• Sections 5.1-5.3 of Anderson.

Problems from Anderson
5.1
5.2

Study Questions

1. How does the flow over a finite wing differ from the flow over a two-dimensional airfoil?
    
2. Describe the flow on a finite wing in the vicinity of the tips.
    
3. Describe the flow downstream of the tips of a finite wing.
    
4. What is meant by downwash? How is it related to the trailing vortices?
    
5. What is meant by the induced angle of attack?
    
6. Explain how the downwash modifies the effective angle of attack.
    
7. What is meant by induced drag?
    
8. How can a drag force exist in an inviscid flow? Hint, use the 1st law of thermodynamics to answer this.
    
9. What is meant by profile drag?
    
10. Why is three-dimensional theory not needed to compute the profile drag of a finite wing?
     
11. What is a vortex filament? How is it different from the line vortex studied earlier?
     
12. What information does the Biot-Savart law give regarding a vortex filament?
     
13. How can the Biot-Savart law be used to compute the velocity induced by a semi-infinite straight vortex filament? What is the end result?
     
14. State Hemholtz's first vortex law.
     
15. State Hemholtz's second vortex law.
     
16. What is meant by washout?
     
17. What is meant by washin?
     
18. What is meant by aerodynamic twist?
     
19. What factors can contribute to lift variation over the span of the wing?
     
20. What value of lift always exists at the wing tips?
     
21. What is a horseshoe vortex? Does it violate the Hemholtz laws? Explain your answer.
     
22. Why is a horseshoe vortex not a good model for a finite wing?
     
23. What simple model did Prandtl adopt for a finite wing in his famous lifting line theory?
     
24. What distinguishes Prandtl's lifting line model from a single horseshoe vortex?
     
25. How are the strength of the trailing vortices in Prandtl's lifting line model related to the lift distribution on the wing?
     
26. Why must there be a continuous vortex sheet behind the airfoil according to Prandtl's lifting line theory?
     
27. How is the Biot-Savart law used to compute the downwash velocity in Prandtl's lifting line theory?
     
28. What type of equation does Prandtl's lifting line theory lead to? What is the unknown quantity to be solved for?
     
29. How can the total lift be computed once the circulation distribution is determined?
     
30. How can the induced drag be computed once the circulation distribution is determined?