Question

plain why the cosine series is not included in Eq. (5.23) to express the tion on a cambered airfoil. y distribu Circulation Distribution for the Cambered Airfoil s.6 143 istribution for the symmetrical airfoil as given by Eq. (5.11). This part is the form of the γ written 2V-A, ltcose later that A,-α when the airfoil is symmetrical; that is, when dzidr ofthe γ distribution depends only on the shape of the mean camber line here including the point at the leading edge. It is convenient to ex- a Fourier series and, following the form used for the first part, we write and is finite everywhere press this part as 2V.2A,sin ne for the contribution of the camber The total y distribution is the sum of the two parts and may be written y@)-2'4 Ao-cost, + ΣΑ,sinn® (5.23) when θ # π, γ 0 for all values of the coefficients; thus, Eq. (5.21) is satisfied. It remains to find the values of Ag and A, that will make Eq. (5.23) satisfy Eq. (5.22). To this end, Eq. (5.23) is substituted in Eq. (5.22), giving π Jo cose-cose, cose-cos6 The first integral on the left-hand side is of the form of the relation shown in Eq. (5.12) The second infinite series of integrals may also be evaluated by Eq. (5.12) if the trigono- metric identity sin ne-sin θ-[cos (n-le-cos (n + 1) θ] is used. After we perform these integrations and rearrange terms, the equation above becomes dz (5.24) dx The station subscript has been dropped, for it is understood that Eq. (5.24) applies to any chordwise station. The coefficients Ag and A, must satisfy Eq. (5.24) if Eq. (5.23) is to represent the γ distribution that satisfies the condition of parallel flow at the mean cam-

Answer 1

숏 inc Ouded becau e ;fwRinclude Coxsine series is no cosine入eues