CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOARD

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Dennis La Varenne
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CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOARD

#1 Post by Dennis La Varenne » Thu Aug 27, 2015 6:26 am

I have written an article below intending to show the disparity between what actually often is and what is purported to be a circular tillered (compass) bow and how to effect a remedy with the use of an accurately plotted tiller backing board showing how, instead of a series of horizontal lines used to trace the progress of a bow's limbs, a board can be drawn which can quite accurately show a series of partial circles from very shallow to the maximum curvature of any bow which form true part-circular bends.

I will post it in parts because of its length.

PART 1. - HOW CIRCULAR IS CIRCULAR TILLERING?

The fact is, that such tillered bows are rarely ever correctly circular if that is the ideal tiller for an ELB.

On investigating this desirable phenomenon, I have always questioned the expression used by Ascham regarding ‘compass’ bows as not necessarily meaning circular at all, but referring to a well-rounded shape to the limbs – having no stiff areas nor areas which ‘come’ too much or create a hinge.

Nowhere in ‘Toxophilus’ does Ascham recommend or enjoin readers that a bow must bend through the handle. That is a derived assumption by today’s bowyers. The error arises from our misunderstanding of his use of the word ‘compass’ to mean circular when there is no actual evidence to support that belief.

Nobody seems to notice that he also describes the trajectory of an arrow as being ‘compass’ in shape. We know today that the trajectory of an arrow is definitely not circular. It is elliptical. In his day, he must have noticed from the side position that the path of arrows differed in shape to that of a bow. Yet he still used the same word for both arcs. So, did the word mean ‘circular’ or simply ‘curved’ or ‘rounded’?

Every ELB-styled bow, that I have ever seen, including all of my own, has had an elliptical tiller. Many bows I have seen progress from shallow elliptical at brace height to distinctly egg-shaped through the middle at full draw, with the outer limbs having arcs of much shallower bend than the middle. This shape of tiller is what Ascham referred to as ‘staffish’ because of the thickness of the outer bow limbs.

It was a surprise and a disappointment to me when I realised this. I then began to do some scale drawings to find out what kind of bend one would need to produce in a bow which, at every stage of the tillering process would take a distinctly circular bend throughout its draw.

What follows is an explanation of what I found.

As many of you have seen, I have used a technique by which I can analyse the tiller shape of a bow whilst on the tiller using three chords of equal length (from nock to bow centre) and having another line standing perpendicular to this chord at its exact middle. The purpose of this perpendicular line is to measure the distance from the base chord to the belly of the bent limb.

That same chord is then placed on the opposing limb at the same position and then finally, a third chord is positioned centrally on the bow with the perpendicular line touching the bow at its exact centre.

For a bow to have a correctly circular tiller, each of these chords must touch the bow’s belly at the end of the perpendicular line and each end of the chord must touch the bow’s nock and mid point as in Fig. 1 below.
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Fig. 1 – An example of a poorly tillered English Longbow. The upper limb is on the right

In Fig. 1 above, each of the red chords and their respective blue vertical depth indicators are of equal dimensions and are placed between both string nocks and then at the middle of the bow. If this bow were circularly tillered, these chords would all touch at exactly the same place and the depth of the bend indicated by the blue line would be also equal.

It can easily be seen from the Fig. 1 that the lower limb on the left has a much deeper bend than the bow’s upper limb and at the bow’s centre, it has a quite stiff section where the blue depth indicator is partially into the bow itself. The same occurs with the upper limb at right which is even worse.

Thus far, of the many bow pictures from eBay (which is a good source for this kind of research) which I have tested similarly, surprisingly few have accorded with this simple test of circularity. Almost all have purported to be circular in tiller, from the common assertion that to be circular in tiller, the bow must bend through the handle. That is not the sole criterion for circular tiller. Most of such bows have had outer limbs with very little bend.

The following is another example which is even worse than the bow in Fig. 1 above. This particular bow is an ELB format but is very short at close to 60 inches.
Very-poor-tillering-of-short-ELB_25cm.jpg
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Fig. 2 – A very short ELB with far too much bend through the handle section.

In Fig. 2 above, I tried another technique of ascertaining the circularity of bend in bows using the principle of radians. This particular bow at 60 inches in length would have a radius of 30 inches. Based on that measurement, I drew the red line which is a true circle based on the radian principle. From the picture, it was easy to find where to place the focus to draw a circle of radius 30 inches.

It can easily be seen that this particular bow has far too little bend in its outer limbs which such a short bow really ought to have in order to spread the bending load over the whole length of its limbs.

The blue circle which contacts the nocks at the bow’s nocks graphically shows just how much bend there is through the handle section – almost two handle thicknesses too much - a dreadful load to put on a deep section bow of only 60 inches. Without those circles, this particular bow easily deceives the eye into thinking that it is truly circular in tiller. Indeed it is far from that.

The same maker of the bow in Fig 2 above has made another example of an out-of-circular limb tiller with this very heavy bow of 74 inches.
Tri-lam-ELB-at-full-draw-_----tiller_25cm.jpg
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Fig. 3. – A 74 inch bow with too much bend in the middle and not enough in the outer limbs.

In this bow (Fig. 3), again we can see how little bend there is in the outer limbs compared to that in the handle section. I have drawn a red circle with a radius of 37 inches (one radian) around this bow to show just how far out of circular that this bow is.
ELB-TRUE-CIRCULAR-TILLER_25cm.jpg
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Fig. 4. – Degree of out-of-circular tiller of bow in Fig. 3 above.

In Fig. 5 below, I edited this picture in Photoshop to bring more curvature into the outer limbs so that they matched the circle I had drawn around the bow above (Fig. 4). If you look closely, you can see the original horns peeping from behind the foreground layer where I have Photoshop-bent the bow’s limbs to follow the red line.
ELB-TRUE-CIRCULAR-TILLER_25cm_2.jpg
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Fig. 5 – Fig. 3 image edited in Photoshop to show correct circular tiller.

The horizontal blue lines were added to estimate the amount of tip deflection needed to bring this bow’s limbs to circular tiller.
Surprisingly, as I have followed the bows this English bowyer lists for sale on eBay, he seems to have a penchant for bows which bend far too much in the middle.

As we know, limbs which bend circularly have the benefit of evenness of load distribution along the limb length which tends to limit the amount of inevitable set and minimises the chance of frets and pinches forming between hard and soft spots along a bow’s belly.

At any rate, debates upon the meaning of the Tudor archery term ‘compass’ are academic and largely unverifiable. However, using an accurately made tillering backboard, it is both possible and practical to tiller an English Pattern Longbow to an accurately circular bend other than by doing it by eye alone. What follows is how to make such a board and the principles behind it.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

QVIS CVSTODIET IPSOS CVSTODES (Who polices the police?) - DECIMVS IVNIVS IVVENALIS (Juvenal) - Satire VI, lines 347–8

What is the difference between free enterprise capitalism and organised crime?

HOMO LVPVS HOMINIS - Man is his own predator.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#2 Post by hunterguy1991 » Thu Aug 27, 2015 7:15 am

Excellent read Dennis, some Great work there mate.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#3 Post by Dennis La Varenne » Thu Aug 27, 2015 1:17 pm

Colin,

I have edited it a bit since first draft but it is mostly the same. I will post the next chapter tonight I think.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

QVIS CVSTODIET IPSOS CVSTODES (Who polices the police?) - DECIMVS IVNIVS IVVENALIS (Juvenal) - Satire VI, lines 347–8

What is the difference between free enterprise capitalism and organised crime?

HOMO LVPVS HOMINIS - Man is his own predator.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#4 Post by Dennis La Varenne » Thu Aug 27, 2015 5:58 pm

Here is the next installment of my thesis on achieving a correctly circular bend in bows which bend through the handle.

2. CIRCULARITY

If a bow is to have a circular tiller, then the arc of the limbs must form part of a circle which has a centre point. The length of the limbs must form a definite proportion of the length of the circumference of that circle. Also, the depth of the curvature at any position along the limb must be the same as at any other part.

The difficult part was finding out how much of the circumference of a circle was formed by the length of the limbs without which proportion, one cannot ascertain the radius of the circle which fits the shape of the full drawn limbs.

I began to find examples of bows at full draw which were as close to being square to the camera when taken so that there was minimal distortion from the camera angle. I had to know the length of the bow and some way of working out a scale. The sellers of bows on eBay supplied the length of the bow and fortunately, a scale was often evident from the markings on the tiller.

Using Photoshop, I began experimenting with overlaying circles of varying diameters over the image of the bow. I found eventually that the correct radius for a bow of any given length was half its length, meaning that all bows had a length of 2 radians. I was astounded.

I tested that finding on several pictures and found that it held.

For those who don’t know what it is, a radian is that length along the circumference of a circle which is equal to the length of the radius of the same circle.

Every circle has a circumference which is 6 radians long or the length of 6 radii. The ends of any radian are 60 degrees apart from the focus of a circle.

So, the distance between A and B in the Fig. 6 below is one radian long and is equal to the distance from A to C or B to C.

Greybeard recently emailed me privately with a note referring me to the observation of Thomas Waring in 1824 suggesting that the arc of an English Longbow was one sixth of a circle (one radian).
RADIANS_25cm.jpg
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Fig. 6 – Radians of a circle

Looking at the illustration in Fig. 6 above, it looks to me that the amount of arc covered by one radian is far too shallow a bend for most straight limbed bows unless they are of prodigious length. Certainly, it is far too shallow a bend for a 6 foot bow or shorter.

At any rate, I found that I could not reconcile the amount of deflection at the tips at full draw of any of my flat longbows or ELBs with a curvature of only one radian, but the technique seems to work quite well with an assumed bow length of 2 radians.

By assumed, I mean that no matter how long your bow is, for the purposes of setting out a correct tillering board, all bows are presumed to have a curvature of 2 radians at full draw, no matter what their relative length.

The reason that this assumption seems to work is because all circles are directly proportional to each other.

This next picture (Fig. 7) is one of the few pictures of a well-rounded tiller in an ELB. I forget the maker on eBay, but I was struck with the near ‘correctness’ of the tiller shape. This bow seems to achieve this shape by being rather thicker in the middle than perhaps we are used to and having a very fast taper to the tips making it take the appearance of a very whip-ended bow which is perhaps what Ascham had in mind when he wrote in Book Two of Toxophilus –
“. . . make him come round compass everywhere, and whipping at the ends, but with discretion, lest him whip in sunder, or else fret sooner than he is ware of;”
$_57-10 copy.JPG
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Fig. 7 – A very nice almost circularly tillered heavy ELB albeit slightly stiff through the middle. This bow is clearly whip-ended.

The significant thing about this bow’s tiller is that a lot of attention has been given to making the outer limbs bend well. Significant to me is that this bow has a very thick mid-section compared to its tips at the horns. My guess is that the tips below the horns appear to be only 1/3 the thickness of the bow at its middle and that this taper is perhaps one of the secrets of making these bows.

These days, very few makers of ELBs make tips at the horns of less than ½ an inch thick, no matter what the bow’s draw weight, prompting the question of overbuilding of the outer 1/3 of the bow’s limbs with consequent excessive outer limb mass and consequently stiff outer limbs. I am as guilty of that as anyone.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

QVIS CVSTODIET IPSOS CVSTODES (Who polices the police?) - DECIMVS IVNIVS IVVENALIS (Juvenal) - Satire VI, lines 347–8

What is the difference between free enterprise capitalism and organised crime?

HOMO LVPVS HOMINIS - Man is his own predator.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#5 Post by hunterguy1991 » Fri Aug 28, 2015 1:32 pm

Hi Dennis,

I have made up a half of the backing board that you described to me in the email for doing some analysis with some of my bows... being an engineer I like to compare things and analyse (sometimes maybe too much) and I have been playing around with a warbow I'm currently making for a friend.

The bow is currently 78" nock to nock and pulling 82lbs @ 30 inches true. I measured out the 39 inches (half 78) and drew up the curves as you described in the email (soon to be posted on this thread I imagine) on some scrap cardboard and fitted it in behind my tiller to check the curve.

On drawing the bow down to 30 inches I noticed that the limbs matched more closely to a 84" bow's curve than the 78" curve I was comparing it to... it then dawned on me that the brace height and therefor string length plays a large role in the curvature of the limbs...The bow currently has a brace around 5.5" which needs to go up to at least 6 for shooting, however, Higher brace height = shorter string = more bend= tighter curve... I feel that even if I upped the brace to 6.5" I still would not match the 78" bow curve.

To very accurately draw a curve to tiller to you need to work out the brace height and therefore string length that matches the curve... I have thought about this fact before but there is some serious maths involved in calculating all of the necessaries to get an accurate curve with many assumptions necessary to make them easier still...

To start this off at least we would know the ntn length of the bow and the draw length at full draw, maybe 80" and 32 " respectively... The issue then becomes the string length to give a certain brace height??

This is where things get very inter-related to on another because the string length is related to the brace height with are both related to the radius of curvature at full draw and the sting to nock angle at full draw...

Messy stuff...

I would suggest that perhaps the backing curve you have worked out here can be used to check evenness of bend along a limb quite accurately, however it may not be a perfect guide to tiller a bow to...

Colin

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#6 Post by clinton miller » Fri Aug 28, 2015 2:45 pm

Dennis La Varenne wrote:
2. CIRCULARITY

If a bow is to have a circular tiller, then the arc of the limbs must form part of a circle which has a centre point. The length of the limbs must form a definite proportion of the length of the circumference of that circle. Also, the depth of the curvature at any position along the limb must be the same as at any other part.

The difficult part was finding out how much of the circumference of a circle was formed by the length of the limbs without which proportion, one cannot ascertain the radius of the circle which fits the shape of the full drawn limbs.

I began to find examples of bows at full draw which were as close to being square to the camera when taken so that there was minimal distortion from the camera angle. I had to know the length of the bow and some way of working out a scale. The sellers of bows on eBay supplied the length of the bow and fortunately, a scale was often evident from the markings on the tiller.

Using Photoshop, I began experimenting with overlaying circles of varying diameters over the image of the bow. I found eventually that the correct radius for a bow of any given length was half its length, meaning that all bows had a length of 2 radians. I was astounded.

I tested that finding on several pictures and found that it held.

For those who don’t know what it is, a radian is that length along the circumference of a circle which is equal to the length of the radius of the same circle.

Every circle has a circumference which is 6 radians long or the length of 6 radii. The ends of any radian are 60 degrees apart from the focus of a circle.

.
so for a 70" NTN bow which forms 2 radians of a circle when drawn requires a draw length of 36.5708". the longer the bow the longer the draw length needs to be to maintain such geometry.

or can it be tillered in such a way that the bow can assume 2 perfect radians with a draw length other than the radius of the circle formed by the radians?
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#7 Post by clinton miller » Fri Aug 28, 2015 3:18 pm

Dennis La Varenne wrote:
For those who don’t know what it is, a radian is that length along the circumference of a circle which is equal to the length of the radius of the same circle.

Every circle has a circumference which is 6 radians long or the length of 6 radii. The ends of any radian are 60 degrees apart from the focus of a circle.
.

the first statement is correct which means that the second statement is incorrect.

a radian is a term of angularity not length. a radian is the angle formed between two points on a circles' circumference that are one radius length of the same circle apart when measured along the circumference. 57.296 degrees.

one radian of a circle doesn't equal one sixth of it's circumference. if it did, you would multiply the diameter by 3 to find the circumference and not by pi which is 3.14159 (infinite decimal places omitted for time saving)

the maths in the last post is actually incorrect because it was based on the incorrect assumption of a radian being one sixth of the circle circumference. but you see the point. bows above 60" that adhere to this geometry will have draw lengths longer than practicable for shooting. unless they can be tillered somehow to make the bow form 2 radians with a draw length other than that of the corresponding radius?
The degree of satisfaction gained from the accomplishment of a goal is directly proportional to the hardships and challenges overcome in order to achieve it.

border black douglas recurve 70# & 58# HEX6-H BB2 limbs
brigalow selfbow with rawhide string

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#8 Post by hunterguy1991 » Fri Aug 28, 2015 3:57 pm

Clinton, you wrote

"so for a 70" NTN bow which forms 2 radians of a circle when drawn requires a draw length of 36.5708". the longer the bow the longer the draw length needs to be to maintain such geometry"

It would need to maintain such geometry if the string to tip angle was 90 degree... however, this is very rarely the case in that the angle is almost always less than 90 degrees...

Here is where the string length and brace height issue comes into it again. Because the bow is braced and the line of action of the force at the tips is not constantly at 90 degrees to the tips you could achieve such curvature at a shorter draw... it could be possible to develop such a bow where the tip angle at full draw was exactly 90 degrees but that would be pushing a piece of timber to its absolute limit if not past it.

I do Agree with what you have considered in that the circumference of a circle is Pi x Diameter or Pi x 2 x radius, which will have an effect on the equations.

Colin

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#9 Post by clinton miller » Fri Aug 28, 2015 5:19 pm

i guess the other thing one has to consider is the bows aren't shot like they are tillered as pictured. the fulcrum might be closer to the top limb tip and the point on the string were it's drawn would certainly be closer to the top limb tip.

this is one thing i've never understood. why are they not tillered using the same two actual points of contact that occur when shooting it?
The degree of satisfaction gained from the accomplishment of a goal is directly proportional to the hardships and challenges overcome in order to achieve it.

border black douglas recurve 70# & 58# HEX6-H BB2 limbs
brigalow selfbow with rawhide string

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#10 Post by Dennis La Varenne » Fri Aug 28, 2015 5:40 pm

Clinton,

I know that the actual angle of a radian is 57.2+ degrees, but for practical purposes of this exercise, there is a close enough relationship between the length of the curvature along the circumference of the circle and the length of a radius that my thesis is workable in practical terms.

Colin has a point in relation to the relationship between string length at brace height and the string angle at full draw. I understand this issue and its implications, but where he finishes his post above
I would suggest that perhaps the backing curve you have worked out here can be used to check evenness of bend along a limb quite accurately, however it may not be a perfect guide to tiller a bow to...
My idea is that as a bow is progressively bent on the tiller, the shape of its curvature can be stage-matched to an ever increasingly tighter curvature as the limbs approach full draw. The point being, that the limbs maintain a curvature which matches a portion of the circumference of a circle of increasing radius at each stage of tillering.

Maintaining circularity of bend throughout tillering is what I am trying to explain.

It also occurrs to me that the length of the string at any intended brace height could be plotted on a scale or full sized drawing of the backing board by the simple expedient of measuring a straight line between the intersection of those two points made along the tracking line of the bow tip and the arc described by an arc which crosses the tracking line where the tips are deflected by the nominated brace height.

The angle which that length of string makes when the bow is drawn will obviously affect the arc of travel of the bowlimbs to some degree, but I am not able to do the very complicated maths involved to be able to calculate that degree of influence.

Rod from FNQ once addressed this very issue in one of my posts a long time ago. In short, he pointed out that the more acute the angle of the string-bowtip intersection, the greater the degree of curvature. There is perhaps some kind of logarithmic relationship between the two and either of you may be able to explain that relationship better than I ever could.

Just the same, I am trying to demonstrate a practical and workable method to guide a bowmaker of so-called compass bow to tiller their bows to have an actual circular bend rather than the many versions of so-called compass bending. By far the majority of these end up having far too much bend through the handle and little outside of mid-limb.

I don't think we can ever achieve an engineering level of accuracy in this pursuit, but I consider that using this method, a far greater degree of accuracy to the definition can be achieved than is achieved presently.

However, I am glad the two of you have pointed out some shortcomings and I hope that they can be addressed through this thread. Later I will continue with the next instalment and you can both scrutinise it in the same way you have thus far. I find it very helpful and useful.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

QVIS CVSTODIET IPSOS CVSTODES (Who polices the police?) - DECIMVS IVNIVS IVVENALIS (Juvenal) - Satire VI, lines 347–8

What is the difference between free enterprise capitalism and organised crime?

HOMO LVPVS HOMINIS - Man is his own predator.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#11 Post by clinton miller » Fri Aug 28, 2015 5:48 pm

is there an advantage to a circular tiller? obviously bows tillered on either end of the spectrum from a circle still work. mollegabet for example. is it more of an exercise in replicating period bows?

i guess i'm used to working in a trade were accuracy counts. that amount of discrepancy would be significant for alot of construction purposes. especially on big circles!
The degree of satisfaction gained from the accomplishment of a goal is directly proportional to the hardships and challenges overcome in order to achieve it.

border black douglas recurve 70# & 58# HEX6-H BB2 limbs
brigalow selfbow with rawhide string

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#12 Post by hunterguy1991 » Sat Aug 29, 2015 8:40 am

Clinton,

Circular tillered limbs produce an even stress distribution along the length of the limb... (or so the theory is anyway)

You would find that the bending section on a well made mollegabet most likely does follow a circular path similar to a short portion of an English longbows limb.

Colin

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#13 Post by clinton miller » Sat Aug 29, 2015 1:55 pm

ok, so it bends in a circular pattern just a shorter portion of the limb.

so this is for selfbows? obviously laminated bows bend alot differently.
The degree of satisfaction gained from the accomplishment of a goal is directly proportional to the hardships and challenges overcome in order to achieve it.

border black douglas recurve 70# & 58# HEX6-H BB2 limbs
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#14 Post by Dennis La Varenne » Sat Aug 29, 2015 2:10 pm

Clinton,

Forrest Nagler worked out mathematically back in the late 1930s that even distribution of load along a bow's limbs can be achieved in an elliptical tiller such as your Møllegabet bow design and most bow designs. Yeoman wrote a good bit about the application of Nagler's pattern of tillering in his article on Ozbow on using maths in making bows a few years ago.

All of this scientific study was published in the volume - ARCHERY: The Technical Side - published jointly by Clarence N. Hickman, Forrest Nagler and Paul Klopsteg in 1946 through the National Field Archery Association. It is a collection of all their papers published earlier in archery periodicals such as the Archery Bowman Review and some of their scientific periodicals. They are very mathematical, but you can get the gist of what they are explaining through the accompanying notes if you are mathematically compromised like I am.

Before that, Clarence N. Hickman had advocated a circular tiller as being the best way distibute the bending load, but Nagler's was even more accurate, particularly with rigid handled bows.

So, how does this correlate with what I have been writing? It doesn't.

Circular tillering offers no greater advantage than elliptical tillering. I am definitely NOT trying to persuade bowyers of the superiority of circular tillering over elliptical tillering.

However, the issue, so far as my thread is concerned is how to achieve the preferred and 'classic' circular shaped tiller in bows which bend through the handle. It is commonly and widespread claimed that this is the correct and preferred tiller of such bows and in my experience does seem to work with this kind of bow. When you make the middle section of a bow rigid, then then you get almost by default, an elliptical shape in your tillering.

Accuracy doesn't result from tillering design. That is purely a human induced effect. Bow's are inanimate objects built purely to perform the function of launching an arrow. Before the bow, arrow construction is more important. When both bow and arrow are built to best practice, then the human factor influences any inbuilt handling characteristics of the equipment.

A bow/arrow combination may be accurate from a shooting machine and very often are. But are almost inevitably reduced when a human does the shooting.

Anyway, here is the next instalment of my thread.

3. HOW LIMBS BEND

The one issue derived from the experimentation above which I applied to several of my own straight ended bows of various types was to test how much tip deflection there was at full draw.

What I found was, that depending upon the bowstring material and how heavily it was twisted, that stretch in bowstrings at full draw brought the tips to a deflection of very close to half the full draw length at full draw. It varied a little, but not much – plus or minus half an inch on average.

The consistency was quite surprising.

I had also thought that only a proportion of the outer limb would bend with each increment of draw length with the inner part of the bow remaining rigid and unbending. But that turned out to also be incorrect according to my drawings.

The middle section of a bow can, should and will bend in the early stages of tillering, but it is barely perceptible until the limbs get to around brace height.
1-RADIAN-CIRCLE_25cm_2.jpg
1-RADIAN-CIRCLE_25cm_2.jpg (26.54 KiB) Viewed 12462 times
Fig. 8 – Circle of bending for an ELB of 72 inches length.

I have always been impressed with the videos of the late Steve Stratton in ‘The Longbow’ series where, in Volume 1, you see him drawing a very heavy bow on the tiller and watching the movement of the outer limbs which seem to curl or roll up as the draw increases.

The curling action of his limbs seems to work its way progressively into the middle of the bow in a very deliberate and engineered fashion with the very last portion of the bow’s middle at the grip area seeming to suddenly bulge into a bend. That lent to the impression that the middle third of the bow was the principal part of the spring action of a bow’s limbs (at least in an English Longbow) with the outer limb following in a whipping action.

That action was a revelation to me and belied the simplicity of the design.

However, after many more drawings and testing against ‘live’ bows, it suddenly dawned on me that at each stage of tillering, the arc of the bow’s bend fitted a circle of proportionately greater radius at each stage of its early draw and progressed steadily to a shorter radius the closer it came to full draw.

I began drawing a circle of best fit for a bow of 72 inches which had a radius of 36 inches (see Fig. 8 above). A base line representing the straight unbent bow was drawn, the middle of which served as the centre point from which the radius was drawn.

The red line represents the circle of bend of a 72 inch bow and the horizontal blue line represents the bowstave itself. The green lines are the paths of travel of the limb tips of this bow. Where the red and green lines intersect represents the maximum travel of the limb tips in forming a circular bend.

However, in real life, this is far too much bend for a draw length of 28 or 30 inches.

How to work out the actual tip deflection was a problem. Empirical testing showed that the actual tip deflection in a straight line down from the base line was within +/- ½ inch of half the actual draw length on a bow of this length. The other variable was, apart from string stretch, changing bow lengths for the same draw length. The amount of tip deflection also changed, but it did so proportionately.

The clue lay in working out that apart from changing bow lengths and string stretch, the amount of bend (and hence tip deflection) would be proportional to the circumference of the circle whose radius was half the bow’s length.

Notably, in each increment of bend from straight to its full draw bend, each of these tillering increments represented part of a circle whose radius was longer at the early stages of tillering and decreased as the bend moved toward full draw shape.

It then became clear that to draw an accurate tiller board showing the shape of the limbs at each stage of tillering, a series of partial circles would be required based upon increasingly larger radii and whose circumference passed through the mid-point along the base-line of the board which represented the unbent stave as in Fig. 9 below.
Progressive-bending-of-circular-tiller-25cm.jpg
Progressive-bending-of-circular-tiller-25cm.jpg (89.05 KiB) Viewed 12462 times
Fig. 9 – Progressive shapes of circular tiller stages based on circles of increasing radius. The toned area represents the backing board.

In that diagram (Fig. 9), the blue horizontal line represents the bow stave and the green curves represent the track of the bow stave’s tips through its normal travel arc. The toned area represents the backing board. It can be seen that because all circles are directly proportional to one another, that a series of circles can be drawn which contact the mid-point of the bow stave (horizontal blue line).

Each circle is numbered. In this diagram, there are 10 circles. It can be seen from Fig. 9, that there are a series of arcs which can be used to represent the stages of bend toward a 2-radian full draw bend represented by the circle numbered 1.

Each circle has a radius plotted away from the stave’s mid-point along the vertical purple line. In Fig 9, the foci of these circles are identified as A to J. Focus A is the focus of the circle labelled 1, focus B draws circle 2, etc., out to focus J which draws circle 10.
If more circles are added with even longer radii, the curvature of those circles becomes even shallower and may be used to represent the shape of a bow’s limbs at even earlier stages of tillering.

It can be seen that the same diagram can be extrapolated to cater for bows of any length. By extending the horizontal blue line to represent bows which are longer than 72 inches or less, and drawing their respective green arcs of limb tip travel, it can be appreciated that the curvatures of the limbs will also follow the same arcs of the circles drawn for the 72 inch bow. The following diagram shows how this is done.
Adaptability-to-various-bowlengths-25cm.jpg
Adaptability-to-various-bowlengths-25cm.jpg (33.51 KiB) Viewed 12462 times
Fig. 10 – Using circular proportionality to show the stages of tiller for bows of different length.

In Figure 10 above, the red arcs of circle can be increased in number to show the correct bending of a bow at much earlier stages than shown in this diagram.

Taking the diagram in Fig. 9, one could increase the number and radius of circles from 10 to perhaps 15 or 16 to show much shallower bends which are to be expected at the earliest stages of tillering. These additional circles could be used to fill the gap between the first circle (1) and the blue (bow) line if it is thought necessary.
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#15 Post by Nezwin » Mon Aug 31, 2015 12:42 pm

Dennis,

It would seem you have missed your calling! This is an Engineers nightmare, but takes me back to my pre-Engineering days with Physicists who loved the challenge of resolving intersecting chords & arcs. Engineers proudly do this kind of thing, but secretly we would rather be making something.

My comments so far;

- The use of 6 radians as opposed to 2 Pi radians demonstrates that this isn't an exact exercise and I think that's a good thing. As all sections of wood are unique, the bowyer has to adapt the bow to the timber. But as a guide for bend-through-the-handle bows, it's very good. I've been modifying the principles as I read to suit stiff-handled bows.

- The 'ideal' tiller could well be the theoretical ideal based on length of bow/radian measurement plus 'a bit'. For instance, a portion of the theoretical 'best' circular arc for a 78" bow might be better suited for a shorter bow at full draw. This would decrease string angle and provide a more elliptical tiller. There's not really a 'best' tiller really, anyway. Much of it is a trade off for performance/feel/accuracy, but at a theoretical level for most energy efficient, this research piece holds well.

- Nagler, et al, have covered the relationship between energy stored in a limb and the curvature of that limb. In your example of using chords (first post) the area under a limb is directly proportional to this stored energy. I, personally, find the relationship between energy stored & curvature an easier one to grasp, so there could well be a method by which this can be modeled. This would also take into account brace height as a form of potential (unused) energy. It would demystify the 'magic' of a skilled bowyer, somewhat - or rather, provide a different avenue for achieving the same results.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#16 Post by Dennis La Varenne » Mon Aug 31, 2015 4:35 pm

Please, NOTE everybody, this thread is NOT about whether or not the circular tiller is the best kind of tiller relative to performance or anything else. It is about HOW to best achieve a genuine circular tiller on bows which bend through the handle such as the classic ELB, and maintain that circularity throughout the tillering process.

I had hoped that it would result in a different kind of tillering back board with a series of curves drawn on it which best appoximate the shape of a bow which bends into a partial circle througout its tillering process.

Most people skilled in tillering ELBs and that family of bows do it by eye with varying degrees of success. Many more do it badly with far too much bend through the handle and too little in the outer limbs. Others again make bows which are too whip-ended and too little bend through the middle section, etc..

Many bowyers use a backing board which is marked with a grid pattern against which the travel of the limb tips is observed to try to ensure that each limb passes the same point as the other and noting that the number of grids under the limbs is close to equal on either side of the tiller.

What I am driving at is that to achieve an ELB pattern bow of any length of which the presupposed ideal tiller is circular or 'compass', that a more accurate fit-to-description by using a tillering board which has a series of partial circles drawn on it against which the bends of the emerging bow can be aligned as those limbs pass through the early stages of bending right out to full draw.

That way, the bowyer can be assured that their bow DOES conform to the ideal of a circular tiller. That's all.

Colin raised the issue of string length relative to brace height. If I use the diagram in Fig. 10 above, I can work out the length of string on any of the 3 bow lengths depicted (60", 72" and 84") at any particular brace height by drawing a line straight across from where the green line bisects the relevant red curve at whatever brace height.

For example, any of these three bow lengths having a brace height of 6 inches, the string length varies around 2 inches of the actual bow length n-n within half an inch. In real life we know that that cannot be right because they are obviously visibly shorter. However this presupposes a string which has absolutely NO stretch.

The strings I use on all my bows is a modern Fast Flight equivalent with fairly low stretch and these strings are rarely shorter than 3 inches less than the n-n bow length. A dacron string on the other hand is usually around 5 inches shorter than the n-n bow length which shows how much stretch there is in this material.

So, I am inclined to think that the drawing and the estimate of string length is demonstrates that the straight line length as measured off the drawing is probably correct. I do know that even with Fast Flight strings, even they show slightly less stretch if I keep as much twist out of the body of the string as possible and the more twist they have in the body, the more they do stretch or more correctly 'unwind' under tension.

Endless strings would be the best kind of string for allowing minimum stretch because there is no twisting in the body if they are made accurately to bow length.

A bigger brace height of course will require a shorter string. So I suspect that the mathematics involved in Nagler's work on tillering and bow draw weight presume a string which has absolutely NO stretch, but in real life, I doubt there is very little loss of draw weight using a real life stretchy string.

Anyway, below is the last part of my discussion.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#17 Post by Dennis La Varenne » Mon Aug 31, 2015 4:56 pm

4. HOW TO DRAW THE TILLER BACKING BOARD

1. The tools you will need to mark out this board are –

(a) A prepared backing board as per 2 below;

(b) A pencil;

(c) A length of non-stretch string of at least 8 feet length (better to have more than necessary);

(d) 10 or more pegs/pins of any kind by which to mark the increasing radii of the circles to be drawn (see A to J in Fig 9 above).

(e) A single peg onto which to attach one end of the string. The other end is tied to the pencil.
2. A flat board of at least the width of the longest bow likely to be made and of a depth of at least the longest draw length to be made. For demonstration purposes, a board of say 7 feet 6 inches (90 inches) x 42 inches deep would cover the above requirement. It should have a surface upon which the arcs of circle would be clearly visible when marked.

3. Draw a horizontal base line representing the bowstave and decide upon an average bow length to be made. Mark the exact centre of the bow. Draw a centre line down the middle of the board at right angles to the base line. In Fig. 10 above, I have used a 72 inch bow and marked the base line thus. (Never mind about the 60 inch and 84 inch marks for the present.)

4. Place the backing board on the ground and fix it in place so it cannot move.

5. Next, set out a series of pegs at 6 inch intervals starting with a point below the base line which is ½ the basic bow length and mark it A. Repeat for another 10 marker points up to J. They must form a line exactly along the centre line of the base board. Start with 10 positions and include more if it is found necessary or desired.

6. The excess string should be wound around the pencil. The peg to which the string is attached is placed at marker A so it cannot move and the string is unwound from the pencil until the pencil reaches to the centre marker of the base line.

7. With the pencil touching the centre marker of the base line, draw an arc extending to the outside edges of the backing board on both sides of the centre line. This is the first and the smallest of the arcs and draws the arc for circle 1.

8. For the purpose of the exercise, you can move the pegged string out to position J and unwind it until the pencil again touches the middle of the base line and again draw arcs on both sides of the board’s centre line. It will be seen that the arc described is far shallower and represents the bend one would expect at an early stage of tillering.

9. You can then repeat the process for as many of the in-between markers as is wished from the shallowest to that with the smallest arc, giving a series of arcs against which one can match the shape of the bend of a bow’s limbs at each tillering stage.

10. When tillering, full draw is reached in the normal fashion when the tillering string reaches that length as marked on the tiller. The correct bend shape is reached at this stage and there is no point in progressing further.

11. With the required number of arcs described on the backing board in pencil, they can then be overdrawn with a more permanent marker and the board then mounted in a suitable place.

12. For bows of other lengths, arcs are described by pinning the string and pencil to the middle point of the base line and extending the pencil out to half the length of the required bow length. An arc is described on one side and then the other side of the centre line bisecting the arcs of bend. Examine the green arcs in Fig. 10 above to see how it is done.

The important thing to realise is that the same arcs of bend used for the basic bow can be used for any other bow length because of the proportionality of circles. So, a 60 inch bow can use the same arcs as the 84 inch bow. The only difference being that the longer bow will have a much shallower bend for the same draw length.


5. A SIMPLE TILLERING TOOL

A very simple alternative to the above is to cut out a semi-circular piece of stiff cardboard (D-shape). This card can be held at arm’s length against a partially tillered bow to check visually for circularity of bend. The size of the semi-circular template doesn’t matter within reason, but around 12 inches diameter is good.

At the earlier stages of tillering when the stave’s bend is very shallow, the bowyer just moves further away from the stave until the picture of the edges of the D-template against the stave touches the bowstave on the belly at its middle.
D-template-showing-poor-tillering_25cm.jpg
D-template-showing-poor-tillering_25cm.jpg (14.35 KiB) Viewed 12429 times
Fig. 11 – D-template showing very poor tiller on an ELB

The D-template should have a centre line which is aligned with the stave’s centre and moved up until the centre of the D-template touches the belly of the stave at its middle.

If the stave is stiff in the middle, the tips will be close to or actually contacting the edges of the tiller but the mid limbs will show a gap. If the outer limbs are too stiff, the tips will always stand away from the edges of the template.

Individual limbs which are not circular will either stand away from the template or be partially or fully covered by the template when it is positioned against the belly of the bow on the tiller.

The bow pictured in Fig. 11 above is the same bow show in Fig. 1 and shows a bow which, while of uneven tiller, has a right outer limb which is too stiff and is partially covered by the template and a left limb which has too much bend at mid-limb and stands away from the template.

The bow in Fig. 13 below shows a nearly perfectly circularly tillered bow. There is very slight stiffening at the bow’s middle, but it is less than half the handle thickness. The individual limbs stand away from the template at the 2/3 mark out from the bow’s middle. This demonstrates that there is a deliberate whip-endedness in this bow. This bow, more than any other I have seen most probably meets Ascham’s criteria quoted above.
D-template-showing-marginal-tiller_2-25cm.jpg
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Fig. 12 – Another bow which is too stiff in the outer limbs.

The bow in Fig. 12 above shows a bow which, while evenly tillered, is still far too stiff in the outer limbs.
D-template-showing-good-tillering-25cm.jpg
D-template-showing-good-tillering-25cm.jpg (16.01 KiB) Viewed 12429 times
Fig. 13 – This is the bow shown in Fig. 7 above. It is a well tillered ELB with whip-ended outer limbs demonstrated by the small gap above the D-template a little past mid-limb.
D-template-showing-fair-tillering-25cm-2.jpg
D-template-showing-fair-tillering-25cm-2.jpg (30.19 KiB) Viewed 12429 times
Fig. 14 – This bow appears to have very stiff outer limbs, but is not at all what it seems.

In Fig. 14 there is an in-between level of tillering skill. It almost makes a circular bend but not quite. The outer bow limbs are still a little bit thick and stiff. Before positioning the D-template (Fig. 15), this bow looks to have extremely stiff outer limbs. But with the template in place (Fig. 15 below) and aligned with the bow’s middle, the edge of the template shows that only.
D-template-showing-fair-tillering_3-25cm.jpg
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Fig. 15 – Showing how well the D-template fits this bow which has outer limbs which are almost but not quite perfectly bent, only needing more bend in the outer ¼ of the limbs.
Marginal-tillering-of-short-ELB-+-D-template-25cm.jpg
Marginal-tillering-of-short-ELB-+-D-template-25cm.jpg (25.52 KiB) Viewed 12429 times
Fig. 16 – Marginal tillering of a very short ELB with stiff outer limbs requiring more bend in the outer 1/3 of each limb.

Figure 16 above with the D-template in place shows how stiff the outer limbs of this bow are for a 60 inch bow. The only way to get these tips to contact the edges of the template would be to induce a much greater bend in the outer 1/3 of the bow’s limbs. This would be very difficult in such a short, stiff section of limb.

Making this bow so short leaves almost no room for error in tillering. A flat bow would have done it easily because of the shallow limb section. However, for an ELB, the tips at the horns would have to be something around 3/8 or ¼ inch diameter to bring the tips around more. Such a short ELB needs a limb thickness taper of around 25 to 30 thou per inch to be bendy enough for circular tillering.

6. IN FINISHING . . .

If the desired shape of an ELB is circular, my view is that this particular tiller back board is the most practical and accurate method of guiding a bowyer through the stages of tillering to the classic circular (compass) bend other than from using mathematical formulae to blue-print a bow before commencing work.
This method can also be used for bows with rigid handles by placing the bow in the tiller’s cradle and aligning it such that the fade-out points (if they can be ascertained) can be aligned on the base line. From that position, one can treat the bending the same as with an ELB.

The middle section of a rigid handle bow will of course have little or no visible bend in its middle section unlike an ELB, where it is mandatory if proper tradition is to be adhered to.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

QVIS CVSTODIET IPSOS CVSTODES (Who polices the police?) - DECIMVS IVNIVS IVVENALIS (Juvenal) - Satire VI, lines 347–8

What is the difference between free enterprise capitalism and organised crime?

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#18 Post by Gringa Bows » Tue Sep 01, 2015 10:36 am

Top post Dennis......When will you be up this way again ?

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#19 Post by Dennis La Varenne » Tue Sep 01, 2015 4:44 pm

Around christmas time I think, Rod. I have a couple of little all-wood recurves made by a young mate over in Michigan that I would like to show you. They are Hickory backed Red Oak. I think you will be interested in them.
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Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#20 Post by Gringa Bows » Tue Sep 01, 2015 8:40 pm

Good one,look forward to seeing them

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#21 Post by BowmanBjorn » Tue Sep 01, 2015 11:38 pm

Hi Dennis,

great work, a lot to digest. in an earlier post you mentioned a reference to a bow at "compass" being 1/6th of a circle and it not making any sense as the 2 radion rule works better. is it possible that the 1/6th of a circle could relate to a bow when at brace?

haven't had a chance to draw it and work it out. if it is the case then for a given bow you could work out the "correct" brace and therefore length of bow string which would also remove 2 more variables from your above calculations?

just a thought
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#22 Post by hunterguy1991 » Wed Sep 02, 2015 8:30 am

Bjorn,

The 1/6th of a circle is just a simplification of the number or radians in a circle as Clinton already explained... Circumference of a circle is Pi (3.1415.....) x diameter or 2 x pi x radius... 2x pi = 6.2803.....

As the radius or curvature is related to the string length and hence brace height as well as bow length and draw length, the process in drawing a curve to tiller to would be to set the bows length and brace height and then use these to figure out the curve...

The issue is relating all the factors in an equation to produce a radius of curvature for the full draw curve (which is quite complex) that works for any combination of the given parameters.

Colin

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#23 Post by yeoman » Wed Sep 02, 2015 7:49 pm

If I might suggest an alternative method of drawing a circular tiller at full scale that takes into account brace height (but not string stretch):

http://www.ozbow.net/phpBB3/viewtopic.p ... 475#p49475

In that link, I show how to plot a circular tiller for a bow that has a rigid handle section. Exactly the same process can be applied to a bend through the handle longbow by not putting a rigid handle section in.

Using that method, you can plot the tiller for exactly the brace height you would like to use. If you feel like putting the work in, your can do several arcs to show theoretical stages of draw. However Dennis' observations on a limb not bending proportionately throughout the whole draw might suggest this is not terribly helpful. Indeed, on bowmaking classes I watch other people pull their bows down to various stages of draw hundreds of times over the course of a weekend and I would have to echo Dennis' point about limb behaviour. I guess it makes sense, as when a bow is drawn the leverage exerted on the limbs changes dynamically through the whole process.

Anyway. To use this method you'd need a very long straight rule, a large set square, a pencil and some plumbline. And of course the sheet of ply or MDF that will form the backboard. The sheet doesn't have to be 11 feet long as would seem apparent. If you do it on the floor, just run off the edge of the board where you need to and you should easily be able to fit a very bog bow on a full sheet of ply.

All that being said, I think there are times when circular tiller is appropriate, and times when it is not. I agree with Dennis that Ascham's 'full compass' does not mean circular tiller, and I think there are many mechanical and practical reasons why circular tiller is not appropriate for a warbow or later Tudor longbow. If there is interest, I'll prepare a piece explaining why this is so, and where circular tiller does in fact become an appropriate and beneficial design feature.

Cheers,

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#24 Post by Dennis La Varenne » Wed Sep 02, 2015 9:17 pm

Bjorn,

As Colin reiterates, equating one radian to 1/6th of a circle is a simplification for the purposes of practicality. Because Pi is a number which never ends ( at least I don't think anyone has calculated an absolute value for it), theoretically, no circle ever closes. In real life we KNOW that they do. That is also a simplification for practical purposes.

One of the ideas which occurred to me in working out this system was the realisation that at every stage of tillering, the shape of the emerging bow, providing that it is circular (another practical simplification), each stage represents a bent shape whose full circle has a decreasing radius the closer the bow comes to full draw - if that makes any sense.

That is why I did the diagram labelled Fig. 9. Each capital letter is the centre of a circle whose radius extends to the blue base-line representing the bow stave. Figure 10 shows the arcs of travel of the bow tips of bows of 3 different lengths. Where they bisect the innermost circle centred on A in Fig. 9, is the maximum amount of bend in a bow of that length before the shape goes out of circular to ovoid.

As I pointed out above, full draw doesn't actually bend a bow to its maximum degree of circularity. Generally, most bows at full draw move their tips about one half of the maximum amount of bend and that seems to be pretty consistent.

So far as 1/6th of a circle goes, it is much more bend than brace height, but less than full draw generally speaking. You can check that on any bow you have presently. Place your bow at brace height on a tiller and measure the amount of tip deflection from straight and then again at your full draw and see what you get.

As everybody has pretty much pointed out, this is not a mathematically precise skill. There are too many variables which presently, we cannot control - string stretch being the worst of these.
Dennis La Varénne

Have the courage to argue your beliefs with conviction, but the humility to accept that you may be wrong.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#25 Post by BowmanBjorn » Fri Sep 04, 2015 7:53 am

Hi Guys,

i understand that 1/6th of a circle isn't the same as 1 radian. the value of pi i use on a regular basis in my day to day job so i understand what your saying.

only reason i suggested it was to try and link together "the observation of Thomas Waring in 1824 suggesting that the arc of an English Longbow was one sixth of a circle (one radian)." to a practical aspect of the "perfect" historically correct ELB.

i'd looked at an ELB in my possesion and thought at Brace it didn't look terribly far off approx 1/6th of a circle.

i don't have the time unfortunately to work the actual numbers out just thought it was worth a mention. but seeing as Dennis has already considered this and that at Brace the bows arch is significantly greater than 1/6th of a circle (for simplicities sake use i know 1 radian isn't 1/6th of a circle) then it doesn't matter :)
Centaur Triple carbon elite 2pce 60# @30"
Thunderstick MOAB 50# @30"
Flat line Raptor 45# @30"
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BowmanBjorn
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#26 Post by BowmanBjorn » Fri Sep 04, 2015 8:06 am

just quickly trying something.

i copied the image from Dennis' earlier post with the 6 radion segments of a circle.

then copied the image of a longbow from http://www.outfit4events.com/eur/produc ... ow-yeoman/

i then super imposed and rotated and scaled the bow image on to the segmented circle.......

the was the 1st clear image of a longbow at brace i could find so it may not hold true but i'll be damned if it doesn't fit the arc of 1 radion of the circle?

i've attached a PDF of the overlay, very simple but it works for the 1st image i found?
Attachments
1 radion ELB at brace height.pdf
(78.59 KiB) Downloaded 171 times
Centaur Triple carbon elite 2pce 60# @30"
Thunderstick MOAB 50# @30"
Flat line Raptor 45# @30"
Norseman Wrath 2pce 54# @30"
Norseman trilam ELB 104# @ 32"

hunterguy1991
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#27 Post by hunterguy1991 » Fri Sep 04, 2015 8:56 am

Scale is off mate, Dennis suggested that a bow is 2 rad long... just coincidence.

Superimposing photos is not really an accurate method of looking at that stuff. Even superimposing curves can be misleading.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#28 Post by Dennis La Varenne » Thu Sep 10, 2015 11:25 pm

Does anybody think that this method of guiding the tillering of an ELB pattern or similar bow through to completion? I can do my own testing, but what I am looking for is corroboration of the technique. It needs somebody else to check what I am proposing who does not have my own bias toward a technique which I devised.
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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#29 Post by Nezwin » Fri Sep 11, 2015 10:49 am

Dennis La Varenne wrote:Does anybody think that this method of guiding the tillering of an ELB pattern or similar bow through to completion? I can do my own testing, but what I am looking for is corroboration of the technique. It needs somebody else to check what I am proposing who does not have my own bias toward a technique which I devised.
I would love to help, Dennis - I've never built an ELB or a bend-through-the-handle bow - but it will be some time before I'm fit enough to get back in the workshop.

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#30 Post by hunterguy1991 » Fri Sep 11, 2015 3:24 pm

I can give it a crack with a bow with some serious weight when I'm good to work in a few weeks Dennis.

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