Theoretical drag of a Tether

[kitefreak]

Every AWE paper ever written, starting with Lloyd, has its flaws. Fortunately, everybody’s errors cancel out, while correct knowledge compounds.

No complete theoretic treatment of tether-drag exists. The first order dimensionless number is tether-length to kite-area. This predicts that if tether-drag is problem, then a bigger slower kite and/or thinner line helps. Within our allotted ~500m high airspace, this suggests big soft kites of ~1000m2 (as proposed by KiteShip and SkySails/North-Sails). For AWES wings like these, tether-drag is most negligible.

Massimo cites an interesting feedback effect, a progressive velocity pitch input provided by tether drag which passively trims the accelerating wings pitch-up moment. The classic kite has similar “passive” feedback loops in all its DOFs.

Sweep is worthwhile up to the tether-drag limit-velocity. Tether drag during reel-out does add power, but paid back during reel-in, unless the kite flies a sneaky pattern back, near the surface.

No-sweep low-drag reel-in, combined with high-sweep high tether-drag reel-out, could actually net positive power. Bravo to Massimo for citing such interesting counter-intuitive tether-drag science.

[tallakt]

@kitefreak I appreciate your comments here, but to be frank you are not getting your message across to me. I don’t understand anything you are saying here. Perhaps if you could the essence of that repeat with a few more words and a “tighter” story?

Looking at the paper, and using your kite size of 1000m^2, we have:

• Area 1000 m^2
• Maximum force at 4 m/s
• Maximum reel out speed 5.5 m/s at 11 m/s wind
• Altitudes of 1000-2000 m
• Glide ratio E = 20 (the flying speed is stated to be 80 m/s in 4 m/s wind)

Lets also add a lift coefficient and rho, and looping radius

• Lift coefficient of wing 1.0
• air density rho 1.225
• looping radius R = 300 m
• drag coefficient of tether 1.0

I’ll leave out the cosine effect for now, to make things a bit simpler. I also assume using a single tether. Double tethers would increase the drag by \sqrt{2}. Also, I will assume that the tether drag cant slow down the kite.

The tether to support this would have to be approx 45 mm diameter. I guess UHWMPE is to be assumed as material (I believe this is quite optimistic though). Putting these numbers through my calculator gives me:

• Tension 7800 kN / 784 ton
• Tether 110 mm
• Power at 11 m/s wind 43 MW

The rig seems to fly well with 2 km tether / 1 km altitude.

So far these numbers look really good, if you believe tether drag does not affect the kite. Then we will look at the exact same scenario, but including tether drag into the total.

The effective glide number E is now E = 3

• Tension 176 kN / 18 ton
• Tether 17 mm
• Power at 11 m/s wind 1.0 MW

It is difficult to say whether the 1 MW rig is still worthwhile. Anyways it seems that if you are planning to fly at these altitudes, even with a 1000 square meter kite, you are not getting much benefit in having a high efficiency kite. Perhaps scale EVEN LARGER? (hint, my calculations show a 2000 sqm kite also has efficiency approx 3 at this altitude).

Now a simple question to “prove” that tether drag exists and slows down the kite: Where does the energy come from, to drag the 6 km x 17 mm tether through the air (total 2D area 100 square meters)? The drag forces are being converted into heating in the air, and energy cannot come from nothing… (it is simple to conclude that only the kite may provide this power)

Anyways, you guys are hijacking my thread. If you believe drag is zero, the whole thread is pointless…

[kitefreak]

Tallak,

Of course all kites have tether drag, that’s a given. “Neglible” means not enough drag to worry about.

The kPower AWES model applies specifically to our FAA designated 2000ft ceiling, and is intended to optimize airspace utilization (not just make tether drag unimportant). “Altitudes of 1000-2000m” does not apply, because it breaks the optimal “stream-tube” efficiency intended. Also, I do not presume downwind reeling, in favor of crosswind cycle motion (Payne Patent fig5).

1000m2 is a reasonable operational scale. Megafly was already bigger, and Mothra1 was >300m2 of blue tarps. SkySails and KiteShip have done fine at ~400m2. No imminent scaling barrier suspected. At some point larger kites would need to be assembled in mid-air (surface-handling limits).

Hope this helps understand kPower design logic, and its relation to tether-drag issue. KiteMill is taking a very different design approach (the EU hot-wing reeling club). A well done fly-off would be nice to settle doubts faster than venture “silo” isolation.

[tallakt]

Do you have any glide numbers for the mentioned kites? This is the most important number to determine if tether drag will be an issue (along with tether length, tether mass and rotational speed during loops)

I am also just considering crosswind kites. If we are not all of us, that could explain our disconnect here.

Kitemill is relevant in this discussion, BUT: Id like to emphasize that we are talking theoretical tether drag for thought up kites, having no direct relevance to Kitemills setup. For comments on that I would have to forward you to our CEO…

[kitefreak]

The problem with using glide-number with power kites is that the numbers vary vastly with loading. An unloaded soft wing floats along at a far higher number than novices expect, and a fully loaded hard wing at high CL has a proportionally lower number.

The simpler tether drag measure is tether length to kite area. That’s a more predictive number than glide number alone.

[tallakt]

I am aware of this, but still the glide number at the Cl you are expecting to output max power at cut-in is the most relevant, or the Cl where you expect to reach peak power production. By saying “it depends” you are dodging getting further into the details, and the discussion will be rather pointless.

The simpler tether drag measure is tether length to kite area. That’s a more predictive number than glide number alone.

Saying this contributes nothing to the discussion of tether drag compared to the drag of the kite itself. The way the number could be predictive is that the tether drag constitutes for much more drag compared to the kite.

[kitefreak]

@tallakt

getting further into the details…discussion of tether drag compared to the drag of the kite itself

Again, without getting lost in details, the ratio of tether length to kite area is kPower’s chosen first-order consideration. Its true that tether-drag most dominates a low-drag kite’s overall drag performance, assuming a constant tether length ratio.

KiteMill just thinks differently about kite fundamentals, so our respective architectures are very different. Let outcomes and future third-party scholars decide who had the better grasp of kite physics.

[Tom]

@kitefreak

KiteMill just thinks differently about kite fundamentals, so our respective architectures are very different. Let outcomes and future third-party scholars decide who had the better grasp of kite physics.

Caveat: I don’t understand the discussion and haven’t followed it. (Which is nice - knowing that there are people here knowing a lot more than I do.)
There is only one real world and one truth. Hypotheses have either been disproven or they haven’t, which means they are valid for now. Hypotheses must be stated clearly enough to be falsifiable. Let’s try to find the truth together, for example by defining hypotheses clearly, thinking about how they can be falsified and if possible run the experiments. If experiments can’t be run at the moment, the speculation on probable outcomes doesn’t get us nearer to the truth.

[kitefreak]

Luke,

Understand the discussion to better judge it.

Its best if Tallak and I differ radically in starting assumptions, and therefore resulting designs. We cover the greatest number of open hypotheses by diversity of thinking. Confidence in future outcomes and scholars to settle technical doubts is not misplaced.

At least please know that tether-drag experiments are constant now for many years. KiteShip, for example, lived on US military R&D into tether drag for years, for lack of a viable ship-kite market.

Anyone reading this can pop up a kite and sight along the line to see wind-shear revealed by the tether-drag profile (see wind-shear thread). What experiments “can’t be run at the moment”? kPower may be able run a scale version, plus scaling law predictions, faster than you seem to think possible,

daveS

[Windy_Skies]

Wayback Machine

The Drag and Shape of Control Lines in Flight

This note documents (briefly) the development and implementation of the methods used computing for a control–line model aircraft the drag and shape of the lines in level flight. Wind and pilot technique (lead/lag) are considered. The wind is assumed to have constant velocity and direction and the pilot flies so as to make the handle rotate in a circle about a fixed point on the ground. The methods developed here have been implemented in a computer code in which the effect of Reynolds number on drag is accounted for as is a nonstandard atmosphere.

[Windy_Skies]

http://dlb.isrc.ac.ir:8080/xmlui/bitstream/handle/isrc/1649811/6.2017-4058.pdf?sequence=1
| Archive link

Influence of Angle of Attack on Profile Drag and Flow Induced Vibrations of Parachute Suspension Lines

To improve the accuracy of the precision air drop systems, parachute suspension line drag and fluid structure interactions, such as vibrations, were quantified. This data was delivered to the Army’s Natick Solider Research Development and Engineering Center (NSRDEC) in order to provide further insight to parachute designers and experimental comparison to CFD modeling. The specific model used for this experiment was a 1000 pound flat, braided Dacron line with a hollow center and a military standard (mil-spec) of MIL-TC-2754 Type II. This work focused on drag and vibration analysis with angles of attack of 75° and 105°, each at a potentially vibrating and a likely static velocity. Tests were completed with Reynolds numbers between 4000 and 8000 and tensions of either 10 or 300 lbf. Drag data was collected at five different heights along the line. A high speed camera was used to acquire high speed video footage of oscillations present in the line. Experimental testing was accomplished in a United States Air Force Academy (USAFA) low speed wind tunnel using the Jones momentum deficit method. Coefficient of drag was lower for the inclined lines than values measured for vertical lines in previous work. However the inherent variability in the drag results provided large, overlapping uncertainty ranges. Drag coefficients for any single line mostly fell between 0.1 and 0.5, with overall averages between 0.30 and 0.32. Given the numerous quantity and long length of suspension lines used in a typical parachute system, the average drag contribution should still be considered useful despite the inconsistencies at any single point location. Contrary to prior testing at 90° AoA, the preferred modes of vibration for this work were transverse or whirling, with some chord-normalized amplitudes approaching three. Unlike torsional vibrations in previous works, the transverse oscillations did not significantly affect the coefficient of drag magnitudes.

Tether and Bridle Line Drag in Airborne Wind Energy Applications - Storm Dunker, 2018

Abstract

This chapter discusses the physics of tether and bridle line drag based on literature, describes the typical flight regimes for airborne wind energy and identifies regimes of elevated drag caused by vortex-induced vibration and movement-induced excitation such as galloping. The presented laboratory tests show increases of aerodynamic drag due to vortex-induced vibration up to 300% and due to galloping up to 210%. Given that tether drag is a primary limitation to an airborne wind energy system’s ability to fly faster and produce more energy, understanding the regimes of elevated drag as well as the mechanisms to suppress the causing phenomena are important. The chapter provides a basic overview of these phenomena as well as potential solutions for drag reduction. The information and material presented should provide an airborne wind energy developer a useful introduction to the considerations of tether and bridle line aerodynamic drag.

[Storm_Eagle]

I remember a patent for a “aerodynamic tether” in a wing profile shape. Will this really be any noticeable difference? And will it be able to self orient for the “leading edge” to face the wind?

[Rodread]

A huge difference
Check out the AWES Book 2
Airborne Wind Energy
Advances in Technology Development and Research
Part I Fundamentals, Modeling & Simulation
2 Tether and Bridle Line Drag in Airborne Wind Energy Applications 29
Storm Dunker

Also looking at the set of Makani videos around
[20171116 RPX-07 - Testing a Faired Tether - Makani M600 - Tether to Kite POV…]
Were all studying line clamped fairings like this.

[tallakt]

I believe Makani had such patents, and by now they are not pursuing any infringement.

The problem with these is they add weight to the tether, which is a big deal with scale, and severly impact handling of the tether. So if you can do without that is much better.

[Storm_Eagle]

Well if Makanis patent does not predate this from 2010 i guess it is not valid anyway because of prior art.
https://patents.google.com/patent/US20110266395A1/en

And here is a identical tether patent just for use underwater from 2011:
https://patents.google.com/patent/JP2018025195A/en

The patent system is really a joke by now. Like the example above just change the application (over water vs underwater) for an identical “innovation” and you have a new patent…

[tallakt]

The patents validity will often depend on a number of features being present. So tether fairing for a seismic vessel would not invalidate a patent for fairing on an AWE kite. I did not analyse those patents towards Makani though, could be an interesting excercise for those who are into tether fairing.

Anyways, between this abandoned patent and Makanis freeing theirs, whether or not any of them are valid is a moot point

[tallakt]

Another really interesting paper on the subject by Philippo Trevisi et al

https://www.researchgate.net/publication/344336638_The_Influence_of_Tether_Sag_on_Airborne_Wind_Energy_Generation

[PierreB]

This figure and other similar figures (see Figure 3C) come from Joeben Bevirt’s patent for the Joby Energy AWES:

US20110266395A1.pdf

[Rodread]

Length of a faired tether is really important.
From what I understand… The resulting aspect ratio of a long faired tether will be very high which will significantly increase the likelihood of flutter occurring
See the tests on flutter TUDelft did for Makani.

Is it fair to say
Fairings on short tethers… Should fair better?
Doesn’t sound very scientific

[tallakt]

Fig 21 title: «aloha»?

I havent seen this before. They have really covered a lot of options in this patent.