Help With Wind Turbine Torque

[Mark59]

I hope that there is someone out there who can help me with working where the torque is measured on a wind turbine

I am trying to calculate the power it can generate, I have tried lifting a weight on the shaft and have calculated

the time that it take to lift a weight within a time.

But when reading the calculations that Betz limit states there is no comparison with what he claims, using the lifting method

it is far less than when connecting a small generator to the shaft,

 

For example if i know what the turbine can lift at the end of the blades and lets say 200 rpm can lift 116 grams at that rpm.

this would equal 1.13 newton of force is the calculation for power then 1.13 x rpm which would equal 23.7 watts or is it

force times distance which would mean 1.13 times the radius let say 21 cm thus 1.13 x .21 = .238 nm this would make 2.9watts

I just can't work it out or if, I am going wrong some where.

 

Many thanks for any help

[Schrödinger's hat]

Well the easiest way to convert torque to energy is integrating over angle. As it's (close to) constant torque, just multiply torque by angular velocity to get power. Make sure you remember to use consistent units.

 

 

F=force at point of contact 1.16N

r=radius of point 0.21m

w=angular velocity

angular velocity is given in rpm

200revs/minute=200*revs/min*(2*pi rad/(1 rev))*(1min/(60sec))=3.33*2pi rad/sec

T=torque

r*F=0.24Nm

P=T*w

= approx 5W

Assuming all your numbers are correct and I haven't had a brainfart.

 

Remember this would be at the shaft, your generator and transmission losses would have to come out of that.

Also you could just use the energy you are putting into the weight you are lifting.

Gravitational potential is mgh, so assuming you pick a weight that is the heaviest weight which will not slow your turbine, time it then power is mhg/t

[Mark59]

Many thanks for your reply, this is what I was told, force times distance, But the big problem is when you look at their claims, I will put this another way, I have a turbine which is well advetised on the web, and I have tested it by lifting weights and timing and have done the calculations to check the power. the area of the turbine is .145M2, and they claim 7watts at 6ms, this is quite high regarding Betz theory.

 

Now their turbine would only lift 45 grams 3 mtrs in 1 second which rates it at 1.33 watts, even lifting a weight on the shaft to double check it makes about the same power.

The turbine would need to lift just over 100 grams 6mtrs in one second to be rated at 5.88 watts, so how can they rate them at 6 watts at this wind speed,

 

But if you connect a small 12v generator to the turbine and use this to charge a battery it will give you about 6watts and this is after all the losses , now here is the question is it making 1,33 watts

or 6 watts if you use some small led lights with the small generator it will give you about 2.6 v at .5 of an amp so the way I look at it, it is rated at 1.33 watts,

not 6 watts all they are doing is putting in a very small voltage into the battery and times the .5 amp to give them 6 watts. So you need to question Betz theory that states that the maximum power in the wind at 6m/s for a turbine having an area of .145m2 is 11.4 watts most turbines are rated between 20-30% efficient. if you go by the lifting theory that makes them about 7% efficient

Edited January 31, 2011 by Mark59

[Schrödinger's hat]

Well there could be other factors for its efficiency. Is it spinning at full speed when you do the weight experiment.The blades could be optimised to turn at a certain speed relative to wind speed. (There are many complex aerodynamical things that I would have to do a lot of reading to understand involved in a well designed wind turbine. As a simplified and slightly wrong explanation, you can think of the blades as wings, and spinning too slow as being a bit like a stall so they don't produce optimal lift.)

 

 

 

6 watts all they are doing is putting in a very small voltage into the battery and times the .5 amp to give them 6 watts

I don't quite follow this. If it is charging a 12 volt battery then it is outputting over 12 volts, even a flat car battery is usually over 10V (under that and they tend not to work anymore).

The current that most generators can output at given rpm is limited (think of it as internal resistance) and so the power you can draw from them will be maximised at a certain load resistance.