Three metrics of AWE kite design

I’ll skip the more practical aspects of designing an AWE rig here, like; will it fly, could it be launched, how much ground and air space used, safety, durability, cost etc etc. Instead I would like to focus on what I believe are the three components of a design that must be selected in a good balance in order to get good performance.

I think we have talked about these things a lot in this forum already, but perhaps with less focus on the fact that its going to be a compromise between more factors.

My mind is on one kite one tether here. I believe the principles apply to multi kite networks also, but that is such a game changer that I am not sure how comparable that would be here.

The metrics are

  1. Lift to weight
  2. Efficiency
  3. Turning speed

Lift to weight: So this factor must take into account the mass of the kite and tether, the wind you expect to produce power and the lift that is generated. Some more definitions have been made, and I will try to suggest a new standard number for this, based on a simulated cycle (loop). Something like the number is given by:

K(w) =\frac{1}{\left(m_{kite}+ m_{tether}\right) \left(t_1 - t_0 \right)} \int_{t_0}^{t_1} L(w, t) dt

w is the wind speed, t is a parameter starting from t_0 at the beginning of a cycle and t_1 at the end, L(w, t) is the lift produced by the kite while flying along the path at a certain windspeed. Basically the formula should state average lift divided by mass over a complete production cycle. For Kitemill/Jojo the parameter t would typically be the angle in a loop starting from t_0 = 0 and ending at t_1 = 2 \pi.

The lift to weight has great importance for performance at cut-in wind speed, but also has adverse effects around nominal windspeed due to overspeeding in the downstrokes.

Lift to weight is also a strong indicator of how far the kite will scale. If the kite itself does not suffer cubic scaling, for sure the tether will.

Increasing this number means increasing wing area, C_L, flying faster, requiring more wind, while using less materials.

Efficiency: I think the KiteGoodness number is quite good to describe this. Unfortunately I could not find the source for this right now. So I will offer my own variant given by:

MyKiteGoodness = \frac{C_L^3 S}{C_D^2}

The drag should include kite and tether. This number must me maximized to get most power output of a rig. Our old favorite, the glide number G_e = \frac{C_L}{C_D} is a bit useless. Rather just optimize the goodness number. This means in practice to increase the lift beyond that of the highest glide number. If one also considers tether drag, it may mean just maximizing the lift period. Also note increasing the kite area but leaving the tether alone increases the goodness number.

Which brings us to our next point:

Turning speed; this may sound a little out of place. But tether drag and mass is such a big deal, that we may assume you want to use a minimum amount of tether. Assuming also that you want to limit the lower and upper elevation angle for safety and minimum cosine losses, we must minimize the turning radius of the kite. If you can turn tighter turns, you can fit more kite area on the same tether, thus increasing the goodness number.

Now from what I have seen, you can opt to have a lot of this or that and less of other stuff, but the overall performance seems to even out. This makes it difficult to say in which direction one should optimize.

Example: A soft kite with lots of drag flies slower but has a high area S. The performance may be on par with a rigid kite flying a lot faster but with a smaller wing area S and a lot less drag. Which is better? Difficult to say.

I don’t know terms for this effect, but I feel choosing compromises for AWE is very elastic. You can choose this or that but the end results are still similar.

Of the three main factors I stated here, we can see that increasing one may easily decrease the others. Eg: increasing aerodynamic efficiency may fly faster and get more energy, but require a large wingspan and need more turning radius. Increasing turning speed may add more actuator drag or reduce the aspect ratio of the wing, thus reducing the goodness number. I believe these are the reasons the compromises are elastic.

(end rant)


Thanks @tallakt
Really appreciate how you break the problem into essential aerodynamic analysis chunks to trade off.

Lift to Weight
Turning speed

Your methods will be a good guide to my design methods going forward. I rely too much on the practical aspects you leave from this analysis.

It will be hard (for me) to apply your analytical design method to the :blossom: Kite-Turbine networks but it will be very worthwhile.

In the meantime, I’m still building my kite design capacity with experimentation. We have a huge amount of performance data still to collect in order that we can design to your standard.
Cheap experiments are a fast method to gather that data. Example - Instead of building a custom backline handling robot… I’m planning to adapt a mini-digger with some sensors & winches. We have concepts ready for the job but the fancy design and build can come later.

With all the money saved by not building a custom prototype… Can we afford to have/hire a nice quiet electric mini-excavator instead of a legacy fossil one?

Indeed (IMHO and if I understand correctly) the last version of Daisy with a single rigid rotor has from the start the correct proportions between the length of the tethers and the diameter (and swept area) of the rotor. So the three metrics could apply as Daisy scales in three dimensions. If Daisy scales with another mean, E.g. by stacking rotors, that could also work if the total area of the rotors corresponds to the tether length.

Concerning other AWES, for example crosswind kites, the three metrics should also work, if we consider correct proportions between the length (and thickness) of the tether and the wing span (so its area). In practice, however, the wing span is very (and too) small compared to the length of the tether. It follows that a very long rope should result in a very large wing span (and area) but which will quickly cause scaling up problems unless one considers networked kites (MAWES for example) if possible.

I think I did not say that the metrics are not free of scaling effects. They may be used to compare only two rigs of comparable power output. The lift to weight quantity though will say something about how much potential a rig has for scaling. Once the number dwindles below 10 or so, its going to be very hard to make useful power. And the number should decrease with scale due to cube scaling of mass (or something more optimistic). Only the gradient effect and reynolds number will improve with scale.