Using the method of characteristics, compute and graph to scale, the contour (using solid lines) and the characteristics (using dashed lines) of a two-dimensional minimum-length nozzle for the expansion of air to a design exit Mach number of 3.

Assume the specific heat ratio is 1.4. For clarity, lay out the design using a schematic, number the intersection points for the characteristics, develop the calculations using a spread sheet and show the spread sheet results for each point for K-, K+, θ, υ, μ, Mach number, x and y for every point. Use at least 8 characteristics for the initial expansion.