Scaling by size


Historic aviation prototypes are often not very “clean”. Mothra is a power kite at heart, if not shown making power in some standard mode (raw lifting, but not traction or pumping). The successful scaling-method proof-of-concept was of cheap tarps aggregated in a simple modular rigging language. Mothra took only two person-days to build, and only 2k USD in materials.

Mini-mothra lifted a 4m diameter HAWT. kPower prototypes are the dirtiest in the game.

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I’m not going after the concept. I’m just saying there is a lot og groundwork remaining, especially in the details. And without these details, I dont see right now how this kite could make power. Flesh out depower, handling, flight path, etc etc. Perhaps then I would be in a position to have an opinion on the viability of the rig. I agree with @dougselsam on this. We know kites pull like crazy given the correct circumstances. The problem is finding a well rounded solution that solves all problems sufficiently well and has a good price… as it stands, I would place the Mothra more in the «showkite» category rather than the «AWE» category.

It does not matter how little time was used if the job is not nearly done. Just look at the efforts of @Kitewinder to bring a relatively simple design to the market

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Of course there is a lot of groundwork remaining. Mothra was just a start. Pierre rightly sees depower in the landing phase.

Toyota’s Mothership is a closely related concept. These kites can make power in-place, much as a human might drive exercise equipment. A kiteplane surging across the sky is not the only motion possible.

KiteMill is of course trying to develop a product, not explore the entire conceptual range of AWE.

Mothra interested me for its double anchoring allowing a better potential of scaling according to Dave’s principle: using the Earth as an element of structure. The problem I saw was the adaptation to wind changes. I found a solution for a simpler ground installation which is also used to prepare the wing for launching.

In the meantime I studied vertical trajectories for Magnus based-effect balloons in yoyo mode, estimating they are also particularly suitable for Mothra, allowing it to benefit from crosswind motion. However the cycle would be short due to the vertical limit, but the recovery phase would be also short. And as it scales, or has longer tethers by being used like a C-shaped wing, the cycle becomes longer.

So I reevaluate this concept. I found it very good, now thinking it has an exceptional potential and looks to be feasible.

Magnus Balloons are scale-limited by bending forces. The largest airships often broke in two, by simple wind shear, even without tethers pulling each end back. Even just bending is bad for a Magnus rotor.

There are some possibilities to lower bending forces. But the big problem is the huge power consumption. So Mothra and its variants to come have more potential. And the envisaged vertical trajectory for Magnus balloon is also very suitable for Mothra.

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How do you keep the pulley loops always in their tracks without a large secondary fairlead boom next to the Magnus rotor?

The strap used as belt should be wide enough and settled between two adhesive foams, and the tension on the tether below should maintain the strap. On the video there are no adhesive foams, so the belt slides a little.

Good Luck seeing the strap adhesive foam idea developed into practical form.

If only Magnus skin-friction itself scaled, like mega-fuzzy skin that grabs air better, like a giant tennis ball. The Magnus effect has historically only been strong enough to make sports balls curve slightly, to make games more interesting.

The strongest power-factors scale best, like highest power-to-weight.

The balloon on the video was about 1 m diameter and 1.8 m span. I experimented also a balloon of 2 m diameter and 8-10 m span with the same drill of 500 W turning the pulley. The tangential speed was about 2 times less. By the plausible equation (3) from

the power consumption should be 45 W, but the 500 W of the drill were fully used. Before I tried with my arms to turn a 2.6 m diameter and 10 m span balloon and it was difficult, for a similar low efficiency.
I believe balloons undergo air pressure which deforms it, adding drag.

Even the well shaped Omnidea’s 2.5 m diameter and 16 m span balloon consumes 400 or 500 W during rotation with a tangential speed of only 6.54 m/s, as showed by a curve (between 9’ and 10’ from the beginning of, while the cylinder on the paper consumes 3 or 4 times less, probably thanks to its more perfect cylindrical shape.

So I will not investigate more about Magnus balloons. The Sharp rotor looks to have more possibility but can be held only by the two ends. With its number curved surfaces it could resist better to bending. Tests of an inflatable rotor are needed. But it is for later.

Dave Culp found the single skin power kite to have the greatest theoretic scaling potential. For years now, I have been flying SS and standard parafoils of similar sizes and masses, and the SS kites are consistently ~2x more powerful by mass, and nicely hold their own by equivalent area.

All other AWE wings can be tested against COTS TRL9 SS kites of all sizes. Kiteship even has its original quiver of SS ship kites available for ever broader experimental AWE testing.

In classical aeronautics and aerospace, best power-to-weight has always been the most dominant design factor. It would be very unexpected if AWE is somehow not subject to shared essential wisdom.

The AWE debate will persist until rigorous testing confirms reality. May everyone have their best wings ready for fly-off.

Another double anchored kite but with tethers is on

Nice modern sea kite. See Old Forum for discussion. At KiteShip I asked Dave Culp to list all the known ways to stabilize a power kite, and “stake it out” was his top answer. That led to Arch studies at the World Kite Museum and WSKIF, where arches are specially celebrated. The Playsail is the archetypical Stone-Age spread-anchor kite. A latter example of scalable multi-anchor topological stability, Neptune with sea-kite-


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Scaling by size and Scaling in numbers rather than size, both ask a question: what is being scaling, an unity, or the kite-farm?

Assuming it is an unity. AWES could scale in a similar way as planes or current wind turbines, all elements scaling in 3D, or in a different way by the number (e.g. the number of the blades or the stacks of blades), the whole forming a well defined unity.

But in all way we don’t know what to do with a 1 km tether(s).

So it becomes a question for a kite-farm, comprising the question whether a kite-farm can be seen as an unity. Thus the question becomes similar.

As an element of response, let us rethink an AWES as a whole. It was possible to make planes or wind turbines then grow, but in the AWES field the tether length imposes to think the whole kite-farm from the beginning, at least for utility-scale.

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Scaling a single wing system by size implies it will either be
1 a massive soft wing with hard control demands or
2 a very heavy rigid wing requiring high-speed operation
both options requiring an extra long tether.

Scaling by number does not change the altitude at which you start flying your turbine.
Your initial tether length doesn’t change.
Tether drag per wing will go down as you scale by adding ring layers upwards.

I think there are some scaling laws that apply to a single kite that are kind of universal:

For a wingspan scaling factor x

  • Area scales x^2
  • Power scales x^2
  • Tether length scales x
  • Tether diameter scales x
  • Flying speed remains constant
  • The size of any path scales by x in size
  • Rotational speed is reduced by \frac{1}{x}
  • mass scales by x^y where 2 < y \le 3

One can always change the design during scaling to get around some of these, but these are some rules of thumb for scaling a single design

I’m going to disagree with some of the generalisation here…
For a wingspan scaling factor x

  • Area scales x^2
  • Power scales x^2
  • Tether length scales x
  • Tether diameter scales x (Need to double-check this (you and Storm Dunker are the tether experts) but … can tether diameter scale <x as speed will be higher, and the key is tether cross-sectional area for strength required. BTW Longer tethers have no chance of adding fairings, again an advantage in network forms. The L/D of whole net form should be considerably higher… )
  • Flying speed remains constant (Wing loading has to go up if mass scales by x^y where 2 < y \le 3 yet the wing area only scales x^2 So surely wing speed has to increase. as per unless we change to using very high lift stacked multi-foil wings)
  • The size of any path scales by x in size
  • Rotational speed is reduced by \frac{1}{x}
  • mass scales by x^y where 2 < y \le 3

EDIT - I’m wrong here about the tether diameter … see Tallaks next message for why

Rod is correct,

Tether Diameter scales less than x and Minimum Stall Speed increases with scale.

A giant power-kite confined under 2000ft FAA ceiling approaches “short-line” tether proportions with area-squared advantage in tether volume. As RolfL points out in Physics World, tether drag is a big issue with small AWES, but DaveC has long taught tether drag is not a big deal at ship-kite scale. Non-dimensional wind velocity also favors the bigger wing’s lesser tether drag factor.

Putting all secondary effekts aside, scaling wingspan will scale the tether force by x^2. Scaling tether diameter by x scales the tether cross-section-area, and thus the strength if the tether by x^2 as well.

If you keep the tether length constant, you are effectively changing the design as tether drag will be relatively smaller than kite drag. And kite will fly faster. But this would be breaking the scaling law above.

But: you could always scale wingspan without scaling tether. At one point, the kite will not fit anymore, as the wingspan and turning radius geometry will limit what can practically be done. Therefor I believe it’s more correct to consider «universal» scaling like I started out, and then say that scaling tether length by a lesser factor should be considered a design change. Also note that the «universal» scaling laws retain effective glide number of kite and tether, which is why it is possible to even state the scaling laws in the first place.

Reynolds number effects i did not put in there, nor wind gradient effects. I believe these should be considered secondary effects. Less important for a «rule of thumb» approach. Probably quite important though for a detailed design.

Wrt fairings, i would consider this a design advantage, that would most likely scale by the said rules once implemented in small scale and then scaled up

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Wing Area is not a “secondary effect” of Wing Span. With power kites like the NPW or C-kites, its the reverse, Wing Span is the secondary effect. Aspect Ratio must decline with scale for rigid wings, but soft arch kites can scale at super-high AR.