# Scaling by size

Because unit-human body mass is not scaling up under Galilean square-cube law, the jumbo-jet can grow bigger than if unit-humans were also becoming giants. Further, as internal volume grows at a cube, lots more constant units pack in.

Scaling limits in AWE are even more complex, and are not understood clearly by many ventures, as their down-select architectures reveal.

I dont necessarily see the correlation between cruise speed and stall speed. Cruise speed depends on glide number for aircraft. Stall soeed/takeoff speed depend on maximum lift…

Generally, most efficient cruise velocity is closer to stall velocity than to max velocity. Biological and engineered flight cases tend to optimize for efficient cruise.

We could also reason from max-velocity by scale to draw the same general conclusion, as well as recognize outliers like a Peter Lynn World Record Kite or an X-15. The calculated mean curve of the flight case-base scatter-plot holds.

This discussion sparked an interest in me to figure out what decides the minimum flying speed of a kite in crosswind flight. I have defined the problem somewhat simplistically by saying that you don’t want to stall when flying at the most vertical part of a loop. (I am still thinking about single kites on a tether.)

The results that came out were quite interesting. If the combined glide number of the kite and tether is around 5.2, the stall speed of the kite flying as an aeroplane should match the minimum windspeed for using it for AWE. The minimum windspeed will increase with better glide numbers, and vice versa.

Though this also means that it’s not easy to directly compare a 747 to a AWE kite, because you need to account for tether drag. But if you have a higher glide number for your 747 and then add tether until the glide number is 5.2, the two numbers should align. That being said, my equations show that minimal windspeed may be reduced to as much as 40% below stall speed, if the glide numbers are very high. OR you could say that a glide numer of 15 relative to 5.2 allows an extra 40% mass to be used while still maintaining minimum flying speed.

Furthermore, I ended up with the following equation:

w_{min}^2 \propto \frac{m}{C_L S}

This basically means that, very approximated and with many details left out, to maintain minimum windspeed for an AWE rig, when scaling, this ratio (mass to lift) must remain constant.

I believe for this kind of AWE rig, this metric is important and useful to describe minimum usable windspeed

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The tether length should be included in the dimensions of the AWE device in the same way that mast is included in the dimensions of a ground-based wind turbine.

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Below there is an interesting example of scaling by size (from Barnard's predictions ) :

For what I remember Mothra1 is an arch of 300 m². As this kite contains several elements it can be seen also as Scaling in numbers rather than size , even as a kind of Kite Networks.

I don’t know the conditions of this test. With a wind speed of 10 m/s, the force could be quite huge, several tons when the kite accelerates by rising.

With some first changes (adding a winch and a generator) and some research (depower for recovery phase) it could work as a yoyo system.

Pierre I think you’re confusing a “kite network” with simply being too lazy to join, sew, or otherwise properly attach the tarps together to better create a solid, high-aspect-ratio wing surface of reasonable efficiency, rather than a punctuated, leaky wing full of “tip losses” every few feet.

The 50 tarps were rigged like a classic ship sail plan, and similarly effective. Not a single “sail” blew out in high wind. Modular wing sections vitally enable mega-scaling. The Megafly parafoil also comes in sections. Choked bypass flow helps with flutter-mode stability and gust resilience. The splayed wings of large birds, the multi-sail golden age of sailing, share those principles.

Dave Culp started the Blue Tarp Kite Village Power challenge. Let anyone do better, more power to them. Mothra was no lazy effort, but more work-kite sooner and cheaper than anyone else at that time, a prophetic flying machine.

The new Toyota Mothership concept closely matches Mothra aerotecture. The Mothership is emerging from US Tornado Alley, not just Japan, via OSU and Toyota’s Midwest network. Proposed final scale is beyond what any AWE player, except kPower, has diligently studied.

From the video I dont see how this kite structure could produce much power. Nor does it seems that the cloth is flying cleanly. While I applaud the effort, there is still a long way to go before arriving at something commercially useful.

I would see this akin to looking at Makani’s first 1-2 meter wingspan experiments and conpating them to the current 600 kW model. Say what you will, but there is a lot of effort that went into developing that. The Mothra it seems needs a similar development effort before one could assess if this is worthwhile.

The Mothra video shows all in few seconds: high power during rising, then depower.

The sand was used to hold the kite at the ground before launching, but in the same time it shows the force (several tons), so the potential of power by multiplying the force with the reel-out speed. As the power of a wind turbine is the torque X the angular speed, the power of a pulling kite is the force X the reel-out speed.

Then on the video we see the kite stung from his nose: it is a potential efficient depower way to study.

I remember some discussions on the old forum, with Mothra lifting turbines. But turbines are not needed. They will be cumbersome and dangerous when the set scaled and will be subject to uncontrollable aeroelastic divergence.

For this the yoyo mode is specially appropriate as during the vertical trajectory (see Magenn) it flies crosswind, certainly on a short trajectory, implying a short power phase since the kite can fly at 26.6 m/s (let us assume a wind speed of 10 m/s, and a L/D ratio of 4, and a reel-out speed of 3.3 m/s). Then the depower recovery phase by the nose could be fast and without too much expense of energy as the video suggests.

A ground installation allowing facing all winds has been documented, but I have some idea for a simpler and more robust installation as it must undergo tons of traction, thousands tons for a 85 MW 1 km span arch. After all if (as @tallakt indicates) “Makani’s first 1-2 meter wingspan experiments and conpating them to the current 600 kW model”, the first 50 m span arch could be a model for a 1 km span arch.

And a complete arch AWES matches the power/space use ratio I often invoke, and that far better than a crosswind kite like Makani.

A quick calculation (always with 10 m/s wind speed) for a 1 km span and 120 000 m² (1km X 0.12 km) arch and 1 km tethers leads to a force of 5100 tons (51 000 000 N) then 170 MW then 85 MW by taking account of the time and the expense of energy for the recovery phase, while Makani could use only one device of 5 MW, perhaps 10 MW in spite of the higher wing efficiency.

So Mothra deserves more analysis, more R&D, and a 300 m² permanent rig on a AWES test site, perhaps Establishing a Highly Windy AWES test site.

Tallak,

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 https://collegerama.tudelft.nl/Mediasite/Play/e51a679525fe491990de3a55a912f79d1d), 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.