Comparing Flight Paths for Airborne Wind Energy Systems: Loop vs Figure-8

Engineering Math & Physics
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Hello All,

I wanted to bring up a topic that has been on my mind - the choice of flight paths for airborne wind energy systems, specifically, the comparison between looping (circular) and figure-8 paths

In airborne wind energy systems, we know that power generation is proportional to the cube of wind speed. Maintaining higher speeds is crucial as even minor increases in speed can lead to significant power output. This brings the focus to the flight path of the kite and its impact on the system’s overall efficiency.

In my analysis, I found that a circular or looping path could provide benefits, especially in high wind conditions. The advantages stem from:

  1. Consistent Speed: The kite maintains a relatively constant angle to the wind in a loop, allowing it to sustain its momentum and speed, which results in more stable power generation

  2. Inertia: Looping paths don’t have significant changes in direction, hence there’s less inertia to overcome. Figure-8 paths, on the other hand, require continuous change in direction, which could lead to speed reductions and thus lower power generation.

  3. Energy Loss: In a figure-8 path, the energy needed to overcome inertia during directional changes could result in efficiency losses.

  4. Control Simplicity: A looping path may simplify the control algorithm due to its single, constant direction of motion.

However, it’s important to note that in low wind conditions, a figure-8 flight path can be advantageous. This path effectively “pumps” the kite, giving it a continuous push and pull, which can keep the kite airborne and moving even when the natural wind force is minimal

Ultimately, the choice between a loop or figure-8 flight path might depend on the wind conditions and specific system design. The capacity to adapt the flight path to best suit environmental conditions can enhance power generation and system longevity.

I’m eager to hear everyone’s thoughts on this matter

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Well said, @ChristianH . Thanks for sharing.

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Hi. Thanks for an interesting post. I will add some of my opinions on this.

First I would like to say, there are two figure of eight modes, one where the «x» part of the path is flown downwards, the other upwards. The upwards version is more interesting to me, because the vertical component of the kite speed is smaller conpared to the other two options, giving the kite less gravitational slowdown. The peak power of gravity on the kite is lessened. This gives better low end performance and more constant speed even in higher winds. (you spend more time climbing, which makes it easier)

Then you have the practical aspect of line twisting which must be solved one way or the other. Fig 8 is the clear winner. Though looping can also solve this simply by alternating loop direction between production cycles.

You are talking about the rotational speed of the kite and moment of inertia. I gather this represents a really small change of energy. I challenge you to calculate what these can be. With larger kites, the moment of inertia will maybe increase by x^3 to x^4, though the rotational speed is reduced by 1/x and the area of the stabilizer/rudder is increased by x^2 and the moment arm CG to rudder increased by x. [x is the scaling factor of a scaled kite, using a dimemension eg wingspan].

My guess is that the effect of rotational inertia change flying figure of eights is not very prominent, even at scale. Though better calculations should be done to be certain.

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Now, figure of eight paths do require more space.

This will maybe affect wind farm density.

For sure it will affect the loss of energy experienced by introducing a larger angle relative to flying directly downwind. This effect maybe less important in practice because if you are flying loops, you my want to place the path of your loop so that the upstroke is mostly placed directly downwind, to compensate for gravity slowdown.

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So to summarize my findings/opinions on this:

1 - Consistent speed; important factor, win for fig 8
2 - Inertia; not a big factor
3 - Energy loss; not a big factor
4 - Control simplicity; not a factor because doing loops and fig 8 both are extremely demanding

For me its about:

1 - Do you want/need to have a motorized tether untwisting tether attachment on the kite?
2 - Are you sensitive to the area spent flying the loop/fig 8.

Also, it could be about; is a loop sufficiently good that you don’t need to worry about fig 8, temporarily. A loop is simpler to reason about, and [as you point out] slightly simpler to implement. Maybe you can be fine with looping then implement fig 8 when you are close to commercialization. This is like an optimization that could occur late in the process

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There are two other factors which you haven’t mentioned. Firstly, there significant cosine cubed losses if the kite is flown at a high altitude. This would favor “lazy eight” path as opposed to circular pattern. Secondly a circular pattern requires a rotary union in the tether with slip rings for electric power transmission.

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Are you assuming that a fig-8 pattern will have smaller size in the altitude direction?

My thinking is that a fig-8 would be as high as a circular loop, but wider. The looping radius would still be the limiting factor for both patterns?

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Yes. Especially with”lazy eights “

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What is a lazy eight?

I believe a kite flying faster should also turn faster, in a smaller radius turn. So either way, the turn in the fig-8 would be limited by turning speed which would probably be at its lowest at the top of the flight path, or close to it

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Elliptical pattern as opposed to circular pattern in the lobes of the figure-of-eight. This means that the altitude change during the flight is minimized.

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And also that cubic losses are increased… I think the pattern ideally is as small as possible, and kite agility is most likely the limiting factor.

Another smaller effect; when flying the «x» in fig-8 path, you dont need to use rudder. This will make the kite fly with less drag. The kite does not want to fly in a loop unless it is asymmetric. But anyhow this is probably very small relative to tether drag

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Drawing from the practical experience of kite surfing, there’s notable value in considering looping flight paths for airborne wind energy systems. In the sport, ‘kite looping’ generates significant pull due to sustained momentum and speed. This aligns with the idea that circular looping paths could optimize energy generation, particularly in high wind conditions.

Looking broadly at high-speed foils, whether in technology, nature, or elsewhere, a continuous looping pattern appears more common and potentially more efficient than a figure-8 pattern. This suggests that figure-8 paths, though convenient for the engineer, may not always offer optimal performance.

Importantly, a system capable of executing continuous loops should, in theory, be able to manage figure-8 paths too. This operational flexibility could be advantageous for coping with variable wind conditions. However, it’s worth noting that figure-8 paths might offer superior performance in specific scenarios, such as in low wind conditions (consider soaring vs dynamic soaring).

Adding to this, the weight of the tether, particularly in airborne wind energy systems like Flygens that use onboard generators and heavy conductive lines, may impact the choice of flight path. In such cases, a ‘lazier’ figure-8 maneuver might offer distinct advantages by managing the weight of the tether more efficiently. That is to say, heavier tether lines are more suited for figure-8’s rather than loops.

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Smaller loops mean less tether drag
Check What Filippo says on the matter Vortex model of the airborne wind energy systems aerodynamic wake - YouTube
Video is a bit noisy

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But this is not terribly accurate because if you use a rigid kite at huge scale, it will be relatively much heavier than a kitesurfing kite.

A huge kite will not have «sustained momentum» because the «momentum», in which I expect you mean the time it takes for flying speed to bleed off, does not scale.

To explain why, you can consider that a larger kite flies a bigger loop, as looping radius is probably very correlated to wingspan. The large and the small kite though fly the same speed, governed by glide ratio of kite and tether vs wind speed (to simplify things a lot). Flying the large loop takes a lot of time but the time it takes gravity to halt a flying object is pretty constant.

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One other aspect is the power required for control. Much higher in eight that in loop. While kiteboating, I noticed that we often used a pattern which is mixing loop in one direction and one in other direction and downloop eight, resulting in a kind of inverted horseshoe pattern. Have a look here Kiteboat AK650 aout 2020 - YouTube

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I’m not sure, because a aircraft style kite will want to fly forward, not in a loop. So for figure-8 some sections will be straight path and thus not require rudder input. My guess is that the rudder input required when transitioning from curved flight to straight and vice versa is very very small, compared to the rudder input required to maintain the loop radius

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Depending on your system design, you might need no power from control at all to maintain your control surfaces (rudder or any differential control) in the same position.

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I want to discuss something I’ve been contemplating, particularly regarding the agility and demeanor of kites.

The tether’s attachment to the kite plays a critical role. With rigid flying components, we usually see one anchor point, necessitating the use of rudders and other control surfaces to navigate the craft. Conversely, soft kites, with their flexible components, have tethers attached at each end. This effectively twists the kite, manipulating the flight surface.

Gravity is less of an issue for lightweight, flexible wings. However, in the context of the kite’s wind window, the most potent wind is found directly downwind of the tether platform.

Examining the geometry, it is clear a loop can access this downwind region more effectively than a figure 8. In the region directly downwind (and closest to the ground), the kite’s tension and steering ability are maximized, and it is well-positioned for altitude gain.

In terms of rudder control, I agree with Tallakt that during a “loop,” the rudder should be aligned straight only when ascending to compensate for lost altitude. The rudder boosts the kite’s power when angled to execute a tighter loop but up to a point. The looping capability is somewhat restricted due to the central location of the anchor point on the fuselage, resulting in larger loops. However, this limitation is counterbalanced by the power of a robust, rigid wing, especially when paired with a Power Take-Off (PTO) system, as seen in Kitemill.

Conversely, a soft kite with two anchor points allows pivot points on both ends. This design can accomplish faster, tighter loops as the pivot point is not centralized in the fuselage, although multiple lines might increase drag.

This suggests that soft and rigid kites might have different leverage points. Soft kites, or those with end pivot points, tend to be quicker and more agile. In contrast, kites with central anchor points are simpiler and more stable. If I were flying inside a tethered plane such as kitemill’s airframe I would certainly pull up sooner when approaching the ground in high speed in a loop maneuver.

The childrens toy plane with a string attached to the wing and spun around is a good base for contemplating such a scenario. In this case the tether point is on the tip of the wing, rather than the center of the fuselage. We could attach another string on the other wing and that would balance the kite in flight but that approximates a “soft kite”'s multiple tether arrangment.

Perhaps a solution in the future are rigid, flexible frames with flexible skins, and two tether points for steering; something like a stunt kite. Such a kite would make Power Take Off easier, it would be less expensive during a potential crash, it would be much lighter… the list goes on.

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I was thinking more in terms of rudder input will create extra drag of the kite, not power to supply the actuator. The rudder drag then reduces the power output overall

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Tallakt,

Does the rudder need power to function? If there is no conductive tether, is it just powered through batteries? If so, does that mean the flight time is limited? Or do you use the props for charging the onboard batteries to power the rudder?

Also if there is a conductive tether, is there some form of slip ring, or are orbital paths not feasible for Kitemill?

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With the conductive tether this is not a problem. With a UHMWPE tether (rope) one usually needs a small turbine (rat) on the kite. The onboard power demands are small.

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As for performing continuous low radius loops. With no control, the kite descends slowly, turning and pulling relatively hard despite the small radius of the loop. Then the kite has to go back up and the cycle starts again. It is also possible to raise the kite a little with each turn so that it maintains its altitude, but this can lead to a cyclical slowdown.

In addition to the possible advantage of a constant speed during several revolutions, the kite is closer to the center of the flight window where the traction is higher, and throughout the loop. But a swivel is required.