AEE342: Aerodynamics
Homework 1 — Introductory Thoughts
Homework Assignment; Due January 27, 2025, 11:35AM in-class
1. Consider a parabola-shaped foil with 12” chord, where the foil surface has this equation:
y = 1.8 − 0.05(6 − x)2 (Upper side)
y = 1.44 − 0.04(6 − x)2 (Lower side)
where x and y are given in inches. The foil is placed at an angle of attack of α = 10◦ and
the free stream velocity is v∞ = 21.5 ft/s. The pressure and shear stress distributions on
the upper and lower surfaces are given by:
pu = 0.01x(x − 12)(x + 3)
pl = 0.005x(x − 15)(x − 12)
τu = 0.2x−1/5
τl = 0.4x−1/5
where x is the distance from the leading edge in inches and p, τ are in psi. Assume the
shear stress τ acts only tangentially to the local surface. Calculate:
(20 points) The contribution of the pressure terms to the axial force, in lb-f/in;
(20 points) The contribution of the shear stress terms to the axial force, in lb-f/in;
(10 points) The lift and drag, also in lb-f/in;
(10 points) If the lift coefficient is unity, what is the density of the working fluid?
Which fluid would you guess would match this density? (Be careful with the units!)
(5 points) For these conditions, what would the drag coefficient be?
2. The power Ẇ required by a propeller is a function of the following variables: The diameter
D of the propeller, the rotation rate n of the propeller, the viscosity µ of the surrounding
fluid, and the density ρ of the surrounding fluid.
(25 points) Find the dimensionless groups that would be appropriate to describe the
relationships between the propeller power and the other variables.
(10 points) If the propeller diameter was doubled, how much lower would the rotation
rate have to be such that the power consumption remains the same? (consider all other
variables remain constant)
Submit your individually-prepared solution in-person, at the end of the class.
AEE342 — Spring 2025
1
Zigunov