Calculate the tail rotor thrust required to trim the helicopter in hover.

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Q1 A helicopter has a main rotor speed of 260 rpm, and a main rotor radius R=5.90m. The gross take-off weight is 30kN. The blades have an average drag coefficient of CD=0.01, and the rotor solidity =0.08. The distance between the axis of the main and tail rotor is x=7.5m. The helicopter is powered by two turboshaft engines with maximum continuous power at sea level of P0=1,150kW, each.
(a) Calculate the tail rotor thrust required to trim the helicopter in hover. [10]
(b) Assume that due to a failure in the flight control system there is an impulsive excess of tail rotor thrust. What happens to the helicopter? Discuss whether the worst-case scenario is during hover or level flight. [8]
(c) The altitude lapse rate for the engine power is a function approximated by P(z)=P0 (/sl)1.35. Estimate the hover ceiling of this helicopter rotor, neglecting the effects of profile and tail rotor power. [7]
Q2 Write a MatlabTM computer program to calculate induced power in level flight. Assume a UK rotor thrust coefficient of CT=0.005, ISA sea-level conditions, and flight at advance ratio = 0.1. The ki of the rotor can be assumed to be 1.15. The rotor tip-speed in hover is 220m/s, and the rotor radius is 12m. You are allowed to make further assumptions if necessary. [25]
Q3 A helicopter rotor is in vertical climb, and the collective pitch is 0.
(a) Show that the rotor thrust T is given by: =123−2−+ 2Equation 1, Question 3 Where is the air density, VT is the rotor tip speed, N is the number of blades, c is the blade chord, R is the rotor radius, is the constant lift-curve slope, i is the non-dimensional downwash, z is the non-dimensional vertical climb rate, and k is the overall linear blade twist. [10]
(b) The helicopter is in steady hover, as a sudden increase of∆̅ is applied to the collective pitch. If the rotor downwash does not adjust its values, show that the equation of motion governing the helicopter’s height (h) above that of the starting position is given by: ℎ̈+14 ℎ̇=16 ∆̅Equation 2, Question 3 where m is the mass of the helicopter. [15]
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Q4 The flapping equation of motion for a rotor blade is given by: Equation 3, Question 4 Where is the flap angle, is the Lock number of the rotor, is the feathering angle and i is the downwash divided with the rotor tip speed. “and ` denote second and first derivatives with respect to azimuth. Using negative Fourier series for and express:
(a) The coning angle as a function of the Lock number, collective and i . [10]
(b) The lateral rotor tilt as a function of the longitudinal cyclic input. [8]
(c) The longitudinal tilt as a function of the lateral cyclic input.

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