ON FULL COMPASS BOWS
Posted: 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.
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.
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.
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.
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.
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.
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.
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.