Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/284

§ 181 resistance, that is to say, least gliding angle, is given by the expression $$\beta_1 = \sqrt{\frac{\xi}{c}} ,$$ and since the aerodynamic and direct resistances are equal we have least value of $$\gamma = 2\ \sqrt{\frac{\xi}{c}} .$$ In Tables VII. and VIII. the calculated angles are given for values of $$\xi$$ ranging from .01 to .03.

'''§ 182. The Aeroplane. Anomalous Value of''' $$\xi .$$—The actual behaviour of an aeroplane presents an anomaly with regard to the value of $$\xi .$$ It has been remarked in the previous section that in the case of the pterygoid aerofoil the theoretical results can never in practice be fully realised, owing partly to the necessity of added surface and partly to other causes. In the case of the aeroplane, in spite of the fact that the same values of $$\xi$$ are employed in the calculation the reverse is the case, and investigation shows that in effect the value of $$\xi$$ is considerably less in the case of an aeroplane than its ordinary value, and may amount to no more than half the coefficient as ordinarily found