Use the computer program developed in Problem 8.22 to make the following assignments.
(a) Change the aspect ratio to 2 and 10, respectively. Keep all other parameters as in Example 8.6. Plot the relation between Mach number and CLδ for sweep angles of 0, 15, 30, and 45◦. Also plot the change in α, θ, and Γ . Based on your results, describe the effect of aspect ratio on the flap effectiveness.
(b) Change the Young’s modulus of the material to 35 and 140 GPa, respectively. Keep all other parameters as in Example 8.6. Plot the relation between Mach number and CLδ for the aforementioned sweep angles. Also plot the change in α, θ, and Γ . Based on your results, describe the effect of material stiffness on the flap effectiveness.
(c) Keep all parameters as in Example 8.6. Plot the relation between Mach number and CLδ for sweep angles of 0, −15, −30, and −45◦. Also plot the change in α, θ, and Γ . Based on your results, describe the effect of forward sweep on flap effectiveness. What adverse aeroelastic effect do you observe?
Problem 8.22
Implement the steps outlined in Example 8.6 in a computer program.
(a) Reproduce the plot of Fig. 8.49.
(b) For the same input parameters, plot (as a function of Mach number) the angle of attack, the twist angle, and the dihedral angle of the wing for each of the sweep angles. Can you explain their behavior?
Example 8.6
Consider the wing of Fig. 8.48. Assume this wing has a planform area of 93.5 m2
and an aspect ratio of 8.4. Furthermore, assume it features a box structure of width w = 0.5cs and height h = 0.12cs. The geometric center of this box is located at 40 % of the structural chord (i.e. e = 0.15). The thicknesses of the box are tskin = 1 cm and tflange = 5 mm. The Young’s modulus of the material is 70×109
N/m2
and the Poisson ratio is 0.31. The flap measures 20 % of the chord, i.e. c f = 0.20c. Assume the wing is sheared with the following sweep angles: Λ = 0, Λ = 15◦, Λ = 30◦, and Λ = 45◦.
(a) Make a topview of the four wings.
(b) Plot the flap effectiveness (CLδ ) as a function of the Mach number ranging from M = 0 to M = 0.9. Assume a static pressure of 26.4 kN/m2
(which is the atmospheric pressure at an altitude of 10 km).