A three-bladed rotor ( ) of radius runs at tip-speed ratio

PHYSICS · Subjective · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch Natural energy flows: rotors, turbines, waves, channels and hot rock

Problem

A three-bladed rotor (

B = 3

) of radius

R = 45\,\mathrm{m}

runs at tip-speed ratio

\lambda = 6

. Its blade section uses a lift coefficient

C_L = 0.8

and the design follows the Betz-optimum chord distribution for

x \gg 1

c(r) = \frac{16\pi R^2}{9BC_L\lambda^2 r}.

Find the chord

c

r = 15\,\mathrm{m}

r = 30\,\mathrm{m}

and

r = 45\,\mathrm{m}

. Which of the three values should you trust least, and why?