# Makani Kite power calculations

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

1. R. Schmehl, M. Noom, R. van der Vlugt: âTraction Power Generation with Tethered Wingsâ. In: U. Ahrens, M. Diehl, R. Schmehl (eds.) âAirborne Wind Energyâ. Springer, Berlin Heidelberg, 2013. doi:10.1007/978-3-642-39965-7_2. Preprint accessible as pdf.
2. V. Salma, F. Friedl, R. Schmehl: âImproving Reliability and Safety of Airborne Wind Energy Systemsâ. Wind Energy, in production, 2019. doi:10.1002/we.2433. Preprint accessible as pdf
3. P. Faggiani, R. Schmehl: âDesign and Economics of a Pumping Kite Wind Parkâ. In: R. Schmehl (ed.) âAirborne Wind Energy - Advances in Technology Development and Researchâ, Springer Nature, Singapore, pp. 391-411, 2018. doi:10.1007/978-981-10-1947-0_16. Preprint accessible as pdf
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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 âpower-to-surface-areaâ 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-

ââŚan 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.â

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, ârated powerâ 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 âFull rated power wind speedâ is â9m/sâ.
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, thatâ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.

Hi @Saqlain
Howâd the presentation go?

Yes, Hi, and what was the calculated result, if any?

aslam o alaikum saqlain .
m also working on it let me clear some of your points as for as i studied.

1. we can mesure height of the kite by mesuring the tether lenght and the elevation angle.
2.second point has also same answer by knowing height we can see the velocity of wind at that height and i have also a formula for that.
3 and 4 th point m looking for the answers but could nt find anything proper trying to search like you iff u have any information about that please tell me also.
03063443228 whatsapp nbr we have a same project we can help each other . thank u
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@PierreB .
i am a student of M-PHIL electrical power. first of al thank you for such data and comments from which i could get basics of the kite energy .
brother you are requested to please help me in some problems that are in this given paper.

1. there are two powers . LIFT and DRAG . Did we have to calculatre both of them and after adding them we will get overall power? because one is pumping kite power and other is on board generator power
2. in drag mode if we see in this paper in equation 29 what is (Ak(area of what) )he use a word of area is where from we will get this area . is it the area of onboard generators or overall area of generators and kite?
3.why we put a=0 in that last equation for drift power ?
4.in the LIFT power output equation is there any will be difference between that lift to drag ratio for both lift power and drag power ? if that as you early discussed difference of 1/3 ?
3. what will be the value of âaâ in the lift ouput power .?
plese help me brother regarding all of these question i will be ery thankfull to u.
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Question 1. No. It is âliftâ or âdragâ power, not both, not âliftâ power + âdragâ power.
Note that I put âliftâ and âdragâ in quotes because their meaning is different or even opposite in the terminology of existing wind turbines: lift devices generally designating HAWT (current three-bladed turbines) with a high power coefficient and being perpendicular to the wind flow, while drag devices generally designating Savonius-type with a low power coefficient and being pushed by the wind.

It is the reason why I prefer use âyoyoâ or âpumping modeâ or âreelingâ, and âflygenâ terms in the place of âliftâ and âdragâ terms.

In flygen configuration (onboard turbine) the kite is slowdown by the turbine, while the swept area remains stationary.
In yoyo (pumping or reeling) mode the reel-out operation assures the power. By Loydâs formula âliftâ power and âdragâ power are equivalent per kite area, all other parameters such like lift-to-drag ratio being identical. In the other hand see The Betz limit applied to Airborne Wind Energy.

Questions 2 and 3. It is about induction factor. For the yoyo mode, a is the reel-out speed in respect to the wind speed. For flygen, a is dependent from the dimensions of the secondary turbines. The larger the secondary turbines in relation to the wing area, the lower the induction factor. If a = 0, there is no induction factor: the induction factor increases with a. A typical value of a for both flygen and yoyo modes is 1/3 (respectively drag of the onboard turbine in respect to the drag of the whole device, and reel-out speed in respect to the wind speed as indicated above), although a value of 0.2 for flygen can be seen as better (lower induction factor).

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thank you soo much for your great response .
as you said that we donât have to calculatre both of them partially and also we donât have to add them to get overall energy .
so is the loyd formula will be used to calculate the overall power generated of the kite (pumping & onboard generator) with the changing of lift/drag coafficient and that lift coafficient used in loydâs formula ?
is that right? than can you please help me with an example of output power like 600kw and lift to drag ( that u will mention ), wind speed density and all other parameters ?
please sir guide me regarding this i will be very thankfull to u !

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thank you soo much for your great response @PierreB .
as you said that we donât have to calculatre both of them partially and also we donât have to add them to get overall energy .
so is the loyd formula will be used to calculate the overall power generated of the kite (pumping & onboard generator) with the changing of lift/drag coafficient and that lift coafficient used in loydâs formula ?
is that right? than can you please help me with an example of output power like 600kw and lift to drag ( that u will mention ), wind speed density and all other parameters ?
please sir guide me regarding this i will be very thankfull to u !

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@khawajaAdnan, the document below provides some useful information. See the equation (2) page 3 about the basic formula of power which works for flygen or yoyo modes:

I donât know exactly the values of lift (2?) and drag coefficients for Makani M600 but you can partially deduce them in order to reach the nominal power of 600 kW, the full rated power wind speed being 9 m/s for what I remember. You can modify some variables.

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@PierreB thank you soo much brother for your help i am reading this paper and it is helping me too much. thank you soo much .

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hy @PierreB with most respect thank you for your concern .
i need a little more help .
now i know how to calculate the output energy of the AWE (moving kite) by that formula.
i have some questions.

1. is it possible to obtain a lift/drag of 40? which is too high.
2. wind speed average i put is 9.
3. lift coaficient of 2 is possible?
beside all of these i want you to please help me in calculating the per KW cost of the kite.
from where i will get the cost of the component used in the makani M600 model.
and also complete capital cost.
please sir help me regarding this . i am writing a coparison of AWE(cross wind kite ) and simple wind energy by turbines.
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Welcome to the forum.
By having a look at the performance of gliders for comparison e.g

L/D 40 would be very low nowadays.

As for cost & LCOE figures, I think there have been estimates on this forumâŚ
but youâre likely going to have to speculate here. The companies involved werenât keen to publish costs.

Is it a university course project? Hereâs wishing you a long successful future in Airborne Wind Energy.
All the best
Roddy

Question 1: a lift-to-drag ratio of 40 is currently not possible (although a higher value is possible but for a wing alone) due to the significant tether drag during crosswind operation. A value of 12 (with tether drag) is more reasonable concerning rigid wings such like Makaniâs wings.

Question 2 : indeed Makani provides a value of 9 m/s for the full rated power wind speed on the Response to the Federal Aviation Authority. Generally the nominal wind speed is 10 m/s or 11 m/s. As an assumption Makani M600 can also be limited by a too high tip speed of the secondary rotors.

Question 3: yes, a lift coefficient of 2, even more, is possible. Planes use flaps to increase lift coefficient. The advantages of using high lift coefficient overcomes the disadvantage of the increase of drag as shown on https://www.researchgate.net/publication/320742362_Drag_power_kite_with_very_high_lift_coefficient.