At 35:56, you are missing a V_\infty in the equation for torque. Furthermore, in case you would insert the velocity to arrive at the same equation as 34:08, you would end up at torque in terms of units, not torque per unit length. Won't this mess up the integration over the span later on in the calculations?
Good catch, I indeed made a typo on the slide and the V_\infty should be there. With the Vinf include you do get the correct units (torque per unit length, N*m/m or just N). Fortunately, when I combine the momentum and blade element parts in the next video I have the V_\infty term back in so everything else is correct - just a typo on that slide.
So from my understanding, for most of the calculations in this video the units are in Torque and Thurst. It is only when you make A_d = 2*pi*r*(dr) and then divide LHS and RHS by (dr) do the equations become Torque per unit length and Thrust per unit length?
There is something wrong with Betz limit if kinetic energy in the wind is 1/2 mass or 50% and Betz limit is 0.5926% then where can the 0.926% come from not the wind ? regards Graham Flowers MEng
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amazing channel, thank you so much for uploading these lessons professor
Thank you so much for the lectures. Learning so much from them
How do we get from T=2a(1+a)
ho\V_inf^2A_d to T ' = 4a(1+a)
ho\V_inf^2 pi r
At 35:56, you are missing a V_\infty in the equation for torque. Furthermore, in case you would insert the velocity to arrive at the same equation as 34:08, you would end up at torque in terms of units, not torque per unit length. Won't this mess up the integration over the span later on in the calculations?
Good catch, I indeed made a typo on the slide and the V_\infty should be there. With the Vinf include you do get the correct units (torque per unit length, N*m/m or just N). Fortunately, when I combine the momentum and blade element parts in the next video I have the V_\infty term back in so everything else is correct - just a typo on that slide.
So from my understanding, for most of the calculations in this video the units are in Torque and Thurst. It is only when you make A_d = 2*pi*r*(dr) and then divide LHS and RHS by (dr) do the equations become Torque per unit length and Thrust per unit length?
There is something wrong with Betz limit if kinetic energy in the wind is 1/2 mass or 50% and Betz limit is 0.5926% then where can the 0.926% come from not the wind ? regards Graham Flowers MEng