A mean camber line with a reflexed trailing edge must have a point of inflection, and therefore, the simplest equation that can describe it is a cubic. Four boundary conditions are required to determine a cubic. Two of them are the condition of zero camber at the leading and trailing edges. Therefore, if a reflexed mean camber line is represented by a cubic, the equation will contain two arbitrary constants and may be written in the dimensionless form z/c = a[(b − 1)(7)3 – b(*/)2 + X/c]
where a and b are the arbitrary constants, and c is the airfoil chord length. Note:
LE » */c = 0 » 27c = 0
TE » */c = 1 >> 27c = 0
One can use thin-airfoil theory and these arbitrary constants to design an airfoil with specific properties. For example, a reflexed mean camber line can be manipulated to yield a zero moment about the aerodynamic center like that shown in class, or, to yield a zero-lift angle-of-attack of zero ( for a cambered airfoil !). Considering the latter case, a) determine the value of b such that the mean camber line has a specified design angle of zero lift, i. e.
AL=0 = - =o= a. 1 (cose – 1) de = 0 also, b) determine the x/c locations for the maximum and minimum camber positions. You may need the following: */c = -1/2 (cos e – 1), (%) = 1/4 (cos e – 1)2 S*cos o do = 0, $cos? do = 5. "cos?o do = 0, $cos* o do =