578 ANNTJAL REPORT SMITHSONIAN INSTITUTION, 196 2 



BACK 



TENSION 



Figure 5. — (a) Section of a stacked limb. CD is the neutral axis, containing CM, the 

 center of mass of the section, (b) Force diagram at this section of the stressed limb 

 showing proportionality of fiber stress and distance from the neutral axis. 



responding distance to the outer surface of the belly. Since the maxi- 

 mum tension and compression occur at the outer surfaces, the back is 

 subject to lower maximum stress in tension than is the belly in com- 

 pression. It is a general characteristic of wood, both from the stand- 

 point of intrinsic strength and of imperfections, that it can withstand 

 greater tension than compression without failure. Thus, in a stacked 

 limb, forces to which the wood is subjected are not matched with the 

 strength characteristics of the wood. This confirms the previous 

 statement that in the longbow the qualities of the wood are not prop- 

 erly exploited. From mechanical considerations it would be better 

 to reverse the shape of the limb, so as to make the stacked side the 

 back and the flat side the belly. It is now evident why the longbow 

 must be long to withstand the stresses to which it is subjected in use. 

 In a working bow, made of wood with suitable elastic properties, the 

 energy in the bent limbs resides in the stresses set up in them as the 

 bow is drawn. Wlien the arrow is loosed, the wood tends to spring 

 back toward its unstressed configuration. The best use of the wood or 

 other resilient material is made when the maximum tensile and com- 

 pressive forces are constant throughout the length of the limbs, with 

 constant bending moment per unit area at any section. The condition 

 can be approximated in a limb of uniform thickness, rectangular in 

 section, bending in a circular arc. In handbooks of engineering one 

 finds that a cantilever beam of uniform thickness, tapering from 

 finite width at the point of support to zero width at its free end, with 

 loading at the end, bends in a circular arc with light loading and 

 small deflection. Hickman pointed out this simple fact and sug- 

 gested that a bow with limbs rectangular in section, of uniform tliick- 

 ness and taper, would more effectively utilize the resilient qualities 

 of the wood than does the longbow. Experiments carried on by Hick- 



