I can handle the Matlab plotting stuff, just need help getting the RK4 method going. I am not sure how to handle the fact that the differential equation is dependent on gamma and L, but gamma and L are dependent on the values that come out of the diffEQ
Microsoft Word - Term Computer Project Assigned 3/2/2021 FLORIDA INSTITUTE OF TECHNOLOGY AEROSPACE, PHYSICS, AND SPACE SCIENCES DEPARTMENT AEE 3150-01: Aerospace Computational Techniques Spring 2021 TERM COMPUTER PROJECT Due April 20, 2021 Project cannot be turned in late for credit. The horizontal and vertical motion of the center of mass of an airplane in the vertical plane can be described using a two degrees-of-freedom (2 DOF) model. In Aircraft Stability and Control, one learns that the equations of motion of the aircraft can be written as: 1 sin ( )cos 1 cos ( )sin x z x V L T D m z V L T D g m where z is altitude and x is the horizontal distance travelled. Other parameters in the equations are: Vx = horizontal velocity T = thrust Vz = vertical velocity D = drag m = aircraft mass g = gravity L = lift = flight path angle Lift, drag, and flight path angle are determined by: 21 2 21 2 1tan L D z x L V SC D V SC V V where Vx and Vz are components of flight speed V in the x and z directions. Assigned 3/2/2021 Note that: 2 2 x zV V V In the above equations, assume that , CL, and CD can be computed using 3 1 2 0 1.225exp( 0.0001 ) (in kg/m ) L L D D z C K CC C e where z is in meters. Consider an aircraft with the following lift-curve slope K1, wing aspect ratio AR, zero-lift drag coefficient 0 ,DC wing planform area S, mass m, and efficiency factor e during flight: 2 1 40 m 15,000 kg 5 0.06 AR 6 0.8 9.81 m s oD S m K C e g For your final project, you are to simulate the aircraft’s undamped phugoid motion. In this case, thrust exactly cancels drag. Assume a constant angle of attack, , of 0.0495 rad. Using the 4th-order Runge-Kutta technique, solve the equations of motion above for the horizontal and vertical components of velocity. The initial conditions are x = Vz = 0, z = 4800 m, and Vx = 210 m/s. Run your simulation from t = 0 to t = 400 seconds with t = 1.0 sec. Plot altitude vs. horizontal distance, altitude vs. time, and flight speed vs. time, each on a separate plot, using proper plotting techniques. You may choose any computer language you prefer (except Python or MATLAB) for your code provided you are not using a commercial or other pre-written application to do the work for you (Mathematica, Excel, and other available software are not acceptable). The plots may be created by importing your data into any available software, including MATLAB. While working in small groups to set up the problem and determine how to solve it is acceptable, all code must be original work. Code that is copied or substantially similar to other students’ work (past or present) will be rejected and no credit for the assignment received. To complete this project, you must turn in an electronic copy of the code listing (in text format with the appropriate language extension on the filename), the plots, and numeric values for Vx, Vz, x, and z only for time steps 0, 5, 10, 15, …, 400, all out to exactly 2 decimal places for each time step using all proper formatting techniques for tabulated data. Please do not email your assignment to me. This project must be turned in by the end of class on the due date to receive credit. No late assignments will be accepted.