Tip Speed Ratio

New topic to move previous discussion on tip speed ratio to.

An easy to understand paper on the subject:


Maybe I worded it wrong. At the moment I lack even the knowledge to use simulation tools. A basis is good, like knowing what a drag polar is.



My design necessitates a very low tip speed ratio. I’d like to learn where I can find airfoils for that and how to evaluate them.

I believe airfoiltools have some profiles for windmills. The selection and design og airfoils for a windmill, if it is to be more than a hobbyist project, I believe is an advanced task that requires very specific qualifications. I could not help you with this except saying that a low tip speed ratio is a good thing because that means you want a low efficiency wing. The next question you might ask yourself is how to best put that waste of efficiency into positive use in your design.

I believe there are some formulas to say somethibg about the L/D of a wing based on the 2D profile curves and the aspect ratio of the wing. You might also find something for windmills. You could use this as a starting point to see what performance you could expect from a design. But these days there are no reasons not to do a computer based simulation before building the real thing

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The proof-of-concept won’t be more than a hobbyist project. I first would need to determine if the thing works at all, only then should I worry about efficiency I think. My thinking is to just choose an airfoil that looks good and call it a day, for now.

I’ve seen it repeated that a low-tip-speed ratio equals low efficiency. I really need to understand that thoroughly to optimize the design, or change it.


I keep wondering if just increasing the number of blades won’t solve the problem.

(Please remember this free advice is totally unqualified)

The wing tip ratio is more or less the windmill version of a wing’s lift-to-drag ratio. Except now the wing rotates instead of flies forward.

If you build the windmill with low efficiency, you could add more blades, and they would not be interfered by the wake of the forward blade. The efficiency I would think is unchanged. You just get a larger wing area. You might have longer blades for the same effect, if that made your build easier.

I am still puzzled why you would design a windmill (?) starting with a requirement of low efficiency. Normally limiting efficiency would be a result of another design choice (eg. the wings are single skin kites and I cant build them with greater L/D ratio than 3).

To use the lower tip speed ratio to good use would be eg: minimizing the radius of your windmill, thicker wings with space for stiffening, bridles, etc, that would make completing your design easier


Noted. This just came up, I had expected the other topic to stay more theoretical.

The paper gives some graphs and tables:

The table and the graph agree I think I shouldn’t try to lower de TSR to much lower than 2. At a TSR of 2, the efficiency looks to be still around 93 percent of the efficiency of a turbine with a TSR of 6.5 (0.515/0.556).

I don’t know how applicable the “empirical observation” that s/r is 1/2, to my design, as my design, like those of @Rodread and @someAWE_cb doesn’t have a hub. Ignoring that, it becomes easy to calculate optimal TSRs:

For 5 bladed rotors: 4pi/5 = 2.5; for 6 bladed rotors, 4pi/6 = 2.1; for 7 bladed rotors, 4pi/7 = 1.8, for 8 bladed rotors, 4pi/8 = 1.57.

To me it looks like I should aim for 6 or 7 blades. 4 blades would have the tips moving at 30 m/s (108 km/h) in 10 m/s wind, that’s too fast.

What would be some things to look out for when designing a 6 or 7 bladed rotor? Maybe it becomes easy for the TSR to get too low? Maybe the band of windspeeds that it would work efficiently in is very small? I’d like to optimize the thing to work well in 8-12 m/s wind.

I thought the Betz limit did not care about the design of the harvesting device. In the graph above it seems there is a dependency on tip speed ratio vs betz’ limit…

I think that graph was copied from a 1980 book.

I looked a bit further, here is the original unabridged paper the article I linked was based on, with more references. I haven’t read that yet.


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