Answers to Study Questions

1. What is the definition of the critical Mach number?
   ans:    It is the free-stream Mach number for which the maximum local Mach number is exactly one.
    
2. Why is the critical Mach number of interest?
   ans:    It tells us the flight Mach number where locally supersonic flow, and hence wave drag begin to exist.
    
3. Will the critical Mach number increase or decrease as the lift produced by the airfoil increases?
   ans:    Decrease. More lift implies more flow acceleration and therefore greater difference between the free-stream and local Mach numbers.
    
4. Will the critical Mach number increase or decrease as the airfoil thickness increases?
   ans:    Decrease. Increased thickness implies more flow acceleration and therefore greater difference between the free-stream and local Mach numbers.
    
5. What is meant by the drag-divergence Mach number?
   ans:    The Mach number where the drag coefficient begins to increase rapidly with increasing Mach number.
    
6. List two factors that contribute to the rapid increase in drag around Mach 1.
   ans:    Wave drag and pressure drag due to separated flow. Shock waves are ultimately responsible for both of these effects.
    
7. Typically by what factor does the drag increase as an aircraft passes through Mach 1?
   ans:    Roughly a factor of 10.
    
8. What is meant by the ``sound barrier''? Does it really exist? Explain your answer.
   ans:    The rapid rise in drag near Mach 1 was once thought to be insurmountable by certain aerodynamicists. We know now that, with enough power, an aircraft can pass through Mach 1.
    
9. State the area rule for transonic flow.
   ans:    Two aircraft with the same longitudinal distribution of cross-sectional area will have the same zero-lift wave drag.
    
10. Does the area rule require a widening or thinning of the fuselage in the vicinity of the wing? Explain your answer.
    ans:    Drag will be minimized if the fuselage is thinned in the vicinity of the wing in an effort to keep the cross-sectional area nearly constant.
     
11. By what factor can the peak drag near Mach 1 be reduced through use of the area rule?
    ans:    By roughly a factor of 2.
     
12. What is a supercritical airfoil?
    ans:    One that is specially designed to weak shocks (and hence modest drag) for a Mach numbers slightly above M_cr.
     
13. What is the advantage of a supercritical airfoil?
    ans:    The drag-divergence Mach number is closer to 1 than for conventional airfoils, thus the aircraft can cruise at a higher transonic Mach number.
     
14. Why does the supercritical airfoil have a concave region on the lower surface near the trailing edge?
    ans:    In order to offset the loss in lift due to negative camber on the forward 60% of the airfoil.
     
15. How will the quarter chord pitching moment coefficient for a supercritical airfoil compare with a conventional airfoil?
    ans:    The moment coefficient for the supercritical airfoil will be greater (in magnitude) since it carries more load near the trailing edge.