Submit your answers to all problems below. Show your working steps in sufficient details.
problem 1: The NACA 4412 airfoil has a mean camber line given by:
By using thin airfoil theory, compute:
a) Its zero-lift angle of attack.
At the angle of attack of 3o, compute the below:
b) Its lift coefficient.
c) The moment coefficient about its quarter-chord point.
d) The location of its center of pressure (x_{cp}/c) and aerodynamic center (x_{ac}/c).
The experimental data for NACA 4412 airfoil are given in the Appendix of this Homework set (from Abbott, I.H., von Doenhoff, A.E., and Stivers, Jr., L.S., “Summary of Airfoil Data,” NACA Report No. 824, 1945).
e) Compare your outcomes from parts a, b, and c above with the NACA 4412 experimental data and express the percentage difference between your outcomes and experiment.
problem 2: A positively cambered airfoil with a zero-lift angle of attack of −3^{o} has a lift slope of 0.1 per degree.
a) Compute the lift coefficient at an angle of attack of 5^{o}.
b) Now the same airfoil is turned upside-down (so it becomes an airfoil with a negative camber). Compute its lift coefficient at the same angle of attack of 5o as in part (a).
c) At what angle of attack should the upside-down airfoil be set to produce the same lift as that when it is right-side-up at a 5^{o} angle of attack?
problem 3: A two-dimensional thin wing was tested in the wind tunnel. The pitching moment coefficient about the leading edge (C_{m,LE}) at zero-lift was found to be −0.02. At angle of attack of 8 deg, C_{l} = 0.7, C_{d} = 0.04 and C_{m,LE} = −0.2. Find out the location of the aerodynamic center of this wing.
problem 4: Spanwise circulation distribution for a wing of span b in an air flow of density ρ_{∞} and speed V_{∞} is parabolic as shown below:
a) Compute the downwash induced by this circulation at any position y_{0} all along the wing span. Compute as well the downwash at the root of the wing.
b) Determine the total lift generated by the wing.
problem 5: A thin spanwise symmetrical wing has an aspect ratio of 10 and straight edges with taper ratio (tip chord/root chord) of 0.8 and root chord of 1 m. This wing doesn’t have geometric or aerodynamic twist and it has symmetrical airfoil profile.
a) find out, by using 4 terms in the expansion, the spanwise efficiency factor, e, and plot its drag polar if its zero-lift drag is 0.01.
b) Find out lift coefficient and induced-drag coefficient of the wing at an angle of attack of 4^{o}.
problem 6: The wing of a light, single-engine general aviation aircraft has an area of 15.8 m^{2} and a span of 9.6 m. The airfoil of the wing is NACA 65-415, which has a lift slope of 0.1033 per degree and zero-lift angle of attack of −3^{o}. Suppose the span efficiency factor of 0.893.
a) If the wing is to generate 11 kN lift while cruising at 190 km/h at standard sea level, compute the geometric angle of attack that the wing must be set to.
b) Compute as well the induced drag experienced by the wing in that condition.