Archery Bow Design Equation

Bow and arrow is one of the ancient combat tool used for defense, hunting and in recent times, used in sports. There have been several improvements in archery since then. Bows, as we know today are made from several components, materials and are available in different shapes and designs. There have been several variations in the bow design, broadly categorized under traditional bow or long bow, recurve bow, cross bow and compound bow. They may look very different and may have different efficiency but their underlying principle of operations have not changed much in past decades. There have been several studies and patents filed for new designs of the bows to improve the efficiency and several accessories have also been introduced to improve targeting, stability, and power. In this study using laws of physics, a design equation has been established which can be used as basis for deriving various aspects of the bow design and can be used for creating new bow designs with added efficiency. The bow design equation in this study is named as ‘RV bow design equation’ which is split into three parts to cover the aspect of arrow mass, energy stored in the bow, and energy transferred to arrow to give designers holistic view of the bow design and ability to monitor several parameters independently and in conjunction to each other. This equation will facilitate designers to make informed decisions about several aspects of the bow and they can use this equation to maximize the energy or velocity output of the arrow with a given design and material used for construction.