Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/326

§ 208 this curve at the blade extremities. This has been done arbitrarily by a pair of ordinates, the thrust grading curve thus completed being the contour of the shaded area, the area itself representing the total thrust. But this “curve” infringes a condition already laid down, that the grading must constitute a smooth curve with no sudden changes of ordinate. Hence we must compromise, and we find that the combined conditions indicate a form such as that illustrated by Fig. 129 (b).

Now the reaction normal to the blade will at every point be equal to the sternward component multiplied by sec $$(\theta + \gamma) ,$$ that is to say, if we multiply the ordinates of the thrust grading curve at every point by sec $$(\theta + \gamma)$$ we shall have the load grading curve Fig. 130 (compare Fig. 136), which represents the distribution of the pressure normal reaction along the length of the blade.

§ 209. Linear Grading and Blade Plan Form.—The linear grading for any radius is the quotient when the load value is divided by the pressure value for that radius ; thus the linear grading curve may be plotted from the other two, the ordinates being calculated by simple division (Fig. 130).

This linear grading is analogous to the aerofoil grading of § 192, and likewise represents the ordinates of the blade plan, i.e., the width of the blade from point to point for constant form of section; that is to say, all sections become geometrically similar.

Whether or not the similarity of sectional form is essential, as it would theoretically appear to be for best economy, must be