Scalability of Skysails, an outsider point of view

So Skysails announced their power curve with 160 kW at around 14 m/s at the kite. I was wondering about their scalability, and what we can make of this from the information we have.

ChatGPT says:

Skysails are typically used to harness wind power for propulsion, especially in marine applications. The weight of a Skysails kite can vary depending on its size and the materials used. Generally, they range from about 100 kg to 500 kg. For instance, a 160 square meter Skysails kite, suitable for a large vessel, might weigh around 320 kg. This includes the weight of the kite itself and the associated control system components.

It seems a 160 sqm kite coincides quite nicely with their 160 kW output, looking at the generic numbers at their web page.

For a 160 kW producing plant at 14 m/s the pull of the kite should be (reel out 1/3 wind speed assumed) 34 kN (approx the weight of 3.5 ton).

So at this point we have a flying gravity force to lift ratio of

\kappa_{160} = \frac{34k}{320 \cdot 9.81} \approx 10.8

Lets assume they want to scale double wing span, achieveing a power of 640 kW. Also lets assume cubic scaling of mass from here on. Thus we have the square-cube law in action. Power and area scales with the square of the scale, the mass by the cube. That means at this scale, the ratio would be

\kappa_{640} = \frac{4 \cdot 34k}{8 \cdot 320 \cdot 9.81} \approx 5.4

Doubling again to 2560 kW gives us

\kappa_{2560} = \frac{16 \cdot 34k}{64 \cdot 320 \cdot 9.81} \approx 2.7

I think a ratio of 5.4 may still work well enough, but a ratio of 2.7 probably won’t.

So we can conclude that when Skysails try to scale above 500 kW, they will need to optimize the weight of their kite.

For the sake of an argument I’ll reply

For your fist paragraph…
I don’t think the phrase “Gradient descent is better than you” applies to you yet @tallakt
We’re still better off with facts in preference to GPT blah.

Square-cube how closely does this apply to a big RAM air inflated pillow?

I’m not sure. At one point, the cloth used for the kite needs to be thicker to maintain the increased tension of it? Or could we see the same cloth being used for a huge kite?

The scaling of the kite control unit and such would probably be close to cubic i suppose?

The fact that they are already on a ratio 10.8 tells me weight is an issue…

The ChatGPT bit looks like a complete hallucination to me, where would it even get that information. And since the kite is bridled, you also can’t assume cubic scaling I think.

I agree that the “information” given by ChatGPT here is not really information rather just speculating that the AI would return a number close to reality. If could do that if it had numbers from its learning set or if it knew about similar kites.

Anyways, take the whole analysis with a big grain of salt.

I think though, that 320 kg sounds like a fair number for such a kite.

We could look at some parts of the kite that would scale (assuming scaling by x):

Control unit: the larger kites would turn slower, so you could spend more time to control steering lines. Maybe the control motors scale x^2-ish? Edit: Though the forces on the control unit would scale, suggesting less optimistic scaling

Bridles: Assuming the number of lines remain constant, the mass scales by x^3 (force scales x^2 and length x). Drag scales x^2 like the lift of the kite, so the relative ratio [bridle drag / kite lift OR kite drag] and scales constant (no scaling). Note though; if you increase the number of bridle lines, mass still scales x^3 but the drag of the new bridle will increase relative to the lift of the kite.

Skin: The skin is just for the pressure. As the pressure is the same for any scale, maybe the skin could be the same thickness, and the mass of the skin scales x^2.

Skin reinforcements: To attach the bridle to the skin, the force on the bridle should scale by x^2. Additional reinforcements would need to increase both in thickness and area, meaning those parts scale x^2

Ribs: The area of the cloth used for ribs scale x^2 assuming the same number of cells. But, the force between the upper and lower skin should also increase x^2 due to larger cells. The thickness of the ribs must increase by x. Ribs should scale by x^3. If you increase the number of ribs though, the ribs still scale by x^3.

Internal strain relief: I’m thinking about the internal webbing that would hold the tension in the kite (eg going from left to right). The length of these should scale by x and presumably all forces increase by x^2 so these should scale by x^3.

I think there are enough components that scale by x^3 to assume scaling will introduce some mass issues.

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Also as a “data” point, for paragliders ChatGPT says

  • 18.1 m² - Weighs 4.2 kg
  • 20.2 m² - Weight not specifically listed
  • 22.4 m² - Weight not specifically listed
  • 24.6 m² - Weight not specifically listed
  • 26.8 m² - Weight not specifically listed
  • 28.1 m² - Weighs 5.3 kg

For the ProDesign CUGA 3, which is a paraglider, with a reference at Performance paraglider - CUGA 3 - Pro Design - single place

Assuming constant mass per square meter, those numbers would put a 160 m2 Skysails kite at 37 kg (relative to 18.1) to 30 kg (relative to 28.1). I believe the reason for this would be that the kites are built to carry the same person mass, so the smaller parachute must be relatively stronger.

ChatGPT also stated in the cloud of hallucinations, that the Skysails kite was 50 kg, without the control unit.

Maybe the control unit could be made a lot smaller, and the kite itself could easily be very large?

A clear low hanging fruit for Skysails could be single skin kites though, like the Flysurfer Peak.

According to ChatGPT, single skin paragliders have half the mass or less, compared to normal design paragliders.

This may also have a positive impact on resource use and cost

I’ve been testing a Flysurfer Peak5 4m
Great kite
They’re still complex to manufacture = pricey

And they might not fit well with the mast inflate / nose tag line deployment method Skysails use.

Skysails did change their leading edge inlet / valve flap design fairly recently
See the cover of the book of abstracts vs 2 years ago where there were many fewer ram air inlets… Did they stall or deform with low pressure previously?

I think the peaks are cheaper than their double layer counterparts.

Peak 5 13 sqm $1100, Soul 2 12 sqm $2550

I guess. But the single skin paragliders did have an inflated leading edge, there may be a middle ground that works, eg more like Gin Marabou

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Yet to try a hybrid
Yeah they look good
Skysails are very good at keeping things no more complex than they need to be
Keeping a single skin kite flying can be a bit more complex as backstall and overflying are more possible

Got to say the power delivery available in the PEAK5 4m is impressive
I was farting around dragging my wellies over the sand at high speed a few weeks ago and after becoming a bit too blasé I got very thrown.

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Luckily, soft-kites do not scale with the square-cube law, as you suggest here. Much of the mass of a soft-kite scales also with the wing surface area, such as the aerodynamic forces. That’s the fundamental difference between soft-kites and fixed-wing kites and that is why I think soft-kites could have an advantage for scaling up. Of course, there is not only mass but also ground handling that plays a tremendous practical role.

Clearly, the differences in mass-scaling behavior of soft- and fixed-wing kites is a very exciting topic and you should soon see some publications about the subject.

I am trying to understand why you may suggest that.

For instance, the bridle would experience cubic scaling. At one point in scaling, the weight of the bridle would become important.

Also look at the skin; you can’t expect a 1 MW kite pulling 25 ton [250 kN] to use the same fabric as the paraglider supporting <150 kg [1.5 kN] load.

At some point, mass scaling will become important. The question is really, at what point is that. Is it in some distant future?

I think the soft kite lower glide ratio is dictating the larger size, which in turn puts you further ahead on the square-cube curve.

I am also sure my dabbling with numbers would not lead to an accurate understanding of where soft kite scaling would end. But maybe it is better than nothing…

I would also like to mention that the air trapped in kite cells scale cubically, and may affect turning speed. (as mentioned by Peter Lynn Kites)

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Here some quick sources:

From Mikko Folkersma’s PhD thesis

Figure 2.5 shows a comparison of the mass per projected area and the scaling of the commercial surf kites. Note that in kite surfing, the designed traction force of the kite remains approximately constant as the kite surface area grows. The larger kite designs are for lower wind velocities, and therefore the tensile forces in the membrane remain rather constant. While in AWE, scaling up aims to generate higher traction force, and therefore, the tensile forces increase linearly with the surface area. Then, the membrane thickness must increase, or more reinforcements and bridle lines are required. Hence, a similar downward trend for the specific mass can not be expected for the AWE kites when scaling up. Generally, a low specific mass is a desirable property as it allows operating the system at low wind speeds. However, lightweight wings are also more prone to disturbances such as rain and gusts, as mentioned earlier.

The mass of the TU Delft LEI V3 kite (25 m2 flat wing surface area, 19.7 m2 projected area) is 22.8 kg. This amounts to a mass/surface ratio of 1.16 kg/m2. Note that this includes bridle line system and kite control unit, which is 50% of the kite’s mass. So, for only the wing, we get to 0.58 kg/m2 which is in the range of conventional surf kites.

From Paulig et al (2013) we know

The specific weight of 160 to 320 m2 kites is around 0.5–0.6 kg/m2

which is in line with the V3 kite (I am not sure whether Skysails refers to flat or projected area). But this at least indicates that in this size range, the mass of the wing scales linearly with the wing surface area.

I do acknowledge that this is only a very rough analysis and I know that kites are increasingly reinforced and/or bridle lines added to increase the wing loading. So, a slightly steeper increase of mass than linear should be expected. But still, this is far from a square-cube law.

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A publication was evoked here. I put again an excerpt of:
Ram-air Wing Design Considerations for Airborne Wind Energy * DOI: 10.1007/978-3-642-39965-7_31. Page 532:

A prime example of the scaling process is documented nicely in the X-Fly family
of Ram-air precision cargo delivery systems from Airborne Systems North America
[9, 11]. 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.

This example concerns heavy RAM designs which lead to a mass penalty, although far lesser than for a rigid kite.

Now some information of the weight of a 200 m² kite by SkySails on:

The weight of the kite depends on its size. A 200 m² kite weighs about 50 kg.

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Thank you for the data provided. It seems we do have more data.

I would like though to point out one piece of data; According to page 561 in the first Airborne Wind Energy Book, Skysails used to use fabric 200 g per m2 when the book was written. I looked up some numbers on ChatGPT stating kitesurf foil kites use fabric 44 g/m2 for top and bottom skin.

This does suggest that some things happen with scale.

I don’t know what the numbers would look like, but if we disregard any technology changes, I expect the scaling of soft kites may also be x^3 or close.

I did present some first principle thoughts about scaling. Seeing that some elements scale x^3 it should be clear that at some huge scale, kites will scale x^3. The question is really if that scale is relevant or not.

I would like to emphasize again, thanks for pointing me to data.

The data I would actually trust though would be some dataset where you first scale the kite to a size where every part of the kite is at it’s necessary strength. For example, you could foresee scaling a LEI kite from 12 sqm to 24 sqm without selecting any other materials, just increase the panel size. This would represent x^2 scaling. At one point though you can’t continue this kind of scaling.

The Kitepower LEI kite presented at AWEC 2024 is a prime example of design optimization at scale, where we have a lot more struts than a kitesurfing kite, and at a relatively much smaller diameter. Also the panels between each strut is curved. This represents just a scaling from eg. 16 sq m (which is a fine size for kitesurfing) to the displayed size of 40 sq m and also increased pull force.

Then, once arrived at the point where increasing size would cause the strength to be insufficient, you would have to scale fabric size and thickness. This would be x^3 scaling. Though of course its not that simple, because for instance the bending moment on an enlarged inflated beam would not scale linearly with scale.

I don’t think I have seen any such numbers yet. Maybe the X-Fly wings could be such an example is each size was optimized in material use and then the weight of each wing was provided. Both I think are not true.

If the Skysails airborne mass is 320 kg, it seems soft kites are in no better situation for scaling huge than rigid kites, as this would be similar to the numbers presented by eg. Ampyx, Twingtex, Kitemill for similar sized power output plants. And with Enerkite claiming only 12 kg for a 6 m wingspan kite [maybe in the 10-30 kW range?], their 160 kW size should have even much less mass [estimated around 260 kg with cubic scaling].

One would have to argue that rigid kites are going to follow a worse scale to mass curve compared to soft kites. If this was true, maybe we should see the effect of that already at 160 kW?

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The big difference of weight, like a jump of mass increase per area, between the 900 m² and 1040 m² wings (13.5 tons and 19 tons), and some points of your analysis could suggest that scalability of flexible kites could go from about to when the kite area increases.

We can only guess, because we don’t have all the elements. And it’s hard to know how much we can extrapolate from cargo delivery systems to flexible AWES.

I was thinking the mass was for the load the wing should carry, not the wing itself. Eg. a 36 sqm wing should be able to lift a 250 kg load… sounds reasonable

If the scaling was not area proportional to wing size, one reason could be that the wing mass itself was starting to make some kind of impact. This is way speculation though, I don’t think I could conclude much from this data.

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Indeed, I had misinterpreted.

But in this case we see that the wing area increases less quickly than the load carried, hence an increase in the wing load as the wing area increases.This would be a positive point on the scalabilty of a flexible wing as argued by @rschmehl, but not enough to conclude in one direction or the other.

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There has to be a limit in the chord length, if you want the kite to be reasonably efficient, fly reasonably quickly, not deform excessively, and have a reasonable turning radius. So my guess would be that you want to try increasing the span of the wing before increasing the chord. I think good questions are: what is a chord length that still makes sense, and what is a good aspect ratio?

A benefit of a smaller chord would also be that you would create less turbulence for the kites above if you decide to go for a kite train, so you can decrease the spacing between the kites.

The 900 m² wing is MegaFly (30K MegaFly.pdf (475.9 KB)). The weight of the canopy is 410 kg. So it is in the 0.4-0.5 kg/m² range.

The modular canopy of the 30K MegaFly is made of five separate segments for ease of recovery.