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):