# Power to space use ratio

A 1.8km radius 1km height cylinder leads to a front airspace of 3.6 km², so a Betz limit (16/27) potential of 1274 MW at 10 m/s wind speed, less losses and unswept area. If reeling yoyo systems are used, the potential becomes 1274/4 = 318 MW, yet a huge value. A fraction of this potential could still be a very high value. Several crosswind AWES with a high efficiency per wing area but requiring high spacing could not fill this space as well as several AWES with lower efficiency per wing area but requiring low spacing.

As an example of filling space the video on

shows large static kites with low spacing.
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I think the idea of “filling” a volume with kites, to an optimal workable energy extraction density is very interesting.
It’s similar, I think, to what you are looking for in

A large area kite, widely tethered, which handles winds from all directions.
I should probably add a lifting network as pictured above into that topic

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Rod, I think a higher value than 10 MW for Daisy would be possible with an appropriate optimization.
I made a sketch of various AWES within a 3.6 km diameter 1 km height cylindrical volume, in plan views.

One of them is Makani M5 (5 MW) with a circling radius of 265 m as indicated on their FAA document. Two units could be added on both sides of the central unit, for a total of nearly 15 MW. Or other arrangements can be studied. M5 would probably be the most efficient AWES per wing area. But it sweeps far more than the useful Betz limit swept area, adding that the 530 m diameter circle doesn’t optimize the cylindrical volume, and is swept only on its periphery.

Concerning OrthoKiteBunch (see a previous message with the video on Power to space use ratio) the rate is far more higher and can be explained by the geometry of the swept area which is a part of the cylindrical volume periphery, the wings being superimposed in 1 km height, and several bunches of superimposed kites needing to share the 120° of the 180° space. It can be not practically possible.

Concerning rotating reel and a yoyo non-crosswind kite, the diameter is the same but the efficiency of the rotor is theoretically higher because of both stationary swept area and crosswind motion.

Of course when I mention < 30 MW or 210 MW or 550 MW we could divide by 2 or 3 or even more. The size of the wings could be also not reachable.

An observation: 3 wind turbines 1 km height side by side on a pivot could achieve 3/3.6 of 1274 W, so 1061 W.

Another evaluation of power/land use ratio is on Multi-kite airborne wind energy systems (MAWES).

kPower sees periodic multi-kite airspace as a metamaterial under applicable science predicting lowest density of overall mass is favored. Too much flying mass in a given space fundamentally limits max power; another way of saying that maximum power-to-weight AWES design is favored, including to maximize airspace capacity.

Lets not forget wind velocity as a driving power-to-space and general design factor. Makani’s M5 concept-blunder would make better sense in a constant but unrealistic hurricane-force wind. Its dead at most-probable wind velocities. Beware of these seductive traps of excess-mass design concepts over-promoted by so many ventures, Its time to discern the practical solutions in a race of few winners, many losers.

Largest and lightest power kites in networks working in tight airspaces is kPower’s bet.

A different analysis minimizing the “effect of flying mass” for flygen systems is given on Flygen

"7.1. Effect of flying mass
In all AWESs, increasing the flying mass decreases the tension of the cables. Since Ground-Gen systems rely on cables tension to generate electricity, a higher mass of the aircraft and/or cables decreases the energy production [107] and should not be neglected when modelling [109]. On the contrary, increasing the flying mass in Fly-Gen systems does not affect the energy production even though it still reduces the tension of the cable. Indeed, as a first approximation, the basic equations of Fly-Gen power production do not change if the aircraft/cable mass is included and this is also supported by experimental data[108]. "

Moreover this topic is about power to space use ratio, not about power-to-weight, excepted if there are connections. Could you support “…that maximum power-to-weight AWES design is favored, including to maximize airspace capacity…”? Can be it due to a possible lower path radius? Or safety concerns?

Let us know which opinion you decide is most pertinent to your topic.

For now finding the connections between power-to-space use and power-to-weight ratios if there is.

Interesting @kitefreak’s post on 2010 about the topic https://groups.yahoo.com/neo/groups/AirborneWindEnergy/conversations/messages/2480 :
"
Sparse v. Dense AWE Arrays
Yahoo

Sent

dave santos santos137@yahoo.com
To:
airbornewindenergy@yahoogroups.com

‎Nov‎ ‎9‎, ‎2010 at ‎4‎:‎33‎ ‎PM

Take a 2mw single-tether kiteplane (like Joby’s model) operating under a 2000ft ceiling. To keep safely clear of neighbors it occupies a circular plot near a mile across. Presume a 3x3 array of nine kiteplanes for 18mw from a 3 mile square kitefarm. The same land developed with conventional 5mw HAWTs, spaced normally, could develop greater than 100mw, presuming that better wind capacity-factor aloft roughly offsets the lowered system availibility of complex delicate aircraft. Conventional HAWTs win overwhelmingly in raw land efficiency without even touching the upper-wind. However, the same land & airspace the nine kiteplanes sparsely occupy can be densely packed with airborne turbines or wingmills, in string latticework based on classic kite methods, for over a rated gigawatt. AWE arrays of cross-linked semi-captive elements seem to have a fantastic advantage in space-efficiency, not just safety & control, over single-tether designs.

I used crude geometric methods to estimate these figures, so it will be fun to see how well someone else’s calculations coincide. A suggestive guesstimate is that there is well over a gigawatt average in a tiny mid-lat crosswind patch of sky, just 100m across & 10km high."/"

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I reckon…
Having highly active AWES, arrayed in volumes, at appropriate densities will have significant impacts on power to space use.
Much as array patterning & density in HAWT farms does.

Also…
The ability to harvest from the whole height, width and depth of your airspace… Is hugely significant.

Of course I have to state… Daisy, a stackable mechanical drag mode autogyro kite, has rotors working simultaneously in lower and higher level winds. Also stacking seems to make the system more efficient with less drag / kite and more line tension for better torque transmission.

More on all that coming

The ratio mainly proposed since M. Loyd’s seminal publication *Crosswind Kite Power http://homes.esat.kuleuven.be/~highwind/wp-content/uploads/2011/07/Loyd1980.pdf is the power to kite area ratio. @kitefreak proposes the power to weight ratio.

I beleive the power to space use ratio allows to think the AWES farm as a whole rather than addition of unities with their respective long tethers. So a system with high power to kite area ratio, generally a crosswind kite power system with its fast moving tether, will have a very low power to space use ratio. In the end AWES seen as less efficient in regard to their power to kite area ratio will be able to reach a higher power to space use ratio if said space can be maximized, for example, by implementing unities that are close each other, or more simply by implementing very large units.

Loyd and I discussed whether power-to-area or power-to-weight is the first-order AWES number and we agreed on the basics. Power-to-weight remains the most predictive number in aerospace; it just happens not to have been Loyd’s starting computation basis, where power-to-area was easier for him to analyze, and gravity was completely neglected.

Its a testament to Loyd’s genius that his paper remains AWE’s founding classic despite its gaps and shortcuts. Loyd himself was rather mortified that the paper came to be so iconic, because he would have worked harder to polish it. Pierre’s special concern with power-to-airspace was also not treated by Loyd as such, but would be a critical factor where airspace is scarce.

Many critical numbers exist in AWES engineering that Loyd did not introduce, like LCOE which in turn might be driven by Insurance Cost. It was reasonable for Loyd to neglect power-to-weight to begin formal analysis, and its now reasonable for us to consider it, especially in the aviation Scaling Law context that Loyd was well aware of. His “C5-A” wing case would logically have been a soft kite, not a massive aluminum transport wing.

The generalised architecture of a networked kite system volume is a dome.
When scaled up, the central area of this dome is flying higher than it would for a smaller land area network.
Therefore the power per land use area improves with scale of networked kite deployment.

The dome may be a self inflating dome shape, some sorta blob, an Alexander Bolonkin dome, or a Santos mothra shape… All allow for better power to land use in the centre.

These could be a lot higher in the middle to achieve the desired effect

Always fascinated when I see this fish farm cage net lift and make this shape…

An AB dome inflation test by KPower

Now I would compare rigid and soft wings as they fly by figure-eight or circle. I will use rough orders of magnitude. The power of a rigid wing is about 10 times the power of a soft wing by considering the wing area. But it can be the reverse if we consider the power to space use ratio, or more precisely the available power in regard to the tether(s) length. The radius of a turn is proportional to the squared speed, and a rigid wing goes two times faster as a soft wing. So the required (useful and useless) swept area for a rigid wing is 16 times that for a soft wing, knowing that in all cases we are far to the Betz’ limit. Add that from these respective areas, the rigid wing uses a thin annulus while the soft wing uses a much larger part of his smaller swept area.

An illustration of what I try to say is on the two documents below:
https://www.researchgate.net/publication/325831964_Aerodynamic_analysis_of_Ampyx’s_airborne_wind_energy_system : the figure 1 represents a fast wing (Ampyx AP3, 150 kW) using a eight-figure of about 600 m wide and 200 m height.
https://www.researchgate.net/publication/320495787_Modeling_and_control_of_a_Magnus_effect-based_airborne_wind_energy_system_in_crosswind_maneuvers : the figure 7 represents a slow Magnus wing (40 m span, 1.5 MW without taking account of the power consumption) using a eight-figure of about 100 m wide and 75 m height.

1.25 W per m² of occupied area for the first, 200 W per m² of occupied area for the second, while the first is far more efficient per wing area. Certainly the result would be far lower than 200 W by using a classic soft wing, but far higher than 1.25 W. Note that here the occupied space is not yet the space use which takes into account of wind changes.

So the use of soft wings by SkySails or by @Kitepower and @rschmehl makes sense.

Pierre,

Agreed, that a kite’s turning-rate and -radius are key to maximizing harvest sweep in the kite window.

Conflating Skysails and Kitepower is problematic, given stark comparisons between them in scaling and other critical engineering dimensions. Its necessary to respond appropriately to Kitepower’s multiple design failure, as revealed by the crash review.

Tweet media dominance aside, what makes Kitepower attractive technically, in the face of the crash conclusions and LEI kite limits? There are other considerable soft reeling ventures, like KPS.

We must address system topology to judge airspace performance. A rigid autogiro turbine that turns-in-place, or a dense kite network, can in principle maximize airspace. These are old findings are worth repeating, along with new insights into turn performance.

In the context of airspace efficiency here, the most pertinent comparison is with USP3987987fig5 crosswind sweep architecture.

The comparison I made is about crosswind kites flying by eight-figure or circle as it is the method used by almost all companies, and concerns rigid vs soft wings (the US3987987fig5 describing a different rig requiring significant developments in order to face the wind). In the scientific publications I would like to see how the “power to space use ratio” leads to a different efficiency but there is nothing about it.

A dense kite network could perhaps maximize the space with static or perhaps rotating kites (imho with a lot of problems as the power is involved), but not with crosswind kites. I know it since my participation in Dieppe kite festival. Crosswind kites require high spacing, so each unity should tend to maximize its own space by taking account of the tether length.

The tether fully modifies the topology. “A rigid autogiro turbine that turns-in-place…can in principle maximize airspace”, but not a tethered autogiro turbine.

Differences between SkySails and KitePower are not about the turning-rate by considering an equal wing area. Other things like crash review are not directly connected to the current topic.

Pierre,

As long as Kitepower is invoked here, unresolved questions about their safety culture and poor scaling prospects beg answering. Their Twitter feeds do not advance either this Topic, or un-responded concerns. Even Skysails and KPS, without Kitepower’s crash stigma, are not really central to the topic.

Kite networks do move interconnected units crosswind together better than un-networked kites can coordinate, by coherent lattice waves, as seen in classic trains and arches. I have attended this annual kite arch event for many years near my NW home, Ilwaco, and developed kPower’s lattice-wave AWES ideas from the dynamics on display-

Dave, the video shows a network of static kites in arches. There is no problem as there is no expected power.
I quoted SkySails and KitePower, illustrating my message about rigid and soft crosswind kites. Thanks to produce more relevant observations.

The positive aspect is that existing companies could significantly improve the power to space use ratio without big changes in the rig, keeping their scheme of crosswind kites in figure-eight or circle in yoyo or flygen modes. R&D could focus to more adapted wings.