Vertical trajectory for yo-yo AWES?

Both chapter 12 and chapter 13 (see also the comment and reply section) in the second AWEbook describe a vertical trajectory for Magnus Effect-Based AWES in yo-yo mode.

I think the same with a classical kite could allow to use a far larger kite than by flying in figure-eight thanks to the absence of turns because the kite rises by its leading edge and descends by its trailing edge. That can lead to a maximization of the space and land use which are delimited by the tether length as radius by considering all wind directions. So the kite span could be equivalent to the tether length: 900 m span kite for 1000 m tether length as extreme value, leading to roughly 150 MW in average before some losses, with a L/D ratio of 4 and 10 m/s wind speed.

In proportions it is like a paraglider with its lines. Of course relatively higher tether length can be used. An advantage could be the simplicity of the flight control and its management, that at any scales.

Today I experimented a vertical trajectory with a four line 4 m² kite, alternating power ascending and depower descending phases. I noted that both went in a similar speed. And the depower can be complete with appropriate maneuvers. This bodes well for the yo-yo reel-in phase.

A low quality video shows these tests, and below another video shows the same between 8:30 and 8:42.

It is true and may be ute ultimate expression of super short tether AWE.

You could probably make a kite to fly up and down well (without resorting to making the kite a «bag»). Going down should make less/no power.

There is a slight issue with flying up/down, and I would rather go right/left. This is to deal with gravity. When going up, you can’t easily point the lift force upwards to compensate for gravity. Doing this will change the angle of attack. If you are flying left/right, this is just a matter of rolling slightly.

Second thought: is this better than a rotating rig with three kites? It takes a while to accellerate the kite for every cycle. With a rotating network the cycles could be longer for pumping, or continuous with drag mode power takeoff.

You raise relevant points but not without possible answers for what I think.

Gravity is a disadvantage during the climb (reel-out phase), but an advantage during the descent (reel-in phase), considering vertical paths.

Both chapter 12 and chapter 13 mention quite vertical trajectories by taking account of reel-out and reel-in phases. The tether reel-out speed results from the increasing of the elevation angle of said tether. During reel-out phase the kite undergoes both the same real and apparent winds in a way that the angle of attack stays the same for what I think.

Yes, but the kinetic energy of the kite is used when the kite ends its raising where the power zone decreases by going towards the zenith. As a result the loss of time to accelerate is compensated by achieving a higher altitude and elevation angle.

Yes, but turns are needed and require place, preventing the kite scaling up beyond some point, unless it is divided into smaller unities whose the management can be quite difficult.

Or even only one kite as for Low radius loop.
It depends, among other things, on how far the kite can scale. The purpose is the same: maximizing the space. For what I think the figure-eight does not allow it enough due to flight requirement.

This works ok with a lightweight kite. e.g. rev or single skin.
The bottom transition (from flying Backwards to going Up again) is where I see a problem for scaling.
OK, you’ll be reeling in when falling so, You’ll not likely have to re establish the flow direction over the wing… That’s ok-ish
but you do have to decelerate the fall and accelerate up from the bottom again where the winds are lower. Power for an apparent wind speed boost will be coming from the yo-yo.
There’s a lot of control needed in this style of flying.Best if all the controls are on the ground.

You’d want the control winding to be closer together and use a longer stroke to span distance than hinted in this old vid…

Yeah that old model was really complex looking.

I tested an arch kite made from 4 windsurf sails a few times. On the last go, it was windy. Having previously flown smoothly and cleanly. This time it galloped and thrashed and ripped. That was some fierce vertical stroke pumping.

This seems to be a bit confuse I think. A nice rendering is not a conceptual explanation. About:

In the bottom of the path, the winds are yet good enough. My 4 m² soft ram wing on the video ascended at full speed immediately after the controlled fall. The explain is simple: its weight is negligible compared to the pull force. Even the kinetic energy due to the fall is low compared to the pull. As an example the weight of my 4 m² kite is 8 N (0.8 kg). Assuming the speed is 20 m/s for the climb as for the descent, the kinetic energy is 192 J, while the pull force is 960 N. The weight/pull ratio is about the same regardless of the size of the kite, or would increase slowly until a critical (?) value which can lead to a huge kite. At worst, a few seconds will be spent on really huge kites, and recovered at the end of the trajectory thanks to the this this time positive kinetic energy during the climb. So I do not see any real problem for scaling in any size. On the contrary, I conceive of this type of trajectory as a means of maximizing the space used, unlike to what results from the figure-eight. And the vertical path, said also 2D (3D being for figure-eight), can also allow the implementation of really small and yet powerful AWES, for example by using a (1.5 kW) 9 m span kite for 33 m tether length.

For general information about vertical path as a start reading carefully chapter 12 and chapter 13, particularly the fig.12. 23. on the page 300 of the chapter 12, showing the vertical trajectory and the swept area that is delimited by the Magnus balloon, and also the table 12.3 on the page 297 where the dimensions of the balloon and its mass are mentioned, respectively 80 m span and 50 tons. Certainly it is a balloon inflated with helium, but the mass of inertia plays a role during transitions, and seems to be taken into account by the author.

Concerning the fig.12. 23, the low position is at about 50 m from the ground, so not too close; and the top position is at 220 m from the ground. As the horizontal distance is about 200 m (do not forget we speak about a vertical trajectory), the elevation angle of the low position is about 14°. The elevation angle of the top position is about 47°, leading to a tether length of 293 m, then 87 m for a reel-out/in phase.

If we extrapolate towards my initial example of a 900 m kite span, the tether length should be about 3299 m, comprising the 980 m for each reel-out/in phase. It is a higher value that the value I initially mentioned, but still low compared to the kite span. This higher value results from the requirement to go far from the winches in order to optimize the crosswind flight in a similar way as the papers indicate.

The mass of a single skin kite is far lower than that of a Magnus balloon, and its weight is two orders of magnitude lesser than other lift and drag forces. So the bottom transition may not be insurmountable.

Thanks Pierre.
It’s a bit early days to be scaling to 900m . . . Slightly ambitious.
Chapter 12 test results on page 291 fig 12.14 Net output power
drum roll
0.0099055W That’s a lot of numbers and zeros …
Just not all on the right side of that pesky point thing.

If you prefer only (1.5 MW) 90 m span for only 330 m tether length, comprising the 98 m for each reel-out/in phase, or even (1.5 kW) 9 m span for 33 m tether length comprising 10 m reeling. As I indicated several times the tether length should not be too high compared to the kite span or the swept area. Even Makani 600 kW is too small compared to its space use. And Google and others will not give a second chance so easily. So a credible method allowing scaling NOW is required.
Other than that, I think I can do without your remarks on figure 12.14, remarks which has little to do with the subject. The only thing to note about this figure is the substantially equal duration of the power and recovery phases which could confirm a rate of climb equal to that of the descent that I mentioned for a classical kite it is true.

True, but the path can become vertical by using yo-yo (reeling) mode. I think the use of a vertical path in yo-yo mode leads to some potential advantages: the implementation of a far larger kite thanks to the absence of turns (which is also possible if the path is not quite vertical), and a really crosswind flight, with no downwind move of the kite during all the climb while the full reel-out phase occurs.

The elevation angle for vertical trajectory (chapter 12, figure 12.17) looks to be higher than for figure-eight (Development and validation of a real time pumping kite model, figure 5-3, page 40 ). I do not know if some other curves could confirm it. If this is the case then the vertical trajectory allows the implementation of a shorter tether, hence an even less land use. Certainly however I would not say that this is the future of wind energy.

Choices on “vertical” are several.


The vertical trajectory in pumping mode on this topic concerns one of the types of verticals on the sketch above. The “Vertical Figure of 8” could not be used as a vertical trajectory such like described on this topic. Going down (during reel-in phase) in half eight doesn’t make sense.