BOWS AND ARROWS — KLOPSTEG 

 H R J K 



579 



Figure 6. — Graphic method of designing a bow. BT, the limb, Is divided into ten equal 

 sections. Its tip, in bending, follows the path TT', a circular arc with center at R and 

 radius t, which is 3/4 BT in length. The length of the arrow is EP; the line CA represents 

 the string on the braced bow, with CP the "bracing height"; ET' represents the string at 

 full draw. Arc BT' represents the bent limb, with radius r, the center of which is located 

 by the intersection of the line BF which is perpendicular to BT, and the perpendicular 

 bisector of chord BT'. Perpendiculars to ET' are dropped from each of the ten equally 

 spaced points B, G', H', .... Q', along the bent limb. The lengths of the perpen- 

 diculars are proportional to the respective widths of the limb at each of the ten locations. 



man and myself some 30 years ago fully substantiated the point. 

 Wlien the deflection is large, as in a fully drawn bow, the bending 

 moment per unit area is no longer uniform along the limbs. To 

 restore uniformity, widths at different points along the limbs must 

 be corrected so as to bring about the desired result of keeping the 

 bending moment per unit area constant. 



Figure 6 depicts a graphic method for determining the correct 

 widths, along its length, for a limb of uniform thickness, to achieve 

 the stated objective. Accordingly, it becomes the basis for the design 

 of a bow with limbs rectangular in section, uniformly stressed. 



Hickman showed that when a limb is bent in a circular arc, the 

 path of its tip closely follows a circle having a radius three-fourths 

 the length of the limb, its center being on the limb. This simple con- 

 struction enables one to draw a circular arc representing the bent 

 limb for any length of draw. The procedure for determining the 



