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Aircraft_perf_notes2

Aircraft_perf_notes2 - Analysis of Air Transportation...

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Virginia Tech - Air TRansportation Systems Laboratory 1 Analysis of Air Transportation Systems Fundamentals of Aircraft Performance (2) Dr. Antonio A. Trani Professor of Civil and Environmental Engineering Virginia Tech Fall 2010 Blacksburg
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Virginia Tech - Air Transportation Systems Laboratory 2 Example of Aircraft Climb Performance The following example gives an idea of the typical procedures in the estimation of the aircraft climbing performance. Assume that a heavy transport aircraft has drag polar of the form, where: AR = 8.0, e =0.87 and C DO (the zero lift drag coef fi cient) varies according to true airspeed (TAS) according to the following table: Mach Number C DO (nondimensional) 0.0 to 0.75 0.0180 0.80 0.0192 C D C Do C L 2 ! ARe -------------- + =
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Virginia Tech - Air Transportation Systems Laboratory 3 The engine manufacturer supplies you with the following data for the engines of this aircraft: For simplicity assume that thrust variations follow a linear behavior between 0 and 300 m/s. The thrust also decreases with altitude according to the following simple thrust lapse rate equation, T altitude = T Sea Level ( " / " # ) .90 (1) 0.85 0.023 0.90 0.037 0.95 0.038 1.00 0.040 True Airspeed (m/s) Sea Level Thrust (Newtons) 0 250,000 300 150,000 Mach Number C DO (nondimensional)
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Virginia Tech - Air Transportation Systems Laboratory 4 where " is the density at altitude h and " # is the sea level standard density value (1.225 kg./ m 3 ). The aircraft in question has four engines and has a wing area of 525 m 2 . A) Calculate the thrust and drag for this vehicle while climbing from sea level to 10,000 m. under standard atmospheric conditions at a constant indicated airspeed of 280 knots. Simulate the climb performance equation of motion assuming that the takeoff weight is 360,000 kg. B) Estimate the rate of climb of the vehicle if the fuel consumption is approximately proportional to the thrust as follows,
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Virginia Tech - Air Transportation Systems Laboratory 5 F c = TSFC (T) where TSFC = 2.1 x 10 -5 (Kg/second)/Newton C) Find the time to climb and the fuel consumed to 10,000 m. D) What is the approximate distance traveled to reach 10,000 m. altitude?
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Virginia Tech - Air Transportation Systems Laboratory 6 Solution The process to estimate the complete climb pro fi le for the aircraft is best done in a computer. There are numerous computations that need to be repeated for each altitude. A suitable algorithm to solve the equations of motion of the aircraft over time is presented in the following pages.
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Virginia Tech - Air Transportation Systems Laboratory 7 Computational Algorithm Flowchart Initial Aircraft States Mass (W o ), Altitude (h o ) Distance Traveled (S o ) and 2) Compute lift coefficient (C L ) Given: Speed profile Typically V as a function of Altitude (h) C L = f (mass, density, 1) Compute Atmospheric values for a given altitude (density, speed of sound, etc.) wing area, etc.) 3) Compute the drag coefficient (C D ) C D = f (C L , Mach, AR, e, etc.) Equation (31) From Table Equation (30)
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Virginia Tech - Air Transportation Systems Laboratory 8 Computational Algorithm (contd.) 4) Compute total drag (D) D = f (C D , V, S, density) 5) Compute the thrust produced (T) T = f (Mach and density) Equation (29) Equation (33)
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