Shop Tips & Tricks #5: Centerlines - Finding, Marking and Using Them! (Part Two)

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Blog entry by GnarlyErik posted 12-08-2012 12:32 AM 13552 reads 7 times favorited 9 comments Add to Favorites Watch
« Part 4: Centerlines - Finding, Marking and Using Them! (Part One) Part 5 of Shop Tips & Tricks series Part 6: Measuring Things - Rulers Versus Tapes »

Here’s a little esoteric ‘how-to’ for those times you can not buy the ‘round’ you need in the size or material you want. This is a basic spar or mast builder’s technique which works for making things round and long.

Almost all wooden masts have traditionally been built with a changing taper, diminishing towards the top. In ancient Grecian and Roman times, many of their architectural columns in their buildings were gracefully tapered from base to capital, and in fact often, the tapers began at the base in a particular diameter, then the diameter increased slightly for a distance before beginning a graceful, curving decrease in diameter towards the top. Some opinions say these changing curves are based on the human figure, and in particular on the female figure – the lovely taper in a woman’s legs in the eyes of a man for example. For whatever reason, the idea of long, graceful tapering columns has carried over for millenia into more recent times in mast and spar building, and many other things too. Tapers also just so happen to be very well suited for making long things like masts smaller (lighter) towards the top, with weight being a penalty against stability the higher it is carried. You even see this in many aluminum light poles along the highways today.

Mast and spar builders over time developed techniques for both rounding something from a square piece of stock, and tapering it towards the end. And, that’s where the two extra holes come in in the little Gee Whiz multi-tool presented in part one of “Centerlines – Finding, Marking and Using Them!” (

The extra two holes on the Gee Whiz are for laying out the facets on square stock to plane to in order to make the piece octagonal, or ‘8-sided’. Once planed to eight-sided, the stock can then be accurately rounded from there (on larger rounds, say over 10 or 12 inches, the stock is often ’16-sided’ after being 8-sided, but the concept is the same, though not the proportions).

In use, the tool is employed exactly as for centering long stock, but the two outermost pencil holes are used in lieu of the center hole. And, no matter the length, or taper, the marks will provide the lines to plane to for the full length of the stock except for the last few inches at the end. Simple as that.

Now, as to how this is laid out, here’s how it is done. First, the stock is squared, obviously. Then, at any point along the length of the stock a square is constructed on the side of the stock, the same as the cross section of the stock at that point (or on a bit of scrap on the bench if you prefer). This is next bisected by diagonals to find the centers, and a circle is drawn to fit inside the square of the stock.

Next, tangents are draw at 45 degrees to the edge, where the diagonals bisect the circle. The point where this tangent intersects the edge of the circle marks the point of intersection of one of the facets of the octagon enclosing the circle – and so on around the circle. The fact is you have only to find two of these points to be able to lay out your work, and here is where the Gee Whiz comes in. These two points are proportional to the width, no matter how wide, and that is why the Gee Whiz works for all tapers, the full length of the stock. By keeping the pins against the sides of the square, you keep the same proportion anywhere along the length – not exactly precise at very steep angles, but generally close enough for ’government work’ as they say. This is done on all sides of the stock, providing all the meeting points of all eight facets. @

I have included a graphic below which demonstrates the laying out of the points, and which should be easier to understand:

Laying out 8-sides using graphical method

Further, since these proportions are always the same, you can use a ruler to do the same thing, albeit not quite as conveniently. A two-foot folding rule is particularly well suited for this, and to watch an old-timer laying out the facets for 8-siding a mast with his folding rule was like watching magic! Here is how that works:

A two-foot rule (or measurement) is laid out across the stock, so that each end touches an edge. Marks are made at the 7” point, and the 17” point. This is done down the length of the stock at convenient points, and then all the marks are connected with a straight edge or batten. Simple as that! (see sketch below)

Laying out 8-sides with two-foot rule

And, any multiples with the same proportions work just as well, for example, a 12” measurement, marked at the 3-1/2”points and 8-1/2” points! Who’d a-thunk it?

@ And, as my old daddy used to say, “Then, you plane off everything that doesn’t look like a mast!”

-- "Never let your dogma be run over by your karma!"

9 comments so far

View shipwright's profile


8711 posts in 3872 days

#1 posted 12-08-2012 01:01 AM

Very good explanation Eric.

-- Paul M ..............the early bird may get the worm but it’s the second mouse that gets the cheese!

View HillbillyShooter's profile


5811 posts in 3367 days

#2 posted 12-08-2012 01:53 AM

Thanks, agree on very good explanation.

-- John C. -- "Firearms are second only to the Constitution in importance; they are the peoples' liberty's teeth." George Washington

View oluf's profile


260 posts in 4113 days

#3 posted 12-08-2012 04:01 AM

I am learning so much and having a great time reading your blogs. I am eighty two years and have been exposed to woodworking all my life. When I was growing up my Father was a production supervisor in a custom millwork and cabinet shop. I spent many hours there with him. My Father was born in Denmark in 1881 and Served a full apprenticeship there and worked as a master journeyman in Europe before coming to the U.S.A in 1912.

While I am sure that my Father had full knowledge and worked with the things you are writing about I didn’t have the opportunity to learn enough from him. He was 49 years old when I was born and with school and four years of navy service we didn’t have enough time together. Thank You again for the great training. Nils

-- Nils, So. Central MI. Wood is honest.Take the effort to understand what it has to tell you before you try to change it.

View GnarlyErik's profile


344 posts in 3209 days

#4 posted 12-08-2012 06:27 AM

Thanks to all for the nice comments! And Nils, you are never too old to learn new things – and I believe learning keeps you young, at least in mind. Besides, at 81 you are only a few years older than me (I’m in my 70’s). My wife claims I haven’t grown up, and she’s still trying to make me behave. My dad also immigrated – from Norway in 1926 – and he had a wealth of experience to share with me. Only, it was more like ‘forced labor’, or ‘sing for your supper’, which was a phrase he often used. In other words, he believed in earning your keep, and fully expected us kids to work in the boat shop (or any other place he assigned as he wished) without pay, or complaint. And, somehow we didn’t even mind! He was generous in everything besides actual money. My dad was a tough task master, but he gave me probably the best grounding ever, for a career which provided for my family and which I enjoyed immensely. Everyone should be so lucky!

-- "Never let your dogma be run over by your karma!"

View lightweightladylefty's profile


3643 posts in 4787 days

#5 posted 12-08-2012 07:12 AM

Erik, Though I may never get a chance to use the knowledge, thanks for another great lesson!


-- “Those who would give up essential Liberty, to purchase a little temporary Safety, deserve neither Liberty nor Safety.” Benjamin Franklin -- Jesus is the ONLY reason for ANY season.

View Nicky's profile


711 posts in 5166 days

#6 posted 12-08-2012 05:58 PM

Thank you for sharing. This (and your other posts) has been very informative.

-- Nicky

View Sylvain's profile


1244 posts in 3574 days

#7 posted 12-10-2012 05:34 PM

I really enjoy this serie about tips and tricks.

Some studies would support the idea that the shape of Greek columns is to provide resistance to buckling.

see at the end of this paper :
see “engineering hypothesis” on the 11th page.

-- Sylvain, Brussels, Belgium, Europe - The more I learn, the more there is to learn

View GnarlyErik's profile


344 posts in 3209 days

#8 posted 12-10-2012 10:01 PM

Hi Sylvain -

While you may be correct on the buckling idea, I still like the more romantic notion they are tapered to achieve ‘perfection’ to the eye. And, most studies seem to agree on that point. Here’s some information on that:

The eye is apparently easily fooled into thinking something is different than it actually is. A good example of this is the common naval architecture practice of changing the rake (lean) of each of the masts in a two-masted vessel. They usually are designed to ‘splay’ or lean apart at the top as much as 5 degrees, so the eye conceives them as parallel, which is the designer’s intention. Otherwise, due to effects of perspective, they can look as though they are converging.

Understand my experience has mostly to do with boats, but another good example of this notion concerns what is called the ‘hood ends’ of the boat. As viewed in a profile on the drawing board, the sheer line (the visual line of the deck or top rail) may look perfect, but if the boat is built to what looks good on paper, because of the three-dimensional aspect of boats, the very end at the bow where all three dimensions converge, (and sometimes the stern too) can look ‘hooded off’ as boat people describe it. In layman’s terms it will look downright droopy. To combat this empirically learned fact, most designers deliberately raise the very ends of the sheer line on their plans by as much as 2 or 3 inches in a 50 footer for example. When built to that line, the sheer then looks visually perfect in three dimensions.

Every trade has its subtleties!

-- "Never let your dogma be run over by your karma!"

View shipwright's profile


8711 posts in 3872 days

#9 posted 12-10-2012 10:27 PM

Two more illusions:
1) Curves must become more pronounced as they get higher above the waterline or they will appear flat.
This applies to the progression… waterline, boot-top, rubstrake line, sheer and to the cambers in deck, cabin-top, hatch cover, etc.
2) Cabin sides must lean in or they will appear to lean out.

The eye is a funny thing.

-- Paul M ..............the early bird may get the worm but it’s the second mouse that gets the cheese!

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