Wind Turbine Power Calculation Equations

recreated · Jul 18, 2014

Glad it's Friday? I will be if you can help me with this :D :

I'm trying to understand an equation about calculating the power extracted by the blades of a wind turbine. I have spent a couple of hours going over it but still not making much more sense.

I'm trying to find out why P = 1/2*m*(v² - v²_d). Why the 1/2? Why the '-' sign?? And why the ² ? I assume it is to do with F=ma, so the v (velocity) is squared to show acceleration but still I can't figure it all out.

Textbook figure of a wind turbine stream tube: air enters at upwind speed v, passes the rotor of area A where the speed is vb, and exits downwind at speed vd.

Two equations from a wind turbine text: m = ρAv_b and v_b ≈ ½(v + v_d) labelled (18.4), and P = ½m(v² − v_d²) labelled (18.5).

Any tips on how they got to the last equation (18.5) shown above would be amazing!

Thank you! Cannot wait for this to make sense

CWatters · Jul 18, 2014

https://www.raeng.org.uk/education/diploma/maths/pdf/exemplars_advanced/23_Wind_Turbine.pdf

RTW69 · Jul 19, 2014

Does K.E.= 1/2 X M X V² look familiar?

recreated · Jul 23, 2014

It does now, RTW69

Wind Turbine Power Calculation Equations

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