TSR vs glide ratio

The speed of a windmill is often specified as tip speed ratio, the speed of the blade tip vs wind speed. For an aircraft, the similar number would be the glide number G_e. For a kite represented as a point looping downwind, zero gravity, the kite would travel at speed w G_e if w is the wind speed.

(please correct me if Im wrong here)

The TSR only applies to the wing tip. I am wondering what is the average «glide number», or mostly equivalent of a windmill. I guess the closest is to take the glide ratio at every point of the swept area, something like this:

\tilde G_e = \frac{1}{\pi r^2} \int_0^r{\mathrm{TSR} \frac{x}{r} (2 \pi) dx} = \mathrm{TSR} \frac{2}{3}

So my conclusion is that when comparing TSR to glide ratio (HAWT vs AWE), a smaller glide ratio would compare to a larger TSR. Eg: a TSR of 9.0 would perform similar to a glide number 6.0 AWE rig. The glide number would include an approximate kite+tether drag of course.

Edit: as TSR is for a loaded windmill and glide number is for unloaded AWE, the comparison is not really useful. In practice, as flying speed is reduced by \frac{2}{3} when loading an AWE rig, the comparison of glide ratio and TSR is probably closer to 1:1

I’m not really sure what you are trying to achieve with this comparison?

Some measure of relative efficiency of the wing? Or just trying to figure out how fast the wing is traveling relative to the windspeed?

A conventional wind turbine will have far less drag than a comparable awe device. Operating at nominal TSR. Induction will be higher, which one might even think of as induced drag in aircraft terminology.

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Yeah, the starting point is sketchy.

There are reasons the TSR of a HAWT do not exceed 8-9 (?). And the glide ratio is such an important number to describe the material use vs energy production in AWE. So eg if both AWE and HAWT are operating at TSR/G_E 8, the kite will have all its wing area working at high efficiency, while the HAWT has the tips working efficiently, but the root running at «low glide number».

The point is to make some kind of cross-technology comparison. Maybe my analysis is completely off, but I think maybe it makes some sense…

If I am right, AWE should have a big benefit in energy/material of the blades. Not only because the tower is missing, but because higher glide numbers are easily available as there is no real limit on looping radius. The only limit for AWE seems to be how fast the kite can fly without excessive wear

To rephrase; There is no point in increasing a HAWT TSR because (in my current understanding) you are hitting the Betz limit, so increasing efficiency will not yield more power. To run at a higher TSR also means running a larger radius…

For AWE we can easily increase radius. But it doesnt make sense unless we are still approaching the Betz limit. That just leaves us with a large swept area and a very low C_p power coefficient.

Next, you may say that for a really large HAWT, the AWE with a glide ratio matching the HAWT TSR will at least initially move at the same speed in the same winds. This would favor the AWE rig as the HAWT sweeps a lot of area at a low speed relative to the wind, near the hub.

Anyways, maybe that explains my initial post a little bit