STABILISERS

The subject of bow stabilisers and what they are for is comprehensively covered by Steve Ellison at the following link:

To summarise a stabiliser system has two main functions

The above two criteria are to be met while keeping a 'manageable' force for the archer on the bowhand.

This page considers the topic of dynamic stabilisation. The biomechnical aspect of 'bow balancing is covered under the heading Bow Hand Loading

In the days of wooden bows when the limbs were attached to the riser and bowstrings had some give, vibration was not a problem. Stabilisers were very rigid to provide high moment of inertia and balance. With the advent of the metal riser (and associated fatigue cracking), free floating limbs and low stretch strings came the 'wobbly stabiliser' period. Stabilisers were designed to damp vibration with the penalty of reducing the 'inertia' effectiveness. The more recent multirod stabilisers aim to give you the best of both worlds; the sideways vibration of the rods provide the damping function while the multirod arrangement maintains the stabiliser rigidity.

One of the functions of a stabiliser system is to reduce the effects of torque swinging the bow around and effecting in what direction the arrow ends up travelling. Where does this torque come from? A commonly used expression is 'bowhand torque' which implies that the bow hand can itself generate torque on the bow. Try the following experiment:- lean a broom handle against your hand and position your hand as you would on the bow grip. Now try and torque the broom handle (sweep the floor using broomhand torque). You don't get very far. The amount of torque you can generate with your bow hand on the bow (without a tight grip) is negligible and to rotate a bow enough to significantly effect the arrow flight needs a lot of torque .

When you are pushing the bow grip with your bow hand you are applying a varying amount of pressure over an area of your palm. This pressure over an area can be represented (it has physically the same effect) as a pressure being applied at a single point - the centre of pressure (COP). What happens is that from shot to shot the position of the COP moves about and it is this variation in COP position that affects how the bow behaves and where the arrow goes. The torque itself is generated not by the action of the bow hand but by the mechanical action of the bow.

The bowhand COP has two effects, static and dynamic. For example suppose the COP is lower then the ideal position, what is often called 'heeling' the bow. (My heels are at the end of my legs not the ends of my arms - but there you go). When you draw the bow the lower COP results in the lower limb being drawn more than the upper limb so you end up at full draw with a limb with a different 'static' configuration which affects what happens on the loose. Again suppose the COP is horizontally dispaced from the ideal position. When the arrow is drawn the bow is twisted, the riser rotating horizontally in one direction and the limbs being twisted in the opposite direction. At full draw you again end up with a different 'static' configuration. When the arrow is released the various bits of the bow/arrow are accelerated 'naturally' generating a variety of torques. How these torques overall effect the bow dynamically is influenced by the position of the COP. The overall behaviour of the bow, and hence the arrow, is affected by the combination of  'static' and 'natural' torques both of which are influenced by the position of the COP.

The torque behaviour of a stabilised bow can be looked at from the point of view of the bow hand COP on the grip being the pivot point of the system. (This is not entirely accurate as the grip can swivel in and push the bow hand around but to avoid a lot of complication it's a reasonable approximation). Appended is an idiots guide to basic concepts of bow rotation. When you draw a bow part of it (riser, stabilisers, some of the limbs) moves forwards and part moves backwards (arrow, string, some of the limbs). When you release the arrow the parts that moved forward try to move back and the parts that moved back move forward. The bow hand is in the way of the parts trying to move back and this has implications for how the bow torques and also for the arrow speed off the bow.

Because on release the riser etc are trying to move backwards the grip presses against the bow hand making the hand-grip contact point (the COP) the (horizontal) pivot point of the system. The following diagrams illustrate the principle.

The acceleration of the bits of the bow that move forward can be represented by force F1 acting on the riser above the pivot point producing a torque which rotates the bow clockwise in the diagram. If the bow centre of gravity were at the pivot point then the bow would rotate on the shot with the top limb tip moving backwards. If you add a stabiliser to move the centre of gravity forward then gravity generates a torque in the anti-clockwise direction. Get the centre of gravity in the right place and then the torques from F1 and F2 will balance out and the bow does not rotate.


In practice what you want to achieve with a stabiliser system is not only to reduce the amount the bow rotates while the arrow is being shot but also to reduce the variation in rotation resulting from variations in how the archer shoots the bow (e.g. bow hand position). To do this not only must the gravity torque on the bow exceed the torque from bow recoil but the bow centre of gravity (cog) wants to be as far forward from the bow grip as practicable.

The two principle torques on a bow being shot are gravity torque (G) and bow recoil torque (R). The angular acceleration (A) of the bow around the hand-grip pivot point is given by:

A = (G-R)/(I+ML2)

Where I is the bow moment of inertia around the cog, M is the mass of the bow and L is the distance the bow centre of gravity is from the bow grip. At a minumum G must be greater than R, easily checked by seeing that the top limb does not jerk backwards when an arrow is shot.(What your actually seeing is not the behaviour of the riser during the power stroke but the effect of the residual angular velocity after the arrow has gone). As the cog is moved forward G increases but I and ML2 increase even faster so the value of A rapidly decreases. The further the distance the bow cog is from the bow grip the less the bow is going to rotate during the power stroke. What is perhaps more important is that variations in the archer's technique affect the value of R with a negligible affect on G so the bigger the value of L the less variation in bow rotation there is and the more 'torque forgiving' the bow becomes.

There is sometimes confusion between the static balance of a bow and its dynamic rotation. The further forward the cog is the more the bow 'feels' forward heavy and the view is often expressed that the bow should balance in the hand. This is a torque disaster as both G and L become zero making the bow torque behaviour very sensitive to the archer's variations.

The fact that a bow will rotate less during the shot the further forward the centre of gravity is in front of the grip is bit non-intuitive so a brief explanation is given.

Suppose you have a mass (m) on the end of a light, stiff rod of length "L" which is hinged at the other end. You hold the rod horizontally and then release it. How fast does the rod rotate? The torque on the rod is the force (gravity on the mass) times the distance to from the mass to the hinge (L) i.e. the torque = mgL (where "g" is the gravitational acceleration). The moment of inertia of the mass/rod around the hinge is mL2. The angular acceleration of the rod around the hinge is the torque divided by the moment of inertia i.e. mgL/mL2 = g/L. The longer the rod (the further the centre of gravity is from the hinge) then the LOWER the angular acceleration and the less the the rod (i.e. bow) will rotate in a given time. This is exactly the same as a pendulum, the longer it is the slower it swings.

In reality the bow is a compound pendulum rather than a simple pendulum and the rotational behaviour is a little more complicated. See Post Shot Rotation

If you push the bow centre of gravity forward with a longer extender or long rod, you can get the illusion that after the shot the bow drop away rotation speed is faster. This is because what archers look at is the movement of the end of the long rod. For a fixed riser rotation speed the longer the rod the faster the end of the rod moves - the speed is directly proportional to the distance the end of the rod is from the grip. So if you double the rod length, with the same riser rotation rate, the end of the rod moves twice as fast giving the illusion of a faster rotation rate

When archer is at full draw the bow and string forces are balanced by the forces exerted by the bow and string hands, there is no net force on the archer. At the release the string force disappears and the bow force (mainly bow recoil plus some gravity effect as the bow is raised above horizontal) pushes the archer backwards. The pressure of the bow hand (the archer's inertia) opposes the riser moving backwards. The less the bow moves backwards on the release then more of the energy stored in the bow goes into the arrow and it leaves the bow at a higher speed. If Mb is the mass of the parts of the bow that try to move backwards and Mf the mass of the parts of the bow that move forward then the percentage contribution to arrow speed from the action of the bow hand is roughly given by 100(1-sqrt(1+Mf/Mb)).

e.g. if Mb was 1500 grams and Mf was 300 grams then the percentage of arrow speed contributed by the bow hand would be around 9.5%. It is easy to see why the arrow speed off a longbow is much more sensitive to the bow hand action then for an olympic bow.

The advantage to 'pushing' the bow forward through the release is that the archer's arm/shoulders act as a compressed spring. As the archer is pushed backwards by the bow on the release the 'compressed spring' exends reducing the amount of bow backward movement. Not that I know anything about it but I guess that if the muscle fibres are contracting at the time of the loose there is less arm collapse (which seems from videos to occur mainly at the bow arm elbow) than if the fibres are just statically holding the load. A major arm collapse is what is termed a 'dead loose'. You get a significant backward movement of the riser, a significant consequent loss of arrow speed and the arrow nose dives on the target.

In general the heavier the riser mass, the less it recoils and the more energy goes into the arrow. More energy into the arrow means a higher string force on the arrow so one consequence of of increased riser mass is the arrow buckles more i.e. the arrow acts 'weaker'.

If there was no bow hand then the overall momentum of the bow arrow system would be zero. i.e. the arrow would end up travelling forwards and the bow end up travelling backwards and spinning (recoil). With a bow hand, during the time the arrow is being accelerated forwards the bow hand is exerting a forward force on the riser (balancing the force of the riser on the bow hand). As a consequence during the shot the bow hand is generating forward momentum in the bow (force x time). When the arrow leaves the bow, the bow ends up with a net forward momentum and so it 'jumps forward'.

Last Revision 1 July 2009