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On 04/03/2008 10:02 AM, Rick Tarara wrote:
The available energy may increase as the cube of the velocity (see below),
I hope that's a typo.
Available _power_ (not "energy") goes like the cube, under these
conditions, more or less.
The force on the blades depends on momentum /transferred/ which
does not scale like the total momentum of the air. You're not
deflecting the air through a fixed angle in the lab frame. It
helps to analyze the system in a frame comoving with the blade,
whereupon the primacy of /angle of attack/ becomes apparent.
You want to fly the blade at the optimal angle of attack, as
nearly as you can. The optimal angle of attack depends on
the lift-to-drag ratio, including contributions from parasite
drag and induced drag. This is nontrivial because induced
drag depends strongly on angle of attack.
At the
generator itself, doubling the rotational speed would double the rate of
flux change and therefore double the induced emf, but that should quadruple
the power through a fixed load V^2/R.
In the immortal words of Richard Nixon, we could do that, but
it would be wrong. Applying a load like that to the rotor
would not allow the rotor to spin at the optimal speed.
In the real world, they control the excitation of the field
coils, so that the torque of the generator matches the torque
of the rotor at an appropriate speed. This costs some efficiency
in the generator.
At the next level of detail, they trade off a little bit of rotor
aerodynamic efficiency to improve generator efficiency at the
lowest airspeeds. Most systems have hubs that can change the
blade angle ... for just this purpose. Of course changing the
blade angle screws up the calculation of optimal twist that we
did a few paragraphs ago ... which explains why the overall
efficiency goes to zero at a non-zero airspeed: At low airspeed,
if you coarsen the pitch too much, the roots will go to /negative/
angle of attack while the tips are still at a too-large angle
of attack.