FYKOS Year 35 Series 4 Problem 5 — Helicopter · FYKOS 35 #35.4.5

Physics · mechanics

Problem

The FYKOS bird started to think about constructing his own helicopter because he was tired of flying using his wings. He started by creating a simple model of the main rotor and wondered what the rotor's angular velocity needed to be. Rotor blades are inclined at angle 45∘45^\circ. Thus, air molecules are pushed directly downwards, creating a momentum flux. Initially, we assume air molecules to be at rest and their collision with the rotor blades to be elastic. The effective part of the rotor blade (i.e., the part inclined at 45∘45^\circ angle) is blade's part that is distant r1=50 cmr_1 = 50\,\mathrm{cm} to r2=6.00 mr_2 = 6.00\,\mathrm{m} from the centre of rotation. The projection of one blade onto the vertical plane has height h=10.0 cmh = 10.0\,\mathrm{cm}, and the helicopter will have four such blades. What is the minimum frequency of the rotor to keep the helicopter of mass m=2 500 kgm = 2~500\,\mathrm{kg} at a constant height?

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