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dazz
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Joined: 15/04/2008
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Posts: 78

Posted: 05:14pm 24 May 2008

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Hi All,

Some of you will be familiar with this formula

rpm = 60 * V * tsr / ( Pi * D )

From Here: http://www.windstuffnow.com/main/wind.htm

Does anybody know what the assumptions are for this formula to work?
I may be wrong, but the formula doesn't seem to take into account any of the usual things we know slow down a windmill, like the load and unloaded drag in a generator system. So I'm thinking there must be some assumptions about the setup.

Any ideas?

I'm trying to create a realistic chart of RPM vs wind speed for a typical setup with say blade diameter 2m, and tsr 6. I imagine such a setup might have a battery load. So alternatively, if someone has a chart of their own windmill RPM as a function of wind speed, that would be perfect.

Thanks, Daryl

Bolty

Regular Member

Joined: 03/04/2008
Location: Australia
Posts: 81

Posted: 11:00pm 24 May 2008

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The value of tsr is not constant! It's value dynamically changes as the load etc. changes. I believe it to be simply a value that indicates the current operating condition of the turbine!

GWatPE

Senior Member

Joined: 01/09/2006
Location: Australia
Posts: 2127

Posted: 01:25am 25 May 2008

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Hi dazz,

Bolty has described a situation that occurs with a windmill that is directly charging a battery.

This is not the case for all windmill applications. I have assumed this discussion is for windmills with a fixed pitch.

I know of windmill generators that are used to pump water. These have quite a constant TSR with increasing windspeed. The maximising cct on my current mill [and the one I am building for my 100S F&P mill] load the windmill to a relatively constant TSR. Combined with the sensing I use, the power output follows a cubic relationship to windspeed. The optimum blade efficiency of energy extraction from the wind occurs in a narrow range of TSR. The rpm should ideally track the windspeed.

I have seen many published graphs from commercial windmills of output power v windspeed. As has been noted by others on this forum, most have quite a linear output v windspeed in the rated power band. This could indicate a changing TSR, or significant generator efficiency change with increasing windspeed.

The wind power increases with a cubic relationship to windspeed. If the generator RPM increases proportional to the windspeed, ie constant TSR, and the efficiency of the generator is constant, then maximum power extraction from the wind will follow a squared relationship. This is still not optimum.

It is possible that a windmill generator that has an iron core in the alternating magnetic field will have significant difference in output to my design. I am getting closer to being able to directly compare performance of a F&P design.

BTW, at 10m/s, the tip speed would be 360kph, and 600RPM. My Lakota 1m blades [2m rotor] give these sort of figures. Approx Wind power = 0.5x10x10x10x3 = 1500W. My mill in furl, has produced 455W in these conditions, just like my avatar pic.

Edited by GWatPE 2008-05-26

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