AWE Power Curves

[Rodread]

So after a bit of tidying I believe the charts for scaling Kite Turbines say the following

Note : These are all reliant on an as yet unproven coaxial autogyro stacking method replacing the old lift kite

Now also spotted a flaw in the codebase where stale documentation lead to a poor analysis of FoS.

Also these are totally upper bounds numbers. There’s a red flag been raised on the momentum calculations for the expansion rings.
Edited overnight. The model now respects momentum theory throughout. Much more reasonable power outputs

[PierreB]

In the section of the video on mass scaling in accordance with square-cube law, the exponent 3/2 is applied and works for SkySails’ flexible kites. The exponent 3 can be applied when the size is considered instead of the surface area.

About Makani, I calculated an exponent of 1.582 (based on surface area), or 3.164 (based on size).

About Ampyx, the exponent becomes 1.88 (based on surface area), or 3.76 (based on size).

In other words, flexible wings scale cubically (about the mass), and rigid wings beyond that.

Traditional wind turbines scale much less, and on top of that, they don’t need to fly.

@PierreB

this expected growth to the power of “3” has been reduced to as low as 2.2.

[derek-rewind]

Rod

Some test data (baseline 10m/s wind speed) :

System Hub Height Power Out swept Area Cp Power/Weight Power/Area*
m kW m² % W/kg kW/m²

Daisy 20 1.28 11.4 0.18 120** 1.1 Ref 1
(optimised)

Bergey
Excel 10 30 6.8 38.5 0.29 119 2.0

Makani M30 93 16 2312 0.01 211 4.0

* = Area of kite, wing, or blade set
** = estimate

Weight is ‘in air’ (aero) only e.g. AWE(kite + tether), AWE(blade set + driveshaft), HAWT(blade set)

It would be interesting to see the Daisy Sim output, with the same Power output & Hub Height of both the Bergey and M30 (at 10m/s wind speed) …

Ref 1 : New model for structural optimisation of airborne wind energy systems with rotary transmission, J Wacker et al (2023)

Pierre

Yes, the data shows that soft kites (excluding pod) ‘scale up’ better than rigid kites (wrt mass), but not better than the ‘cube square’ ratio.

[PierreB]

I couldn’t find the mass (8 kg) of the 30 m² SkySails prototype, nor that (120 kg) of the 180 m² PN-14.

Besides, I weighed two of my old 4-line Buster power kites: the 4 m² kite alone weighed 0.795 kg, and the 9 m² kite alone weighed 1.72 kg, which is a mass scaling slightly less than the surface area, so slightly less than squared.

[PierreB]

About scaling of flexible kites:

Scalability of Skysails, an outsider point of view

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 ther…

@rschmehl

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.

[derek-rewind]

Pierre

There are references everywhere, and they are all different. It’s a ‘reasonable’ estimate (in video), since there’s no Skysails published data.

Some sources →

30m² kite → AWE Book, U Ahrens et al (2013) : page 431 plus Deformation and Aerodynamic Performance of a Ram Air Kite, A de Wachter (2008) page 26

PN-14 kite → AWE Book, U Ahrens et al (2013) : page 554 & 561 plus
Analysis of the Maximum Efficiency of Kite-Power Systems, S Costello et al (2015) Table I

[PierreB]

Derek,

Thanks for these references. Unfortunately, I only have access to two publications.

In page 26, Aart de Wachter does not mention (for what I saw) the 30 m² kite with a mass of 8 kg, but Flysurfer Pulse2 6.0, 6 m², with a mass of 1.6 kg, for a normal wind range of 6.5 – 21 m/s.

“Analysis of the maximum efficiency of kite-power systems” (S. Costello), table 1, mentions SkySails’ kite of 400 m² with a mass of 320 kg.

400/6 = 66.66…
320/1.6 = 200.
The exponent is 1.262 (or 2.524 if the size is the basis).

@rschmehl

But still, this is far from a square-cube law.

Maybe not as far as we initially thought, regarding the flexible wings.