Bob Kooi's Archery publications

You can download the manuscripts of papers on Archery from this homepage.

The manuscripts of the papers are available in PDF [P] and PostScript [A] format. You need Acrobat Reader to be able to read and print the PDF files. PostScript files can be printed only on PostScript printers or viewed on the screen with GhostView.

If you make a citation to the papers, please refer to the published version in the scientific journal. Notice that the numbering of the Equations, Figures and Tables generally differ from those in the original paper. Therefore, please check these numbers when you really want to refer to Equations, Figures or Tables.

There are three categories. The first two categories are Mechanics of the bow dealing with the behaviour of the bow where the arrow is treated simply as a point mass, and Mechanics of the arrow dealing with the motion of the arrow and where the model for the bow is rather simple. The third category is formed by the papers published in the Journal of the Society of Archer-Antiquaries. Information about the Society of Archer-Antiquaries is given here: SOAA.

Mechanics of the bow

These papers deal with the modelling of the dynamics of the bow where the arrow is assumed to be a point-mass which is attached to the middle of the string. A numerical scheme for the solution of the governing equations is developed. Different types of bows are distinguished and their static and dynamic behaviour are studied. The performances are assessed by comparison of quality coefficients such as the efficiency. In the introduction of the PhD-thesis an overview of models for the dynamics of the bow published in the literature is given.

In the article written together with Dr. C. Tuijn (University of Amsterdam, The Netherlands) an experimental set-up is described to measure the velocity of an arrow accurately. This technique was also used by Ide-Teknik, Bertil Olsen. The paper with Dr. C.A. Bergman (Northen Kentucky University and 3D Environmental Services, Inc. 781 Neeb Road, Cincinnati OH 45233-4625, USA) describes the modelling aspects for those who do not like formulae.

Kooi, B.W. & Sparenberg, J.A. 1980 On the static deformation of a bow. Journal of Engineering Mathematics, 14(1):27-45.
[ ]pdf-file (216 Kb) [
  ]PostScript-file (694 Kb)

Kooi B.W. 1981 On the mechanics of the bow and arrow. Journal of Engineering Mathematics, 15:119-145.
[X]pdf-file (262 Kb) [A]PostScript-file (721 Kb)

Kooi B.W. 1983 On the Mechanics of the Bow and Arrow. PhD thesis, Rijksuniversiteit Groningen.
[ ]pdf-file (1.36 Mb) [A]PostScript-file (3.5 Mb)

Kooi, B.W. 1991. The 'cut and try' method in the design of the bow. In Eschenauer H. A., Mattheck C., and Olhoff N., editors, Engineering Optimization in Design Processes, volume 63 of Lecture Notes in Engineering, pages 283-292, Berlin. Springer-Verlag.
[ ]pdf-file (318 Kb) [A]PostScript-file (723 Kb)

Kooi, B.W. 1991. On the mechanics of the modern working-recurve bow. Computational Mechanics, 8: 291-304.
[ ]pdf-file (372 Kb) [A]PostScript-file (923 Kb)

Kooi, B.W. 1994. The Design of the Bow. Proc. Kon. Ned. Akad. v. Wetensch, 97(3), 283-309.
[ ]pdf-file (329 Kb) [A]PostScript-file (697 Kb)

Tuijn, C. & Kooi, B.W. 1992. The measurement of arrow velocities in the students' laboratory. European Journal of Physics, 13:127-134.
[ ]pdf-file (195 Kb) [A]PostScript-file (473 Kb)

Kooi, B.W. & Bergman, C.A. 1997. An Approach to the Study of Ancient Archery using Mathematical Modelling. Antiquity, 71:124-134.
[ ]pdf-file (209 Kb) [A]PostScript-file (1062 Kb)

Back to top

Mechanics of the arrow

In these article I deal with the motion of the arrow when it is released from the bow. The mathematical model is derived by considering the arrow as a vibrating beam with time-dependent boundary conditions. The governing equations are solved numerically. In the second paper our model is compared with a model proposed by Pekalski from Poland who did experiments in addition to modelling. The last paper is a review of published articles on the ``The Archer's Paradox".

Kooi, B.W. & Sparenberg, J.A. 1997. On the Mechanics of the Arrow: Archer's Paradox. Journal of Engineering Mathematics, 31(4):285-306.
[ ]pdf-file (335 Kb) [A]PostScript-file (694 Kb)

Kooi, B.W. 1998. Bow-arrow interaction in archery. Journal of Sport Sciences, 16:721-731.
[ ]pdf-file (276 Kb) [A]PostScript-file (552 Kb)

Kooi, B.W. 1998. The Archer's Paradox and Modelling, a Review. History of Technology, 20:125-137.
[ ]pdf-file (249 Kb) [A]PostScript-file (425 Kb)

Back to top

Journal of the Society of Archer-Antiquaries papers

The following articles are published in the Journal of the Society of Archer-Antiquaries are written for non-mathematicians. I tried to explain the train of thought with building a mathematical model (without describing it with formulae) and to define quality coefficients which describe the quality of a bow-arrow combination quantitatively.

Kooi, B.W. 1991. Archery and Mathematical Modelling. Journal of the Society of Archer-Antiquaries, 34:21-29.
[ ]pdf-file (169 Kb) [A]PostScript-file (361 Kb)

Kooi, B.W. 1993. On the Mechanics of some Replica Bows. Journal of the Society of Archer-Antiquaries, 36:14-18.
[ ]pdf-file (147 Kb) [A]PostScript-file (231 Kb)

Kooi, B.W. 1996. Functioning of ears and set-back at grip of Asiatic bows. Journal of the Society of Archer-Antiquaries, 39:73-77.
[pdf]pdf-file (205 Kb) [A]PostScript-file (383 Kb)

Lanting, J.N., Kooi, B.W., Casparie, W.A. & van Hinte, R. 1999. Bows from the Netherlands. Journal of the Society of Archer-Antiquaries, 42:7-10.
[ ]pdf-file (195 Kb) [A]PostScript-file (473 Kb)

Other references and links

I was involved in testing the Mary Rose bows together with Prof. P.Pratt from Imperial College of Science & Technology, London. This work is reported in:

Hardy, R. The Longbow Patrick Stephens 1992, page 209-221

Strickland, M and Hardy, R. The Great Warbow Sutton Publishing Phonix Mill, Thrupp, Sroud, Gloucestershir, GL5 2BU, UK, 2005, page 3-33.

See also: Paterson, W.F. 1980, "Mary Rose" - A Preliminary Report Journal of the Society of Archer-Antiquaries, 23, 29-34, and Paterson, W. F. 1981, "Mary Rose" - A Second Report Journal of the Society of Archer-Antiquaries, 24, 4-6, and the comments I made in the article in the Journal: Kooi, B.W. 1991, Archery and Mathematical Modelling., Journal of the Society of Archer-Antiquaries, 34:21-29.

You can find more information on the mechanics of archery on Joe Tapley's home page: Some notes on the Mechanics of Archery


Back to top


Bob Kooi
Fri July 16 2004

Valid HTML 4.01!