Kite Numbers, Ratios, Parameters, Factors

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Aug 8, 2020, post by Dave Santos

z-Factor is primarily an explanatory number to relate wing types from SS to rigid-composite. Its strongly corelated precedent number in aerodynamics is Wing Loading: the ratio of an aircraft's weight to its wing area. One of my many mentors across aerospace was George Parks, a savant from youth who designed and built countless world-champion RC gliders, with peers like Paul McCready. George and I built many crazy sUAS concepts in the '80s and '90s, and every one flew just as intended. George's number-one Number for an experimental design was lowest possible Wing Loading.

In classic kites, Lowest Wing Loading is also the most important performance parameter. All expert kitemakers know it, if not the respective mathematical aerodynamics, including top intuitive empirical power-kite designers. And yet, most AWE researchers completely disregard Lowest Wing-loading in favor of highest L/D or piling on parasitic-flying-mass, like eVTOL capability and avionics.

The modern SS power kite or paraglider has the Lowest Wing-Loading of any utility wing. The lightest models (62gr/m2) are less than half the Wing-Loading of a Monarch Butterfly (168gr/m2), the Lowest Wing-Loading charted on WP. Note the WP paraglider number includes pilot payload mass, but an unloaded AWES SS kite is far less loaded and is maximally "floaty". Lowest Wing-Loading is a very useful AWES property during lulls, where minimum sink-rate wins, with lowest wind velocity for sustained flight (zero-point energy of flight) and lowest cut-in (AWE free-energy and capacity-factor).

All champion kite foilboarders know these things. Dave Culp was teaching AWE players SS Lowest Wing-Loading superiority a generation ago. The SS NASA Power Wing and Barish's first PG was based on Lowest Wing-Loading, over 50 years ago. z-Factor based on wing-thickness is simply another way of expressing the virtue of Lowest Wing-Loading, for reasoning better about optimal AWES wing selection

Wing loading

More Kite Numbers Proposed- Some Topological Numbers

A single long-lined kite and a kite-train can have the same tether-length-to-area, but are distinct topologies, with distinct flying characteristics. A kite-train's proportionally smaller unit-kites suffer less from unit-scaling laws, and train unit-kites develop lift all along the tether. Kite-trains are well known to reach higher altitudes than single-kites (~10km v. ~5km, within atmospheric boundary) just as multi-stage rockets reach higher orbits than single-stage rockets of equivalent mass.

Thus we need a Kite-Number to characterize the multi-kite relation, much as a polymer molecules are numbered from monomer to polymer as Mn. So let us similarly number a kite-train by Kn. We can also use Kn for arches, stacks, meshes, and 3D lattices. We can use An for Anchor-Number, for multi-anchor topologies like classic Kite Arches and Playsails.

There there are the well-known multi-line Line Numbers, or Ln here, of a Single-Line Kite, Two-Line, Three-line Four-Line, and so on. These have not been reasoned-over much, but this will change. Topologically, a Two-Line Kite is a Kite Arch, and there is a dimensionless geometric number for Bar-Spread or Anchor-Spread ratios. Lets call this the Anchor-Spread Ratio.

Multi-r refers to multiple radius lines of radially symmetric kite formations. "3r", as coined by TUK, is the minimal radial-footprint number, and multi-r formations offer redundancy and scalability. Call these r-Numbers. There are more topological kite numbers coming for self-similar and/or fractal dimensioned kite formations (in prepublication). All these numbers will become increasingly important to the emerging new phase of AWES R&D.

"Dynamic mechanical analysis is a sensitive method for exploring the structure, the processability and the end use performance of many materials. It enables characterization of the structural differences between materials and provides information about how the materials will process. Such information is important both for product development as well as process design and optimization. Most materials are viscoelastic and full characterization of a material’s rheology requires elasticity information in addition to viscosity information. Dynamic mechanical analysis is a uniquely powerful method because it measures both properties simultaneously."

Aut. 7, 2020, post by Dave Santos

Let's define just what a AWE "Kite Number" is to us. A Kite Number is any dimensionless number unique or deeply inherent to kites. We have identified many of these numbers over the years.

A typical example that comes to mind is the ratio of tether length to kite area. Lately, I have been flying a 1.2m2 two-line parafoil on 70m lines, which very "long-lined" proportion. At the other extreme, we have been reviewing advances in Race Kites, where a super-hot 20m2 parafoil be "short-lined" at 15m tether length. Interestingly, both of these extremes are similarly demanding technical-flying.

There are many dimensionless Kite Numbers awaiting identification. An especially rich vein of Kite Numbers are inherent to Kite Dynamics. We have only been discussing static Numbers so far here. Kites are a mathematical wonderland.
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Thanks Max, very helpful. There is a lot of old analysis to update regarding the issues you raise.

A major heuristic assumption is that a dominant AWES architecture will tend to standardize greatly across many diverse markets, just as an popular automobile will prevail in different climates, service altitudes, road conditions, and use patterns. The same goes for standardized aircraft that operate over remote ocean, mountains, or cities alike. Similarly, AWE may have the same fundamental design parameters in remote or populated locations. Multi-r someday ideally may operate directly above cities, or out to sea.

Existing HAWTs are not optimal by frontal airspace because they cannot reach superior wind 500m high. The prime AWE resource that can save the world is beyond the limits of towers. It is trivial to calculate that a large wind-farm footprint of AWES will far outproduce HAWTs. The wider the farm the higher we can go, while the HAWTs are stuck in surface wind. We can even operate above HAWTs in principle.

"Footprint" is a complex subject that includes the full zone of significant impacts. For example, Makani's M600 can break free of its single tether to kill or destroy almost anything up to several km away. A giant single line kite might drag disastrously even father, sustaining flight. Many connected topologies like multi-r can always stay inside their field, self-killing passively.

Joe and I can produce archived discussions of all these topics, going back over a decade. In may seem that the AWE community is unduly quarrelsome, but it is actually more like family quarrels, because the serious players all realize that we are on the same team ultimately, we just disagree on details.

The high-complexity "energy-drone" players have now burned through >$500M, much of it public funding, and are unable to stay in the air more than a few days before game-over crashing. It is now time for low-complexity "rag and string" architectures to be comparably tested. This is an AWE R&D issue of optimal experimental design, not a pretext for emotional distraction.

I have been concerned if the frequency and quantity of comprehensive AWE posting is a burden on Maja and Nicolas, that perhaps you should be the one to review the whole moldy hay stack for golden needles, that they then help polish.

Thanks again to you all for opening up a new paradigm in the academic trajectory.