Yes @Saqlain, Loyd’s formula is used. The gliding ratio can be defined as the lift-to-drag ratio. If L/D =

4, (CL/CD)² = 16. So this ratio is important to determine the efficiency of a crosswind kite.

The value obtained by this formula is multiplied with the cubed cosine. As an example if the elevation angle is 30°, the cubed cosine is 0.65.

# Makani Kite power calculations

I guess Makani would be using a glide ratio 8-20? This is pure guesswork of course. I would not use the energy formula, rather just calculate the power, speed etc. There are many ways to do this, differing in perspective…

You could read some paper which are quite detailed about this, eg. Kheir et al 2019, DOI: 10.1016/j.jweia.2019.04.010

Air density of I.2 is an average value at ground level. Of course the air density varies with altitude and temperature.

As full rated power wind speed, 10 m/s is an often used value. Other values can be chosen. http://www.energykitesystems.net/FAA/FAAfromMakani.pdf Makani provides a rather low value of 9 m/s.

Because the conversion system (the turbines aloft for a flygen like Makani, but also the reel-out phase for yoyo mode with the generator at ground) should slow down the device for 1/3 in a standardized calculation.

“Verification: 33 x 1.2/2 x 70.666666 x70.666666 x 70.666666 x 0.0857575 = roughly 600 kW.”

If I remember correctly I used the classic wind energy formula, multiplying the full area of the secondary turbines (33 m²) with air density/2, and with cubed apparent wind speed.

I added a coefficient of 0.0857575 to obtain 600 kW, because the turbines are very large in regard to the expected efficiency in regular flight, that due to vertical takeoff requirement. Indeed 33 m² of secondary turbines is a huge value compared to the wing area.

Some precision; I do not know what are all features of Makani M600, so I complete with hypothetical numbers in order to obtain 600 kW. If we consider the 9 m/s wind speed value as specified by Makani (instead of 10 m/s), some other variables should have a higher value.

How much value should I choose for density? what would you suggest. For height of flight only range is given from 110-310.

A little less, perhaps 1.1. There is a curve for air density below:

https://www.engineeringtoolbox.com/air-altitude-density-volume-d_195.html

Another point: there are losses due to the irregular power according to the place of the wing within the wind window. The sound varies during the figure as we can hear on the videos below.

Circular figure:

Figure-eight:

.

Hi Saqlain,

Welcome to this forum!

How much time do you have to complete your project? You have chosen a very complex question, and it will take some time to locate key references scattered in the domain literature.

Be sure to calculate square-cube and other parasitic up-scaling factors, which are predicted to be starkly evident between Makani’s 30kW Wing7 prototype and the M600 prototype. Its quite possible the M600 is netting very little power due to looping cycle phase losses, and high energetic cost of just maintaining its large mass in flight.

. Thank you for your help brother. I have another question related to this topic that why we can not use blade element momentum theory beyond induction factor of 0.5?

You’re most welcome, Saqlain. Given the short time frame, it will be very hard to produce a correct estimate. Blade element momentum theory as such omits many critical parameters, including the parasitic effect of maintaining high mass powered flight.

The 600kW claim has limited objective public data basis. Makani has not provided key data, like how much platform and tether weigh, nor the tested thermal limits of their larger motorgens, and other electrical losses. They likely would have shared power curves that met optimistic claims.

There is one source of good public data; Videogrammetric parameters, to derive flight pattern scale and time values. A sufficiently deep video analysis, including the audio track and wind-velocity clues, in principle suffices to derive close net power-out estimates.

Here is a well documented paper below:

I also provided the link on Limitations of Blade element momentum theory.

Hello Saqlain,

Have a look at this preprint of an AIAA JGCD paper that I published last year together with co-authors from Makani:

https://www.researchgate.net/publication/326954168_Aeroelastic_Analysis_of_a_Large_Airborne_Wind_Turbine

It is focused on the aero-elastic behavior of the wing but does contain many design parameters that might be of use for you.

You may access the published paper also via http://doi.org/10.2514/1.G001663

Roland,

Why are there no tested M600 power curves publicly supplied by Makani? Why no Norway Mishap Report either?

It seems the likeliest reason these numbers are secret is that the M600 is not delivering enough power across the lower wind range, due to predictably severe scaling law limits on its architecture. A similar logic of investor/public-relations damage-control seems also to explain the missing mishap report.

Surely TUDelft has an informed opinion about what hidden M600 data would reveal. We should all press for full disclosure, on academic and safety culture grounds. Are any of the AWEurope folks under Google NDAs?

Hi @rschmehl,

I propose to introduce the ratio power / land and space used which is more realistic than the usual power/wing area ratio.

The initial question was about M600. Its tether length is 440 m, being also the radius of the minimal covered land area of 0.6 km², leading to a density of 1 MW/km² with difficult or no secondary use due to safety issues, that compared to about 8 MW/km² for the current wind turbines with possible secondary use.

By supposing that 600 kW is really reached (is there a power curve?), a farm of kites of this type would multiply the issues.

As a result IMHO architectures maximizing the land and space used should be more investigated.

Hello @PierreB,

I also think that the power-to-surface-area-used ratio is a useful metric, especially once AWE systems have reached higher TRLs and are operated in relevant environments. Only then we will have more certainty about the surface-area-used parameter.

The power harvesting factor \zeta=P/(P_wS) that is now often used in theoretical studies [1], was introduced as a result of dimensional analysis. It uses the wing surface area S because this is the only area measure that is constant for an AWE system. Other than wind turbines, where the blades of the rotor are always sweeping a constant area A=\pi l_b^2, an AWE system will not necessarily harvest from a constant swept area. This is also the reason why it is not straightforward to formulate the Betz law for AWE systems, which has been the subject of a number of recent studies.

While we can now determine the power output and annual energy production (AEP) of AWE systems with reasonably good accuracy, both by measurements as well as by computational simulations, the surface area used by AWE systems is a less tangible parameter. It will be influenced by the specific type of AWE system (e.g. rigid wing vs flexible membrane wing), operational safety characteristics and regulations. I think that you will agree that there is little data available on this. Also the cost of this surface area needs to be taken into account (offshore vs onshore). Your estimate of drawing a circle with the maximum tether length around the ground station is only a first guess, which will probably be contested by industry. In recent publications [2,3] about flexible wing systems we have introduced a spacial layout of kite parks that is requiring decidedly less space. See, for example, Fig. 4 in [2].

But I do agree that AWE architectures maximizing the surface area by concept used should be investigated more thoroughly.

**References**

- R. Schmehl, M. Noom, R. van der Vlugt: “Traction Power Generation with Tethered Wings”. In: U. Ahrens, M. Diehl, R. Schmehl (eds.) “Airborne Wind Energy”. Springer, Berlin Heidelberg, 2013. doi:10.1007/978-3-642-39965-7_2. Preprint accessible as pdf.
- V. Salma, F. Friedl, R. Schmehl: “Improving Reliability and Safety of Airborne Wind Energy Systems”. Wind Energy, in production, 2019. doi:10.1002/we.2433. Preprint accessible as pdf
- P. Faggiani, R. Schmehl: “Design and Economics of a Pumping Kite Wind Park”. In: R. Schmehl (ed.) “Airborne Wind Energy - Advances in Technology Development and Research”, Springer Nature, Singapore, pp. 391-411, 2018. doi:10.1007/978-981-10-1947-0_16. Preprint accessible as pdf

Hint: you cal use Latex markup in this forum by enclosing it in $ signs. Eg. \zeta = \frac{P}{P_{ws}}

Did use \LaTeX in my post, but see also that the notification email does not render it.

Highest “power-to-surface-area” is a power-kite design trap of high wing loading. It especially does not scale because wind velocity remains constant, while scaled-up stall speed increases, and turn-rate decreases. Highly wing loaded wings are not crashworthy. In AWE such wings will take decades to reach TRL9 MTBCF statistics (<1 mishap per 100khr). Wikipedia-

“…an aircraft with lower wing loading will be able to take off and land at a lower speed (or be able to take off with a greater load). It will also be able to turn at a greater rate.”

Guessing that TUDleft signed Google-Makani NDAs, locking them into helpless acquiescence to the withheld M600 Mishap Report and power curves, unable to champion open M600 data.

Highest power-to-mass remains the top number in aerospace generally, and will prove so in AWE. The M600 scores far poorer than any power-kite in this most predictive parameter.

A heuristic approximation of M600 power is that hover and vertical climb power-out is approximately equivalent to max power-in, under similar electrical-thermal limits. Comparable power-out/in RPM data may be evident from audio track. Has anyone found accurate test wind velocity and mass numbers for tether and aircraft? Its likely prior mass estimates were overly optimistic.

Also, “rated power” is a bad metric if the wind velocity basis is poorly probable. WECS developers have often simply raised the rated power wind velocity to fit a chosen power number.

On http://www.energykitesystems.net/FAA/FAAfromMakani.pdf and concerning M600, it is specified that the “Full rated power wind speed” is “9m/s”.

It is a rather low value.

The initial 9m/s estimate was years before actual M600 testing, and now real data exists (but is secret; as unfair business practice if Google is wrongly believed better in AWE). The hidden picture may be cut-in around 9m/s, and rated output now at rather higher wind velocity. Poor M600 low-wind performance may hide in simply motoring around the loop. The audio signal can reveal struggling in the upward phase.

Here is a more refined estimation heuristic-

Look up max power rating of the M600 motorgen, multiply by eight, then start subtracting parasitic factors (drag, mass penalty, electrical loss, overheating, etc). This may not give precise wind velocity, but does give a certain top power limit that is almost certainly being risked in testing, and may have caused the crash.

If M600 aerodymamic and motorgen estimates correspond, that’s good, but not very realistic. In real wind, that varies a lot moment to moment, the system may have high loss due to motoring through lulls and popping up to chase transient gusts. Practical estimation of M600 power capacity must account for borderline conditions.