Understanding Tiller



Part One

 

There are three major sections used to cover this topic.  The first is an introduction, which establishes basic concepts and definitions.  The second section deals with tillering primitive or traditional bows.  And the third section covers tiller of compound bows.

 

Definitions

 

Definitions of certain terms and phrases mean different things to different types of bowmen, depending on their background and the type of bows with which they have familiarity.  The following definitions may not be universally understood as presented here, or agreed upon by all, but these define how they will be used in this presentation.

 

TILLER

To a bowman of compound bows tiller means taking two measurements, one from each limb cup to a reference line between the cam element’s axels.

 

The term “tiller” to a bowyer of primitive or traditional bows means the flexing profile of a bow stave.  And can also be measured in a similar fashion to a compound bow.

 

SETTING TILLER

The “setting tiller” phrase to a bowyer of primitive or hand-made traditional bows translates to scraping, filing, shaving, sanding, whittling, planning, or rasping to shape the limbs of a bow to achieve a smooth graduated flexure of the stave as it is drawn to the desired draw weight and draw length.

 

To bowmen of compound bows and manufactured break-down traditional bows it means adjusting the limb securing bolts to achieve the desired tiller measurements.

 

TILLERING

For both bowyer of organic staves and bowmen of manufactured bows, tillering is the act or process of setting tiller.

 

It is critical to this subject to reflect on the GOAL OF TILLERING.  The goal of tillering for any and all styles of bow is to achieve the most efficient and accurate launch of the arrow toward a target. 

 

There are a few other phrases, which are very important to understanding the subject but, are not widely used nor fully comprehended.

 

STATIC TILLER

Current methods, practices and tools deal only with static tiller.  Static tiller is what you see, measure, feel or set.  Static tiller exists between the point where a bow and arrow are at rest and where it is held at full draw and everywhere in between.  Static tiller is the condition of the bow at continuous equilibrium.

 

DYNAMIC TILLER

Exists between the instant the arrow is loosed and the point at which the arrow nock leaves the string.  The forces, vectors, accelerations, torques and energy of this process cannot be dynamically measured or seen directly, but must be derived mathematically.  Unfortunately, this is the tiller that determines the flight characteristics of the arrow shot.  It is however, approachable and understandable.  Good dynamic tiller is a product of bow design and cannot be achieved by adjusting a poor dynamic design.

 

CENTER OF PRESSURE

The center of pressure (C.O.P.) of a bow is the point, or pivot, or fulcrum, which holds the bow against the pulling force of the string.  The COP in relation to the nocking point of the string determines how the limbs load and store energy, and consequently how they are poised to unload that potential energy turning it into kinetic energy to launch the arrow.  The limbs of a bow will always try to unload their energy in a reverse relationship to the way they were loaded, which means that too will be somewhat relative to the COP.

 

CENTER-SHOT BOW

There is only one style of bow where the static tiller and the dynamic tiller are certain to be equal and where the drawing vector and the arrow vector are coincidental and have a zero angle of attack.  That bow is a true center-shot bow where all things are precisely symmetrical and identical.  This perfect bow is highly theoretical and serves as the basis of most mathematical models and mathematical analysis.  It is possible to design and build such a bow, but a vast majority of all bows available today are not this style and cannot be adjusted to perform as well.

 

The closest primitive bow to a center shot bow can be found among certain aboriginal tribes in South America.  A straight stave bow is made and tillered symmetrically and then shot in a horizontal attitude, pulled against the butt of the bow hand positioned directly under the arrow rest.  This arrangement strives to place the COP in alignment with the path or vector of the arrow with the smallest possible offset in the weak plane of action, between the actual arrow rest and the actual COP.  The bow is pulled and released with the fingers, which will induce the archers’ paradox, but in a vertical plane instead of horizontally.  This style of shooting accomplishes several things.  Bow making and tillering becomes a symmetrical, simple and straightforward process.  It renders a more efficient transfer of energy from the bow into the arrow, while reducing the parasitic stresses between the bow and the arrow.  It will aid in the task of making arrows with more dynamic consistency.  And it helps prevent the bow hand from choking the grip and inducing counterproductive stresses into the shot.

 

EQUILIBRIUM

A bow is a closed system of riser, limbs and string expressing forces, torques, mass, accelerations, stresses, and tensions.  The system as a whole during the draw will always adjust itself to remain in equilibrium.  The good aspect of this reality means that when the archer nocks an arrow and pulls the bow, it will respond automatically to adjust those forces.  And when the archer releases the string, the system will seek equilibrium again, as fast as possible, and shoot the arrow in the process.  This will take place in a generally acceptable fashion regardless of reasonable changes in nock point placement, changes in COP, changes in the position of the arrow rest, and characteristics of tiller.  The challenge presented by this system is the fact that it tries to unload those forces in response to the way they were loaded, which is relative to the COP.

 

GEOMETRIC DISTORTION

Any deviation from the theoretical balanced configuration of the center-shot bow can be viewed as a geometric distortion of the ideal configuration.  For instance; moving the grip, to a lower center of pressure would qualify.  Also, moving the nocking point of the arrow on the string from its central position would also constitute a similar distortion.  Likewise moving the arrow rest position upward is also a distortion from ideal.  In common upright bows all these distortions are present.  These changes distort the geometric and mechanical operation of the bow.

 

How these definitional aspects of a bow interrelate while shooting an arrow, drive the task of seeking a tiller that will attempt to correct, or rebalance some of the forces, which have become out of balance because of the geometric distortions.

 

These definitions and concepts will be generally addressed in relation to different bow styles in the appropriate segment.

 

Part 2 of this series on understanding tiller will deal with the concepts of tillering a primitive or handmade traditional style of bow.  However, compound bowmen should understand these things to appreciate how they apply to compound bows, since the same theories apply.

 

Part 3 of this series will deal with tiller of compound bows in general.


Understanding Tiller

Part Two A

 

Primitive or Handmade Traditional Bow Styles

 

It must be understood from the beginning that every bow that has any geometric distortion can NEVER be made to come back into ideal dynamic tiller where all the force vectors balance and the arrow is driven with a zero angle of attack, and the forces cooperate precisely to drive down the vector of the arrow shaft.

 

What can be done through modifying tiller is to compromise some of the distortion of those factors to gain slightly better shot dynamics.

 

Considerations

An important concept to keep in mind is the difference between static and dynamic tiller.  They must be considered as two separate functions linked somewhat through the COP.  Static tiller will determine the smoothness of the draw, but dynamic tiller will dictate the performance of the arrow shot.

 

Another concept to keep in mind during the tillering process is the realization that the limbs of the bow will try to unload their stored energy in a similar way, but in reverse from the way they were loaded, but based on different forces.  That said, there are approaches, which can help. 

 

One of the first things a bowyer must consider is where the Center Of Pressure will finally reside.  If the archer shoots with a wrist-high, or wrist-low position, that difference will move the COP.  The wrist-high position is the best, because it keeps the COP closer to a central plane between the COP and the arrow rest, and causes less dynamic imbalance.  But either way, the COP is extremely important and must be anticipated. 

 

The tiller philosophy must be determined before a single shaving hits the floor.  Will the bow be essentially symmetrical vertically and one of the limbs weakened, or will one limb be shortened to strive for a better balance?

 

The type of wood, or material combination has the greatest affect on the range of the final draw weight desired.  Judicious selection of materials will greatly influence the final outcome and result in a better overall bow.

 

The arrow nocking point on the string is another critical element concerning tiller.  Its position is SLIGHTLY moveable during tuning, but is heavily considered in the tiller geometry of the bow.

 

Keep in mind that when the finished bow is at full draw there will be one limb that will have a greater angle between the string and the resultant arm of the limb to which it is attached.  This angle should not go over 90 degrees at its maximum draw length on a primitive or traditional bow.

 

Also, any angular force on the nock of the arrow, which deviates from a zero angle of attack will induce and amplify oscillations in the dynamic forces acting on the arrow.  These variations in the stresses felt on the rear of the arrow will have greater effect on the attitude of the arrow in determining its general flight path and its stability during the beginning of the launch rather than after the arrow has established some momentum and inertia along a flight vector.  Put simply, jerking the back of the arrow around at the beginning of its flight will have a greater effect on its flight behavior than after it starts to travel.

 

All these considerations are in play for the primitive, or handmade traditional bowyer, because each bow made is always a custom made bow, and should be produced for the individual who will shoot it.

 

Mistakes to avoid

One of the most common mistakes made is blocking or clamping the riser of the bow during the tillering process.  Doing so defeats knowing where the Center Of Pressure is located and means the limbs are functionally tillered separately as though not connected to the same riser at all.  The bow must be viewed as a single, cooperative unit.  Initial limb strength and flex testing can be done a variety of ways.  They can be flexed against the floor, have weights hung from their tips over the edge of a table, or even stressed over a knee, but when the act of setting the tiller begins, the bow must pivot over a Center Of Pressure.  It makes no difference what apparatus is used.  Regardless of whether a tillering board is used, or a chord and pulley arrangement is used, the bow must balance on a pivot representing the Center Of Pressure to see the relationship of one limb to the other in relation to the riser and how it will be shot.

 

Another pitfall is rather haphazardly choosing the point at which to draw the string during the tillering process and allowing that point to wander with little attention to it.  This point of contact is where the arrow nock will contact the string.  The nocking point is a very important part of the bow geometry and therefore the process of setting the tiller.  Whether a long chord is used prior to stringing the bow for the first time, or during the later stages of tiller with the final bowstring, the relative position of the nocking point to the ends of the string or chord must remain consistent and as accurate as possible.

 

Apparently, it is thought by some that a symmetrical tiller where both limbs are made to flex evenly with the same curvature and flexing the same distance from their beginning point is correct all the way to full draw and final draw weight.  This is true if the bow will be shot as a center-shot bow, which of course, it won’t be.  The tiller process can begin this way, but it is not correct if the Center Of Pressure and rest point of the arrow will be offset from each other in the final arrangement along with the nocking point, which of course, they will be. 

 

Starting to Tiller

 

A reasonable way to start to tiller a bow is to get the limbs fundamentally balanced and flexing the same.  At some point the bow will be put on a tiller board or some apparatus for pulling the limbs with a chord or string.  A small notch should be made on the riser.  This notch can be where the valley of the grip will be made, or it can be at the measured center of the bow stave.  At first it should be small, but rounded and saddled to provide a single pivot point.  Working the limbs with the preferred tools to shape them for flexure and strength begins the tillering process.  Leave as much strength in the limbs as possible at this point while checking for anomalies.  When the point is reached for the first stringing of the bow, other measurements can be made.

 

Once the bow is first strung the initial, relative strength of the limbs, one to the other can be determined.  If the balance notch was placed in the measured center of the bow stave and the pulling point has been the center of the string or chord, the center of the string will fall perpendicular to the notch if the limbs are balanced in tension.  Additionally, if the flexure curves are the same, a measurement from the ends of the riser to the string will be equal as well.  If the balance notch is not the measured center of the bow stave, only the measurements from the riser to the string will indicate basic equality between the limbs.  This is where the practice of measuring tiller from the end of the riser spawned.  Note however, this is just a preliminary and very gross measurement and does not reflect any refinement in bow tiller.  Relatively subtle, but important changes in limb loading during the draw will result in very slight changes to these measurements at its brace height.

 

Before continuing some mental modeling must take place, which will guide the rest of the tillering process to its completion, when it is resumed.


Understanding Tiller

Part Two B

 

Mental Models

STATIC TILLER

Imagine a line between the point on the grip where the web of a hand between the thumb and the index finger would rest, and the middle of the bowstring.  With a wrist-high grip, this will create the Center Of Pressure force vector.  If the arrow rest is above that COP, as it must be, and the bow is pulled to its full draw position, it becomes clear that there is an angle formed between the COP vector and where an arrow would lie.  That angle changes only slightly if we move the nocking point upward on the string to be closer to perpendicular to the arrow rest, at the brace height position, which is a standard configuration.  When the bow is drawn it remains in equilibrium and adjusts the forces, and angles to exactly compensate for its distorted geometric configuration.  This defines the current static tiller.  What must be realized is that the upper and lower limbs have loaded unevenly with respect to each other and the riser even though the forces felt at the nock of the arrow are identical.  The reason for this is seen in the difference in the angles between each string segment and the limb, to which it is connected and the angles created by the flexing of the limbs.  Imagining a line from the root of the limb to a point near the nock of the limb can approximate a representative straight line for the limb. Primarily because of the travel of the nock point, the upper limb will have a greater string angle, but the upper limb has flexed less relative to the riser than the lower limb.  The lower limb will have flexed more, but will have a smaller angle.  What this means is that even though the upper limb has stored less energy and is exerting less force, the greater angle allows more of it to be felt at the nock of the arrow.  Conversely. The lower limb has stored a little more energy, but less of it is felt at the arrow nock because of its angle, but it is just enough to equal the upper limb. All this is just static tiller and the bow system has been continuously in equilibrium during the draw.

 

The fundamental understanding that comes out of this exercise is that the greater the distance between the COP and the arrow rest, and the more off-center the nocking point, the more out of balance are the stored forces, and increasingly the geometric imbalance is exacerbated.

 

DYNAMIC TILLER

Dynamic tiller grows out of the static tiller setup, but is not just a sped up version of the latter in reverse order.  Dynamic tiller occurs between the instant the arrow is released and when it leaves the string.  The model now changes character somewhat.  During the draw, the COP was king.  Its relation to the nocking point of the arrow was all-important, and the entire balance of the pulling force was focused at that point.  It defined how the energetic forces were stored in the limbs.  At the instant of release the influence of the COP is diminished and continues to diminish until it is nonexistent.  What begins to matter more beginning at the instant of release is the mass of the bow.  The part the bow hand plays now can be viewed as lending mass to the bow only.  The COP during the draw is the absolute pivot point of the entire system, but on release, the mass and inertia of the bow does not allow any meaningful pivoting until after the arrow is well on its way to the target, unless the mass of the bow is far too little for the magnitude of the forces being stored.  If this lack of mass is the case, some slight rotation can be present.  Dynamic stability is enhanced by the use of balancers and dampeners, or an increase in the non-working, or dead mass of the riser. What matters now is how the limbs will unload the energy they have stored against the relatively tiny mass and inertia of the arrow.  During the dynamics of the shot nothing is in equilibrium, so it becomes important to recognize the greatest influences on the geometry and forces of the bow, and how the arrow is being pushed.

 

Since the mass of the bow makes it something of a fairly stable platform, attention is focused on the limbs.  Assuming the limbs to be pretty much equal in length and mass, primary consideration becomes the force stored in each limb and their resulting accelerations.  If the limbs are of unequal lengths and mass, this visualization is somewhat more complex, but is still generally understandable. 

 

An instant after the release of the string, and assuming the mass of the limbs to be equivalent, the limb, which has stored the greatest energy, will exhibit the greatest acceleration trying to pull the nock of the arrow toward that limb.  It will also bleed its stored energy more quickly.  Once its resultant and relative force weakens relative to the other limb, that limb will try to pull the nock of the arrow its direction.  This sets up an energy oscillation, which may not be observable, that will persist through the shot.  Evaluating the effect of these oscillations, it would be best if they are small at the beginning of the stroke and ideally they would diminish as the launch progresses.  This is usually not the case, but can be influenced somewhat by the tiller.  In the case of unequal limb lengths, the shorter limb will store greater tension.  Uneven limbs also make a bigger issue of the torque-moment of each limb, which should be considered and factored into the understanding and calculations as well.

 

Manipulating only the overall strength of the limbs relative to each other, moving the nock point, or adjusting the position of the arrow rest is much like hanging a carrot from a stick anchored to the head of a horse, which remains just out of reach to the horse’s mouth.  It can be pursued, and the carrot may swing closer, or further away, but it will never wind up between the horse’s teeth.  Applying this analogy to a bow; when a limb is weakened, or the rest, COP, or nocking point is adjusted, it changes the static tiller and in so doing the beginning conditions of the dynamic tiller.  The best configuration of tiller that can be achieved is akin to when the carrot swing is closest.  That becomes the best achievable tiller.  To improve the best achievable tiller requires limbs of complimentary, but different pressure curves, which render compatible, but not identical flexing geometry.

 

Finish Tiller

The final tiller process is to get the limbs to unload with the same force and acceleration, which puts the nock of the arrow on a path to the arrow rest with the least amount of vertical oscillation at the beginning of the launch.  Specific steps cannot be dictated for two reasons.  First, every bow is different.  And other aspects of the bow, which have not been addressed herein, affect how it must be designed and tillered, such as the length of the riser.  The general considerations do not change, but the geometry of the bow does.  Second, understanding tiller is different than dictating how to achieve good tiller.  Creativity must be allowed to flourish. 

 

One of the best tools for designing and planning the tiller of a bow is a Computer Aided Design program.  Fastidious care must be taken when developing a geometric model to avoid misunderstanding how to plot critical elements and their reference planes to their relative geometric relationships.

 

Tiller of a traditional bow style manufactured with modern materials having separate limbs and riser is more restricted.  Moving the rest, nocking point, and limb angle, which relates to limb strength, are the only parameters that can be adjusted after it is manufactured and assembled.  The only real improvement to be made in tiller would be in replacement of identical limbs with dynamically complimentary limbs engineered for a specific riser and a specific draw length.

 

Any bow that has been properly fine tillered for optimum performance will specify precise positions for the COP, arrow rest height from some specific point, and a specific nocking point on the string.  Fine-tuning can be done to account for minute anomalies, but they should not deviate any significant amount from the design parameters.


Understanding Tiller

Part Three

 

Compound Bows

The primary and most fundamental question to be asked is; why a compound bow?  What is gained over a traditional longbow, or deflex-reflex, or recurve?  The simple answer is that a little more energy can be transferred from the limbs into the arrow during the stroke and the holding weight is less to assist the archer in aiming and waiting at full draw for the best shot timing.  Oh yes, and they look cool.

 

In terms of tiller though, all the fundamental principles apply.  The COP still determines the pivot point of the draw.  The offset between the COP and the arrow rest still creates a geometric distortion and imbalance, along with the placement of the nocking point of the arrow on the string.  For a maximum draw weight, brace height and draw length comparison between styles, no more energy is stored, it’s just stored differently.  It does however, allow a little more energy transfer into the arrow during the stroke.

 

Understanding compound bows can be made clearer by tracing their evolution.  Compound bows emerged in the 1960’s sporting eccentric wheels with the buss cables attached to the riser, which soon became anchored to the opposite limb tip. The use of wheels and a separate riser design accomplished one thing that allowed for three advantages.  It allowed the string to be drawn past 90 degrees from the resultant limb vector, which resulted in a peaked and rounded pressure curve instead of just linear and also a lower holding weight.  The compound bow concept is all about mechanical advantage during the draw.  The limbs initially have the mechanical advantage over the string until the wheels roll over enough to give the advantage to the string.  This means that during the shot there is less pressure at the beginning of the arrow launch, which increases to the pressure hump and then decreases.  The moderated beginning is less radical before the arrow begins to establish some momentum and inertia.  The only complication became the timing or coordination of the wheels at the point where they transitioned from the string having the mechanical advantage, to the limbs having the mechanical advantage.  The main goal was of course, to get the maximum overall energy out of the limbs with a lighter holding weight.

 

Next came the designs with cams instead of wheels.  This enhancement gave a better pressure curve profile.  The limbs of a two-cam compound bow are more directly coupled beyond just their connection to the riser, because of the cam elements integrated into the tip of the limbs and their connection to each other through the cables.  When the string is drawn, the upper string portion uses the upper limb tension and its buss cable cam section to draw the lower limb.  The lower portion of the string likewise, uses the lower limb tension and its associated cam section to draw the upper limb.  The string ends also run over cam elements, which enhance its mechanical advantage over the limbs when it is pulled beyond what is felt as the pressure hump.  This arrangement describes a symmetrical, mirror image, two-cam bow design. 

 

A single cam design operates a little differently as do the cam and a half and modified cam designs.  This process though, still defines static tiller where everything remains in equilibrium to full draw.  The inherent dynamic tiller challenges still remain.

 

The proposition of dynamic tiller remains the same.  Once the limbs are loaded they should theoretically and ideally unload their energy into the arrow as equally as possible with the best balance of the force vectors at the beginning of the launching stroke and the smoothest transfer of energy along a vector down the shaft of the arrow.  As always though, little has been done to correct the inherent tendency of the limbs to unload unevenly in direct response to the COP and the way they were loaded.  Consequently, dynamic tiller problems remain as much of a problem and challenge as they ever have been and they have not been actually addressed in any meaningful way.

 

With the advent of the single cam bow design virtually all the variable mechanical advantage resides in the lower limb.  This design philosophy has one advantage and two disadvantages.  Its advantage is that it does not require the timing of cams, which historically proved to be somewhat difficult.  Some of the previous difficulty was undoubtedly attributable to poor dynamic tiller design, but blamed on cam timing.  The disadvantages are that because there is no cam timing possible, no corrections can be made to improve the coordination or relative balance of the limbs, and additionally, it results in a very lopsided dynamic tiller scheme.  The emergence of this design coincided with a change in philosophical priorities, which shifted from stability and accuracy to arrow speed.  The idea being that a faster arrow is a straighter flying arrow.  While it is true that a faster arrow with more kinetic energy will have a flatter trajectory, it is not true that it will possess better dynamic flight characteristics or any other benefits.  The shot just happens faster and the problems are harder to see.  This design is also very sensitive to draw length; hence the more forthcoming manufacturers disclose that their design is the best compromise, which they could arrive at between all the critical elements and a change in draw length requires different components.  The geometric and force distortions are so extreme that plotting the static tiller from brace height to full draw cannot yield a straight nock travel in the strong plane of movement, which is a deviation back and forth between the limb tips during travel.

 

The emerging designs are now modified dual cams.  They are hybrid designs that have a better balance between the limbs, but don’t allow for any significant re-timing of the cam elements to be done without actually replacing some of the components.  They do shoot arrows at a higher speed, but do not seem to possess any better dynamic tiller than any other generally symmetrical design.

 

Summary

There are several realizations, which come to light.  Both static and dynamic tiller are a function of design, and coordinating static tiller with dynamic tiller involves more than just weakening one limb over the other, moving the arrow rest, or moving the point at which the arrow attaches to the string.  Therefore, improving tiller coordination is not really adjustable once the bow is made.

 

Any bow design, other than a true center-shot bow, can never be made where the static and dynamic tiller are functionally identical and in balance so the forces load in reference to the COP and unload in reference to the arrow vector, although, some compromises are better than others.  It may however, be possible to come even closer with improved designs of corrective and complimentary cam elements and limbs.

 

Any bow that has been made with attention and true consideration given to dynamic tiller will specify an exact draw length, rest position, COP position, and arrow nocking point on the string for optimum performance of that particular bow.  Moreover, the limbs will have been shaped, or screened, selected and paired as either identical or matched for complimentary characteristics.

 

Tiller is the most fundamental and important design aspect and setup consideration of any bow.  It is at the heart of bow performance and therefore, arrow performance.

 

Smoothness, quietness, forgiveness, accuracy, stability, reliability, tune-ability efficiency, and all other good or bad characteristics of a bow’s performance grow out of tiller.

 

How a bow is shot is either compatible with the design objectives and tiller of a bow, or deviates from them, which will degrade performance.  In the cases where shifting the COP by using a wrist-low grip or pulling the string with three fingers under the arrow nock improves the launching of the arrow, it can be definitely concluded that other parts of the bow are poorly designed or misaligned and any improvement though purposeful, is accidental and somewhat serendipitous.  In a vast majority of bow setups deliberately misaligned parts during tuning such as the arrow rest, limb tension, and nocking point are compensating for poor shooting technique and bad tiller.  These improper and inadequate adjustments express themselves in undesirable and unwanted results such as excessive hand shock, noise, excessive arrow flexing, unreliable shot to shot accuracy, lower than ideal arrow speed, poor arrow flight dynamics, excessive dynamic vibrations, and greater wear and tear on the bow, which shortens its useful life.

 

True and accurate analysis of static tiller can only be accomplished on the Bow Lab.  Dynamic tiller can only be anticipated with geometric and mathematical analysis.

 

Lastly, archers will have bows designed with better, and more coordinated tiller when they begin to demand it for the price they are asked to pay for higher priced bows. 

 

The foregoing is intellectual property of G. Wesley Stagg

 

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