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Tutorial Problems Performance

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457 views5 pages

Tutorial Problems Performance

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Uploaded by

Ayaz Ahmed
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AIRCRAFT PERFORMANCE 189 SMcComick, B. W., Aerodynamics, Aeronautic, and Flight Mechanics, Wiley, New ‘York, 1979. ‘Boyle, D, “Windsbear, Taming the Killer” Interavia, an. 1985, pp. 65-66, SLewis, M., "Sensing Change inthe Wind Aerospace America, Jan. 1993, p20 ‘Mulgond, S.'S., and Stengel, R. F, “Target Pitch Angle forthe Microburst Escape Maneuver" Journal of Aircraft, Vl. 30, No.6, 1993, pp. 826-832. Stengel, RF, “Solving the Plot's Wind Shear Problem" Aerospace America, March 1985, pp. 82-85. Problems 2.1 Show tthe maximum endurance of ies ven by 3s pan = 2, me av 2.2. A glider weighs 4500 N and has a wing loading of 600 Nim, and its drag polaris given by Cp = 0.01 + 0.022C. tis launched from a height of 400 m in Still ar. Find (a) greatest possible ground distance it can cover, (b) the maximum. time t can remain in ir, and (c) effect of 10 m/s tailwind foreach ofthe above two cases. Answer: (a) 13.484 km, (b) 6.72 min, and (c) AR = 3.52kmand Ai 2.3. Acenain sirpane weighs 4440 N and has a wing loading of 1433.55 Nin? ‘The drag polaris given by Cp ~ 0024+004C2 and Cr may ~ 1-2. Forapowerott glide from 600 m, determine (a) the maximum distance it can cover and (b) the ‘maximum ime tcan emai inthe ai [Answer (2) 16,6066} and (b) 210.1255) 24 A piston-prop aircraft has a wing loading of 1600 N/m, and its drag polar is given by Cp = 0.025 + 0.05CZ. The maximum lift coefficient is 15, The reciprocating engine develops 750 KW at sea level, andthe propulsive efficiency ofthe engine-propeller combination is 085. Draw the power-available and power required cuves at sea level, Determine the maximum and minimum speeds for level fight at sea level. ‘What isthe minimum power required for level light at sea level? Determine the corresponding velocity and lift coefficient. 25 Alightturbojt airplane weighs 30,000 N, has a wing loading of 1000 N/m?, tnd prodges a sea level thst of 4000 N. The thas vaies with ale a Too, Assuming Cp = 0.015 + 0.024C} and Cras = 1-4, find (a) maxi ‘mum and minimum speeds in level light at sed level and (b) the absolute ceiling of the airplane, (Answer: (a) 119.2149 mus and 32.9914 m/s and (b) 13.30 km.) 2.6. Whatis the trast required fora turbojet airplane weighing 50,000 N, witha ‘wing loading of 1800 N/m? and a maximum sea level fight speed of 241.83 mis? Assume Cp = 0.02 + 0.04Cf, and Cymax = 1.5. (Answer: 20,000 N.] 2.7 For the propeller sirplane of Exercise 2.4, determine, the maximum climb Angle and the maximum rate of climb at sea level as well a the velocities and lit coefficients at which they occur 160 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL, 28 _A propeller sisplane has a wing loading of 1750 N/a, wing area of 30 m, Cy = 0.02 -+0.04C2, and Ci max = 1.5. The propulsive efficiency is 0.85. What should be the power developed by the reciprocating engine to achieve a maximum rate of climb of 12 m/s a sea level? 2.9 ‘The drag polar of a turbojet airplane is given by ct p= Coo + SE + eae Assuming that the thrust is independent of fight speed, show thatthe dynamic ‘pressure when the rate of climb is maximum is given by _t T we ** GSCo0 * \ 6SCo0 * 3eAeS*Coo 2.10 An areraftis powered by a turbojet engine and has a maximum speed of 790 kaw at sea level The aross weight ofthe vehicle is 160,000 N, wing aea is 50:m?, and Cp = 0.02-+ 0.04C2. Find (a) the thrust developed by the eng (b) climb angle and rate of climb when flying at 75% maximum aerodynamic efficiency, and (c) maximum rate of climb and velocity at which it occurs. (Answer: {@)30,118.94N, (65171 degand 14.5229 mus, and (©) 14,547 avsat 129.06 8 2.11 Atasea level speed of 200 m/s, the pilot of a certain jet aircraft can achieve a rate of climb of 20 m/s. Instead of climbing, the pilot choosesto accelerate, holding the altitude constant. Determine the maximum speed achieved at sea level. Assume W=200,000N, $= 601m, and Cy = 0,021+0.042C?. (Answer: 257.8538 m8) 2.12 A jetairplane weighs 160,000 N and has a zero-lift drag coeficient of 0.008 ‘and a wing area of 42 m*. At 100 m/s at sea level, the rate of climb is 11.5 mis. The thrust developed by the engines is equal to 27,000 N. Determine the maximum rate of climb and the corresponding fight speed at sea level. (Answer: 22.75 mvs and 211.06 mys.} 2.13 A jet aircraft weighs 150,000 N and has a wing area of 30m? Its drag polar is given by Cp = 0.015 + 0.025C2. The sea level thrust Tis equal to 23.200 N, and the thrust at alttade is given by T= Tyg. The specifi fcl consumption a sea level cis 1.2 N/Nh and, at altinde, ¢ = cya. Determine (a) the most economical cruise altitude and (b) fuel load and cruise velocity fora Breguet range of 2500 an. Tnswer: (2) 12.31 km and (b) 6030.0 N and 205.166 ms} 2.4 Ifthe aircraft in Exercise 2.13 encountered a steady tilwind of 35 km/h ‘uring the cruise, how much fuel is saved” (Answer: 492.19 N.] 2AS Ifthe aircraft in Exercise 2.13 followed a constant-altiude range program, find (a) cruise altitude and (b) fuel required to cover a sil-ar range of 2500 km, (Answer: (a) 11.2059 kam and (b) 6361 N.] AIRCRAFT PERFORMANCE 161 2416 _A jet aircraft has the following data: W = 50,0000 N, Cp=002 + 0.04C}, Crm = 1.2, $=30 mt, T = 145000 N, © = 1.50% NIN, oil consumption = 1 N for every 25 N thrast, and Wy = 20,0000. Determine (a) sil-air range and endurance at an altitude of $000 m (a = 0.60) and (b) reduction in the range ifthe srcraftencounters.a steady headwind of 20 m/s daring the cruise. [Answer (—) 2074.988 km and (b) 391.166 km.] 2.17 _A jet sizcraft has the following data: W = $0,000 N, Co = 0.025-+ O.03C%, Cr = 0.084, $=30 m2, = 15,0000 N, and ¢ = I.0a"? NINB. ‘ifthe airplane cruises atan angle of attack of 5 deg, determine the percent change in the fuel consumption compared tothe minimam possible fel consumption to Cover a range of 1500 ki at an altitude of 11 km (o = 0.293). Assume that the pilot consanily monitors the speed to prevent the aircraft from gaining alitude. [Answers 3.4681] 2.18 A propeller airplane weighs 60,000N and has a wing loading of 2000 Nim. ‘The aspect rato ofthe wings is 6, zr0-lit drag coefficient is equal to 0.021, and Oswald's efficiency factor is equal to 0.920. The airplane produces a thrust of 750 KW at a propulsive efficiency of 0.82 and a specific fuel consumption of 3.5 NAkWih. What fuel load should the airplane cary (a) to cover a sill-ar range ‘of 1500 km and (b) to remain in air for 8h? Assume that the airplane operates at an altiude of 24 km (¢ = 0.7892). (Answer: (8) 6985.3523 N and (b) 9160,7026N.] 219 (a)Foracoordinated constant-velocit tur ina horizontal plane, derive the ‘expressions forthe turn rate and radius of turn for fight at limit oad factor for et aircraft. (©) Show that for MSTR and SST, the lit-to

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