Agreed. Poorly written...
No matter what you feel in your lines or how you fly your kite, the power available has a cubed relation with wind velocity. For those interested here is a derivation of the Wind Power Formula.

I see what you're getting at. I suspected it might be the case.

To put some practical perspective on this concept:

Suppose you're cruising along on a beam reach on a foil kiteboard.

The wind speed doubles. You (somehow) manage to maintain kite trim as line tension quadruples (squared function of air speed over kite).

As a result, your speed increases, stabilizing at double your original speed, with quadruple the resistance (again, squared function of water speed over foil).

Because wind speed and your speed both doubled, the apparent wind direction remains unchanged, and so does the direction of pull in your lines. Therefore, the forward component of line tension quadruples along with overall line tension.

So, you end up going twice as fast, against four times the resistance (force). Power = velocity x force, and since velocity is doubled and force quadrupled, that means your power is multiplied by eight. In other words, a cubed function of wind speed.

Btw, I used the example of a foil board because a planing kiteboard doesn't necessarily exhibit the same resistance function.

Edit: Further, while my example illustrates the theoretical cubed power function, it's not a practical example because a kiteboarder who experiences quadrupled line tension won't be able to maintain original trim, so the power increase of the kiteboarder/gear system will be limited. For what it's worth, my guess is that the highest kiteboarding power (generated during speed runs) is somewhere around 5 hp.

Cheers,
James

An obvious mistake. The energy in the wind passing through a given area has a cubed relation with wind velocity. I believe the intention was clear...

Thanks for clarifying Hansen, and thanks JS for the didactic example.

I wasn't taking into account the increase in boarspeed, which, multiplied by the new force, will give the new power.

As a sidenote, I would say that how the kite is flown does alter the power available, because we're actually transforming muscular energy into kite's both kinetic and potential energy. Because the lines lenght is relatively long, this effect is far from negligible (as would be in some other sail/aero sports) and is one of the things that make kiting so unique!

The BS comes from claiming a fairly typical inflato kite, board & rider system just barely capable of planing in 10 knots will work in 6 knots. The cubed velocity-power relationship requires a much larger power conversion factor at 6 knots which would require a much different system - say race board and/or large foil (which still may not have sufficient power conversion capability.) As the wind diminishes, at some point, there simply is not enough power available and kiting in little-to-no wind becomes a dream rather than reality.

As long as there's enough wind to keep a particular kite airborne, it's mainly a function of board lift/flotation and efficiency whether or not that kite will do the job.

There are boards now (race, mostly) that allow certain kites to perform in wind speeds that would have been considered a joke a few years ago.

For illustration, here's an extreme example: You can go upwind in 5 knots of wind with a 3m trainer kite. You just have to use the right board... a stand up paddle board or old one-design windsurf board will do the trick, albeit slowly.

Btw I added an explanatory edit to my previous post.

Cheers,
James

We don't feel "Power" (P=dw/dt) on our kites we feel "Energy" (integral(Fdx)) both of which have precise definitions in physics, as does "Force" (F=dp/dt), but when kiters say "Force" they mean "Energy", it is what you feel when you go kiting, it does NOT vary as the velocity cubed it varies as the velocity squared. When I say "Force" to kiters I mean "Energy" aka 1/2 mv^2, this is also called "Power" though it is neither "Power" nor "Force" though it is called both "Power and "Force".

In summary, stay away from precise physics definitions, and use velocity squared to measure the strength of the wind, unless you are running a wind electricity plant, then by all means use velocity cubed.

Friction varies as the square of velocity for kiters.

If you can get going with a 16 meter at 10 knots you would need a (10/6)^2 * 16 = 44 meter kite at 6 knots for the same pull.

...OR in laymans terms, to go kitesurfing, you need some wind. LOL. Low wind kitesurfing IS BS, even if you do manage to stay upwind or whatever with a huge sail and a door for a board. After about 30s of 'tootling' about you can start to smell the BS, as well as the light feeling in your wallet. As the saying goes, 'you've been had'.