The plunger button is a fine tuning device enabling control of how much
rotation the arrow has in the horizontal plane when leaving the bow. The
aim is to have the 'perfectly shot' arrow leaving the bow with zero horizontal
rotation. Rotation is generated by the action of the string force on the
arrow where a torque is generated if the string force does not run through
the arrow centre of mass.
Basic Torque Concepts
In the diagram the string force initially runs through the arrow
centre of mass - no torque and no rotation. In the middle drawing the arrow
has been rotated clockwise.
This moves the centre of mass to the
right and there is now a torque generating a clockwise rotation. In the
right hand drawing the arrow has bent to the right moving the centre
of mass to the right and there is now a torque generating a clockwise rotation.
The bigger the perpendicular distance between the centre of mass and the
line of the string force then the larger the resulting torque. While the
arrow is being accelerated by the string it is continuously rotating
and bending. As a consequence the arrow centre of mass is continually changing
position moving towards and away from the bow. At the same time, during
the shot, the direction of the string force is continually changing because
of the archers paradox effect and the nock moving forward. The magnitude
of the string force is continually changing as the nock moves forward.
Basic Spring Concepts
The more you compress a spring then the higher the force the spring exerts.
The relationship between the force exerted by the spring and the amount
of spring depression is given by:
Force = constant x depression + preset
The spring 'constant' is how much the force exerted by the spring increases
as you depress it. If you look in your button package the spindly looking
spring has a low spring constant and the one that looks as though you could
use it in a pogo stick has a high spring constant. The 'preset' is how much
initial compression there is in the spring (the starting force). As you
'tighten' the spring you increase the preset on the string. The above graph
illustrates how two springs behave (one spring has two different presets
hence the three lines). Lets suppose the aim is to compress the string
to reach a specific spring force - the green line. The blue and red lines
are the same spring (same spring constant hence the slope of the two lines
are the same). The blue spring has a higher preset then the red spring
so the button (spring) depression required to reach the green line for
the blue spring is lower than for the red spring. The blue spring starts
off with a higher spring force and over the same distance of travel the force
from the blue spring is always higher than from the red spring. The action
of an arrow 'bouncing' off a plunger button is a dynamic situation
i.e. it is time dependant. The time taken for the plunger button to reach
the green line will probably be shorter for the blue spring than for the
red spring so the effect on the arrow will be different for the blue and
red springs. The purple line represents a diferent spring with different
spring constant (line slope) and different preset.
Plunger Button Operation
There are two forces on the plunger button. The arrow shaft exerts a force
Fa towards the bow and the spring exerts a force Fs away from the bow.
The overall force on the plunger is Fa-Fs and this net force equals the
effective mass (plunger + spring + friction) multiplied by the acceleration
of the plunger towards the bow. The higher the spring force then the lower
the plunger acceleration and so the less it depresses in a given time.
In the following discussion a right handed archer is assumed and direction
of rotation is as seen looking down on the archer.
Over the whole shot one of the effects of the overall torque history on the arrow is to have the arrow leaving the string with some angular momentum
(rotation) in the horizontal plane (fishtailing). This rotation can be in
a clockwise or anti-clockwise direction depending on the torque 'history'
during the shot. If the arrow leaves the string with clockwise rotation
then drag will accelerate the arrow to the right. If the arrow leaves the
string with anti-clockwise rotation then drag will accelerate the arrow
to the left.
What we want to achieve is that when the arrow leaves the string it has
zero angular momentum (rotation) in the horizontal plane (ignoring bow
elevation). In this case the arrow will fly straight towards the target.
The plunger button allows the archer some control over the rotation the
arrow has leaving the bow because with it you have some control over the
sideways movement of the arrow centre of mass and hence some control over
the torque input to the arrow.
There are two main adjustments you can set with a pressure button, the
initial position of the button (screw it in or out) and the spring characteristics
(initial spring force and how the spring force varies as the button is depressed).
What complicates the tuning process is that these two adjustments are not
independant of each other in terms of what the arrow ends up doing.
At full draw prior to release the string force normally runs on the
bow side of the arrow centre of mass (the arrow is is normally set up with
the pile rotated anti-clockwise away from the bow).
The diagram illustrates the basic effect of the intial button position.
As the button is screwed out the arrow centre of mass moves away
from the line of the string force increasing the initial (anti-clockwise)
torque setup. (The torque lever is the perpendicular distance from the
centre of mass to the line of the string force). There are recommendations
from arrow manufacturers and general archers 'lore' on about where this
initial button position should be.(ref)
With the finger release the nock is accelerated away from the bow so the arrow is rotated clockwise.This moves the arrow alignment towards the plane of the bow and puts a bend in the arrow sufficient for the string force when it comes onto the end of the arrow to produce a clockwise orientated torque on the arrow and buckle the arrow in the sense for the nock to move away from the bow. This clockwise torque and the buckling force is dependant on the intitial arrow orientation before release i.e. the initial button centreshot position.
The combined effect of the string torque and arrow buckling is to rotate the front part of the arrow
shaft into the bow. The shaft accelerates the pressure button plunger into the bow. The force between
the shaft and the plunger depends on the effective mass of the plunger (plunger weight, spring weight,
spring force and friction) and the rate of plunger acceleration (determined by the string torque and
amount of shaft buckling). The overall force between the arrow and plunger will depend on factors
like the draw weight and the arrow length as well as the centreshot position. My guess is that for a
typical male archer with the draw
weight in the 40-50 pounds region the force between the shaft and the plunger will lie somewhere
around 400 to 600 grams weight equivalent.
As the button is depressed the arrow as a whole rotates towards the bow. The combined effect of the button force on the shaft and the pile inertia act to bend the front section of the arrow in the sense that the shaft in front of the button moves away from the bow and the shaft behind the button moves towards the bow. Overall the more the button is depressed the more the arrow centre of mass moves towards the bow and hence the higher the string torque on the arrow generating clockwise rotation (producing a 'weaker' arrow).
When you adjust the pressure button spring you are making fine adjustments to the effective mass of the plunger. If you increase the spring
strength you are effecively increasing the effective plunger mass. This increases the force between the shaft and button
(the front of the shaft will bend more) but more importantly you reduce the amount the arrow rotates into the bow reducing the clockwise
string torque and hence the clockwise rotation. The bending/rotation effects act against each other with respect to movement of the arrow centre
of mass so spring force adjustment is a very sensitive control of how much horizontal rotation the arrow ends up with.
The weaker the arrow the more it will buckle at the rear end and the more clockwise string torque will be generated. The arrow rotation into
the button will increase. To tune a weak arrow therefore you have to increase the button spring tension to keep the arrow centre of mass way from
the bow and thereby reducing the amount of string torque on the arrow you get. For a stiff arrow you need to do the opposite, reduce the button
spring force.
To summarise the centreshot position and the button spring provide control of the sideways movement of the arrow centre of mass in the initial part of the shot (while the arrow is in contact with the plunger button) and hence some control of the amount of overall angular momentum (rotation) the arrow ends up with when it leaves the string. The principle is straightforward. If you reduce the initial clockwise string torque with the pressure button you reduce the angular momentum in the clockwise direction the arrow has when it leaves the string and vice versa.
Suppose using whatever tuning method you like, it appears that the arrows
are leaving the bow rotating clockwise (weak). It means that the initial
clockwise torque is too high i.e. the arrow centre of mass is initally moving
to much towards the bow - too much clockwise rotation. You need to increase
the preset spring tension reducing the amount of button depression and keeping
that centre of mass away from the bow reducing the clockwise torque. If
the arrow acts stiff it means that the arrow is leaving the bow rotating
in an anti-clockwise direction - not enough initial clockwise torque. The
initial clockwise torque can be increased by reducing the spring preset
tension, moving the arrow centre of mass towards the bow.
Note that for normal tuning the control of movement of the arrow centre
of mass is done by controlling the arrow rotation. Movement of the centre
of mass via the bending of the arrow by the plunger button is secondary.
This is not always the case. Suppose your arrows are too weak (whippy). Up
to a point you can increase the spring tension reducing button depression
and keeping that centre of mass out there but the resulting increased button force
on the shaft means its going to bend more and arrow bending moves the centre
of mass towards the bow. Bad news! Ultimately the arrow bending effect on
the position of the arrow centre of mass is going to outweigh the
button depression effect. If and when this happens your tuning guide falls over.
Say your bare shaft hits to the right of the fletched shaft. You increase
the spring tension and try again. The bare shaft hits the same distance
or even further to the right of the fletched shaft. All you are basically
doing at this point with the button spring is increasing the amount of arrow
bend 'weakening' the arrrow instead of 'stiffening' it.
You don't have the above problem with an arrow that is too stiff. Dropping
the button spring tension to increase the clockwise spring torque doesn't
have any significant effect on the bending of the arrow by the button. The
'tuning window' is wider for a stiff shaft then a weak one.
When you do a basic tune like the bareshaft method you end up with a plunger
button setup where the average (perfect) arrow you shoot leaves the bow
with no horizontal angular momentum. The button setup you have is not the
only one that that meets the tuning requirement. There are an infinite number
of centreshot/spring setups that will give you a bareshaft tune. For example your button
came with a variety of springs. You can normally change the spring and
repeat the basic tune just as well. You can go beyond a basic tune using
a more advanced approach, 'tuning for groups', 'microtuning', whatever you
want to call it.
Only a few of the shots we make are perfect, most are mediocre. Advanced
tuning involves looking at many different button setups to try to find one
that has the maximum damage limitation. I.e. with a given (mediocre) shot
one button setup will have the arrow leaving the bow with less angular momentum
than another button setup. Advanced tuning includes looking for the most
forgiving button setup.
The archer with most to gain from finding a forgiving setup is the average
archer, he does more mediocre shots than a top archer. Perversely it is
usually the top archers who spend the time and effort in search of this holy
grail.
Archers have long been aware that how much the pile of the arrow extends beyond the plunger button has some effect on how 'forgiving' the setup is. Various theories (some completely off the wall) relating to the arrow's nodal points have been put forward
to explain this effect. The following is my suggestion as to why this effect
occurs. My view on how/why nodal points come into it is also presented.
When an arrow is shot it bends with the pile moving away from the bow
(RH archer)so that the shaft flexes and rotates towards the bow. The following
diagram illustrates (bearing in mind that the arrow is moving forward) how
the amount the shaft moves into the plunger button varies with where the plunger
button is located with respect to the pile.(this results from the pile inertia as regards lateral movement)
As can be seen the further the plunger button is initially located behind
the pile then the more the shaft at the button moves towards the button
i.e. the more the button is depressed.
The force exerted on the plunger button relates to the mass of the plunger
multiplied by the acceleration of the plunger. The bigger the distance the
arrow moves into the button the higher the plunger acceleration (the 'flex'
time is the same along the shaft) and hence the higher the force on the plunger
button.
If an arrow is shot poorly, say 'weak' then the shaft bends more and flexes
more into the button. The plunger acceleration is higher and so the force
on the plunger is higher than for a perfect shot. Conversely if a poor arrow
is shot 'stiff' then there is less less arrow flex into the button, the plunger
acceleration is lower and the resulting force on the plunger button is less
than for a perfect shot. The button therefore provides a negative feedback
mechanism compensating for the effects of poor shots in terms of how much
sideways movement of the arrow centre of gravity there is.
The further back the button is from the pile then the larger the difference
there will be between the shaft flex into the button between the perfect
and the bad shot and hence the larger the plunger button force difference
between the perfect and the bad shot. The further back the plunger is from
the pile the more bad shots will be compensated for by the action of the plunger
button.
There are practical limits to how large an initial gap you can have
between the arrow pile and the plunger button. As the plunger button has
to be vertically above the grip pressure point to reduce the effects of bow
torque moving the pressure button itself is not an option. The only mechanism
available to increase the pile to button gap is by making the arrow longer
so it projects more beyond the plunger.Making the arrow longer will reduce
its stiffness, increase its mass and increase the shaft drag area. The main point is that the arrow needs to be matched to the bow for optimum grouping so there is a limit to
how much longer the arrow can be. As usual its coming up with the best overall
compromise between several different factors.
Nodal points do not form on an arrow until after the arrow has left the bow so there is no direct link between their positions and the action of the plunger button. The free vibrational properties of the arrow and hence position of the front node (whichever one you pick - see finding the nodes) is determined by the stiffness of the shaft material, the shaft length, shaft weight and the pile/nock/fletching weights. These are the same arrow properties which determine how well the arrow is matched to the bow. (This is why arrow selection programs can be based on a simple vibrational model of the arrow). What someone noticed (a guy developing an arrow matching program for Easton) was that if the front node was kept behind the pressure button position at full draw, you would keep an acceptable arrow match. This provides a guideline to how much the arrow pile can be extended in front of the plunger button. For example if the pile weight was increased the arrow would act weaker and so the maximum arrow length for an acceptable match would be reduced. Increasing the pile weight would move the front node forward indicating that less arrow 'overhang' was permissible.
In the diagram the string force initially runs through the arrow
centre of mass - no torque and no rotation. In the middle drawing the arrow
has been rotated clockwise.
This moves the centre of mass to the
right and there is now a torque generating a clockwise rotation. In the
right hand drawing the arrow has bent to the right moving the centre
of mass to the right and there is now a torque generating a clockwise rotation.
The bigger the perpendicular distance between the centre of mass and the
line of the string force then the larger the resulting torque. While the
arrow is being accelerated by the string it is continuously rotating
and bending. As a consequence the arrow centre of mass is continually changing
position moving towards and away from the bow. At the same time, during
the shot, the direction of the string force is continually changing because
of the archers paradox effect and the nock moving forward. The magnitude
of the string force is continually changing as the nock moves forward.
The more you compress a spring then the higher the force the spring exerts.
The relationship between the force exerted by the spring and the amount
of spring depression is given by: 
The diagram illustrates the basic effect of the intial button position.
As the button is screwed out the arrow centre of mass moves away
from the line of the string force increasing the initial (anti-clockwise)
torque setup. (The torque lever is the perpendicular distance from the
centre of mass to the line of the string force). There are recommendations
from arrow manufacturers and general archers 'lore' on about where this
initial button position should be.
As can be seen the further the plunger button is initially located behind
the pile then the more the shaft at the button moves towards the button
i.e. the more the button is depressed.