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Fiber Stresses in Bows
Part 4 of 5

The reason for selecting these two sections on the bow was to show that the maximum stress exists where the bow took its greatest set. There was no set near the handle but it was very great about 15 inches from the ends of the bow.

On first thought this may be confusing to the reader because we have previously stated that the fiber stress occurs where the bow is thickest. That statement however applies only to a bow the limbs of which bend in arcs of a circle. Obviously this bow does not bend in the arc of a circle. However a casual observation would not reveal this difficulty. An apparently small change in curvature will make a big difference in the stresses.

There is one more point in connection with the cross-section of a bow which should be mentioned. Many bows arc worked beyond the elastic limit, but of course not beyond the modulus of rupture.

It has been shown by the Forests Products Laboratory that the modulus of rupture for compression is much lower than the modulus of rupture for extension. In all of the tests which they make in determining the modulus of rupture for static bending, it is the compression side which gives way first. This moves the neutral plane closer to the extension side so that the radius of curvature is increased at this point until finally the extension side gives way.

The archer must not be confused by the fact that a bow always breaks on the back. This happens only because the belly gives way and thus causes greater extension stress along the back by the shift of the neutral plane. The archer does know that a bow will break where there is a bad chrysal on the belly side. Here he observes the belly fault before the break occurs.

In most woods which they have tested, the modulus of rupture for extension is over twice as high as for compression. (By modulus of rupture is meant the maximum fiber stress in pounds per square inch at the breaking point.)

In like manner the elastic limit for extension is over twice as high as the elastic limit for compression.

The orthodox cross-section of a bow is such as to make the fiber stress on the belly or compression side greatest. On the other hand, wood will not stand as much compression as extension. Why then do we not construct bows with the belly side flat and the back side narrow so as to take advantage of the greater elastic limit of extension?