The basic physics of archery has in principle been understood for around 80 years. The last topic to be theoretically described was vortex shedding (aerodynamics) in the 1920's related to developments in the aircraft industry. While the principles of archery are understood, in practice the behaviour of the bow/arrow/archer system (termed 'interior ballistics') and the arrow in flight (termed 'exterior ballistics') are somewhat complicated. In order to understand the mechanics of archery computer models are required.

Models related to interior ballistics have been developed over the years becoming more realistic (and complex). A few related papers are listed below:

**Kooi, B.W. 1994. The Design of the Bow. Proc.Kon.Ned.Akad. v. Wetensch
, 97(3), 283-309**

The design and construction of various bow types is investigated and a mathematical model is used to assess the resulting effects on the (point mass) shot arrow.

**Kooi, B.W. & Bergman, C.A. 1997. An approach to the study of Ancient
Archery using Mathematical Modelling. Antiquity, 71:124-134.**

Interesting comparison between the characteristics and performance of various historical and current bow designs.

**Kooi, B.W. & Sparenberg, J. A. 1997. On the Mechanics of
the Arrow: Archer's Paradox.
Journal of Engineering Mathematics 31(4):285-306 **

A mathematical model of the behaviour of the arrow when being shot from a bow including the effects of the pressure button and bow torsional rigidity. The string forces applied to the arrow are derived from the bow model referenced above.

You can download most of the archery papers by Bob Kooi et al (in PDF/Postscript format) from the following link Archery Mechanics Papers. While inevitably many of the papers have a highly technical content there are non-mathematical versions which cover the general concepts and conclusions.

More recently a similar approach used by Kooi for lateral arrow behaviour has been used by Ihor Zanekvskyy to model recurve bow behaviour in the vertical plane addressing issues of arrow and bow behaviour, biomechanics, bow tuning and stabilization. A few of these papers are listed below.

**Zanevskyy Ihor 2006 Archer-Bow-Arrow behaviour in the vertical plane
Acta of Bioengineering and Biomechanics, Vol. 8, No. 1, 2006**

A model which incorporates the archer, the bow and the arrow as an interactive mechanical system.

**Zanevskyy Ihor 2008 Modeling and Computer Simulation of Bow Stabilization in the Vertical Plane
International Journal of Sports Science and Engineering Vol. 02 (2008) No. 01, pp. 03-14**

The aim of the research is to develop a method of mechanical and mathematical modeling and computer simulation of dynamic stabilization of bow rotation in the vertical plane intending to get practical recommendations for the sport of archery.

**Zanevskyy Ihor 2006 Bow tuning in the vertical plane
Sports Engineering 05/2006; 9(2):77-86.**

The goal of the research was to create an analytical method to determine an optimal combination of bow parameters, which ensures zero angle of attack for an arrow launched from a string. Mechanical and mathematical models of bow and arrow geometry in the vertical plane in braced and drawn situations were investigated.

Realistic mathematical models for the exterior ballistics of arrow flight, while simpler than the interior ballistics, are as far as I know non-existant. You can at least download a couple of (incomplete) models from this site.

Recently a group in Japan have been carrying out wind tunnel and free flight experiments to investigate arrow aerodynamic properties. Some related published papers are listed below:

- Aerodynamic properties of an arrow: Influence of point shape on the boundary layer transition K Mukaiyama et al, Procedia Engineering 13 (2011) 265-270
- Aerodynamic properties of an archery arrow Takeshi Miyazaki et al,
- Free flight and wind tunnel measurements of the drag exerted on an archery arrow K. Okawa et al, Procedia Engineering 60 ( 2013 ) 67-72

For downloads or links to these and other articles also refer to the bibliography.

I have attempted here to put together a basic (laymans) guide to the bow/arrow system and arrow flight. The guide is not complete and comprises bits and pieces added when and if I have the time and inclination.

My thanks to those archers who have commented on the content and pointed out ommissions and errors I have made.

Joe Tapley June 2000

*Last Revision 4 July 2014*