2. Consider a helicopter rotor in a wind tunnel. The rotor is spinning and the wind...
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2. Consider a helicopter rotor in a wind tunnel. The rotor is spinning and the wind is turned on. The equation for the rotor flapping was derived in class for this situation. Note that =  +C/2 = CT/2 for this case since as is forced to zero. (a) For the following rotor characteristics and operational conditions, solve the flapping equation using a numerical method (such as MATLAB's ode45). You may use initial conditions of 3 = 0 and 30. CT=0.006, p = 0.2, y = 8, 80 = 20.67, t = 0, and = 0.1. It is helpful to make time dimensionless by letting = Qt. Plot 3 as a function of dimensionless time for 5 rotor revolutions. (b) Perform a 20harmonic Fourier transform (discrete) on your result for s(t) and find the Fourier coefficients. Compare the results to the flapping coefficients you would calculate using the trun cated series solution we derived in class. Comment on the appropriateness of using the truncated series for solving the flapping equation. Note the following: i. In order to remove the transients from your computed solution, you may want to start your Fourier analysis after one revolution, i.e., at t=2. ii. Since ode 45 does not use constant time steps in solving the ODE, you cannot use stan dard FFT or DFT methods to perform the above Fourier transform. You may have to numerically perform the integrals for finding the Fourier coefficients in the formula 3(t) = ao +an cosnt + b sinnt (or redistribute the points to make them equally distributed). 00 12= 2. Consider a helicopter rotor in a wind tunnel. The rotor is spinning and the wind is turned on. The equation for the rotor flapping was derived in class for this situation. Note that =  +C/2 = CT/2 for this case since as is forced to zero. (a) For the following rotor characteristics and operational conditions, solve the flapping equation using a numerical method (such as MATLAB's ode45). You may use initial conditions of 3 = 0 and 30. CT=0.006, p = 0.2, y = 8, 80 = 20.67, t = 0, and = 0.1. It is helpful to make time dimensionless by letting = Qt. Plot 3 as a function of dimensionless time for 5 rotor revolutions. (b) Perform a 20harmonic Fourier transform (discrete) on your result for s(t) and find the Fourier coefficients. Compare the results to the flapping coefficients you would calculate using the trun cated series solution we derived in class. Comment on the appropriateness of using the truncated series for solving the flapping equation. Note the following: i. In order to remove the transients from your computed solution, you may want to start your Fourier analysis after one revolution, i.e., at t=2. ii. Since ode 45 does not use constant time steps in solving the ODE, you cannot use stan dard FFT or DFT methods to perform the above Fourier transform. You may have to numerically perform the integrals for finding the Fourier coefficients in the formula 3(t) = ao +an cosnt + b sinnt (or redistribute the points to make them equally distributed). 00 12=
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Related Book For
Physics
ISBN: 9780077339685
2nd edition
Authors: Alan Giambattista, Betty Richardson, Robert Richardson
Posted Date:
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