Scaling Laws in AWES Design

Starting with Galileo’s Square-Cube Scaling Law, various scaling laws have been identified and explored in AWE domain literature. This topic is to review and add to understanding of scaling laws in AWES design, in order to predict how well various architectures can scale.


It is a main topic. For what I know from Yahoo forum is the constance with which @kitefreak advocated soft wings vs rigid wings, developping Mothra
Scaling better is also a mean to optimize the land/space use, another potentially main topic.

There is a Storm Dunker’s paper on then click on request full-test blue button.
Page 532: “The development originated as an Advanced Concept Technology Demonstrator
research program from Natick Soldier Systems, whereby iteratively heavier
weight requirements were levied (0.25 ton, 1 ton, 2.25 tons, 4.5 tons, 13.5 tons, and
finally 19 tons). The wing sizes were 36 m2, 102 m2, 250 m2, 350 m2, 900 m2,
and 1,040 m2, respectively.”

Now waiting for Dave’s precisions about quasi 2D flexible kites, and quasi 3D rigid wings, their respective potential and so on.

I’m convinced networks are the best way to scale AWES.
Both Storm Dunkers parachutes and @kitefreak’s mothra were so large they had to be made modularly.
The loading on a large wing becomes so huge that the material needs to be heavy this results in limited workable conditions.
Yes finding an efficient span is important but it must also be able to tolerate the strongest winds and calm.
Spreading multiple loads across wide anchored rope networks works wonders for scalability.


That can be dealt with by bridling on kites in contrast to planes. And planes are quite a bit larger than any awes at the moment. Larger wings have less wingtip losses.

Most things become more efficient with size. Thinking of planes and ships.

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Large aircraft have large minimum take off speeds. Same will go for large AWES minimum working wind speed. See the Makani test video. Bold statement time… Thon thing was definitely powered to complete the upward part of the loop.
Yes aircraft can be tethered… That’s an AWES. Makani, twing, Ampyx etc is like an aircraft kite.
However , Just like biplanes with ties and struts between wings… there’s a lot of extra drag with lots of added tether.
Conversely with networks … it looks like a lot of tether, but it’s a lot more kite per tether length. Each kite is only responsible for a short section of tether , the tethers share function with all of the connected kites.
There are seagulls flying backwards outside here today (over 20m/s wind ) a 747 sitting on it’s tail on a kite string still won’t take off.

That isn’t because of the size. Airliners and other large aircraft have other design priorities.
Solar impulse with a span of ~ 60m has a takeoff speed of under 10m/s.


That is a good argument that scaling exists. A EDO slow flier flies well at (?) 2 m/s. A butterfly much less.

Positive scaling laws: Kites could have bridles, this is not so easy for aircraft.

Tether scales with sqrt(X) where X is the scale factor in force. So double force only gives sqrt(X) increase in diameter. The force scales with the cut area of the tether, while drag scales with diameter.

This scaling also has a «evil cousin»: If you split tether load on N tethers, you need a factor of sqrt(N) more diameter to withstand the same force.

I think perhaps something that wont scale well is a beam, for instance one to stiffen the wing. Someone with mechanical background should be able to shed more light on this.


I’m not buying any of the “larger planes planes need higher speed for take-off”.
It’s not that I’m very much convinced of the opposite. It’s just that the arguments have so far been unconvincing.

A butterfly is practically a VTOL. That would mean that I could use an Osprey as an argument that larger planes don’t need any takeoff speed.

Just imagine a simple rigid board as a kite. If it’s larger it will take off in less wind since the area increases faster with size than the losses on the edges. Or imagine a multitude of those kites alone vs connected.

Is there a rigid wing AWES design which suggests it needs no power to assist launch?
I’m all for drone assist in launch and recovery. but once deployed that is dead weight and aught to be shed.

Imagine a perfectly rigid, unbreakable, and weightless material, and try to make a perfectly efficient wing out of that. How long can you make the chord before drag becomes too much of a problem under normal circumstances at ground level and at your desired flying speeds?

There you have another scaling limit I think. And the more your material of choice is worse than that ideal, the sooner you reach that limit.

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One more on tether scaling: The melting point of dyneema/spectra is constant. The ability to shed heat from the tether reduces with diameter with reduced skin area vs volume. At some point tether heat dissipation could become a limiting factor

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Thought excercise: Imagine a foam wing at 30 cm wingspan. There is no issue with weight or structural strength at a given airspeed, say 5 m/s.

Now scale that foam wing to 100 meter wingspan. Structurally, it will not be stiff enough to hold it’s weight anymore. I’ll leave that exact calculation to someone who knows mechanics.

The lift of the wing is proportional to the area, so the lift should now be (assuming no change in Reynolds number) X^2, where X = 100/0.3. The mass of the wing will have changed by a factor X^3, as volume scales in three directions X, Y and Z. The ratio (lift/weight) has been reduced by a factor of X.

As if this wasn’t enough, the Reynolds number itself will have changed in a way that the polar curve of the wing is not as good looking anymore, in particularly at the low wind speeds.

It’s not easy to put all these relations into a simple formula. I believe for any scale, the calculations should be redone mostly for that scale.

That being said, I believe there are scaling problems to be found, but we do not need to scale to infinity. A useful AWE wing can be 10 kW or 1 MW. The useful question is not: “Will AWE scale to 100 MW in one wing?”. Rather we should be asking “Can we design a useful wing at X kW?” or even “How many kW can we currently design a wing with a certain design?”. When you get to that maximum number for a design, you can only scale by incremental improvements or by changing the design. At this point, saying something about the maximum scale of an AWE rig has a lot less uncertainty. Changing the design will be a story of diminishing returns.

Being such a young industry, we are quite certain to still see large incremental change and also perhaps sweeping design changes compared to whatever people are doing now.


Another consideration when scaling is, that if one has a tested and prooven smaller scale awes and possibly even a production line, just cranking those out is relatively cheap.
So even if there are efficiency gains in larger awes, in such a situation the prooven design would be more price efficient for quite some time.

If we look to windmills, small scale is in general not cost effective, with prices around 0.11 - 0.25 € per kWh. With massive scale, the price drops towards 0.025. This argument tells us that AWE probably needs to scale in some way to be cost effective for general electricity production.

Re is not a major scaling barrier, in kPower’s view since, at our target winds ~500m high, as unit-scale grows, most-probable-wind-velocity does not. The two factors tend therefore tend to cancel.

Rigid wings can be bridled like soft wings to handle large loadings. The practical scaling limit on rigid wings is vulnerability to even slow impacts, like “forklift accident” in aviation, or landing hard on an AWES cradle.

A simple survey of aircraft classes shows larger rigid airframe aircraft generally do require proportionally greater take-off and landing velocities. The exceptions are large very fragile very expensive aircraft, like human powered aircraft, where the engineer trades away normal airframe robustness for maximum lightness.

If economy of scale does apply in AWES as it does in related fields, then we need to be thinking of GW scale kitefarm units of networked unit-kites rated at a few MW each (shipkite equivalents). An applicable scaling law is the largest soft-kite unit that can be handled as a bundle on the surface, given delicate kite fabric.

As the unit-kites and their kite networks scale up, rope load-paths take the aggregated forces. Ropes scale far better that rigid wing structure. We have two scalable media to depend on- the rigid surface of the kite field and the pressure field of “wing-in-ground-effect” of giant kite networks in FAA-designated airspace <2000ft AGL (above ground level).


Just like the largest wind turbine blades are not solid, so would the largest airplanes not be. So this would not hold I think if I understand you correctly.

I think a probable design for a giant wing is some sort of rigid or semi-rigid envelope around a pressurized chamber, probably using that “tensairity” principle, composed of multiple sections so that even if your parachute or other safety mechanism failed to deploy, you wouldn’t lose the entire wing in a crash. You could maybe even add crumple zones. You would I think want to look at the thickness vs length of the wing so that the wing is more resistant to bending, but wouldn’t that also reduce the efficiency of the wing?

Why is that? Because of higher wing loading? Because of the wings being designed to work better in higher speeds for example?

You want your wing to fly fast, right? To reduce material usage? How fast?

I think the question is too vague. More useful would be: what are all the ways that you can imagine building a wing, and how large can you reasonably make that? How much would those cost in material? How much power would each of them be able to extract from the wind?

The question attempts to get a quick overview of the thing by asking about everything at once. That’s too wide a question to reliably give rise to useful discussion. Better to ask about every single thing separately. [1] How big can you make this? [2] …? Slow down to speed up.

It seems to be the “sports car fallacy” to “want your wing to fly fast”. Look also at draft animals, the strongest are the slowest.

As for “material usage”, the theoretic maximum is 100% polymer at its rated work load. Anything less is parasitic. A rigid wing is unable to distribute working loads as efficiently as tensile structure.

Tensairity loses to ram-air parafoil structure because it does not progressively stiffen with greater velocity as needed, and requires the added parasitic mass and failure modes of air pumps. This is basically the same scaling limit as LEI airbeams.

Right, a tensairity structure is always at optimal inflation pressure. That’s bad? Needing a few pumps is an engineering challenge, not a scaling limit I think. It makes up for the extra complexity by being superior in other ways.

Yes, a fabric kite will scale the most. It will not be the fastest. I want a wing that goes fast so I can make use of the cubic increase in power, and make it smaller and cheaper over the long run if it doesn’t crash. The only snag is that it is more brittle. I gave an architecture that is not so brittle and added some safety features.

Disclaimer again: I know nothing.

I think my argument about the foam wing holds, here’s why:

Even for a carbon skin wing, the skin of a bigger wing will probably be thicker, thus you (very simplified) still have X^3.

When you say that a large wing would have tensairity, you have already done some optimisation, scaling using better materials rather than just scaling up the foam structure. I believe such optimization is probably quite necessary, but it does complicate the scaling discussion without changing the fundamentals.

The @kitefreak arguments about «the forklift problem» is very well thought through, there seems to be quite a lot if insight in those paragraphs

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