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The tip speed ratio is given by TSR = w.R/v where w = rotational speed of the turbine, R = radius and v = wind speed. Now the speed of the tip is a function of the energy extracted from the wind, but the energy extracted from the wind is also a function of the TSR.

  1. Under a no-load condition, the turbine is free to spin, and I would imagine that the TSR is a simple function of the pitch angle. The TSR should be able to go right up to the value dictated by the Betz limit.
  2. Under loading conditions, the rotational speed of the generator should be such that the power output from the turbine is in equilibrium with the marginal load in the system, and therefore the TSR is a function of the rotation speed, and therefore the output of the WT.

If the above thinking is correct, then what is the use of the TSR or the Cp in wind turbine calculations? Aren't they determined by the external load, and not by the wind turbine design, under loading conditions?

hurreechunder
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    This is not an EE question: TSR is largely determined by blade design. As design TSR increases blade count usually drops. I have seen TSR 10-12 designs with a single blade (and counterweight). Erosion is high (dust & rain start to matter muchly) and noise tends to be high. If an airfoil is designed for optimum TSR then it is liable to stall under light loads as TSR goes far above design. Betz limit is on Cp, not on TSR. Power is proportional to torque x RPS, & higher TSR leading to higher RPS leads to lower torque for the same power. So TSR, RPS, Cd ... are all interelated but not linearly .. – Russell McMahon Oct 15 '20 at 03:08
  • Cp is vitally important as it relates energy in air to energy extracted.| Power in airflow is 0.5 x density x Area x Velocity_cubed . Multiply that x Cp to get actual output. Betz is about 58% max. Best HAWT may give 40%+. Best VAWT 30%+ (Darrieus). Other lift based VAWT up to over 30% but usually 20%+ for a good design. | Many designs end up in the 0.1 - 0.2 range. || TSR is useful in designing alternator and matching to load. As TSR rises RPM rises and alternators need less resources (magnets, copper, ...). Many VAWTs tend to run in TSR 1-2 range making alternators more expensive. – Russell McMahon Oct 15 '20 at 03:13
  • At no-load, Betz is irrelevant since you aren't extracting significant power. –  Oct 15 '20 at 08:05
  • Thanks - perhaps my question wasn't clear enough. Basically, given a load, a pitch angle, and a wind speed - all independent variables - can you determine the TSR? If so, then what is the formula for that? – hurreechunder Oct 16 '20 at 04:36

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