Journal of Engineering Mathematics

, Volume 31, Issue 2, pp 285–303

On the mechanics of the arrow: Archer's Paradox

  • B.W. Kooi
  • J.A. Sparenberg

DOI: 10.1023/A:1004262424363

Cite this article as:
Kooi, B. & Sparenberg, J. Journal of Engineering Mathematics (1997) 31: 285. doi:10.1023/A:1004262424363


In ancient bows the grip of the bow was in the way of the arrow. The arrow needed to get round the bow while being accelerated; this phenomenon is called the ‘Archer's Paradox’. In the forties it was observed experimentally with high-speed cameras that the arrow vibrates in a horizontal plane perpendicular to the vertical median plane of the bow. These movements are started and controlled by the movements of the two points of contact with the bow, viz. the middle of the string in contact with the rear end of the arrow and the grip where the arrow slides along the bow. The latter contact imposes a moving-boundary condition. The numerically obtained results are satisfactorily in agreement with experimental data. The model can be used to estimate the drawing force of ancient bows of which only the contemporary arrows are available and also for the design of new archery equipment.

Archeryarrow motionArcher's Paradoxfinite-difference techniquemoving-boundary problem

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • B.W. Kooi
    • 1
  • J.A. Sparenberg
    • 2
  1. 1.KudelstaartThe Netherlands
  2. 2.Department of Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands