Real efficiency of "Crosswind Kite Power" measured at the kite height?

As everyone knows “Crosswind Kite Power” is the title of Miles L. Loyd’s seminal paper, and is the basis of a good part of AWE projects.

“Crosswind Kite Power” has been discussed in many threads but among other considerations.

This is why it may be interesting to return to the basics and compare its supposed efficiency with the results of two test reports that I had the opportunity to comment on but in topics for which the efficiency of the “Crosswind Kite Power” was not the first consideration. These two publications are, to my knowledge, the only ones reporting crosswind tests concerning flexible kites in yo-yo mode (pumping mode) flying by figure-eight. Although almost 10 years apart, the results were very similar, all things being equal. A comment and two quotes from another comment are therefore placed just after the two documents, and relate the two test reports.

The main power equation is summarized in the page 3 of

Page 3:

The power P that can be generated with a tethered airfoil operated either in drag
or in lift mode had under idealized assumptions been estimated by Loyd [8] to be
approximately given by P = 2/27ρAvw³CL (CL/CD)²
where A is the area of the wing, CL the lift and CD the drag coefficients, and vw the
wind speed.

Subsequently, to begin refining the basic formula, we multiplied it by a coefficient integrating the cubed cosine loss, for example 0.65 for an elevation angle of 30 degrees.

The main question (hence the topic name):
But what are measurements taken a few meters from the ground worth when the kite is flying hundreds of meters from the ground, where the power (wind speed cubed) is of the order of 3 times greater or even more?

Usually the wind speed of a conventional wind turbine is taken at the nacelle level.

It would therefore be more judicious, if possible, to place the anemometer on the kite, take the wind speed when stationary and in the middle of the flight pattern. In these conditions the efficiency would then likely drop. And knowing the reasons could help. I myself had noted the irregularity of figure-eight flight, preferring by far the more regular Low radius loop one. But there may be other reasons: perhaps the winch loses a lot of its effectiveness as the kite accelerates and slows down, unless the unwinding speed is stabilized in spite of kite speed variations.

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Hi @PierreB,

The point that you raise has been discussed intensively, especially which wind speed to use for performance characterization.

In our early work, we used the wind speed at the ground, for the simple reason that this is where we were able to measure conveniently, without a Lidar or any advanced onboard sensors and estimation techniques. An example is our 2013 Springer book chapter about the TU Delft kite power system:

van der Vlugt, R., Peschel, J., Schmehl, R. (2013). Design and Experimental Characterization of a Pumping Kite Power System. In: Ahrens, U., Diehl, M., Schmehl, R. (eds) Airborne Wind Energy. Green Energy and Technology. Springer, Berlin, Heidelberg. doi:10.1007/978-3-642-39965-7_23 (preprint available from here).

However, with the advancement of technology and more groups operating systems, it was decided to use wind speed at the operating height of the kite. This is also described in the glossary available from Airborne Wind Europe, which was compiled after extensive exchange between all teams operating hardware.

If not directly measured, the wind speed has to be estimated. A rather simple way to estimate is to assume a certain vertical wind speed profile. But this clearly has limitations, as clearly visible from these works:

Schelbergen, M., Kalverla, P. C., Schmehl, R., and Watson, S. J.: Clustering wind profile shapes to estimate airborne wind energy production, Wind Energ. Sci., 5, 1097–1120, 2020. doi:10.5194/wes-5-1097-2020

Sommerfeld, M., Dörenkämper, M., De Schutter, J., and Crawford, C.: Impact of wind profiles on ground-generation airborne wind energy system performance, Wind Energ. Sci., 8, 1153–1178, 2023. doi:10.5194/wes-8-1153-2023

It is quite often not the case that the wind speed at higher altitudes is so much stronger. There are many variations to this early simplification. In this work

Dylan Eijkelhof, Roland Schmehl: Six-degrees-of-freedom simulation model for future multi-megawatt airborne wind energy systems. Renewable Energy, Volume 196, Pages 137-150, 2022. doi:10.1016/j.renene.2022.06.094

We distilled from the above-mentioned Schelbergen et al (2020) two characteristic wind profiles, one for onshore and one for offshore conditions (see Fig. 6). Both are in the Netherlands, so the onshore is on quite flat terrain. You can see that the offshore profile is nearly constant above 200 m. And that wind profile is the most frequently occurring profile.

In terms of measuring the velocity at the kite, we presented in the following paper an interesting approach, using the measured kite speed and the measured apparent wind speed:

Mark Schelbergen and Roland Schmehl: Validation of the quasi-steady performance model for pumping airborne wind energy systems. Journal of Physics: Conference Series, 1618, 032003, 2020. doi:10.1088/1742-6596/1618/3/032003

We will soon evaluate how this estimation technique performs using additional Lidar data taken upwind of an operation kite power system.

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Adding to what I wrote earlier, Mark Schelbergen will defend his PhD at TU Delft on Monday 18 March at 3pm (CET). The title of his dissertation is Power to the airborne wind energy performance model: Estimating long-term energy production with an emphasis on pumping flexible kite systems. The presentation and public defense will be broadcast online. We will distribute a link ahead of the defense.

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Hi Roland,

Thank you for your analysis. Indeed the last document is interesting, starting with Figure 1 including “Measured 6 m”, and “ERA5 (reanalysis) wind speeds at three heights (10 m, 150 m, 250 m)”.

Is it not possible to settle an anemometer at 6 m, then another anemometer on the kite when it is stopped, taking measure at least in the middle, and if possible also in the bottom and the top of the flight path, that before and after operation when kite and apparent wind speed are measured?

Then compare the results with the other techniques and reanalysis tools you mention. It is because the only measured kite and apparent wind speed can diverge a little from the deduced real wind speed at some places such like turns, due to the variations of the effective L/D ratio during figure-eight.

In the same time the combined measures of real wind at various heights and the kite and apparent wind speed could perhaps improve the knowledge of the efficiency of the crosswind kite and the L/D ratio at different places of the path.

Everything I describe does not allow simultaneous measurements between the real wind aloft and the speed of the kite in operation and that of the apparent wind.

For this, at least one other kite (with an anemometer), this time a static kite, would be needed to measure the wind at the altitudes at which the power kite is evolving, and flying close to it (without hitting it!). A Lidar, or, failing that, a navigational compass, would allow to control the evolution of the altitude of the static kite, and the average altitude of the crosswind power kite, so that they converge.