For lifter kites, the aim is to obtain maximum tether tension at the maximum tether angle. Unfortunately, as the tether angle increases, the tether tension decreases due to cosine cubed losses. This is counteracted by the fact that, as the tether angle increases, the altitude of the kite increases, and it experiences higher wind velocities which increases tether tension. The following analysis attempts to quantify these effects. In the analysis, I have assumed that the tether force varies linearly with the effective area of the kite. This effective area is the full kite area at zero tether angle and zero at 90° tether angle. The tether tension also varies with the square of the wind velocity. Using a baseline of 8 m/s at 50 meters I assumed a linear increase in wind velocity to a value of 13 m/s at 2000 meters. I did the analysis at two tether lengths, one at 1000 m and the other at 2000 m. The results show that there is a definite advantage of having a longer tether. TETHER TENSION.pdf (138.9 KB)
The results are summarized as follows:
1000 meter tether: Maximum tether force is at 13.2° tether angle (17% above baseline)
Tether angle at baseline force = 24°
2000 meter tether: Maximum tether force is at 33.5° tether angle (51% above baseline)
Tether angle at baseline force = 66.3°
Clearly, there is an advantage of having a longer tether. The lifter kite operates at a much higher altitude where the winds are more steady and more consistent. It can operate at a higher tether angle, which is beneficial for lifting. This is counteracted by the fact that the tether weight increases (doubles) and a much larger ground area is required for operation. Longer tethers will benefit all non-crosswind kite systems, and especially the Kitewinder system where the turbines are oriented to face the wind and do not suffer cosine cubed losses.
The horizontal axis shows the elevation angle, the vertical axis wind speed squared times assumed projected area (cosine of the elevation angle). The light blue line is the 2000 meter tether, the dark blue line is the 1000 meter tether.
Tether length
Elevation angle at maximum
Kite altitude at maximum
Wind speed at maximum
1000
27
454
9.04
2000
37
1204
10.96
3000
42
2007
13.02
4000
44
2779
15.00
10000
50
7660
27.51
Here is a graph of a 3000 and 4000 meter tether.
I still don’t understand this, for example:
We can see for the shorter tether its maximum is at 1.17 on the vertical axis, so I think that gives us the 17% above baseline, but I don’t understand the various elevation angles.
Im not sure if this is valid for a lifter kite. The kite is mostly stationary. You can’t choose the elevation angle other than choosing a different kite.
To get a high elevation angle, you need a kite with a high L/D ratio and high pull to counteract tether sag. High pull could mean bigger kite, but bigger kite only helps so much because the tether scales cubic in mass and the kite force scales square relative to the area of the kite.
Net effect i presume is you can scale up kite and tether, but the relative length of the tether length to diameter/kite chord must decrease.
A higher elevation angle will have a positive effect on tether sag. Though high L/D lifter kites would need active control?
Also not mentioned; the lifter must work well in the wind speed range the plant must operate. Low wind is where tether sag will hurt you and also steal from you altitude and wind gradient. High winds you need a heavier tether.
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I think lifter kites are a bit difficult to implement. For serious business we would be looking at something with a big depower range and very high L/D. Probably we would be looking at something looking like a paraglider or LEI kite and with a control pod. The lifter should be able to swerve left and right to increase lift in low winds, but in those cases, there probably cant be anything hangig on the tether.
Luckily Kitepower has these kites already, one just needs the software to make it a lifter rather than a looper.
As a lifter kite for Daisy, with its elevation angle comparable to its own (25-35 degrees, as for any crosswind kites in the average angle), so in the axis of Daisy (optimizing the traction force), and with a huge pull thanks to high coefficients.
The question is really about stability as a kite in different wind speeds, as well as how, if necessary, to control them. Do you need a passive system (bridles and springs) or a full fledged control system with winches and sensors. And how to attach the load to the kite, if it flies on multiple tethers.
If you have a control pod or ground based controls, then any large kite seems viable. And Kitepower do have these, tested and ready to fly if you go the control pod route.
For example this one on the video below, the suspension lines (bridles) connecting the single line which is tied to Daisy as for any lifter kite. Indeed tests about passive stability would be useful to see if this is really workable.
The other solution, with control pod looks interesting, but two kites could be better to mitigate oscillations due to the traction force on Daisy when only one looping kite is implemented.
So the old Peter Lynn Single Skin Lifter we had
Was a bit similar and worked great with a couple of extra lightweight lines tied to the B2 bridles to keep it steady or steered from the ground.
It wasn’t full control of tension or stability though
Of you read through some of Peter Lynn’s blog posts he is very clear that a kite design, for each size, has a wind speed range where it flies stably on a single line. Higher or lower wind speed and it will crash.
The thing I can conclude from his posts and also now the Rogallo video where NASA could not afford to finish the Rogallo design is that designing soft kites like this is extremely time consuming and/or expensive. So for those of us wanting to produce electricity, starting with designing the kite is probably not a good idea. An actuated kite though is less costly, though kind of brute force «ish» you will probably get it working until someone else can supply a single line lifter that does the job more elegantly.
The designer himself, Rogallo, has declined the eponymous wing using several manufacturing methods for the same one which is a wing “composed of two partial conic surfaces with both cones pointing forward.”
The Parawing is a flexible wing. But there are Rogallo wings including a frame consisting of a keel separating the two lobes.
As far back as I can remember, Rogallo hang gliders posed problems similar to those described by NASA, leading to crashes, particularly following feathering during too sudden maneuvers. Hang gliders with a more complete frame then followed.
The Rogallo rescue parachutes that I often cite have other requirements, and other characteristics such as much more complete and elaborate suspension lines. It may not be so difficult to make a kite out of it, if it hasn’t been done yet.
And also were the wings used for AWE designed for this purpose in the first place?
If these rigid wings have been designed for specific AWE use, then the same can be true for a flexible Rogallo Parawing kite based on Rogallo rescue parachute, and for a tether-aligned use, or as a lifter kite for some AWE designs like Daisy, benefiting from a strong thrust coefficient.
Indeed stability is an issue for a single-line kite, whether it flies as a lifter kite or as a tether-aligned pumping mode AWES. This is the reason why many lifter kites are equipped with stabilizing elements such as a long tail.
A simple way to convince yourself of this is to fly a two-line power kite, then fly it statically by holding the handles without moving them: the kite falls very quickly to one side or the other if we remain too passive. The higher aspect ratio of a power kite accentuates instability in static flight, but crosswind flight is not problematic, the air-speed of the wing being a stabilizing element.
Perhaps even for a single-line kite, a piloting pod a minima would be useful, at least just to compensate for the differences and stabilize it: this would be an active stabilizing element. It would be still better by working in different wind speed ranges.
That said, it must be admitted that the Kiwee ​​remained passively in the air for a very long time (but in the same wind speed range?).
My philosophy is to land the kite whenever wind conditions are not suitable. If the winds are too low, then the system will not produce much energy, and there is a danger of the lifter kite falling to the ground. It is, therefore preferable to land the system, and wait for more favorable winds. Conversely, it if the winds are too high, there is a danger of damaging the equipment and the kite must be landed to avoid this. In this way we can design the kite for a suitable wind range and we do not have to over-design to handle high winds.
