You have been tasked to investigate lift and drag forces around airfoils exposed to hypersonic flows. You are specifically asked to experimentally characterize both forces employing a force balance system in pressurized wind tunnel experiments. With this type of system, a load cell is used to measure the lift and drag forces in an airfoil. Knowing that both forces are expected to vary non-linearly with Reynolds number, Mach number, and angle of attack, please answer at the best of your knowledge the following questions: a) What are the response variables of such an experimental setting? (5 pts)
b) What factors would you consider in your experimental design? Please express your answer in terms of controllable variables (e. g., air velocity, pressure, temperature, etc) (10 pts)
c) What is the minimum number of levels that you need to define for each factor? Why? (10 pts)