Aerodynamic performance and power limit of crosswind kite systems

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A new perspective on the aerodynamic performance and power limit of crosswind kite systems
Mojtaba Kheiri , Vahid Saberi Nasrabad ,Frederic Bourgault

Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, QC, H3G 1M8, Canada
New Leaf Management Ltd., 500-1177 West Hastings Street, Vancouver, BC, V6E 2K3, Canada

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Some explains on and also
abstract and full text on request on

And about “induction factor”:

By some tests I made, there are significant losses during crosswind figure because of the variation of power from that of cosine, above all for very large figures.
Small figures like on Low radius loop seems to produce roughly the same power. It is because the lesser swept area is compensated with a better swept area closest to the centre of the flight window, as a result lesser power variations.

$37… and I hardly even have time to read the free/open ones on my bucket list…

As usual, we await a free view, but the abstract is serviceable meanwhile.

The paper looks good in summary, but uses the old “Lift Mode” and “Drag Mode” terms that are mostly confusing to new readers and even some longtime analysts. Loyd told me he was mortified how his paper became so classic that this improvised choice of terms became baked into AWE.

In fact classic-kite “Lift Mode” does develop useful Drag in proportion that it “powers-up” by higher AoA. Thermodynamically, Lift Mode is equivalent to “Drag Mode” of “turbine-on-a-wing”, which Loyd only chose as the quickest idealization to calculate, not as a configuration down-select.

The first thing to check when we see the full paper is whether power-kites are considered in fully powered-up mode with useful high Drag, or depowered in “pure” Lift Mode. No way turbine-on-a-wing beats a powered-up power-kite by power-to-weight. Hopefully this paper got that right.

The paper does go on some about “swept-area-normalized [power coefficient]…not practically important”, but best-informed AWE analysts have long known that.

Ok. So I had a chance to read both papers and they are really good. I guess any discussion of the Betz limit (or as the paper states, B-J limit, only an academic could come up with that? :slight_smile: ) may well have these papers as a starting point to clear a lot of noise. Furthermore, the inclusion of the induction factor a is important.

So I’d recommend these papers to anyone into AWE.

Now for the bad parts: There seems to be a bias towards drag mode vs lift mode AWE which is fine and well grounded. But the plots I believe use a value of glide number (G_e = \frac{C_L}{C_D}) that is quite high (G_e = 10). These numbers are probably only realistic for a multi kite AWE rig (eg. dancing kites). We are in 2019 now and we should not need to publish papers not taking a nominal tether drag into account. Hint: D_t \approx \frac{1}{8} \rho v^2 C_{d,t} l d. For a 15 mm tether of 1 km that you might use for a 10 m2 wing, the area of that tether facing the wind is a whopping 15 m2. It will affect the glide number in a big way. A conductive tether a lot thicker, and with further detrimental mass effects to boot.

Also, the large simulated kite has a wingspan of 54 m and looping radius of 120 m. Again this would probably only be viable for dancing kites due to extreme centripetal forces required and also the difference in airflow along the wingspan of the kite. At the same note I believe these numbers are infeasible for a Makani type of rig due to tether mass (and then indirectly drag).

The speed we arrive at in the paper is thus > 90 m/s, which would be nice, but I doubt it will happen in near future. I would expect the blades for a drag mode turbine might even exceed the limit for subsonic speeds 273 m/s in this scenario

The author thus arrives at some plots showing that the induction factor described is of more importance than would be in real life situations.

Still a good paper. Though I wish we as an industry could stop overselling the potential of AWE


Also please, if the authors are reading - this stuff deserves to be open to the public. Please no paywall…

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Same goes for TUDelft’s Springer AWE Textbooks, “deserves to be open to the public. Please no paywall…”

Still have not read the 2nd textbook :^(

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Many thanks to Rod Read for introducing this amazing forum to me. For those who do not have free access to the following papers, I recommend either contacting me at mojtaba.kheiri[at]concordia[dot]ca or visiting my profile on the ResearchGate. I have shared the recent paper on the ResearchGate and will also share the other one shortly.

A new perspective on the aerodynamic performance and power limit of crosswind kite systems
Mojtaba Kheiri, Vahid Saberi Nasrabad, Frederic Bourgault
Journal of Wind Engineering & Industrial Aerodynamics 190, 190-199, 2019

On the aerodynamic performance of crosswind kite power systems
Mojtaba Kheiri, Vahid Saberi Nasrabad, Frederic Bourgault, Samson Victor
Journal of Wind Engineering & Industrial Aerodynamics 181, 1-13, 2018

Unfortunately, I cannot share the journal-formatted version of the papers on the ResearchGate due to Copyright issues but can do that through email. Hope you will find the papers interesting and useful!

In my next reply, I will say a few words about the two papers. Cheers.


Welcome Mojtaba,

I was just starting to study your publication on

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Mojtaba @mkheiri
It’s an honour for me to have been able to introduce you and Concordia University here.
Your work is an impressively honest and clear signal on how AWES should progress.

If there is any way I can assist your AWES research… I’m right here.