The following diagrams illustrate schematically the behaviour of an arrow (blue line) when being accelerated by the bow. The red line represents the plane of the bow. The diamond markers represent from left to right the full draw position, bracing height and pressure button.

The sideways acceleration of the nock away from the bow by the fingers and the load on the arrow from the bow string start to buckle the arrow. At this point there is no interaction with the pressure button. Note that the rear part of the shaft bends away from the bow not as sometimes described the shaft bending towards the bow.

The arrow continues to buckle and the shaft is rotated into the pressure button. The resulting force between the arrow and button result in the shaft section in front of the button bending away from the bow and consequently the shaft section to the rear of the button swivelling into the bow. At this point the arrow shaft sections in front of, and to the rear of the button have different mechanical behavior. This is plausibly the origin of the problem of "arrow forgiveness" if the length of shaft in front of the button is too great.

The nock of the arrow has now reached it's maximum displacement out of the plane of the bow. There is now no force between the arrow shaft and button. The shaft has 'stabilised' into a smooth curve and the entire shaft (ignoring effects of the pile insert) now behaves as a single mechanical unit.

Because the nock of the arrow was displaced sideways out of the plane of the bow there is a torsion spring effect (the twisting of the limbs) pulling the nock rapidly towards the bow. At the same time the bent shaft starts to spring back and of course the string force applies a bending moment buckling the arrow. The result is the shaft quickly forms a bent shape opposite to the original one and the arrow nock is bent/rotated towards the plane of the bow.

When the nock of the arrow reaches the plane of the bow, because of momentum, it keeps going and travels a short distance past this point before reversing the directon of motion. The curvature of the arrow is still away from the bow. As the nock travels back towards the plane of the bow the string exists the nock groove. The combination of the string deceleration direction with the orientation and rotation of the arrow nock are aimed at minimising any lateral tweak on the nock from the string at exit. One condition for this to occur is that the arrow shaft is near maximum bend i.e. when the nock transverse velocity is near minimum.

After the arrow leaves the string it starts to vibrate as a free-free beam so the nock end of the arrow starts to move away from the bow. The aim is to have the end of the arrow having sufficient clearance with respect to the bow riser (shaft selection) and the arrow to have overall near zero rotation (tuning).

The following graph shows the displacement of the arrow nock from the plane of the bow (the horizontal dotted line flagged '0') as function of time as calculated by the Kooi/Sparenberg Archers Paradox model (see reference on Contents page). Nock paths for stiff/weak arrows are included for comparison with a well matched arrow.

The red dots approximately correspond in sequence to the schematic drawings above.

The following graph shows the physical behaviour of the arrow based on measurement and on mechanical modelling (Pekalski and the Kooi/Sparenberg Archers Paradox model (see reference on Contents page).

The following are video based graphics from high speed films illustrating arrow behaviour from Bertil Olssen's web site. Use the back button at the bottom to see the other goodies available on the site.

Last Revision 1 July 2009