Using thin-airfoil theory, design an airfoil camber line that meets the following three requirements: ⚫ The lift coefficient is c₁ = 0.5 ⚫ There is no leading-edge suction peak • The airfoil has 10% static stability, SM = 10% a) Based on the requirements, determine the thin-airfoil theory constants B1 and B2. b) Assume that the camber line is given by Ze =a = a²² (1-2²) (1+6²) с Determine the constants a and b, and the angle of attack a, such that the design requirements are met. Provide a computer-generated plot of the camber line. c) Plot the difference in pressure coefficient versus x/c, Acp(x/c) = Cp,lower (x/c) - Cp,upper (x/c), and verify numerically, using point values of Acp and trapezoidal integration (trapz) that ce == 1 A(z) dz

2. The table below shows experimental data for the shape and pressure distribution on the upper and lower surface of an airfoil at zero angle of attack. X 0 0.25 0.5 0.75 1 Y Fx = Yu 0 0.0952 0.0922 0.0588 0 (Pu dYu dx - Calculate the drag and lift force on the airfoil by numerically evaluating the integrals Fy (P₁-P₂)dx = √ ( P₁ - 1 Pi Y₁ 0 -0.0254 -0.0144 -0.0052 0 dv) Y = Yu (x) dx y = Ye (x) Pu 1.000 -1.640 -0.786 -0.212 0 x Pi 1.000 0.589 0.426 0.322 0 Use finite difference approximations of the derivatives and the composite Simpson's rule to evaluate the integrals. Hint: Use central differences to estimate the derivatives wherever possible since they are more accurate than forward or backward differences.

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2. The table below shows experimental data for the shape and pressure distribution on the upper and lower surface of an airfoil at zero angle of attack. X 0 0.25 0.5 0.75 1 Yu 0 0.0952 0.0922 0.0588 0 Fx = dYu dx 5 Y₁ 0 -0.0254 -0.0144 -0.0052 0 PL Pd) d: dx Y = Yu (x) Calculate the drag and lift force on the airfoil by numerically evaluating the integrals = S₁² ( P₂₁ = ['(P₁ - F (P₁ - Pu)dx 0 y = Y₂ (x) Pu 1.000 -1.640 -0.786 -0.212 0 Fy x Pi 1.000 0.589 0.426 0.322 0 Use finite difference approximations of the derivatives and the composite Simpson's rule to evaluate the integrals. Hint: Use central differences to estimate the derivatives wherever possible since they are more accurate than forward or backward differences.