Beginning with the November issue 1930 of Ye Sylvan Archer, Dr. Hickman published a series of articles dealing with the static strains and stresses in bows. The first article was on "General Formulas for Static Strains and Stresses in Drawing a Bow". In reproducing these articles the nomenclature will be changed to conform with that used in Hickman's later work. All of the articles have been edited to delete unessential material.
Development of Formulas
It is possible to express mathematically, the tension in the string, the force on the drawing fingers, the motion of the bow tips, the strains in the bow and the work as functions of the draw.
There are many ways in which these expressions may be obtained. The method used here was selected as being best fitted to the solution of the many problems to be presented.
It must be understood that in the development of these equations, certain assumptions must be made relative to the manner in which a bow bends. The results will therefore not be exact for all bows. However, the bending of most bows is sufficiently similar to the assumptions made here so that no serious errors will be introduced. It will be shown that the mathematical results agree very closely with experimental data.
Let us assume that the bow is made up of a short rigid middle section and two limbs, which, for all positions of the draw, bend in arcs of circles. This assumption is reasonable because practically all bowyers construct their bows so that they bend in this form. In the articles referred to above, it has been shown that a very simple design having this form of bending will stress all sections of the bow equally. It is believed that for most bows this form of bending is desirable. If for some particular bow another form of bending is desired, the method used here may be applied to it.