is shifted forward would counterbalance wing distortion from the increased wind. It's a lot easier to imagine these things than to actually get them to work, though.
In the "old days" kites were made from porous fabrics and they'd only fly in quite heavy winds, but in my experience, and for the light-wind conditions I like to fly in, porous deltas aren't very interesting - so I can't comment on porous deltas or deltas with porous panels.
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