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Aerodynamics Question From Foundations of Aerodynamics by Kuethe and Chow, Probl

ID: 1996673 • Letter: A

Question

Aerodynamics Question

From Foundations of Aerodynamics by Kuethe and Chow, Problem 6.5.1

A wing with an elliptical planform is flying through sea-level air at a speed of 45 m/s. The wing loading WIS = 1000 N/m^2. The wing is untwisted and has the same section from root to tip. The lift curve slope of the section m_0 is 5.7. The span of the wing is 10 m, and the aspect ratio is 5. Find the sectional-lift and induced-drag coefficients. Find also the effective, induced, and absolute angles of attack. What is the power that is required to overcome the induced drag of the wing?

Explanation / Answer

Given data:

Free stream velocity (v0) = 45m/s

Wing loading (W/S) = 1000N/m2

Slope (m0)                   = 5.7

Wing span(b)               = 10 m

Aspect ratio(AR)       = 5

To find:

                  Rho = 1.225kg/m3   ( density of air at sea level)

Since the wing is an elliptical platform the sectional lift coefficient is equal to wing lift coefficient.

         = (0.8062)2/(3.14*5)

   CDi = 0.041

      = 0.8062/5.7

    = - 0.041/0.8062

   = - 0.05 rad

     = 0.1414 + 0.05

     = 0.1922 rad

                                    Di = CDi * 0.5*rho*v2*S

                                          = [(CL)2 * 0.5*rho*v2*S]/ (pi*AR)

                                     Di = [{W/(0.5*rho*v2)*S}2* 0.5*rho*v2*S]/ (pi*AR)

                                          AR = b2/S       

                                          5 = 102/S,

                                          S = 20 m2

    W/S = 1000,     W = 1000*20 = 20000N

Equating we get

                              Di = [1/(pi*0.5*rho*v2)]*[W/b]2

                                    = [1/(3.14*0.5*1.225*452)]*[20000/10]2

                                                      = 1026.54 N

Power Required           PR        = Di * v0

                                                 = 1026 * 45

                                                  = 46194 N

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