A Simplified Drag Estimate for a Tether with a Belly

Hi. I made a better drag estimate of a tether subject to centrifugal forces, but not requiring numeric integration or simulation.


a_simplified_drag_estimate_for_a_tether_with_a_belly.pdf (181.1 KB)

Note: I updated the document after a revision.

I am having a few doubts though; is all the tether drag absorbed by the kite, or is some also absorbed at the ground station side.

I think maybe the answer is different for TRPT and for Yoyo. For TRPT all the drag must be dealt with by the kite. For Yoyo some part of the tether drag may be dealt with by the ground station. The difference may be 30% more drag for a similar TRPT vs Yoyo

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I’m not going to pretend to have the competence to validate any of your formula derivations @tallakt . Waaay over my head.
Very impressed.

The natural interpretation I can relate to is skipping rope.

Can these points summarise it for lay folks as… ,

1 More tension & shorter lines = less belly for same speed, line type and radii?

2 A belly will add drag but a spiral will tend to decrease drag.

Is it fair to say - A belly would increase torsional rigidity? The shaft is wider with higher 2nd moment of inertia but the line is less taught straight.
A spiral initially increases torsional rigidity then beyond 90 deg reduces it.

Must inspect my old videos for belly… The one I posted on YouTube yesterday had a 47 year old belly showing and I’m not prepared to measure nor share the radius details

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I agree with your observations, more or less. Thanks for digesting this. I am very busy right now with the TRPT rig and upcoming AWEC, so I find it hard to make time to put a lot of effort into the presentation side of things. And - to be fair, I am the only likely user of these equations for now.

Thought I’d share for those curious.

I think you would always want a straight as possible tether. The “belly” due to centrifugal forces on the tether is more dominating when the tether tension is relatively low (relative to rotational speed, radius tether mass etc). When the belly occurs, the tether radius will increase, then the airflow over the tether increases which in turn increases tether drag.

The “belly” is interesting because it can be solved separately and I included it in an improved tether drag calculation/approximation in this document.

The spiralling part is less interesting because it only affects drag in the sense that tether is shortened because of it, and I don’t think any sane AWE implementation would see much spiralling. At least not for one unsupported shaft section. Also solving the spiral shape I have not been able to do analytically, so it must be solved numerically.

I think yes, it is definitely interesting to make the “belly” shape on purpose to increase the moment the shaft can carry (the \Lambda value). I haven’t done any calculations on this though. Keep in mind that increasing the radius of the soft shaft also increases drag, and the balance between tether drag and shaft length and \Lambda requirements is very delicate.

Maybe if you added mass to the tether by applying fairings, you could have increased mass (and higher \Lambda, or more moment transferred) and also have lower drag. This would be a win win. Though handling gets more complicated. I think these are not just theoretical options for such a TRPT rig, but real options that could be considered.

Let me end with saying that the point of this whole exercise was to arrive at a better tether drag estimate that took the “belly” into account, but still being easily calculatable without numerical methods or simulations. I think the functions I arrived at are better used than the onces previously commonly used in AWE that only consider the tether to be straight.

Also, I believe the distinction between tether drag approximation for TRPT and other AWE is a new thing. Maybe…

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