ON FULL COMPASS BOWS

How to make a Bow, a String or a Set of Arrows. Making equipment & tools for use in Traditional Archery and Bowhunting.

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Dennis La Varenne
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ON FULL COMPASS BOWS

#1 Post by Dennis La Varenne » Sun Feb 22, 2015 12:33 am

The modern use of the term 'compass' in reference to the shape of well-tillered ELBs is taken directly from the use of the same word by Roger Ascham in his 1545 book 'Toxophilus'. He uses the word quite often in describing the shape of the drawn bow AND the shape of the trajectory of the arrow. Reading and re-reading the book, especially where he uses the word has caused me to come to the conclusion that it does not match the modern word 'circular' or the expression 'arc of circle'.

Furthermore, it is my present opinion that the tiller shape of the ELB is definitely NOT circular as we have all come to believe, but in fact, it is eliptical.

My understanding now is that in Ascham's time, the word 'compass' was a word which would be used interchangeably with our modern word 'curved' and that the Tudor expression 'full compass' as it applied to bows meant in fact that a bow was curved (evenly) over its full length and was not necessarily derived from a circle at all.

Nowhere in Ascham's book does he use the word 'circle' or 'circular'. He uses the word 'compass' or other versions of it to describe any form of curvature. A circle as we understand it today has specific properties which can be described mathematically, such as the relationship of its circumference to its radius and its diameter and the measurement of chords drawn between points along the inside of its circumference.

Today, we understand that a truly circular bend in the limbs of a bow seems to be the best shape by which to distribute the optimum (and maximum) stress along the limbs of a bow before the wood begins to fail. So, presuming that the optimum bend for and ELB was also circular, I tried to work out a way of drawing a bend which was the length of a given bow from nock to nock which, at full draw, formed a truly circular bend and which, if continued out past the nocks, would join again at a point 180 degrees away from the centre of the bow and directly across the circle's diameter.

There is a branch of circular geometry dealing with finding the circumference of a circle from the measurement of chords and the distance of their midpoint from the circumference. In this case, the chord of the circle in question is the distance between the nocks of the full-drawn bow. The shape of the full drawn bow represents the partial circumference of the circle and the distance from the middle of the chord and at right angles to it out to the bow itself is the distance of the chord from the circumference of the circle.

Unfortunately for me, my mathematical skills are not up to the application of that level of maths. However, I realised that if the curve of an ELB at full draw was truly circular as we have always believed, then applying the concept of radians, that if half the length of an ELB were treated as the radius of a circle, its length would be two radians.

For those who do not know, a radian is that partial length of the circumference of a circle which is equal in length to the radius of that circle and spans a distance along the circumference of almost 60 degrees, so that there are 6 radians to a full circumference for practical purposes.
Tannhillman bow_1.jpg
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Above is a picture of a bow made by an English bowyer which is 77 inches nock to nock. He advertises that his bows are full compass bows meaning that their shape is truly circular. The picture has been rotated 180 degrees for this post.

In fact, the bend of this bow is eliptical at the full draw of 30 inches in this picture, but could possibly be truly circular if it were drawn to 38.5 inches or half the bow's lengh. The standard drawlength used by the English War Bow Society is 32 inches which is far short of 38.5 inches.
Tannhillman bow_2.jpg
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In this picture above, by scaling the picture in Photoshop, I have overdrawn a circle in red which has a radius of 38.5 inches, the focus of which is well below the V of the drawn string on this bow. You can easily see from the shape of the circle that the shape of the bow's limbs DO NOT form circles. The curves are much shallower at the bow's 30 inches of draw on the tiller and would not increase significantly in curvature if drawn to 32 inches.
Tannhillman bow_3.jpg
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In this third picture above, I have drawn a series of chords labelled A, B and C on the picture using chord A as the standard. The chord is drawn from the bow's exact middle to the nock and I have copied it exactly and used it for the other two chords labelled B and C.

I have then aligned chord B from the bow's middle toward that limb's nock showing that the curvature of that limb is greater than the left limb. Lastly, I have place the centre of the chord C with the bow's centre which shows that the curvature of this section of this bow is far greater than either of its limbs indicating that this bow certainly bends through its handle. If the bow were truly circular, all three chords would touch the bow at each end and the vertical blue lines from the middle of these chords would touch the belly of the bow. They do not.

The other pale green lines labelled D and E mearly show the difference in distance from the V of the drawn string to the centre of each limb further demonstrating that the curvature is different between each limb.

I have done this same experiment on many pictures of full-drawn ELBs and found the same thing. You simply cannot get an ELB or other non-rigid handle bow to form a true partial circle at full draw.

This experiment is not meant to point out any kind of tillering faults in ELBs. We can and do tiller them very well indeed. What it is meant to point out is that we have most probably and erroneously misapplied Ascham's term to mean the conventional geometric shape we understand today, when clearly, it does not. We have then become slavishly attached to endeavouring to meet this criterion and assuming that this was how it was back then and trying to emulate a standard which most probably did not exist.

As I pointed out above, Ascham also uses the term to apply to the trajectory of an arrow which most certainly is elliptical because the shape of its trajectory steepens as it loses velocity at the end of its range and begins to descend more steeply as gravity draws it down against its every decreasing velocity.

This distinct use of the term in two completely different applications seems to me to indicate that 'compass' was a common Tudor language term (not necessarily an archery term) which applied to anything having a well curved shape. It is also quite possible that, even with a Tudor understanding of the mathematical nature of circles which they most certainly had, that the same word had been used to also apply in common language to anything which appeared to be circular including the bent shape of a bow and the trajectory of an arrow and which APPEARED to be circular even though in reality, it wasn't.
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.

hunterguy1991
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Re: ON FULL COMPASS BOWS

#2 Post by hunterguy1991 » Sun Feb 22, 2015 9:15 am

Dennis,

I completely agree with you on your thoughts on the term "compass" in Ascham's text... Unfortunately I have to deal with the term being misused often when talking to bowyers from the UK...

As far as that bow you posted goes... pretty terrible tillering job I think as its visibly far to stiff in the last 8 to 12 inches of both limbs. Unfortunately I often see this from guys on Facebook as well because they don't understand the 'Whip' tiller that should be used. I have often had to tell them that to get a proper well formed whip tiller it is a matter of a half inch or so, rather than very exaggerated.

This is an image by Lee Ankers, a professional bowyer from England, who I have had several discussions with on tillering bows.
Lee's tiller plus circle overlayed.jpg
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Lee claims to tiller to a perfect Circle and when a big enough circle is laid over the photo it would appear that he does as the limbs follow the red circle arc pretty much perfectly.

Dennis La Varenne
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Re: ON FULL COMPASS BOWS

#3 Post by Dennis La Varenne » Sun Feb 22, 2015 4:10 pm

Colin,

That picture shows a bow with a circle overlain which would have a focus much further from its circumference than on my example where I treat the bow's curvature as having a value of 2 radians in length. And yes, the outer limbs are way too stiff as you say. It is very apparent and quite visible in my third picture.

The bend through the handle is about 0.5 inch greater than at the middle of the limbs which is considerable for this kind of bow and makes me think that the concept of a bow which bends through the hand is being made a more important aspect of tillering ELBs by some bowyers than it really ought. What is wrong with just the hint of bending through the handle and whipped ends to minimise handshock.

Personally, I think that this bow would kick badly because of the amount of stiff timber at the bow's tips. Somewhere on this site in the ELB section http://www.archers-review.com/, I remember reading that handshock in an ELB is a given. I disagree with that entirely and have made none which did so, but have had several which I bought from overseas which certainly did. All had too much bend through the handle, had far too rigid outer limbs and anything BUT a circular bend.

Using my method of assessment using radians could well be incorrect, but if I could work out how to apply the maths for calculating the circumference of a circle from the length of a segment bisected by a chord, it would be the correct way in which to be able to figure out a circle to draw against a wall by which to match the bow's tiller. I could then be able to work out from that how long a bow would need to be in order to meet the accurate circular bend criterion to within a few percent relative to a specific draw length.

Are you any good at that sort of thing? Your maths would be light years ahead of mine.

Also, when I look at your picture carefully, although it is small, I think I perceive an inconsistency of shape between the shape of the circle and that of the bow. Can you see it? If you let your eyes go out of focus slightly, you can see it better. I think he has placed the circle contiguous with the bow's belly rather than its back because the bow seems to sit above the curvature of the circle. I wish the picture were bigger. Just the same, it is quite apparent how little visible bend there is through the handle than on my example.

I wonder how he worked out what radius he needed to use to match his bow.

By way of an aside, I wonder why the EWBS picked on 32 inches for a standard draw length when the average length of arrows from the Mary Rose was 30 inches by all accounts?
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: ON FULL COMPASS BOWS

#4 Post by greybeard » Sun Feb 22, 2015 4:41 pm

Dennis and Colin,

My original interpretation of ‘coming around compass’ was that when a bow was at full draw the limbs formed a semi circle i.e. 180°.

Perhaps forming a segment of a larger circle may be closer to the mark.

I have always referred to my bows having elliptical tiller, perhaps 'oval' could be another description.

Dennis, having viewed the photograph posted by Colin I decided to do similar to a photograph of a Mary Rose bow on the tiller posted by you some time back.
Mary Rose War Bow On The Tiller.jpg
Mary Rose War Bow On The Tiller.jpg (80.76 KiB) Viewed 2919 times
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!....

hunterguy1991
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Re: ON FULL COMPASS BOWS

#5 Post by hunterguy1991 » Sun Feb 22, 2015 5:00 pm

Daryl and Dennis,

In the image I posted the red arch does lie along the back of the bow... I have a larger version here that I can look at to verify that.

As far as compass being to 180 degrees, that's not possible as the string would be straight up and down, like the blue lines in Daryl's photo...

By setting a string to nock angle at full draw you have a starting point for calculating the arc as this give a quarter of a circle... this can then get you the string length by doubling it and from that a range of potential bow lengths...

From what I have seen tho the string to nock angle on the large draw weight bows is not close to 90 degrees (minimising deflection to maximise allowable stress since large stress plus large deflection equals failure) so you cant make that assumption... you somehow need to relate the radius of curvature at full draw to the string to nock angle at full draw and the string length...

There are a lot of factors that come into play, string length, bow length, brace height, brace profile, string angle, draw length... list goes on!!

I will go over some calculations at some stage and try to work it all out but for now I'm happy to set a bows length and desired draw weight and tiller that bow to as close to a circle or slightly stiff in the handle by eye... Worked fine for me so far so that's what I'm sticking to :biggrin:

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mikaluger
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Re: ON FULL COMPASS BOWS

#6 Post by mikaluger » Sun Feb 22, 2015 9:22 pm

I have a head ache.
I agree with Colin, some guys in the UK are so Mesmerised by this full compass idea. But if you make and shoot enough of them, and put aside the ones that shoot the best, this is what I have found.
Crowned back, slightly stiff handle with an even tiller to tips and braced correctly = Better shooting bow with little or no hand shock.IMHO......

Now if you splice a handle in the afore mentioned formula................... geez, still working on that one........some success and some expensive faliures. Ask Roadie.
Such is bow making...........

alaninoz
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Re: ON FULL COMPASS BOWS

#7 Post by alaninoz » Mon Feb 23, 2015 7:57 pm

Minor point unrelated to bows - the trajectory is actually a parabola if you ignore air resistance. It gets a lot more complicated if you include air resistance.
Alan

hunterguy1991
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Re: ON FULL COMPASS BOWS

#8 Post by hunterguy1991 » Mon Feb 23, 2015 8:26 pm

Still an arc tho as it is my understanding that arcs don't have to be a segment of a circle, just a curved path.

Including air resistance and atmospheric effects, I do believe arrow trajectory follows a cubic function similar to that of a bullet.

Colin

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Re: ON FULL COMPASS BOWS

#9 Post by hunterguy1991 » Tue Feb 24, 2015 6:43 pm

Only a little related to the thread but I thought Dennis could appreciate this photo...

One of several great shots we managed to get during a little warbow shoot today. This one is of me at full draw with my 115lber shooting a 54gram, 31.5 inch long EWBS Standard arrow.
DSCN0732 (480x640).jpg
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The belly of this bow is riddled with Chrysals now after shooting it for so long ( hence my saying Grey Ironbark is not the best warbow wood) but still comes round to a gorgeous slightly whipped bend. The dam thing just wont break!! But its getting a little sluggish now, so I have an excuse to make a new heavier one :biggrin:

We also managed a photo at about one third into the power stroke of the shot and also one with the arrow about a foot and a half off the bow after the shot where you can still see some of the archers paradox in the arrow.

Oh and Mick, I am wearing shoes in this photo :wink:

Colin

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