Theoretical drag of a Tether

I think the results kind of also debunk the larger kite -> higher altitude. I think it is not necessarily true that scaling the wing or wing area by x will give you more tether than x times the tether you had before scaling.

Or, to rephrase, I think tether length may scale with wingspan or wing area. So there may not be a magic size where tether drag does noe matter anymore.

Welcome @Massimo !
For what I know the review looks to be correct.

Nooooo! Please, a kite behavior like a glider could be described with 3 forces: lift, drag and weight. The case of the kite see the weight replaced by the tether tension. No other differences, the weight thrust the glider as the tether tension do with kites. The tether tension in C shaped kites is always axial, no licit vector decomposition, the link between wing and tether is a 5DOF. This is a classical newbie error or the desperate tentative of the wind industry to undermine tropospheric wind exploitation trough corruption of the well established science, as happen in other sectors. We are preparing a page explaining again the issue but we are very surprised of the widespread poor understanding of the matter.

This is probably relevant:

Yes Luke, thank you, this is very relevant and introduce the key elements of understanding, the difference
with KiteGen is that our tether isn’t linked to the CoM and the tether drag induce only moments (pitch) to our wing, the opposite of Ampyx case. I agree with the paper that tether model is crucial for accurate evaluation, it is the only model that cannot run in real-time despite parallel computing, because of the insane propagation speed of the axial tension forces. The moment imposed to the KG wing stretch asymmetrically the wind power spot and limit the length of straight paths at full power (before the wind angle is too much aligned to the wing chord). But this isn’t an issue because of continuous and cyclical lemniscates, with direction changes (U-turns) well before those derating limits and before wasting too much energy.

1 Like

See also KiteGen Research High Altitude Wind Generation... and also KiteGen Research C-shaped semi-rigid Power Wing. If Massimo’s statement is verified it could be good also for Optimization of a soft wing with turbines aloft as it is also a two lines C-shaped wing.

1 Like

So if figure A is correct we are in agreement as far as I can tell. It should be clear that if the kite/plane/plite is heading directly forwards the tether may be decomposed as a tether force aligned with the lift force of the wing, a tether force aligned with the drag of the kite, and perhaps also a sideforce component not easily seen on a 2D drawing.

So, if we are in agreement so far: The curvature of the tether is linked to the tether drag and the tension of the tether. More tether length with the same tension inevitably gives more curvature in total and the incidence angle og the tether changes so that more force is allocated in the direction of the drag

I’d appreciate being corrected in this if my understanding is inacurate

1 Like

With regard to the paper cited [“A reference model for airborne wind energy systems for…” eq 17] the formula for tether drag is actually cited incorrectly. The original text is in the first “Airborne Wind Energy” book on page 67, eq 4.6. Anyways, this is a fine simplification of tether drag. Though it will not take mass effect into account. The formula should of course be:

T_d = \frac{1}{8} \rho C_T d_{tet} l || v_a || ^2

(the …^2) is missing in the text

(Note that the formula is similar to my previous post with K=1/4)

1 Like

Aye, it’s a fab paper, great research, really neat match to real life and I can’t wait to see it applied to my work. …
However, in the intro to (PDF) A reference model for airborne wind energy systems for optimization and., As ever, awareness of AWES concept space is missing in the text
The two most promising approaches to AWE are the pumping and drag mode
Most promising and most studied are not, in this case, the same thing.
I guess I’ll never change this institutionalised perspective… I will have to admit. . .
Kite turbines are drag mode. Mechanical drag mode rotary kites.

No.
One of the first envisaged AWES was (and still is) Sky Windpower. It was studied to harness jet-stream at several km from the ground level, following or perhaps preceding C. Archer’s prescriptions. But the weight and the drag (even for a stationary system) of such a long electric tether may have been a problem.

After companies investigated crosswind prototypes, shortening the tether year after year, that due to weight and drag concerns mentioned in several scientific publications of which Bas Landorp’s.

However knowledge about the tether drag concern can be still incomplete. So waiting for a KiteGen scientific paper with peer review about Massimo’s statement, and comprising both computed and real measures.

False, systems without CoM force application thus axially aligned to the lines, the tether drag only appear exactly as tether tension both on ground generator and wing sides, the tether drag finally add generating force. The energy wasted by the tether is paid by the reel out speed that is slightly reduced for geometrical reasons and wind spot deformation. This affects production only in very low wind condition when the reel out speed isn’t nominal yet. Look here for the potential buffer in presence of de-rating bound conditions:
https://www.researchgate.net/publication/331312828_KiteGen_Research_High_Altitude_Wind_Generation_Tropospheric_Wind_Exploitation_Under_Structural_and_Technological_Constraints

Line drag cannot be added to the wing drag because it acts axially, like gravity to a glider, without limiting the flying speed, hence the system AE.
The delay that the line imposes to the path in airspace affects only the angle with respect to the wind and is never a degradation, because it only modifies the power spot shape.

This does not at all counter any of the arguments I have previously set forth. It basically just states a precondition for the analysis which is clearly untrue.

To prove it’s untrue: Its not hard to imagine the tether facing in the drag direction, providing only additional drag and no force to counteract the lift force of the wing. (This happens every time the tension is very low and flying speed is maintained)

In practice, the tether points slightly backwards providing the force you describe in addition to an extra drag force in the ditection of the drag. It may also provide a sideforce, but then we are complicating things too much for this discussion.

My advice would be to rethink tether drag and then after having understood tether drag, reread your paper… I think you might need some adjustments.

True but only if the wing goes downwind without crosswind figures. These generate an apparent wind, resulting a higher tether drag without generating any useful force.

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.

1 Like

@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…

1 Like

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.

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…

1 Like

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.

1 Like

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.

1 Like

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.