Arrow Vibration - Introduction

The opinions disseminated about arrow vibration and nodes during the bow power stroke have probably generated more nonsense than any other topic in archery. Somehow the knowledge that an arrow bends became "transposed" into the arrow undergoing a simple spring type oscillation. Then the opinion that arrows had vibrational nodes was invented. Then the opinion that these "nodes" travelled along the plane of the bow was invented. Then the opinion that the alignment of these nodes had something to do with tuning was invented...oh dear....rather like someone looking at a map of the world in at atlas, not realising that it was only a schematic representation and going away believing that the world was flat.

Arrow behaviour on the bow is extremely complicated. For a (simplified) treatment of arrow launch mechanics I suggest you read through the technical papers of Bob Kooi (these at least are available on the web).

When the arrow leaves a bow it's bent and vibrates all the way to the target. We can maybe have some speculative opinions about the effect of arrow vibration on arrow flight

Arrow Euler Buckling

The various models of arrow behaviour during the launch phase on the bow (Pekalski, Kooi etc.) have all started from the basis of the arrow being a vibrating beam. This is, as was known by the authors, technically incorrect. The reason for starting with a vibrating beam is that the mechanics is "do-able" in terms of producing results and the approach is justified on the basis that there is a good agreement between the modelling results and the observed arrow behaviour.

In practice the bending of the arrow during launch is the result of a mechanism known as slender column buckling. If the axial load on the arrow exceeds a critical value then the arrow shaft will bend (and fail). The problem is that a mathemetical description of the actual dynamics of arrow behaviour on the bow, in terms of buckling, is extremely complicated and to date no one has attempted to climb this Everest (assuming it's possible).

The following comment is from Liston's book on archery physics (relates to a conventional aluminium arrow):

`The author tried nocking an arrow and gradually pushing against a block. When the bow was about half way drawn it became obvious that the arrow was becoming unstable and would break if the experiment were continued.'

The above experiment demonstrates quite a number of facets of arrow on-bow behaviour:

• The first point is that the forces on an arrow during launch have nothing to do with the draw force curve. The instantaneous load on an arrow shaft is the product of the arrow mass and the instantaneous arrow acceleration. For example with two identical bow set ups if with one setup you added a 1Kg weight to each limb tip then while the two bows would still have (excluding gravity effects) the same draw force curve the arrow accelerations (and hence initial arrow speeds) would be very different.
• Clearly the draw force of the bow far exceeded the critical (buckling) load for the arrow shaft. That an arrow bends during launch for a recurve bow indicates that the arrow critical load is being exceeded. Conversely for a compound bow or crossbow where there is no riser clearance "Archer's Paradox" requirement an arrow design parameter is that the critical load is not exceeded during the launch phase i.e. the arrow doesn't buckle. Any shaft bending with a compound/cross bow would generate torque on the arrow and you would be in the same "tuning" situation as for a recurve.
  Blythe in his paper Ballistic Properties in ancient Egyptian Arrows derives an "archers" version of the buckling equation in terms of the "spine" value for an arrow and illustrates the calculation of the critical load for an arrow shaft. (see also Arrow selection & buckling).
• It is worth re-emphasising that the Archer's Paradox bending of an arrow shaft is not, as sometimes stated, a result of the action of the archer's finger release on the arrow. Variations in the finger release will effect the arrow shaft behaviour but is is only an "initial condition" as regards arrow behaviour.
• An interesting point about Liston's experiment is that although the critical load was exceed the arrow shaft did not catastrophically fail but just bent. The reason was that there is a built in safety mechanism. If the critical load is exceeded and the shaft starts to buckle then the amount the arrow is drawn reduces, dropping the load on the shaft below the critical value. An arrow being shot normally from a bow has a similar safety mechanism which is when the critical load is exceeded and the shaft starts to bend a consequence of the bending is an increased acceleration of the free front of the arrow. This topic was discussed previously under the heading Archers Paradox. Of course there are limits to the spine to mass ratio for an arrow shaft as regards failure during launch. To quote from Blythe's paper:

  Common sense suggests that there must be some absolute lower limit to the stiffness of an arrow, in relation to its weight or mass, below which it will not leave the bow at all, but collapse under its own inertia. In practice, Mr. Hardy has described to me how a flight arrow designed for a 40 lb. bow seemed to explode when shot in an 80 lb. bow.

Last Revision 24 January 2013