Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A horizontal axis wind rotor is to be designed for a tip speed ratio of 1.5, rotor diameter 3.3 m and angle of attack (the angle at which the wind will strike the blade) 5°. If wind velocity in each part of the swept area of the rotor is reduced to one-third of its upstream wind velocity, the blade angle in degrees at the tip of the rotor will be
Options:
(A) 14
(B) 19
(C) 24
(D) 29
Official Answer Key:
B
Step-by-Step Solution & Explanation
At the blade tip, the tangential (blade) speed = TSR × V∞ = 1.5V. The axial induction reduces the wind velocity approaching the rotor plane; taking this reduction as one-third of upstream velocity (i.e. the local wind speed at the rotor plane = (2/3)V, consistent with the standard actuator-disc induction picture), the relative flow angle φ is: tan φ = V_local/(tip speed) = (2V/3)/(1.5V) = 0.4444 ⟹ φ = 23.96° ≈ 24°. Blade (pitch) angle β = φ − angle of attack = 23.96° − 5° = 18.96° ≈ 19°, matching option (B). (Note: φ itself, 24°, is listed as distractor option (C) — the common error is reporting the relative flow angle instead of subtracting the angle of attack to get the blade angle.)
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