Problem Set 3 - 09 Feb 2024-1

1 MAE 3306 – Flight Performance & Stability Spring Semester 2024 Ian Maynard • NH 125A E -Mail: ian.maynard@uta.edu HOMEWORK P ROBLEM S ET 3 D ISTRIBUTED : 09 F EBRUARY 2024 D UE DATE : 19 F EBRUARY 2024 Name: ID: Problem 1 Write a computer program that uses the vortex panel method that was [50%/100%] described in Sec. 1.6, and do the following: (1) Compute and plot the C p vs x/ c pressure distribution on a NACA 2412 airfoil. (2) Generate a table of the section lift coefficient 𝑪 ̃ 𝑳 , section leading edge pitching moment coefficient 𝑪 ̃ ? ?𝒆 , and the section quarter-chord pitching moment coefficient 𝑪 ̃ ? 𝒄/𝟒 as a function of angle of attack 𝜶 from -12° to 16° in 2° increments. (3) Plot 𝑪 ̃ 𝑳 and 𝑪 ̃ ? 𝒄/𝟒 as a function of angle of attack 𝜶 (4) In one plot, plot 𝑪 ̃ 𝑳 vs 𝜶 using thin airfoil theory, plot 𝑪 ̃ 𝑳 vs 𝜶 using the vortex panel method, and plot the experimental NACA 2412 𝑪 ̃ 𝑳 vs 𝜶 data from Fig. 1.6.6. Compare and discuss the results. Notes: • Use 100 nodes with 99 panels. Verification Data: • Using 100 nodes, at 𝛼 = 2 °, 𝐶 ̃ 𝐿 = 0.50247 , 𝐶 ̃ 𝑚 𝑙𝑒 = −0.18441 , and 𝐶 ̃ 𝑚 𝑐/4 = −0.05887 • If you are not matching with these results, set your number of nodes to 12 and check your code’s results with the following: • The A matrix for 12 nodes (note that python indexes start at 0, not 1):

2 • Vector for solving for gamma (using 12 nodes): • Gamma values (using 12 nodes): • Summation vector for calculating Vx and Vy (using 12 nodes): This is a matrix of eleven (n-1) 2x1 matrices • The upper surface Cp values (using 12 nodes): • The lower surface Cp values (using 12 nodes): • 𝐶 ̃ 𝐿 summation vector (using 12 nodes):

4 Homework General Requirements: » Use MATLAB, Python, or another programming language to generate the answers and plots for all problems. » Keep the programming codes neat and organized. » Use professional plot formatting when generating plots. » Include all the programming code that you have coded for your homework in your submission. Homework Formatting Requirements: » Use engineering paper for all written solutions » The header should include the student’s last name, then first name, class information (MAE 3306), homework number, date, and page number information » Problem statement summaries are required (no need to rewrite entire problem statement if it is long, just summarize) » List the inputs given, show all work in deriving the solution, and box or highlight all final answers . Plotted answers DO NOT need to be boxed. ---------- o0o ----------