Dynamics of the Bow and Arrow

Ahyoung Choe, summer UTRA, 2013

 

Goals:

The basic principles underlying the operation of a bow and arrow are well understood. Surprisingly little is known, however, about how a bow's design affects its performance. The goals of this project were:

• To measure and characterize the deformation and motion of three representative bow designs as they fire an arrow under controlled conditions in the laboratory
• To compare the forces exerted by each bow under static and dynamic conditions
• To measure the dynamic efficiency of each bow (the ratio of the kinetic energy of the arrow after it is fired to the work done to draw the bow)
• To model the behavior of the three bows using finite element simulations, and compare the model predictions with experimental results.

Experimental Method:

Three bows were studied: (i) an Asiatic recurve bow; (ii) a traditional English longbow; and (iii) a modern, compound bow (see the figures below)

• The bows were rigidly mounted on a test-stand, and fired using a handheld bow release
• Static force-v-deflection curves were measured by drawing each bow with a spring-scale.
• The motion of the bow and the arrow were recorded using three synchronized high-speed cameras (NAC Memrecam, kindly loaned by the Naval Undersea Warfare Center, Newport) at frame rates of between 3000fps and 6000fps
• The displacement of the arrow as a function of time during a shot was determined by tracking a mark on the arrow using digital image correlation software in the MATLAB image processing toolbox (see the figures below)

 

         

 

 

    

 

Experimental results:

Selected results from the experiments are stored in the comma separated value files listed below:

• Static force-v-draw data for recurve bow (two columns: draw in m, force in N) >>
• Static force-v-draw data for longbow (two columns: draw in m, force in N) >>
• Static force-v-draw data for compound bow (two columns: draw in m, force in N) >>
• Dynamic position-v-time data for recurve bow (two columns, time in sec, position in m). Initial draw distance 47cm, arrow mass 0.031kg 3000fps >>
• Dynamic position-v-time data for longbow (two columns: time in sec, position in m). Initial draw distance 51cm, arrow mass 0.0391kg, 3000fps>>
• Dynamic position-v-time data for compound bow (two columns: time in sec, position in m). Initial draw distance 54cm, arrow mass 0.0374kg, 4500fps>>
• High-speed video of recurve bow (Initial draw distance 47cm, arrow mass 0.031kg 3000fps) >>
• High-speed video of longbow Initial draw distance 54cm, arrow mass 0.0391kg, 3000fps>>
• High-speed video of compound bow Initial draw distance 51cm, arrow mass 0.0374kg, 4500fps>>

 

The static force-v-draw curves for the three bows are plotted in the figure below