Cosine Functions in Kite Physics

See my reply about moving the topic here: Questions and complaints about moderation.

I was expecting a reference from the kite domain, at the very least from aerospace or a related field…


Do not be surprised to see AWE terms-of-art first emerge on our Forums. “AWE” itself emerged on the Old Forum, and many other terms. We know who and when these terms first appeared, like Dave Lang coining “flygen” in a Drachen Foundation Newsletter.

Consider Antenna Design cosine-gain usage as naturally applicable to Aerospace Design, without controversy. What better dynamic for introducing new terms in AWE is there, than to encourage users to do so?

“cosine gain” as a term might make sense in a universe where in all planets that had an atmosphere, the energy available in the atmosphere as a function of density and wind speed only ever increases the higher you go. In our universe, that’s not the case. There is not always more energy available at 200 kilometers up than there is at 0.5 kilometers up.

What you do in our present universe is to measure the wind speeds at different altitudes and design your system to target a favorable and achievable altitude, keeping in mind our current understanding of “cosine loss”.

What you are trying to get at is better said by just saying: look at the wind measurements at different altitudes and try to target the altitude where the wind speed is favorable currently or has been over a period of time.

If you want to introduce a new term, do your homework and quantify it, qualify it, and support it with empirical and theoretical data.

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On this planet “cosine gain” makes perfect sense to me. Its no scientific law, just a term of art, just like “cosine loss”, which is no law either.

This is more about an anonymous authority abusing moderation powers than an actual “scrapyard” topic. If we knew who you were, perhaps we could judge better what’s going on. Perhaps you are underage or have some other weird motive to moderate crudely from anonymity. Cosine gain usage as such is just a small part of the wonderful kite cosine math-physics topic, but it all got put in scrap regardless, and only you know who did that.

The KAP usage example stands as a cosine gain case, given a high flying angle is so desirable. I have both observed and practiced KAP, with pros. Ask a KAP pro:

“The kite has a high flying angle, allowing me to maneuver in tight spaces.”

Having reviewed trigonometry, the only recognized Laws are Law of Cosines and Lambert’s Cosine Law. Neither is violated by either “cosine loss” or “cosine gain” terms of art. The KAP vs power-kite cosine issue is covered under trigonometric identities, as reciprocal (ie. sec theta) cases. There is no conflict in using cosine “loss” or “gain” in context, as standard descriptors.

No one commenting on the cosine subject has done the homework better than this. Relegating proper kite cosine physics discussion to Scrapyard is the poor-homework decision.

Concluding trigonometric analysis between KAP and power-kite cases, note that each has its own adjoining right-triangle whose theta vertex is the anchor-point. The two thetas are reciprocal values of each other, by orthogonal principal axes of operation.

Economic science is a clear model for how “gain” and “loss” usage applies to the KAP or power-kite case, consistently in context. Its mistaken to insist only “cosine loss” makes sense for kite cases, that “cosine gain” usages are somehow meaningless or wrong.

No Rod, its simply that Cosine Loss for a power kite is Cosine Gain for KAP.

Payne’s 1975 “self-erecting tower” criteria comes to mind, where Cosine Gain is the geometric property of value.

In Chapter 18 of the 2nd Springer AWE Texbook, “Cosine Efficiency Gain” is used equivalently to “Cosine Gain” here, for the gain in power given by flying a power kite on top of a tower. Windy Skies has made no objective case for relegating this topic to “Scrapyard” due to “Cosine Gain” usage (while creating Topics so generic (adhesives, where to find weather data) they are not even AWE or kite topics as such)


Good on you for trying to find a source. I’ll move the topic back over. 18.2 Cosine Efficiency and its Maximization, 18.2.4 Numerical Results, page 449: “Even if the tower height is only half of the kite’s altitude, an efficiency gain of up to 1.89 in case C is possible.”

WIndy Skies. Stop moderating anonymously, from ignorance, without remorse. This was always a well-formed and well-informed Topic in its proper Category.

If @PierreB ‘s quote is correct, you are wrong to say that cosine gain was used in the book.

I have to disagree. For what I saw “efficiency gain” expression is used, and not “Cosine Efficiency Gain” as such. However the used words are in 18.2.4 subsection which is a part of 18.2 section whose title is Cosine Efficiency and its Maximization as I precised in my previous message. So one hardly can doubt that “efficiency gain” refers to “Cosine Efficiency”. So the concept of cosine gain is used in the book.

Another quote on the same page 449:
" However, as visualized in Fig. 18.7, a considerable efficiency gain is only achievable if the tower height to operation altitude ratio is not too small. Consequently, the efficiency gain and effectiveness of
a tower would be rather low for kite operation altitudes above hk ≈ 1000m."

Pierre and I have quoted different instances. In fact there are various “cosine…gain” variations in the literature. This is not about who used the term with a clear precedent, but about who is able to use technical language in both original and correct ways. As the creators of the AWE knowledge domain, its up to us to develop our semantics, there is no fully settled nomenclature yet for pedantry to depend on.

At least “gain” really is clear in any specific engineering context.

Focusing on just one word of that troubled sentence (is), to reflect the truth in the world and not initiate a falsehood, you would need to either change that to read something like I propose is or cite evidence that the term is already in existence and has the same definition you give it, because you cannot of course say something “is” when it “isn’t”.

If you would like to go for the second option, the onus is on the writer, not the reader, to give the exact reference and quote it accurately.

If you would like to go for the first option, you would need to expand on it. Now you’ve just given a definition. Support it with more work, ideally exactly citing previous work, to improve reception.

Yes, Cosine Gain is here properly defined canonically, as the inverse of Cosine Loss. Too late to “propose” such usage; Cosine Gain is already in use, in the established KAP case example, including cited reference.

Its not to be expected that initial “reception” of ideas counts for much; inherent correctness and long term usability counts most.

Please give an exact quote and reference. “cosine gain” does not give results in the 2018 AWE book (

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As Pierre rightly notes, the gain concept is evident in redundant usage like “cosine efficiency gain”. Lets also define here “cosine inefficiency” as a valid equivalent of “cosine loss”.

For a definitive example of proper “cosine gain” use, this Cosine topic can serve well enough until maybe a prior use case emerges. Let future use also come to validate cosine-gain usage beyond all denial.

It would be nice to know the identity of the person asking for so much help.

A post was merged into an existing topic: Questions and complaints about moderation.