Torque in Wind Turbines: Calculating Power Output

[sundaravadivel]

【 mod note: moved to H/W forum so homework template is absent 】

Dear all
i am trying to calculate torque in HAWT from the measurements using Rope brake dynamometer set up with a blower. i had wound a string over the turbine shaft. The string is connected to a spring balance on its one end and the other end have provisions to add weights.
firstly i'd calculated the turbine free wheeling characteristics ie.. i allowed the turbine rotor to rotate due to blower wind (5m/s) and i applied load in steps of 10 gm and correspondingly I've noted the RPM (310 RPM). When a particular load is reached (200 grams) , the turbine shaft, does not able to overcome the load and stop its rotation. The blade length is 20 cm (0.2 m).
The swept area = pi*r (squared) = 3.14*0.2*0.2 = 0.1256 m squared.
Power available in wind is = 1/2 rho A V cubed= 0.5*1.225*5*5*5 = 9.6125 watts

from the measurements i got
torque = (load - spring bal. reading)*9.81*(radius of shaft +radius of rope)
torque (Nm) = (0.01-0.001)*9.81*0.011 = 0.00088Nm

power produced = torque *angular velocity=0.00088*31.34= 0.0304 watts

The power produced is very much lower than power available (Cp is very low). where i am going wrong,,any one please help...

 

[CWatters]

Your equation seems OK but...

Have a think about the expected efficiency of a turbine that has no load (or a very small load).

Work the numbers for the other data points and see what you get. I'd use a spreadsheet so you can plot some graphs later.