On the mechanics of the arrow: Archer's Paradox

  title={On the mechanics of the arrow: Archer's Paradox},
  author={Bob W. Kooi and Johan Adolf Sparenberg},
  journal={Journal of Engineering Mathematics},
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 Archer's Paradox and Modelling, a Review
In this paper I review physical and mathematical models dealing with the interaction between the bow and the arrow, especially the ‘Archer’s Paradox’ that is, how the arrow can follow a straight path
Arrow behaviour in the vertical plane during and immediately following the power stroke of a recurve bow
It is shown that by suitable selection of the arrow’s location on the string, the archer can obtain zero angular velocity and minimal angle of attack.
Lateral deflection of archery arrows
A whole mechanical and mathematical model of an arrow–bow motion system, which accounts for arrow deflection in the lateral plane, has been created. The arrow is modelled as a shaft within the
Arrow behaviour in the lateral plane during and immediately following the power stroke of a recurve archery bow
The method used by Kooi and Sparenberg to remove subjective components has been extended to include the carbon fibre composite arrows now used almost exclusively in competition and to consider the arrow after it has left the bow.
Bow-arrow interaction in archery.
  • B. Kooi
  • Economics
    Journal of sports sciences
  • 1998
A full description of the model of the flight of the arrow during its discharge from a bow is given and it is predicted that the arrow leaves the pressure button before it leaves the string, as reported previously.
The Behaviour of An Arrow Shot from a Compound Archery Bow
The behaviour of an arrow exiting an archery bow is of interest in relation to equipment selection and optimization, as well as to the performance of the arrow down-range. In particular, it is a
Compound-archery-bow nocking-point locus in the vertical plane
In general, the path taken by the nocking point of an archery bow in the vertical plane is not a straight line perpendicular to the rest position of the string; it may vary significantly from that.
Design and Materials in Archery
  • B. Kooi
  • Materials Science
    Materials in Sports Equipment
  • 2019
A significant part of bow tuning is vertical adjustment that strives for a zero angle of attack of the arrow. This requires laborious procedures through a lengthy and tedious trial and error phase. A
High-speed video analysis of arrow behaviour during the power stroke of a recurve archery bow
The manner in which an archer holds and releases the string of a recurve bow causes the arrow to flex during the bow’s power stroke and on its way from the bow to the target. While an experienced


On the mechanics of the modern working-recurve bow
Characteristic for the bow are the slender elastic arms or limbs. The bow is braced by putting a string shorter than the bow between the tips of the limbs. Additional deformation energy is stored in
Experimental and theoretical research in archery.
The mathematical model and computer simulation were used to describe the arrow's movement for various initial conditions and various parameters of the equipment, based on which a nomogram was constructed of the optimum arrow parameters for bows of various draw forces.
A New Method to Measure Lateral Bow Accelerations During Shooting in Archery
During the release of an arrow the bow undergoes vibrations and torsions caused by the impact of the bowstring with the tips of the limbs of the bow. These vibrations are transmitted to the entire
On the mechanics of the bow and arrow
SummarySome aspects of the dynamics of the bow and arrow have been considered. The governing equations are derived by means of Hamilton's principle. The resulting non-linear initial-boundary-value
On the static deformation of a bow
SummaryThe storage of deformation energy in a bow with or without recurve is considered. Some numerical examples are discussed. For a simple bow it is shown that theoretically a shooting efficiency
Modelling and simulation research of the competitor—bow—arrow system (in Polish)
  • PhD thesis, Academy of Physical Education, Warsaw
  • 1987
  • Patrick Stephens, Sparkford, Nr Yeovil, Somerset
  • 1992
Archery: the technical side
  • National Field Archery Association, Redlands (Ca)
  • 1947
A ”Mary Rose” archery symposium
  • Journal of the Society of Archer- Antiquaries, 26:49–51
  • 1983