Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/346

§ 218 (5) Calculate the values of $$V^2$$ for different points along the blade (§ 207), and divide the values of the ordinates of the load grading curve $$c\ c\ c$$ by the corresponding values of $$V^2 ,$$ and draw a curve representing the quotient. This is the linear grading curve $$d\ d\ d$$ and represents the relative height of the arched section at every point along the blade. (Compare § 192.)

(6) The "plan form" or "development" of the blade may now be laid out. If we proceed on the lines indicated by present theory, the plan form will be everywhere proportional to the linear grading; thus we have to settle the aspect ratio of the blade, lay off the maximum width, and draw a curve whose ordinates from point to point are proportional to the linear grading ordinates (Fig. 137 (a)). If we adopt this design of blade the sectional form, will be constant throughout the length, varying only in its scale; that is to say, the materialised $$\alpha$$ and $$\beta$$ angles will be everywhere the same (Fig. 137).

The theory may possibly be incomplete; as discussed in §§ 190, 191, 192, etc., there may be some unformulated objection to the pointed extremities to which present theory gives rise. If this is the case the section will become flatter towards the extremities, the linear grading remaining the same and the width of the blade becoming greater. If we take the elliptical aerofoil as our model we may derive the corresponding blade form by the construction given in Fig. 138, elliptical ordinates being substituted at every point for the corresponding parabolic or segmental ordinate.

(7) If such a modified plan form is adopted the sectional form