Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/224

on the plane for all angles from degree 0 to 90 degrees, we have curves plotted as follows:—

(A)	The Newtonian or sine2 law—
$P_{\beta }=P_{90}\ \sin ^{2}\beta ;$
(B)	According to an empirical formula proposed by Duchemin
$P_{\beta }=P_{90}\ {\frac {2\ \sin \beta }{1+\sin ^{2}\beta }};$
(C)	From the experiments of Langley;
(D)	From the experiments of Dines.

Fig. 93. It will be noticed that the Newtonian curve does not accord with any of the experimentally ascertained curves, which latter do not even agree very closely amongst themselves. Perhaps the most salient facts connected with these curves are the close agreement between Langley and Duchemin (an agreement pointed out by Langley in his Memoir), and the remarkable disagreement in the curve of Dines, characterised by an erratic “kick up,” a maximum being recorded at or about 55 degrees angle, at which point the pressure is actually greater than when the plane

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