Probably bullshit, but what if one would “vibrate” the tether at maybe 50Hz with an amplitude of 1dm?

You could make some assumptions like:

- Compare to yoyo at 1/3 wind speed reeling
- zero force reeling out in the sine
- same force reeling in in the sine

If we assume for a period T that the constant winch speed reels out o_c = \frac{1}{3} w T lengths units of tether, then the vibrating tether running at frequency f would have the same useful reel out length of o_v = T f a where a is the amplitude in length units of the sine vibration.

Setting o_v = o_c yields a = \frac{w}{f}

In practice though the vibration reel in tether force would not be zero. Lets make the more practical assumption that the ratio of forces are on average 1:2. The losses would make the number a increase a lot, perhaps by a factor of 3? (wild guess).

Now considering the tether curvature and the elasticity of the tether (the latter less important I believe), with the two prescribed tensions, what is the difference in length? You have to compensate for this difference in length by further increasing a. The smaller a (larger f), the more dominant this effect will be. This effect will be largely attributable to aerodynamic loss, so the energy will not be recovered.

I think what you might end up with is a frequency f that is a lot larger than 50 Hz. Also, the time spent in production and return is equal, so the tether power transmission utilization is reduced compared to yoyo/flygen. This leads you to limiting the tether length somewhat (perhaps not a big deal)

For a certain tether length and thickness, you could plot the losses of power conversion on a scale where frequency f in on the x-axis. Just place f where the losses are acceptable

If you had a dual system with Y arrangement you could make them deliberately out of balance with each other by either lift or mass with one down looping as the other up loops. That would create a relatively slow axial vibration while acting against a constant tension.

I am sure there would be many other practical issues with such and arrangement.

Some additional thoughts: These calculations are interesting for any yoyo where the return phase and production phase form a single loop/cycle. If my instincts are right on this one, for a smallish rig, say 100 kW, f will be smaller than 0.1 Hz. So you maybe cannot go high frequency without incurring large transmission losses, but you would very much like to support the “natural” frequency matching the cycle period. But it might not be easy to design for the “natural” cycle time and low losses.

If the tether and kite can do this, building the ground based equipment could be simpler, due to no weight/size constraints.

Also, at this point, it’s no longer a vibrating sine wave I guess, rather a periodic function that is probably not sine shaped

I was considering this option as pure power transmission, not like a very short yoyo cycle. The kite wouldn’t get a chance to change orientation and the force needed to pull it in would be the same as could be generated by it pulling.

For the most simple implementation: Consider a static kite with a propeller. There is some smoothing by a spring system ot something and then the torsion is transferred to a crankshaft on the kite. On the “crank handle” the tether is fixed. The tether tension and is balanced in such a way that the kite stays more or less static while the tether moves back and forth.

Another implementation could be a flapping device.

I think the killer could be the damping related to tether shape. If the force difference reel in/reel out is very small, then the energy transfer is very small also. If it is big, the energy transfer is bigger, but the damping factor will be large.

I guess a good next step would be to do some simulations/calculations… I don’t know directly the relation of the damping wrt force difference…

I did some testing of the 75m Skybow arch kite By Roy Mueller

Some videos on youtube from around this time…

It’s a mad spinning ribbon kite… Rotation up to 20kHz in a strong wind.

Works on magnus effect across the whole ribbon.

Adding any more torque than a fingernail dragging on the ribbon edge will stall the rotation.

And I couldn’t be bothered making a coordinated controlled generator each side…

However the tug vibration into the anchor is potentially a source to tap…

Whole kite makes a very loud howl best heard at the focus of the ribbon.

The ground around the anchor is really made to vibrate.

But nowhere near the 10cm stroke you are looking for.

There may be a way to hold the bearing housing so that the 20kHz can be tapped.

Note I’ve also flown this ribbon between 2 lifters… Q… Can you array ribbon generation up 2 lines?