CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOARD

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#31 Post by greybeard » Fri Sep 11, 2015 7:36 pm

Dennis,

Every time I think about circular tiller I keep coming back to the point of the relationship between the length of a radian and the draw length of the archer.

I cannot vouch for the accuracy of the illustration used by Horace Ford; the bow length would appear to be less than two radians but as it conforms to part of a circle we cannot refer to it as elliptically tillered.
Horace Ford Diagram.jpg
Horace Ford Diagram.jpg (66.57 KiB) Viewed 1864 times
In the following image the blue and the black lines are of equal length. As you can see the red line indicating the curve of a bending bow limb is longer. I believe the point of intersection of the green arc is not correct.
Full Length Of Bow.jpg
Full Length Of Bow.jpg (134.99 KiB) Viewed 1864 times
I think the only way to get the true path of travel of the limb tips would be to attach pencils on the tips of the limbs and bring the bow to full draw on the tiller board thus marking the tips travel on the board.

Daryl.
"And you must not stick for a groat or twelvepence more than another man would give, if it be a good bow.
For a good bow twice paid for, is better than an ill bow once broken.
[Ascham]

“If a cluttered desk is a sign of a cluttered mind, of what, then, is an empty desk a sign?” [Einstein]

I am old enough to make my own decisions....Just not young enough to remember what I decided!....

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#32 Post by Dennis La Varenne » Sat Sep 12, 2015 12:43 am

Thank you both Colin and Neil. The technique does need verification in case I am barking up the wrong tree.

Darryl, I know where you are coming from. The amount of bend at full draw does not come completely around to two radians of bend because of stretch in the string, but thus far when I have measured the curves of some of my own full bending bows, the amount of bend measured against a half circle protractor with 3 radians drawn onto it show that the bends are almost 2 radians, consistent with string stretch using fastflight. The degree of bend would be much less using dacron or something with similar stretch.

You will notice in your quote above that the last sentence does say
However, in real life, this is far too much bend for a draw length of 28 or 30 inches.
Measuring the length of both dacron and fastflight against the n-n length of the bow, dacron is short by almost 5 inches and fastflight by only 2.5 to 3 inches. From that observation, I knew that string stretch would make a difference

I have probably explained myself badly, but my idea only began with noticing that the bows which I matched against circles drawn over their full drawn shape was what gave me the idea of their bending over 2 radians of curvature, but I later wrote that string stretch would have an influence on the degree of bending. I would not have had the temerity to insist that they actually bent over 2 radians. But it is pretty close for practical purposes.

Again, matching my 'protractor' against a full drawn bow on a tiller, I just cannot get the shape to fit a curvature of only one radian or even close to it. However, as you propose, the bent shape is still partially circular with which I quite agree.

I realised that even if a bow did not bend to a full 2 radian curvature, the shape at any stage of bending throughout the tillering process would still be partially circular. From there I went on to devise a way of drawing up a series of '12 o'clock' interesecting circles of increasing radii (Fig. 9) with the idea/realization that as the bend increased along the bow's length, that shape would/should match those intersecting circles and hopefully, maintain a partially circular shape to the entire bow right out to full draw.

Hopefully, this technique would overcome the tendency of so many bowyers making this kind of bow to make handle bending bows which bent excessively in the middle or left the middle too still and too much bend in the outer limb creating an elliptical shape in both cases where the deepest part of the curve of each limb was either in the outer or inner part of the bend rather than in the middle.
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

#33 Post by greybeard » Thu Sep 17, 2015 3:31 pm

Dennis,

I taped a few strips of bamboo together to represent a 68 inch n t n bow. As the bow has minimal draw weight somewhere between five and ten pounds string stretch is not an issue.

To obtain circular tiller the bow had to be draw to 32 inches to follow the pattern. Incidentally my draw length hovers on 27 inches.
Sixty Eight Inch Bow.jpg
Sixty Eight Inch Bow.jpg (107.37 KiB) Viewed 1848 times
The average lengths of the Mary Rose bows are 78 inches which would suggest a radian of 39 inches.

As an estimate the bow would have to be drawn somewhere near 45 inches to achieve a circular tiller.

Daryl.
"And you must not stick for a groat or twelvepence more than another man would give, if it be a good bow.
For a good bow twice paid for, is better than an ill bow once broken.
[Ascham]

“If a cluttered desk is a sign of a cluttered mind, of what, then, is an empty desk a sign?” [Einstein]

I am old enough to make my own decisions....Just not young enough to remember what I decided!....

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#34 Post by Dennis La Varenne » Thu Sep 17, 2015 3:56 pm

Daryl,

Like I did originally, you've fixated on 2 radians being the only form of full circular draw. I tried to explain that it was my early observation that the bows I drew circles against appeared to have a radius of half of one radian. I knew that that would raise just the issue that you are now raising and that in real live, nobody would draw that kind of draw length even allowing for string stretch.

That is what drove me to try to work out how could one maintain a circular tiller throughout the tillering process to the stage of full draw and still keep the shape of the arc truly circular. Realising that all circles are directly proportional to each other, I realised that at every stage of tillering, even at less than brace height, that the shape of the arc could be kept circular because the shallower the arc, the greater the circle of which the length of the bow was only a partial curve.

I had to think long and hard about how to maintain the circularity of the arc of the bow from end to end and found that the only way that it could be achieved was to draw that series of intersecting circles in Figure 9, where each circle was predicated on progressively longer radii. So, even though an early-tiller staged bow was bending but a few inches, the shape of its arc from end to end could still fit the curve of a circle, albeit a much shallower curvature at that early stage.

Perhaps I ought to have left that part about 2 radians out completely. It is clearly confusing people. I included it only to demonstrate my thinking processes and how I arrived at the conclusions that I did. There was a huge jump in concept from first thinking that a bow bent around 2 radians of arc to the later concept that 2 radians would not work because of a preposterously long draw length to the later idea that of matching the shape of the bow's arc to circles of increasingly greater radius.

As you can see from your experiment, both the 34 inch radius circle to which you have matched your 'bow' is a circular bend, but so is that of the shorter radiused 27 inch curve. It is just that one is a smaller circle around which to bend a bow. BOTH ARE CIRCULAR BENDS. They are just of different radii. If you were to bend your test bow to match a circle causing a bend where the draw length would be nearer your real life draw length, the circle would still be circular - only it would be of a larger radius circle with a much shallower bend.

As you proposed earlier that Waring (???) considered that the full draw bend of a long bow was one sixth of a circle or near enough to one radian of curvature, I have not been able to match that shallow a curve with any of my ELBs which go from only 66 inches up to 75 inches. I get a result above 1 1/2 radians for the longer bows at a 28 inch draw and close to 1 3/4 radians with the shorter bows using my protractor.

So, what's the point of it all?? Authorities on the subject insist that handle-bending bows like the ELB are/should be of circular bend if their interpretation of Ascham's term 'compass' is to be believed and insisted upon. Few bows seldom are and most I have seen bend far too much through the handle in what looks to me to be an exaggerated attempt to induce a visibly circular or 'full compass' bend in their bows. Others appear to have ends which bend more than the bow's middle, but this happens much less because such made bows are clearly NOT 'compass' bending.

Therefore, starting with the observation that many pictures of full drawn bows on tillers appeared to me to have a curvature of 2 radians, I thought I had solved the problem of inducing correctly circular bows. However, as you rightly point out and with which conclusion I completely agree, that a bow of 2 radians in length which is bent to that degree of arc requires arms the length of which no gorilla ever had. So, my original contention was wrong. The rest of what I wrote above followed from that error in thinking.

My apologies for the confusion.
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

#35 Post by hunterguy1991 » Thu Sep 17, 2015 4:37 pm

Daryl,

Your bow is drawn to 32 inches at 68 inches long, following the maths Dennis put forward in his discussion and I follow what you have done with the bamboo. However, notice that your bow has a string to tip angle of very close if not 90 degrees... the last thing you wrote was that the MR bows would need to have a 45 inch draw to achieve a circular tiller... I disagree... To have the same relationship Dennis put forward they may need the 45" draw but a circular tiller just means the bow bends the arc of a circle, it does not specify the radius of curvature that the bow takes...

I have seen some bows made to MR spec by Ian Coote (A world renowned English warbow maker) that bend pretty much an exact circle. I will look and try to find the photos of the bows if I can. both laminates and self Yew bows. The difference with these bows is that the string to tip angle is not as close to 90 degrees as yours which would indicate a larger radius of curvature.

Here lies my issue with relating bow length to brace height/string length to nock-string angle to the radius of curvature.

It is a much more complex issue than whats been put forward in this thread.

I agree however that Dennis's tillering method of drawing a series of circles on the tillering board of varying radius to tiller to through the entire tillering process is a solid idea and one worth trying should that be the desired tiller shape.

I have had a chance to do a little testing of different tiller shapes recently with 2 bows I have made personally for a friend. the theory by UK and European bow makers is that a circular tiller will throw a heavy arrow further and a whipped tiller a lighter arrow further... NOT my experience.

I have tested a 75lb@ 30" whipped tiller (with some set) and an 80lb@30" circular tiller (bow is straight when relaxed) both shooting the same 31" 52g arrows and there is little difference in the cast of each bow... The release angle of the shot plays a larger role in the overall distance.

Colin

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Re: CIRCULAR TILLER BOWS AND DRAWING AN ACCURATE BACKING BOA

#36 Post by greybeard » Thu Sep 17, 2015 9:00 pm

hunterguy1991 wrote:..........However, notice that your bow has a string to tip angle of very close if not 90 degrees......
Colin, I was well aware of the string to tip angle.

Although there was a lot of information to go through I believe the following image clouded the issue.
Dennis Image.jpg
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Daryl.
"And you must not stick for a groat or twelvepence more than another man would give, if it be a good bow.
For a good bow twice paid for, is better than an ill bow once broken.
[Ascham]

“If a cluttered desk is a sign of a cluttered mind, of what, then, is an empty desk a sign?” [Einstein]

I am old enough to make my own decisions....Just not young enough to remember what I decided!....

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