Page 225 - Aerodynamics for Engineering Students

208 Aerodynamics for Engineering Students

2 A thin aerofoil has a camber line defined by the relation yc = kc<(< - 1)(< - 2).
Show that if the maximum camber is 2% of chord then k = 0.052. Determine the
coefficients of lift and pitching moment, i.e. CL and CM],~, at 3” incidence.
(Answer: 0.535, -0.046)
3 Use thin-aerofoil theory to estimate the coefficient of lift at zero incidence and the
pitching-moment coefficient CM~/~ for a NACA 8210 wing section.
(Answer: 0.789, -0.172)
4 Use thin-aerofoil theory to select a NACA four-digit wing section with
a coefficient of lift at zero incidence approximately equal to unity. The maximum
camber must be located at 40% chord and the thickness ratio is to be 0.10.
Estimate the required maximum camber as a percentage of chord to the
nearest whole number. [Hint: Use a spreadsheet program to solve by trial and error.]
(Answer: NACA 9410)
5 Use thin-aerofoil theory to select a NACA four-digit wing section with a coeffi-
cient of lift at zero incidence approximately equal to unity and pitching-moment
coefficient CM],~ = -0.25. The thickness ratio is to be 0.10. Estimate the required
maximum camber as a percentage of chord to the nearest whole number and its
position to the nearest tenth of a chord. The CL value must be within 1% of the
required value and CM], within 3%. pint: Use a spreadsheet program to solve by
trial and error.]
(Answer: NACA 7610, but NACA 9410 and NACA 8510 are also close.)
6 A thin two-dimensional flat-plate aerofoil is fitted with a trailing-edge flap of
chord lOOe per cent of the aerofoil chord. Show that the flap effectiveness,

where a is the angle of incidence and 7 is the flap angle, is approximately 4&/~ for
flaps of small chord.
7 A thin aerofoil has a circular-arc camber line with a maximum camber of 0.025
chord. Determine the theoretical pitching-moment Coefficient CM~/~ and indicate
methods by which this could be reduced without changing maximum camber.
The camber line may be approximated by the expression
yc = kc[; - (3’1

where x’ = x - 05. (Answer: -0.025~)
8 The camber line of a circular-arc aerofoil is given by

Derive an expression for the load distribution (pressure difference across the aerofoil)
at incidence a. Show that the zero-lift angle a0 = -2h, and sketch the load distribu-
tion at this incidence. Compare the lift curve of this aerofoil with that of a flat plate.
9 A flat-plate aerofoil is aligned along the x-axis with the origin at the leading edge
and trailing edge at x = c. The plate is at an angle of incidence Q to a free stream of