Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/349

Rh of the blade should be designed at every point to suit the width and grading, the angles $$\alpha$$ and $$\beta$$ having appropriate values assigned from point to point, according to the value of the constant $$\epsilon$$. It is possible that the constant $$\epsilon$$ ought to vary from point to point along the blade; if this is so it is a matter on which we have so far no information; for the present it should be taken as the aerofoil value of $$\epsilon$$ proper to the value of $$n$$ employed.

In Fig. 137 the blade is supposed continued to connect to the boss. Such continuation is always necessary, unless a boss of very large diameter is employed, the continuation being of stream-line section symmetrically disposed about the pitch helix. It will be observed that the linear grading falls with extreme rapidity as the inner "extremity" of the blade is approached, and thus the change of form from the pterygoid to the symmetrical stream-line section is very abrupt. It is probably advantageous to carry the pterygoid section beyond the theoretical blade limit and so merge it more gradually into the simple form. No cognisance of this structural feature has been taken in the hypothesis.

It should be remembered that the $$\theta + \gamma$$ spiral is at every point the analogue of the horizontal line, and the one from which the $$\alpha$$ $$\beta$$ angles are laid off; on this basis the setting out of the section is the same as for an ordinary aerofoil, but the full "dip" forward can be given to the section, since the possibility of the loss of equilibrium is no longer a factor (§ 138).

Parenthetically it may be remarked that the $$\theta + \gamma$$ series of spirals does not form a helix, for the angle $$\gamma$$ is constant at all points. This would usually be expressed by saying that the pitch of the blade increases towards the tip, but we know that the ordinary manner of defining the pitch by the mean angle of the blade is unscientific.

(7) Number of blades. The determination of the maximum number of blades permissible has been discussed in § 211, and it has been shown that this depends but little upon the