Nice Axe Handle - traced plan

[bugbear]

Recently I saw a rather lovely little 1 1/4 Lb axe by Whitehouse appear on eBay.

It turned out to be offered by our own mahking51.

I didn't need another axe, but the handle looked gorgeous, and good axe handles are much
rarer than good good axe heads.

Mark was kind enough to send me the additional images I asked for, and I carefully traced them.

So - herewith, with permission, for the general good, I present copies of the measured plan I made. The lines
inside the outline are the proportional "octagon" lines.

(I would have preferred the plan to be in PDF, but the forum doesn't allow it)

BugBear

 

[Harbo]

Thanks BB - nice profile - will file away for future use.

Rod

 

[matt_southward]

Looks like a nice profile, and I have a head in need of a handle so I'll definitely try that shape. I'm not sure what you mean by 'proportional octagon' though - could you explain please?

 

[bugbear]

Looks like a nice profile, and I have a head in need of a handle so I'll definitely try that shape. I'm not sure what you mean by 'proportional octagon' though - could you explain please?

The normal way to make a round (or elliptical) object from a square blank is to first make an octagon;
this is so common that a "spar gauge" embodies the arithmetic for it, and many steel squares
also have an octagon or "8 square" scale.

http://www.boat-building.org/learn-skil ... par-gauge/
http://www.pettigrews.org.uk/lm/page030a.htm

BugBear

 

[matt_southward]

Ok, got you. I'm familiar with the concept from green woodworking- just didn't quite follow your meaning. Thanks.

 

[bugbear]

I asked for some thickness numbers, which I've added to the diagram as cross sections;
Thickest point is around 30mm.

BugBear

 

[Billy Flitch]

Thats a real nice helve easy on the eye and probably easy on the hand, I hope you don't mind if I talk about the spar gauge. Its a ancient Shipwrights tool and was probably being used before the maths of the tool was fully understood.
you posted two good links to explain the tool but they where both just a little over the top on the maths .

I thought I would explain it the way it was explained to me when I was a boy. Shipwrights just like most Carpenters in the past worked in proportions in this case we will work in 12 th`s. To make it easy to check back and see just how it works we can call each 12 th a centimeter, so if we draw two lines on a x y basis that dissect each other and around these two lines we form a 12 centimeter square.
We go to the top of the square and where the line crosses the square with a set of compasses we mark 2.5 centimeters either side of the line, repeat it at the bottom of the square and to the left and right sides of the square.
We now join these points together and we have now formed a octagon. when we measure across the top of the square we we can see that the measurements are 3.5 5.0 3.5.

When using 12 ths we know that proportions are 3.5 5.0 3.5 but this is only the start of the spar gauge because we know that spars are tapered and when we place the spar gauge on the spar and run it along the spar, then the spar gauge scribs adjust with the gauge and keep the proportions 3.5 5.0 3.5 no matter where it is on the spar.

So if you looked at the end of the spar you would have a perfect octagon if you where to take a hand saw and cut the spar at any point regardless of what size the spar was and at what point you cut it the spar would show a perfect octagon even though it is changing its size all along the spar.

The simplicity of our ancestors is matched only by their brilliance.

 

[Plumberpete]

Hi Bugbear,

I've got a couple of old 7lb axes with 36" handles. If I sent you dimensions/photos would you be up for making patterns for them to share?

Cheers,
Pete.

 

[bugbear]

Thats a real nice helve easy on the eye and probably easy on the hand, I hope you don't mind if I talk about the spar gauge. Its a ancient Shipwrights tool and was probably being used before the maths of the tool was fully understood.
you posted two good links to explain the tool but they where both just a little over the top on the maths .

I thought I would explain it the way it was explained to me when I was a boy. Shipwrights just like most Carpenters in the past worked in proportions in this case we will work in 12 th`s. To make it easy to check back and see just how it works we can call each 12 th a centimeter, so if we draw two lines on a x y basis that dissect each other and around these two lines we form a 12 centimeter square.
We go to the top of the square and where the line crosses the square with a set of compasses we mark 2.5 centimeters either side of the line, repeat it at the bottom of the square and to the left and right sides of the square.
We now join these points together and we have now formed a octagon. when we measure across the top of the square we we can see that the measurements are 3.5 5.0 3.5.

When using 12 ths we know that proportions are 3.5 5.0 3.5 but this is only the start of the spar gauge because we know that spars are tapered and when we place the spar gauge on the spar and run it along the spar, then the spar gauge scribs adjust with the gauge and keep the proportions 3.5 5.0 3.5 no matter where it is on the spar.

So if you looked at the end of the spar you would have a perfect octagon if you where to take a hand saw and cut the spar at any point regardless of what size the spar was and at what point you cut it the spar would show a perfect octagon even though it is changing its size all along the spar.

The simplicity of our ancestors is matched only by their brilliance.

As I'm sure you know, the numbers you quote are an approximation to the true (irrational!) numbers, but are certainly
good enough for practical purposes - these lines, after all, define a roughing process!

Further, the spar gauge is only accurate for "long" tapers. If you sketch a spar gauge on a strongly tapered item (1:3 or something silly) it gets the answer wrong.

None of this detracts from it's extreme utility for setting out an actual spar, of course.

BugBear

 

[bugbear]

Hi Bugbear,

I've got a couple of old 7lb axes with 36" handles. If I sent you dimensions/photos would you be up for making patterns for them to share?

Cheers,
Pete.

Sure; if you can:

1) make/draw/find a piece of squared paper big enough to sit the axe on. The size of the squares doesn't matter, as long as it's documented. This grid allows any perspective errors to be corrected, and the size of the plan to be corrected.

http://gimp.pixtuts.com/gimp-tutorials/ ... destortion

2) write on the axe at various stations (probably using pieces of masking tape as label) labelling the thickness at that point, so we have a thickness profile as well as the more obvious side profile.

3) Set the axe on the paper, and take a photograph (at last!) using a lens of 100mm (35mm equiv) or longer, and from a good distance away (4 foot or more); the long lens helps to avoid any barrel distortion. Make sure the labels are readable

4) Send me the photo!

Something like this (in this case, the thickness stations are just spots, and I wrote the thicknesses on a piece of paper, and my squared paper could have been better)

BugBear

 

[Billy Flitch]

Bugber your quite correct the numbers are aprox I think you would have to add 0.035 to the measurement of 3.5 but if I was to do that then Iàm missing the whole point of the gauge. The gauge is not offered at right angles to the spar but canted and is based not on mathematics but proportions. It was in the 1500`s that mathematics where introduced into shipbuilding when young Shipwrights like Mathew Baker and his contemporary's where sent of to Holland and Venice to learn the most up to date way of building ships.

Before this time ships where built on custom and practice methods (just like the spar gauge) ships would be inspected by the kings master Shipwright who would either give the ship the the thumbs up or down and that was called the rule of kings thumb and is where we get the modern day saying ` rule of thumb`.
So as you rightly say any method that has a dis function of so small an amount would be excepted just as Archimedes taught us in his writing a result to within a grain of sand is quite exceptable .

Working with tapered objects on a small scale with the gauge is feasible but really finicky this is my gauge for the shop fully adjustable with a tapered octagon handle on a chisel.

 

[bugbear]

The gauge is not offered at right angles to the spar but canted and is based not on mathematics but proportions.

I think proportions, ratios, fractions et al come under the generous umbrella of maths!

Obviously altering the angle of the gauge doesn't alter the ratios.

I would be slightly sad at someone using this who didn't understand where
the ratios come from, but just use the "special" 7/24 value.

I supposes that sort of thing was "Guild Magic" and all the worse
for it, IMHO.

BugBear

 

[bugbear]

I would be slightly sad at someone using this who didn't understand where
the ratios come from, but just use the "special" 7/24 value.

I supposes that sort of thing was "Guild Magic" and all the worse
for it, IMHO.

BugBear

I just found a pamphlet on the use the the "Steel Square". It mentions that
most steel square have an exact "Octagon scale" on them, but also mentions
that the "Steel Square" can be used to proportionate an approximation
by using the body (24") diagonally across the beam, and marking at 7" and 17"
which is (of course) your 3.5/12. Steel Square practise is of course very much
expressed in the language of ratios.

Now, the real ratio is (approx) 0.292893219
7/24 = 0.291666667 (error 0.0012265523333)
interestingly, 5/17 is a better approximation, despite having a small denominator, but few people have scales
marked in 17ths.
5/17 = 0.2941176 (error -0.0012244280)
(12/41 is even better, but nobody cares)

BugBear