If the tether is perpendicular to the take up wheel, then the power transfer is almost 0. If the tether is parallel to the take up wheel, then the power transfer is maximum. Please tell me why there is not a drastic, reduction in power if the tether is at 80to90 degrees to the take up wheel as in the case of the pyramid. This has nothing to do with the cosine cube losses, which relate to the angle of the kite or the turbine to the wind
Yes, it is correct and can also apply to winches used for reeling systems during power reel-out phases, although, for the lever (wheel) systems, I would say “if the tether is parallel to the axis of the wheel, the power transfer is almost 0, and if the tether is perpendicular to the axis of the wheel, the power transfer of the wheel is maximum.”
Perpendicular to the axis of the wheel or “parallel to the take up wheel” (for lever systems the two expression can design the same as mentioned above) leads to an optimal transmission without restriction of length. Note that the same applies to the transmission of a reeling yo-yo kite during power reel-out phase, and with less materiel and greater adaptability: regardless of the elevation angle, the tether is always “parallel to the take up wheel” (to take your words here quite suitable unlike my expression (“the tether is perpendicular to the axis of the wheel”)) at the point of its exit from the winch.
For TRPT like Tiira, things are different: the tether angle is between 90 degrees and 0 degrees. So the transmission cannot be optimal if the tether length is without restriction. But TRPT work also by the axial force (tension by the power kites or blades, and the lifter kite if applicable). Under tether length restriction and a high axial force, the torque transfer can be maximum. If one imagines an unlimited axial tension, then it would function like a rigid structure for which perpendicularity would have no importance.
Now the calculation for TRPT is complex because of a lot of parameters: the axial force, the torque, the length of the tethers, the number of tethers, the phase lag (expression that I had forgotten and that Tallak reminds me of)… It is not “tether angle losses” as such, but among parameters that constitute the TRPT, knowing that it is about determining the maximum possible distance between the wheel and the rotor (blades or kites) while having maximum efficiency or almost.
Said like that, I can only agree, and that’s what I suggested, just like you from the very beginning.
In the end we can agree that the rope-drive transmission allows avoiding tether length restrictions while maintaining optimal efficiency.
More and more, I will lean towards a traditional wind turbine or rather a Kiwee-type because lighter, at least concerning the rotary devices, separating (just like you suggested if I remember correctly) the lift function from the power generation function.
For Tiira, the distance between the kites and the wheel (rotating ground station) as represented in the image seems theoretically possible. But in the real world, this could roughly correspond to the distance between Daisy’s rotor and the ring just below.
1 Like
Hi
I am sorry I have not been able to better explain, I don’t mean to dismiss you without any discussion. I will try to rectify this slightly.
I am adding the “The Pyramid” PDF to this topic as an attachment, in case you had issues reading it.
the_pyramid.pdf (2.9 MB)
So. To see things from a very birds eye view, TRPT AWE consist of two rotating rings. One at the kites and one at the cartwheel/carousel at the ground. The tension between these, the phase lag of the two rings and the rotary speed of the wind turbine determine how much energy one can transfer from kite to ground.
Rotary speed is influenced by lift-to-drag (kite and tethers) or how fast the wind turbine rotates for a given wind speed. Less drag gives faster rotation and thus more energy transferred. Primary factors to reduce drag is to shorten the tethers, use thinner tethers or improve kite design. Lets assume kite design can quite easily be made the least significant source of aerodynamic drag. So this pushes the design towards shorter tethers and also finding the best material for tether (strength to diameter) and also maybe pursuing drag reduction of the tethers (fairings and such). I would say this is largely determined by current tether material technology, something I don’t see huge improvements to in the near future.
I would also add that increasing the kite looping diameter will reduce the rotary speed of the turbine (with the assumption that kite speed is mostly determined by wind speed), so keeping radius to a minimum seems important as well. I did though show that you can scale “The Pyramid” to larger scale and get similar performance, scaling depends on many factors.
The phase lag is largely limited by the fact that the tensile shaft (tether based shaft stiffened by tension) will collapse due to geometry when the phase lag kite - carousel/cartwheel exceeds a certain value which is probably close to 90 degrees. I named this the MTR factor or the lambda factor. “Moment to tension to radius” would be the acronym expanded. This is a parameter that is decided by the radii of kite and cartwheel rotation and the distance between them. Larger radii and shorter distance increase the lambda factor. The trick is finding the exact lambda factor that is necessary to generate the required power. I have shown in the document that it is indeed possible to find lambda values that are useful for wind turbines like these. Increasing radii and shortening tethers are of course undesirable design motivations:
- increasing cartwheel size increases the bulk of the ground equipment and the need for a tower to elevate the cartwheel. For ships it increases the moment applied to the hull.
- increasing kite radius decreases the rotary speed and thus the energy transferred
- decreasing tether length reduced the wind increase from wind gradient and reduces the distance to ground obstacles or third person
It seems important to get the lambda factor right, and also that one must be operating the wind turbine close to the point where the shaft would buckle, where the energy transfer is maximized. This also implies phase lag kite - cartwheel must be precisely controlled.
–
The final component - tension is slightly difficult to reason about. You can add more area to the kite wings to get more lift and more tension. Reducing drag and increasing speed also generates more lift without increasing the wing area. But the tether needs to be thicker to support more lift, and thus generates more drag.
I think its easy to see that there are a lot of design problems around the subject of generating tension. For instance, low drag kites would be high aspect ratio. This would again mean that the difference in airspeed at left and right wingtip of the kite would be quite different if the looping radius was very small. Choosing a smaller kite would effectively mean that the tether length is effectively elongated (meaning that kite size and turbine scale are tightly coupled)
–
What I am trying to get across here is that designing something like “The Pyramid” involves a lot of compromise work between different design parameters. The question really is: “Is there a sweet spot in there that would be useful?” I tried to explain why I think the answer to that is “yes” in the PDF. I explained this step by step, with calculations and figures showing every design decision. An I believe the evidence is quite solid to say that this could work.
So you might understand why it is a bit frustrating when you and quite a few others (not in this forum) simply brush off the whole idea by saying “its not possible that that could work, because it seems too unlikely to”. And I could not explain why it would work in less than a few pages of calculations…
–
Let me also add that I am not necessarily hijacking the Tiira thread to talk about “The Pyramid” - these principles apply to both designs and I presume also many other TRPT designs.
1 Like
Where you have
- increasing kite radius decreases the rotary speed and thus the energy transferred
I presume that statement comes with caveats on which parameters stay similar… Because surely torque could also increase with flown radius
But also risks of flying loops closer to the ground…
Yes, I was trying to talk about the fact that kite vs wind speed is fairly constant (in a very simplified sense), so increasing kite looping radius would decrease the rotary speed of the shaft. You are right that this would also increase the lambda value of your design (more possible moment transfer through the shaft). Maybe these two effects would cancel each other out?
In my studies of this, I have figured that the kite looping diameter is more limited by how close you want the turbine to be to the ground… So a practical minimum ground clearance dictates shaft elevation angle and looping diameter, then the other parameters must be chosen to match well… finally optimize for maximum power output at the winds you are interested in .
1 Like