To find the thickness of a blade at any points from the tip to the
root it will be sufficient to calculate the bending moment on section
at B,C, and D, fig. 49, and at corresponding points XYZ on a radial
line ZK, to draw ordinates XN, YM, and ZQ, which in length repre-
sent, on a convenient scale, the magnitude of the bending moment
at those points. That at any other point is measured by the length
of ordinate intercepted by the line OK and the curve QNK.
To find the bending moment on any section, say B, it will be
necessary to imagine the blade surface from B to A divided into
a number of narrow strips — say an inch wide. Multiply the length



174



MARINE PROPELLERS.
of one EF ( — b) in inches by the pressure p, when the load will
be bxp. This is acting at a distance BG- ( = #) so that the bending
moment = (& xp)xx inch pounds.
The B.M. due to each strip can be
calculated in the same way, and finally,
when all are added together, the sum
is the bending moment due to the
pressure on the surface BEAF.
Now if b is the breadth of blade
at a section of which it is desired to
know the thickness t and B.M. is the




Fig. 49. — Showing Curve of
Bending Moments.
Elliptical Hump Backed

Fig. 50. — Typical Screw Blade Sections.
bending maximum moment on the section, then

t--



v*



M.x/



bxs



(1)



/is a factor which, for semi-elliptical sections, may be taken as = 13
and for humpback or triangular sections 15. (Vide fig. 50.)

For best cast iron 8 = 5000, which will mean a factor of safety of
about 7.
