Induction factor

A simple calculation is performed in secondary rotor concept (Peter Jamieson). This study is also applicable for the AWES of type flygen like the wings of Makani. It is explained that a “secondary rotor axial induction” of only 0.2 can be better that the usual 1/3, implying a larger secondary rotor area.

The “INDUCTION FACTOR FOR A CROSSWIND KITE” is well explained in the publication below, both for “Crosswind Kite in Lift Mode” and for “Crosswind Kite in Drag Mode”:


@mkheiri as author, @Rodread mentioned a more detailed and recent version on Aerodynamic performance and power limit of crosswind kite systems. The tether drag issue is another significant limit. As a result if tether drag is taken into account, this can explain the significant dimensions of the area of ​​the rotors compared to the area of ​​the wing, in addition to the induction factor issue.

See also https://www.sciencedirect.com/topics/engineering/induction-factor.

This paper reveals the typical beginner’s flawed approach to wind energy based on ignorance and denial of the basics of wind energy. No matter how many formulae are presented, they cannot overcome the ignorance from which the entire approach originates.
The glaring ignorance that jumps out at a person familiar with wind energy starts with two typical beginner errors:

  1. believing that surfaces being dragged downwind, entailing a non-power-producing upwind return journey for the working surfaces, is a more effective approach to wind energy. It starts with not even understanding the difference between a lift-based machine, and a drag-based machine, according to long-established wind energy terminology;

  2. believing that “this time it’s different” regarding the applicability of the Betz coefficient to a given configuration for a wind energy extraction device.

As to point 1, lift machines versus drag machines, the longstanding convention in wind energy is that “drag-based” operation is exemplified by a Savonius-type device, with the most common example being an anemometer, where cups are pushed downwind by thrust force from the wind, then must fight their way back upwind on the return journey, contributing negative power to the device on this return trip.

It is possible to fly a kite back-and-forth, or in a circle, figure-8, etc., to achieve the a larger amount of downwind thrust, like a larger non-crosswind surface would have. However, if the power is extracted by allowing the working surfaces to travel downwind, with the energy extracted in the downwind direction, from the downwind thrust force, that is still fundamentally a drag-based machine, (that uses lift to achieve greater downwind drag), and it still suffers from the same detractive aspects of any drag-based machine, which is the reduced power from the downwind-traveling surfaces due to reduced relative wind speed impinging on the working surfaces in that downwind direction, plus the power lost on the return trip. It’s the same basic operation as a savonius turbine, as though one is using a parachute dragged downwind, then folded as it returns upwind, which is instantly recognized in the actual art of wind energy as a drag-based machine.

Similarly, in established wind energy, lift is used to pull a blade in a circle against the “drag” of a generator at the center of rotation, however this configuration is called, by long convention, a “lift-based” turbine, and using lift to pull in a circular path against the “drag” of a generator is called “lift mode”, NOT “drag mode”. The lift versus drag naming convention refers to the working surfaces themselves, not the load, which normally induces “drag”.

So just as a start, Loyd and his followers have the entire basis of wind energy backwards, calling lift-based machines “drag”-based, and vice-versa. To jump into wind energy and start reversing the most basic naming conventions just shows an ignorance of how wind energy actually works, and how it has been understood and analyzed for a hundred years, including the naming conventions for the most basic distinctions in types of wind energy extraction approaches.

What is missing is the fact that “lift” has a forward component, and that the tips of wind turbine blades, once traveling, are effective at a zero or even negative setting angle. Watch a hang-glider in flight: the motion is propelled forward, while the wing is angled backwards. Why? There is a vacuum above the front of the wing that pulls it forward. That is called “lift” by long convention, since it results in flight. The fact is a wind turbine blade pulls forward against the “drag” of a generator, on the basis of lift. The same would be true if, as is often discussed but seldom if ever tried, the central generator were replaced by small rotors mounted on the blades themselves. The machine would still be “lift-based”, though perhaps less efficient.

Next, the notion that the Betz coefficient, which is a universal factor, somehow “does not apply” to kite-based or airborne wind energy systems due to the small effect the kite has in such a large area is in error. One could make the same claim for any newbie-inspired first stab at a wind energy device. After all, a typical wind turbine rotor can have a solidity as low as 2%, yet is capable of extracting close to the Betz coefficient. If one were a beginner in wind energy, one might similarly construct a large yet inefficient rotor, incapable of extracting a large percentage of the energy from its swept area, and claim that the Betz coefficient does not apply to it since it does not even approach the betz coefficient anyway. This may be true, but that’s like saying the rules on a racetrack do not apply to a wheelbarrow because it is incapable of winning a race. The fact of a less-effective approach to wind energy does not mean the limits to power extraction don’t apply, just because the given approach does not approach that level of efficiency.

So my opinion is that the two most glaring ignorant mistakes beginners make in wind energy are manifest in this approach to AWE:

  1. Not even understanding the difference between a lift machine and a drag machine;
  2. Arguing that the Betz coefficient “does not apply” to ones pet new configuration.

Once that is established, it is easy to see that the understanding of AWE remains at the level of beginners who do not know the ropes or understand the basics of the art to which they aspire.

:slight_smile: - Doug Selsam, June 24, 2020

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I think Peter Jamieson mentions secondary rotor concept in his book page 128.

Below there is two sketches. The first sketch is the usual secondary rotor concept such like described by Peter Jamieson.The second sketch represents the same concept with secondary rotors close to the root. Makani and other companies (Windlift, KiteKRAFT) use this concept. Note that Peter Jamieson does not mention “lift-based machine” as the paragraph is about conventional HAWT, indicating that the second rotor concept is a way to avoid a too high mass when the wind turbine scales a lot.

Secondary rotors

@dougselsam do you allude to the secondary rotor concept as sketched above, and mentioned by Peter Jamieson?

Other than that the inversion of the terms “lift” and “drag” that you mention is problematic.

Initially the induction factor problem was even overlooked because it was considered minimal due to the very small area of ​​the kite compared to the covered space. The last publications I mention tend to correct this approach.

Indeed instead of trying to correct and correct it would be better to use the terminology applied in current wind energy, such like Betz limit or Betz coefficient, of where a significant induction factor. Reaching Betz limit is also a mean to tend to maximize the space use which is (imho) a major issue for utility-scale AWES.

Yes Pierre, I was thinking the same thing, to come as close to the Betz coefficient as possible is the same thing as what you often talk about, maximizing the use of a given swept area. As far as exactly where a propeller would be placed on a blade, it does not affect what I was talking about. My point was that the misapplication of the word “drag” to describe a machine with a gliding wing that “drags” a wind turbine through the air seems silly to me, since any working wind energy surface could be said to “drag” whatever is producing the electricity. Yes, a generator causes what could be called “drag” on a wind turbine blade, (actually we call it a “load” in the field of wind energy) just as a small wind turbine mounted on a larger blade could be said to cause “drag” on a wing, whether free-flying or operating as a wind turbine blade itself. Just because someone labels a “load” on a wind energy system as “drag” does not make the device a drag-based machine. It just blows my mind how these people keep thinking they are coming up with new concepts, when it is apparent they do not even understand the old concepts. Crosswind: the only way anyone who knows what they are doing has harnessed wind energy for the last 2000 years.


Sure, there are the learning-impaired who still create vertical-axis turbines that beat themselves to death while being less efficient - what can you do, there will always be people of high cranial density in this world. But how can supposed wind energy innovators start out by calling lift-based wind energy devices “drag” machines, and calling drag-based machines “lift”-based? I mean, seriously, I knew more about wind energy than 99% of today’s supposed innovators after reading my first pamphlet on wind energy way back in the 1970’s!
https://books.google.com/books/about/Wind_machines.html?id=tBLcHfOgVo0C
the version I had, I ordered from the U.S. Government printing office and it looked more like this version,

but as I recall was not very thick, and not very many pages. Later versions had hundreds of pages. I thought I remembered something like 30 - 50 pages at most. Still, it covered most every type of wind turbine existing to this very day. Who knows, maybe it is still around here somewhere in some pile of books and papers.
:slight_smile:

We have been using lift power and drag power in AWE since 1980. I dont see an issue with possible collission of naming relative to HAWT. We should all know what lift and drag power means if we are serious about AWE.

From this seminal publication, page 107:
“Since calculations of kite performance have resulted in Betz efficiencies of a few percentage points, the induced effects of the kite slowing the wind are assumed to be negligible in this paper”.

However a recent publication (among others) mentions page 4: “The present paper aims to provide a new theoretical perspective on the aerodynamic modelling and power limit of CKPSs by taking into account the effects of the induction factor.”

I think @dougselsam’ comparison between yoyo (said “lift” but in fact “drag-based” according to him) mode and drag-based Savonius-type device is particularly relevant: both are “pushed” (via reel-out tether downwind motion for the one) by the wind, and have a phase against the wind, unlike lift-based wind turbine or Makani-like device. And also the paper on https://www.sciencedirect.com/science/article/abs/pii/S0960148118304427 confirms that comparison in some way as "AWE drag power systems can harvest up to 16/27 of the power available in the wind " and "AWE lift power systems can harvest up to 4/27 of the power available in the wind ", “AWE lift power systems” being yoyo systems.

Loyd’s analysis and following papers study the efficiency by taking account of the kite area, while current wind energy considers the swept area within the actuator disc, the blade area (a.k.a. kite area) being only an element.

Little by little the traditional analysis elements for HAWT are gradually arriving in the field of AWE: Betz limit, Betz coefficient, actuator disc theory, induction factor…

Tallak: Who is “we”? I doubt you were even born in 1980. The terminology is not “relative to HAWT”. It applies to all wind energy devices. Most drag-based machines are vertical-axis, because “Professor Crackpot” is never satisfied with making just one mistake - he insists on making ALL of the mistakes! :slight_smile: Nobody paid attention to this paper until the recent smartphone generation, in response to the global hype. Not surprising they don’t care about facts. Too busy looking at their phones. The fact that Loyd had everything backwards doesn’t make it right. Loyd’s ideas may end up having very little, (or nothing) to do with any eventual success in AWE. Meanwhile, let’s review the basics of wind energy. Maybe this link from Paul Gipe will help:

The first and most important categorization of wind energy extraction devices has always been whether they are based on “lift” or “drag”. To start, you throw away any and all “drag” machines. Lift is where the action is. After that, the split is between vertical-axis and horizontal-axis. You then throw away all “vertical-axis” machines. At that point it is telling that drag machines are usually vertical-axis machines (Coincidence? No. Ignorant wind-wannabes tend to always tilt in favor of doing everything the wrong way.) The next categorical distinction is method of overspeed protection. Pitch control, stall control, (or sideways furling for small turbines). Passive stall control was how the industry got started (The Danish Concept) but today most utility-scale machines are pitch control. Next distinction is “pitch-to-feather” or “pitch-to-stall”. But back to lift versus drag devices: Either you understand the basics of wind energy, or you are doomed to repeat all the past mistakes. Of course some people see no problem with ignorance and doing everything backwards, starting with not understanding the most basic categorizations of wind energy devices and the requisite terminology. Oh well, one thing we in wind energy have learned: you can’t help people who just don’t care about the facts. They will always be there, and you cannot “fix” them.

2.4. Wind turbine with tip-rotors

About the axial induction factor for secondary rotors.