By E. Houghton, P. Carpenter
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Additional info for Aerodynamics for Engineering Students
57) and from the geometry Basic concepts and definitions 39 Fig. g. the stagnation pressure in the free stream). 58) can readily be converted into coefficient form. 59b) where the contour integral is evaluated by following an anti-clockwise direction around the contour C of the aerofoil. Similar arguments lead to the following relations for X. 6Xu = pubs sin E, 6Xe = pe6s sin E : 6s sin E = 6z, giving where zmuand zme are respectively the maximum and minimum values of z, and AC, is the difference between the values of C, acting on the fore and rear points of an aerofoil for a fixed value of z.
The force coefficients CX and CZ are parallel and perpendicular to the chord line, whereas the more usual coefficients CL and CD are defined with reference to the direction of the free-stream air flow. The conversion from one pair of coefficients to the other may be carried out with reference to Fig. CR is both the resultant of CX and C Z ,and of CL and CD;therefore from Fig. 19 it follows that CL = CR COS(^ + a)= CR COS y COS Q - CR sin y sin a But CRcosy = CZ and CRsin y = C x , so that CL = CZ cosa - Cxsina.
Consider what is happening at some point y along the wing span (Fig. 21). 1). This causes the flow over that section of the wing to be inclined slightly downwards from the direction of the undisturbed stream V (Fig. 22) by the angle E , the induced angle of incidence or downwash angle. The local flow is also at a slightly different speed, q. It is this effective incidence that determines the lift coefficient at that section of the wing, and thus the wing is lifting less strongly than the geometric incidence would suggest.