Figure 2 shows an uncambered, rectangular wing with span b, chord c and aspect ratio AR-b/c=10.

Model this wing using a single horseshoe vortex with a constant strength F and its bound vortex at

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(a) Calculate the induced velocity (V) of the horseshoe vortex at the control point P (=

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,0,0). (10 %)

(6) Continuing with the flow model from (a), determine the strength of the filament such that flow tangency is satisfied at the control point for an angle of attack, a. Assume that the thickness of the wing and the angle of attack a are small. (10 %)

(c) The lift on the wing can be found using a three-dimensional form of the Kutta-Joukowsky theorem, specifically, L =p. V.b. Combining this with the results from (b), find the lift slope (i.e. dC/da) for this wing with AR=b/c=10.

Figure 2 shows an uncambered, rectangular wing with span b, chord c and aspect ratio ARb/c=10. Model this wing using a single horseshoe vortex with a constant strength r and its bound vortex at the quarter-chord line (xc/4) of the wing as shown in figure beloy. 816=8y (a) Calculate the induced velocity (Vi) of the horseshoe vortex at the control point P(=43c,0,0).(10%) (b) Continuing with the flow model from (a), determine the strength of the filament (C) such that flow tangency is satisfied at the control point for an angle of attack, a. Assume that the thickness of the wing and the angle of attack a are small. (10%) (c) The lift on the wing can be found using a three-dimensional form of the Kutta-Joukowsky theorem, specifically, L=0Vwb. Combining this with the results from (b), find the lift slope (i.e. dC2/d ) for this wing with AR=b/c=10. ( 10%) Hint: From Biot-Savart law, he induced velocity of a straight vortex filament segment AB at P is V=4d1(cos1+cos2)