Starting with a 2D airfoil that produces the following upper and lower velocity distributions: Ulower = U (1 + 1.3x.5 (1 x)) Uupper = Uo(1+ 3.1x05 (1-x)) A. Plot the incompressible pressure coefficients on the upper and lower surfaces B. Apply the Prandtl-Glauert correction to the incompressible pressure coefficients, plot the compressible pressure coefficients on the upper and lower surfaces for Mach 0.6 flow, and calculate the lift coefficient. C. Calculate the critical pressure coefficient for Mach 0.6 flow and then plot this limit on top of your compressible pressure coefficients. Show that a shock occurs on your upper surface. D. Calculate the value of the minimum Cp value and locate its x position. E. Using the equation: CP.A 2 YM (PA :- 1) calculate the max Mach number at the location of the minimum Cp value. F. Using the value of your maximum Mach number, what is the value of the subsonic Mach number immediately after your normal shock. G. Calculate the Cp value for the subsonic March number immediately after your normal shock. H. Estimate the lift coefficient loss caused by the presence of the transonic shock. Draw a vertical line from the min Cp to the Cp value at the end of the normal shock. Draw a horizontal line at the Cp value at the end of the normal shock until it intersects the Cp distribution on the downstream side. Integrate this area. 1. Make up for this lift coefficient loss by "adding" an equivalent amount of lift to the lower surface. Modify the velocity distribution on the lower surface to restore your lift coefficient to its intended unshocked value. Congratulation! You have just inversely designed your first transonic airfoil. Now if only you could describe its actual shape!! You can start by trying something like: Ulower = U (1+ (1.3x.5(1 x)) * K * sin(Lx)) Ulower = U (1 + (1.3x.5(1 x)) * K * sin(Lx)) Where K and L are scalar constants. But don't be afraid to try other more interesting functions!! -Ve Clarit Cpmin DC== x=1 (Pupper of -Ve Clarit Cp at Mend of shack Cpmin Xa 'CPMIN DC== x=1 X=1 CL transanic = Compressible sez Pupper of shoul