Low radius loop

Yepp. Another approach to this thought experiment. But how could one extract power from this? How would one depower the kite(s) for the reeling in phase?

Better add a swivel and vane next time.

First one would have to control the rotation.

The laws for turn rate are not a law of nature, I would be hesitant to conclude something is not possible based on that law. Rather they provide a way of estimating the design envelope for current kite designs.

For a kite i believe its simple, just integrate «L/D» over the wing. The difference in left and right should state the natural radius of flight for a wing.

Furthermore, kite networks complicate this, tethered wings will turn at any radius. The fit of natural radius and forced radius will show itself in roll control. The cross influence yaw-to-roll becomes more important for smaller loops.

I would also state that for rigid wings with tail, turning rate works differently than a kite providing some drag at either tip.

The maths is there for anyone who cares to go into the details. Many things are possible. Turning rate is of course affected by AR and wingspan, but there is so much more to it that one should not draw conclusions.

One conclusion we could draw, is that for a single wing on a tether, in order to loop (in smaller radiuses with high speed), it must have the sum force pointed somewhat towards the center of rotation. This is a cosine loss of sorts, and cant be avoided.

Rotokite theorized it with two kites that would be controled like for all yoyo systems.
The same with only one kite, unless a mechanical means is found in order to lift the kite in every rotation then depower it by stopping the rotation.

The same for all AWES, the cubed cosine loss increasing as the elevation angle increases, about are the considerations of flight path with large radius (Makani) or small radius (here) or rotating with joined wings (Rotokite) or figure-eight.

For all yoyo systems I think a simple way to calculate the power is the force x 1/3 wind speed reel-out x 4/9.

As Goldstein indicates half of power for a rotating kite in regard to crosswind flight, can deduce half of force. So all other things being equal a Rotokite with two joined wings would have 6 kg (60 N) force, so 30 N for a single wing, perhaps less.Taking also account of Betz limit 4/27 for yoyo systems.

I was talking about a second (third, fourth?) cosine loss due to having to «roll» towards the center of rotation in order to provide a sentripetal force, not the cosine loss due to elevation above horizon. (Im not sure if that was clear)

Also I wonder where you get the 4/9 factor?

The same for other systems. And the variations of the elevation angle are very low.

The power = force x reel-out speed. As the reel-out speed is 1/3 wind speed, the initial force is multiplied by 4/9. Indeed the apparent wind is 2/3 wind speed. 2/3² = 4/9. So the 40 N force with 4 m/s wind speed becomes 17.7 N with 1.33 m/s reel-out speed, the power being 23.5 W.

Today I remade the experiment of autorotation with only one other wing then I obtained the same result as on the following video I put again:

4-5 kg regular traction measured with a steelyard on the line taut with 4 m/s wind speed while I obtained 3 kg surge traction in crosswind larger figure-eight and for one of the two lines, the other line giving a lower value in the same time, and the total value being irregular and probably lesser.

So it looks like an autorotation with low radius loop could generate more power and using less space than crosswind large figure-eight that are generally envisaged.


Continuous operation in the kite window “power zone” will improve the quality and magnitude of power output from any AWES design.
Even those crazy Daisy ones. The higher line tension will allow them to transmit torque more effectively.

Thanks for sharing your experience @PierreB

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Yes. My experiment I recently remade with the same result allows to guess the power during reel-out energy phase. Wind speed = 4 m/s, Force = 50 N, Power = 50 x 1.33 (reel-out speed) x 4/9 = 29.5 W.
If the swept area was 4.9 m² for 1.25 m radius, the (here) soft 0.8 m² kite achieved the 4/27 Betz limit of the 4.9 m² swept area. I think the real swept area was rather 7 or 8 m².

But for Daisy it can be different as it is stationary, the Betz limit being the16/27 well known limit. Using rigid blades or more soft blades could theoretically allow achieving this limit.

After there are other parameters (traction or torque, spacing…). My experiment was to introduce a small loop in yoyo methods.

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Flight control of tethered kites in autonomous pumping cycles for airborne wind energy.pdf (1.1 MB)

See the figure 21 with the huge variations of force (so power) during large crosswind figure-eight, apart reel-in phase. Numerous papers show similar curves. The variations of force imply a big loss (about 1/2) of power.

It would be possible to obtain the same or a little more power by using a low radius loop. After some problems can occur as a swivel requirement or other.


For a high aspect ratio wing, having low speed on one side and higher on the other makes things difficult. This effect is reduced with increasing radius. I expct there is a practical sweet spot, say diameter is 10x wingspan that will be established as a rule of thumb with more experience.

I think a wingmill represents the tightest possible loop while eg Makani represents the «untightest». Som design considerations:

  • starboard/port airspeed
  • radius vs centripetal force generation
  • bridling or other centripetal support
  • cosine loss due to roll based generation of centripetal forces
  • smaller radius allow for faster rotational speed giving easier torque transfer
  • multi wing AWE may place additional requirements on radius for power transmission due to geometry constraints

Im sure i forgot some…

I also subscribe to @PierreB concerns about smoothness of power delivery as a function og gravity slowdown/speedup during the loop. These concerns dimminish with smaller radii.

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In fact it was a peak of 3 kg for one of the two lines, and far less for the other line in the same time. So I correct the following: the low radius could allow using less space with a likely higher efficiency.

Gravity can be a concern, but I rather think about both the more efficient central power zone and the various power within the flight window as the lemniscate figure is large, involving different cosine.

Sorry my default thinking is always circular/spiral not lemiscate. This is probably a topic for a separate thread though. Circular is simpler to analyze though, thats one reason to choose that for a mental model of a kite

If I understand well enough, I agree your thinking concerns several aspects of a circular/spiral of which the gravity, while my thinking of a low radius loop is in regard to a large lemniscate, and in a lesser way a large radius loop.

It looks like the (0.7 m², weight 0.145 kg) kite made more (regular 4-5 kg) traction in full autorotation (2.5 or 3 m diameter swept area) on only one line, as I released the second line, descending at 1 or 2 m/s (wind speed 4 m/s).

When I tried to maintain altitude by pulling then releasing the second line in each rotation, the total traction appeared to be lesser. It is true that a part of the traction was transferred towards the second line during pulling (not during the full rotation). I wonder what the traction would be if a Delft module piloted the rotation by maintaining altitude. Does anyone have any answers or assumptions? @Rodread, @tallakt, @Tom, @Windy_Skies, @dougselsam, @Derek, @JoeFaust

I don’t really get the question… so I’m just going so say things related to what I think it was about. :stuck_out_tongue:
When rotating just by bridling and falling in altitude, the plane of rotation is more orthagonal to the wind direction. Steering it so that the kite keeps altitude might skew the plane of rotation so that the swept area (projected onto a plane orthagonal to the wind direction) is lower and the apparent wind less favorable.

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It looks to be a serious possibility. Thanks.

The apparent wind generated by descending can also be an explain.

Pulling the second line at every turn can break the flow of the rotation.

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There are various kite power simulators now available as stand alone open source software or MATLAB simulations. You can likely program an altitude maintaining near-circular flight path into these simulators and be fed line tension parameters as output… Any experts on the packages available available?

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