As discussed in class, if we make some simplifying assumptions (including that the density of air is that at sea level and angle of attack is 6°), then wing loading, W/S = 0.38V2. (where W is weight, S is wing area as viewed from above, and V is cruising speed). In the questions below, note that your answers to earlier questions may be very helpful in answering later questions, so if you feel stuck, for insight you can look back at relationships you have already figured out. To avoid any confusion, stick with SI units (e.g., newtons) — non-SI units (e.g., approximate tons) are shown just to help orient those of us who don’t have a good intuitive sense of the SI units. 

(1) If wingspan = b and we assume isometric scaling, 

a) what is S proportional to? 

b) what is W proportional to? 

c) what is wing-loading (W/S) proportional to? 

d) Write an equation relating W/S to W (you can use c to indicate some unknown constant relating two quantities that you know are proportional to each other).

(2) A Boeing 747 weighs W = 3.5 X 106 newtons (~400 tons) and has wing area S = 511 m2. 

(a) What is the wing loading for a 747? Show your calculation. 

(b) What is the cruising speed for a 747 (for this and all subsequent questions, assume that the plane is cruising at an altitude where the air density is 30% that at sea level)? Show your calculation.