ENAE 631 Homework Problem Set No. 6

  1. The Cierva company designed a heavy-lift helicopter with three main rotors, with a layout such that the rotors were arranged at the corners of an equilateral triangle (two rotors at the back in a lateral arrangement, and one rotor at the front), with all three rotors turning in the same direction. How is torque reaction compensated for, and how would the aircraft be controlled?
  2. A helicopter is operating in level forward flight at 210 ft/s under the following conditions: shaft power supplied = 655 hp, W = 6,000 lb, r = 0.00200 slugs/ft3. The rotor parameters are R = 19 ft, s = 0.08, WR = 700 ft/s, k = 1.15, Cd0 = 0.01. (i) How much power is required to overcome induced losses? (ii) How much power is required to overcome profile losses. (iii) What is the equivalent flat plate area, f ? (iv) If the installed power is 800 hp, estimate the maximum rate-of-climb possible at this airspeed. (v) If the installed power is 800 hp, estimate the maximum level flight speed.
  3. Estimate the vertical autorotative rate-of-descent in forward flight at sea-level conditions for a small light-weight helicopter with the following characteristics: Weight = 1370 lb, rotor radius = 12.6 ft, rotor solidity = 0.030, tip speed = 700 ft/s. Estimate the autotoratve rate of descent for the same helicopter in forward flight as a function of forward flight speed. repeat the calcualtions for a desnity altitude of 10,000 feet and comment on your results.
  4. Describe the procedure a pilot would follow if the engine of a single engine helicopter failed in hover. How might the procedure differ (if any) if: (a) two engines were installed and one engine failed, (b) the tail rotor failed. Estimate the autorotative rates of descent of three substantially different (in terms of gross weight) single-rotor helicopters of your choosing. Explain how these results would be affected by the weight of the helicopter and the density altitude at whicj it operates. Comment on your results.
  5. You are asked to design an optimum rotor for a large helicopter whose primary mission is to lift logs and heavy construction equipment in the mountains at elevations above 10,000 feet MSL. If the gross weight is given as 100,000 lb, rotor diameter is 120 ft, average operating altitude is 15,000 ft, and tip speed is 650 ft/s, calculate the tip chord (assuming seven blades), equivalent rotor solidity, and mean rotor lift coefficient for the helicopter. How much shaft power would be required to hover out of ground effect at the design condition? Choose and obtain data on an appropriate airfoil.

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