Airfoils and Airfoil Systems of Finite Span

Abstract

The subject of this Chapter is the investigation of the forces experienced by an airfoil of finite span and by airfoil systems. The basic idea for the following deductions has been indicated at the end of III 32. The only point we have to add is that in the case of a single wing of ordinary type we may substitute the lift per unit span l for Λ (see III 31), and consequently take l as the principal unknown quantity. Then III (27.7) becomes:

$$ w = \frac{1}{{{e^V}}}\int\limits_{ - b}^{ + b} {dn\frac{{{{dl} \mathord{\left/ {\vphantom {{dl} {dn}}} \right. \kern-\nulldelimiterspace} {dn}}}}{{4\pi \left( {y - \eta } \right)}}} $$

((1.1))

and III (31.9), neglecting the difference between φ and tan φ:

$$ \varphi = \frac{w}{V} = \frac{1}{{{e^{{V^2}}}}}\int\limits_{ - b}^{ + b} {dn\frac{{{{dl} \mathord{\left/ {\vphantom {{dl} {dn}}} \right. \kern-\nulldelimiterspace} {dn}}}}{{4\pi \left( {y - n} \right)}}} $$

((1.2))

Now suppose that the geometrical angle of incidence of an airfoil section. defined with reference to the x axis, or what comes to the same, with reference to the horizontal velocity V, has the value α; then the effective angle of incidence i, measured from the downward sloping effective velocity, is given by¹:i = α ‒ φ