Comparison of the traction force of a static parachute kite and a crosswind kite, both with the same projected surface

[PierreB]

Some measures of crosswind kites were performed, reference wind speed perhaps at pattern height, perhaps at mast height (figure 15).

I myself tried to see a little more clearly, both for circular and eight figures.

@PierreB

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

The comparison between circular and eight figures could perhaps stand (both being close each other in term of produced average traction force), but 4 m/s was the reference wind speed at my height, not at flight height. And the difference is very large when we compare the wind speed at 1-2 m height to that of 20 m (kite) height.

Moreover it is difficult to see on the weighing scale (steelyard) and the anemometer in the same time, especially since values were constantly and rapidly changing.

To get around these difficulties, I flew one after the other and for quite a long time (a few minutes each) a good crosswind kite (Peter Lynn’s Vibe that I have used many times), and a parachute kite, having noticed that their projected surface, of about 0.5 m², were almost identical. The wind speed was 5 to about 9 m/s (measured and estimated, the gusts being at ground level (and notably during the highest gust on the kite parachute that led to a traction force of 2.7 kg) as well as at 25 m altitude). I used a weighing scale (on the photo below).

The elevation angle of the parachute kite (40-45 degrees vs. 30 degrees for the crosswind kite) and its height were higher (about 25 m vs 15 m), but it was quite unstable and tended to descend at times. The higher values of traction force of the parachute kite were measured when this kite was close to the ground as well as at maximum height, and during gusts.

Parachute kite: peak traction force: 2.7 kgf. A value of 2 kgf was often achieved.
Crosswind kite: peak traction force: 4.5 kgf, with eight and circular figures. A value of 4 kgf was often achieved.

The second line was not measured this time, but given the past measurements, and the fact that the traction felt was much less, we can assume that the whole traction force was 3/2, leading to 6.75 kgf for the peak traction force, and 6 kgf for often achieved value.

The proportions of the traction force between the two kites did not seem to change too much according to the wind speed.

One might have expected that the lift-to-drag ratio of 4 of this crosswind kite would make a much bigger difference, but it seems that in this case (and maybe in general?) the average traction force of the crosswind kite is only 3 times that of the static parachute kite.

Many refinements would be useful for better measures, and to better know the parameters such like the lift and drag coefficients, the losses from the crosswind kite due to the variations of the traction force within the flight path, and so on.

[PierreB]

@dougselsam

I’d say Pierre has scrutinized this one as much as anybody, and his question about the height of the anemometer is appropriate - that’s a corollary to that first basic question of even having a power curve.

Skysails present their power curve at 10am today (22 March 2024 CET)

Could it be the same curve as in the figure 15? If yes, the deduced efficiency would be far higher if the reference height was the pattern height instead of the mast height as specified in the figure 15, given the wind gradient as suggested in the text (see the quote on the commentary on which this post is based).

@PierreB

This would be a big difference from the wind speed measurement at mast height as indicated in figure 15 (link also above). An excerpt on 4.1.1.:

A specific measuring campaign achieved an uninterrupted automated flight of 42 h that featured day and night flight with an average power production of 62 kW, in wind conditions varying between 4 and 13 m/s (1-min average measured at a height of 10 m) and estimated wind speeds at flight altitude of 6–19 m/s, showing the robustness of the implemented flight and power cycle automation algorithms and all system components at relevant load conditions.

A value of 12 m/s wind speed at mast height of 10 m) would lead to a value of approximately 18 m/s, if we take into consideration the high range of the two evaluations mentioned in the above quote or, in a lesser degree, the difference between the reference height of wind speed at 200 m (on the video) and that at 10 m.

If the kite keeps its efficiency at high wind speed (this may not be the case), its power at 18 m/s wind speed would be about 3 times its power at 12 m/s wind speed or also, to be more careful and keeping the same proportions of the wind gradient, 12 m/s versus 8 m/s.

Now, 3 times is also the (low) ratio of the traction force that I measured between the crosswind kite and the parachute kite in the photo above. The traction force is used to determine the power in reeling mode, by multiplying it by the reel-out speed (2/3 of the wind speed to simplify), and then by 4/9 due to the loss of 1/3 of the wind speed by going downwind.

My home experiments could better agree with the measurements in Figure 15 with the wind speed at 10 m from the ground, although with the reference to flight height, we would be closer to the theoretical maximum with an L/D ratio of 4, i.e. an increase in the traction force by 4².

My home experiences have highlighted the huge losses of crosswind kites. To be convinced of this, it is sufficient to take a look at the power curves in real time, for example the curves in Figures 15, 17 and 18 which zigzag.

[PierreB]

@PierreB

the losses from the crosswind kite due to the variations of the traction force within the flight path

In previous experiments, I had felt a more regular pull on the low radius loop than for long figure-eight trajectories, leading to equal or almost equal power with less traction peaks.

Losses due to relatively large figure-eight trajectories can be explained by the fast variations of traction force within the flight window. The position of the kite is always changing in relation to the central line of the flight window. This leads to increasingly greater losses as the kite moves away from that central line.

In addition to these losses, there are losses due to the irregularities themselves. For example, if you drive a car for an hour, covering 75 km, you will consume much less energy if you drive constantly at 75 km/h (by analogy with a regular traction force of a static parachute kite) than if you accelerate and decelerate (by analogy with an irregular traction force of a crosswind kite) constantly for the same average speed of 75 km/h.

In addition to this, the angle of attack is optimized to favor the L/D ratio of a crosswind kite, while the thrust coefficient is favored for a static parachute kite.

This seems to explain why I get only 3 times the average traction force for the crosswind kite compared to that of the static parachute kite. In reeling mode, the power obtained would also be 3 times higher. Indeed:

@PierreB

The traction force is used to determine the power in reeling mode, by multiplying it by the reel-out speed (2/3 of the wind speed to simplify), and then by 4/9 due to the loss of 1/3 of the wind speed by going downwind.

[dougselsam]

I also remember one video where the crew were taking their own data, trying to fill in a missing part of the power curve that was not filled in in previous days. Not sure how that comports with the bit about forty-something hours of continuous operation.
Pierre, you point out an inability to determine the anemometer placement or reference height of an estimated wind speed. How any of this matches what would be expected from an independently verified power curve meeting professional industry requirements for certification, I don’t know.
Given all of these uncertainties, I’m not sure what was being celebrated about this power curve announcement. Maybe someone with knowledge of the situation could clarify the story. To me, credibility in AWE remains an open , empty space, ready to be occupied, as usual.

[PierreB]

Hi Doug,

I have to say that after my own experiences related above, I am less curious to know whether the figure 15 prevails (which I think), or if it is the curve with the reference height of wind speed at 200 m on the video, and this is all the more so since another example that I have already mentioned also provides a reference for wind speed a few meters above the ground for performances comparable to those indicated in Figure 15, all else being equal.

@PierreB

@PierreB

On the first paper: Table 8 page 44, dataset 5: Mutiny (25 m² kite, see page 8), 8 m/s wind speed, 5.19 kW average power, 14.1 kW average generation phase.

On the second paper: Figure 15 (average power 92 kW, with peaks of 300-400 kW.

The wind speed was measured a few meters above the ground, and the flights were carried out at several hundred meters altitude, if I was not mistaken in reading both documents.

The wind must therefore be much stronger at the height of the kite, which would considerably reduce the real efficiency such as measured with a wind speed close to the ground.

[PierreB]

@PierreB

The second line was not measured this time, but given the past measurements, and the fact that the traction felt was much less, we can assume that the whole traction force was 3/2, leading to 6.75 kgf for the peak traction force, and 6 kgf for often achieved value.

This has been verified once again.

May 11, 2025: Vibe test with two weighing scales, like years ago, and with similar results. This test consisted of attempting to see the values given by the two weighing scales at the same time when possible, and then to observe the evolution of the pulling force on a single weighing scale throughout the trajectory in eight then also the trajectory in loop.

A peak of 4.5 kgf on both weighing scales simultaneously (9 kgf in all) was achieved during a short gust (about 6-8 m/s), and during the flat part of a large figure-eight towards the middle of the flight window.

Then (with slightly lower wind) a regular (as expected) traction force of 3 kgf plus 1 kgf was achieved on very tight loops (about 3 m in diameter like in the old video of Low radius loop that showed the traction force on a single line, with the second handle having been released and the two lines wrapping around each other).

Then the wind did not exceed 3-4 m/s: during figure-eight, traction force on the same weighing scale of maximum 2.5 kgf and about 1.25 kgf on the other weighing scale exactly at the same time, these values being reversed during the trajectory.

On the same weighing scale, the traction force varied from 2.5 kgf to less than 1 kgf, partly due to moving closer to the edge of the flight window where the kite loses its power, partly due to the change of the global traction force during the trajectory, and partly due to the sharing of forces on the two lines (unlike SkySails’ kite which operates with a single line). The outer side of figure-eight or loop experiences more traction due to the greater speed compared to the inner side, and in a proportion depending to the amplitude of the trajectory and its curved (more difference) or flat (less or no difference) part.

[PierreB]

@PierreB

Losses due to relatively large figure-eight trajectories can be explained by the fast variations of traction force within the flight window.

@PierreB

In addition to these losses, there are losses due to the irregularities themselves.

These last losses are due to the kinetic energy increase when the kite goes faster within the trajectory, and having to be dissipated when the kite slows down, at the cost of enormous energy consumption.

It’s as if, in a car, you were constantly accelerating and braking instead of maintaining the same pace, for an identical average speed.

To my knowledge, this point has not been taken into account in the various equations derived from Loyd’s model.

These two types of losses (the second resulting from the first) are not observed in traditional wind turbine rotors, whose entire surface remains perpendicular to the wind and whose blades rotate at the same speed throughout the entire rotation.

[PierreB]

@PierreB

These last losses are due to the kinetic energy increase when the kite goes faster within the trajectory, and having to be dissipated when the kite slows down, at the cost of enormous energy consumption.

Kinetic energy is dependent on mass and velocity squared. We saw that kinetic energy worsened the mass issue, both preventing to maintain speed in the climbing path.

@PierreB

The wind speed aloft (first circle in the left) was about 8-10 m/s. The kite speed was between about 38 and 56 m/s. The power generation was negative about half of the time (kite slowdowning), and between 0 and -500 kW, the positive power generation (kite accelerating) having the same values. So there was roughly no generation in average.

A mean to partially solve both cosine and kinetic energy issues would be using a tower. In the process, you replace the crosswind kite with conventional wind turbine blades.

Or, if one wants to stay within AWE, to capture high-altitude winds, tether-aligned of type parasail AWES, although still underestimated, could be a possibility. This is what the trials mentioned on this topic could lead to, showing that the superiority of the crosswind kite over a parachute kite of the same area is far from overwhelming: one should not confuse peaks of force or power with the average force or power (see below).

@PierreB

it seems that in this case (and maybe in general?) the average traction force of the crosswind kite is only 3 times that of the static parachute kite.

This rough estimate made on a small scale could be corroborated by (in French) SkySails — Wikipédia:

La voile peut opérer à une altitude comprise entre 100 et 300 mètres où l’on trouve des vents plus forts et plus stables et délivre 2 à 3 fois plus de puissance au mètre carré qu’une voile conventionnelle.

Translation:

Sailing can operate at an altitude between 100 and 300 meters where stronger and more stable winds can be found, delivering 2 to 3 times more power per square meter than a conventional sail.

[PierreB]

@PierreB

These last losses are due to the kinetic energy increase when the kite goes faster within the trajectory, and having to be dissipated when the kite slows down, at the cost of enormous energy consumption.

It’s as if, in a car, you were constantly accelerating and braking instead of maintaining the same pace, for an identical average speed.

To my knowledge, this point has not been taken into account in the various equations derived from Loyd’s model.

Can they be corroborated by other tests than mine, whether for flexible or rigid wings in crosswind flight?

Regarding flexible wings, some hints are exposed again on Annual Reviews: Autonomous Airborne Wind Energy Systems - Engineering / System Design - AWESystems Forum.

Regarding rigid wings, flying in circular path:

Multiple Wing Systems – an Alternative to Upscaling?

1: 47: “wing area of 1 m² generates 40 kW (at 13 m/s wind speed and L/D of 15).”

3: 08: “10 kW for 4 m² plane [Vander Lind 2013] at 8 m/s wind speed,i.e. 25% of potential.”

I wouldn’t even consider the example on the left side of the image, which is still far less favorable.

The 4 m² plane can have a L/D ratio of 15. If that’s the case, what leads to only 25% efficiency, apart from the irregularity of power (and perhaps tether drag in a lesser level), hence the losses of the power generated by the accelerations and decelerations during the path, assuming that the L/D ratio of 15 partially or fully includes the tether drag?

See the curve of a Makani wing on:

Makani Power Autonomous Flight. June 18, 2010 - HD

@PierreB

Then (with slightly lower wind) a regular (as expected) traction force of 3 kgf plus 1 kgf was achieved on very tight loops (about 3 m in diameter like in the old video of Low radius loop that showed the traction force on a single line, with the second handle having been released and the two lines wrapping around each other).

It is possible that large-radius circular trajectories, such as those of the Makani wing, result in fewer losses due to irregularities compared to figure-eights which likely produce more accelerations and decelerations.

[PierreB]

@PierreB

An underestimated problem may be the significant kinetic energy as the kite descends, preventing it from ascending.

@PierreB

These last losses are due to the kinetic energy increase when the kite goes faster within the trajectory, and having to be dissipated when the kite slows down, at the cost of enormous energy consumption.

It’s as if, in a car, you were constantly accelerating and braking instead of maintaining the same pace, for an identical average speed.

To my knowledge, this point has not been taken into account in the various equations derived from Loyd’s model.

Perhaps some Makani’s videos could provide some clues.

20190430 CW-07 - First Night Flight of Makani M600 [Full Flight, Data Overlay]

At 14:34: wind speed (in the left) aloft: 12.7 m/s. M600’s speed: 40 to 60 m/s. Tension on the tether: 45 to 125 kN. Power: -250 kW (negative power) to 750 kW (positive power).

I don’t remember exactly M600’ surface area, but with its span of 28 m, an area of 35 m² seems to be plausible. Its lift coefficient (Cl) seems to be only about 0.65. Average M600’ speed: 50 m/s.

Average tether tension force: about 80 kN. Lift-to-drag ratio (glide number) is noted as: (L/D). Rough calculation:

35 x 1.2 (air density) / 2 x 12.7² x 0.75 (cosine² for an average elevation angle of 30 degrees) x (2/3)² (M600’ velocity² with turbines in relation to M600’ velocity² without turbines) = 1.129 kN: so, 80 (kN) / 1.129 (kN) would provide 0.65 (L/D)² (without turbines) = 70.86, leading to (L/D)² = 109, so (L/D) being about 10.44 (without turbines).

For a rigid wing, it is a slightly lower value than expected 12 (without turbines) by taking account of tether drag. And if the area and the Cl are higher, the (L/D) would be still lower for a same tether tension of about 80 kN. We can note that 50 m/s (M600’ average speed) / 12.7 m/s (wind speed aloft) lead to a (L/D) value of about 4, which is a far lower value, but requiring correction due to the circular trajectory in relation to a supposed straight trajectory.

We can therefore think (without yet having formal proof because of unknows) that in connection with the losses due to the variable cosine according to the position in the flight window, we have the losses by speed variations that result from the consequences of variations in the cosine, exacerbated by the mass aggravating the force of gravity, so kinetic energy issues towards the ground.

[gordon_sp]

I assume that this phenomenon occurs in crosswind yo-yo systems as well.

[PierreB]

@PierreB

My home experiences have highlighted the huge losses of crosswind kites. To be convinced of this, it is sufficient to take a look at the power curves in real time, for example the curves in Figures 15, 17 and 18 which zigzag.

Whether it’s in yo-yo mode, as specified on:

@PierreB

Now, 3 times is also the (low) ratio of the traction force that I measured between the crosswind kite and the parachute kite in the photo above. The traction force is used to determine the power in reeling mode, by multiplying it by the reel-out speed (2/3 of the wind speed to simplify), and then by 4/9 due to the loss of 1/3 of the wind speed by going downwind.

Or in flygen mode, as specified also here.

This topic is about the big losses in crosswind flight traction, due to variable kite velocities. The possible implications on the flygen and yo-yo modes have already been mentioned, with references to support.

On the other hand, it seems to me that rotary devices like Daisy with a good power coefficient (Cp) of around 0.15, AlphAnemo and The Pyramid experience less or even no such variations due to the tether arrangements making them to work like rotors.