Review: Acer-Ferrous Sector
Review: Robert Howard
The sector is a very old mathematical instrument that has become relevant again as an aid to design, but up until now it was very difficult to find one. The arrival of this Acer-Ferrous Toolworks sector from Red Rose Reproductions satisfies that need.
So, what can a sector do? The sector can be used, in conjunction with a set of dividers, to find proportions (including Golden Ratios); find the radius, diameter or circumference of circles; find the length of the side of any polygon (up to 12 sides) to fit a given circle; set out given angles, or measure given angles (from 6–90°).
Finally, for chairmakers, it can calculate resultant and sightline angles from any given rake and splay angles. This greatly simplifies the drilling of any compound angle hole, such as the leg mortises on Windsor chairs.
All of these uses involve working from a known dimension – in metric, imperial or degrees – to set the sector, and then using dividers to read off or set out the dimension that is required. A few simple steps are all that are needed.
A quick example: what is the length of each side of an 11-sided polygon drawn to touch the circumference of a circle 187mm in diameter? 1. Draw a circle with 187mm diameter. 2. Set dividers to the radius of 93.5mm. 3. Set the sector by placing the dividers, set to 93.5mm, into the holes marked ‘6’ on the P scale. 4. Finally, with the sector remaining set in that position, re-set the dividers in the holes marked ‘11’ on the same scale. That is the required length of each of the 11 sides.
I deliberately chose the odd numbers to emphasise how easy these problems become (and yes, I did test it, and it worked without any discernible error). Note also that I do not need to know the actual length in millimetres, but just step it out with the dividers.
The most exciting possibilities however, are to be found in its use for finding proportions.
George R Walker and Jim Tolpin, in their two books (By Hand and Eye, and By Hound and Eye), detail their discovery of how traditional designers used proportions as the basis of design. This method has been hiding in plain sight for over two centuries, and offers a way to take the guesswork out of the many design decisions that need to be made when drawing up a design. In the space I have here I can only point you towards their books. The method is simple in concept, but tricky in execution. However, if I was 40 years younger I would make mastering it an urgent priority.
The sector itself is of high quality, likely to survive regular use over a long career. The two arms are made from anodised aluminium, and are joined with a brass hinge much like those used in the old, folding boxwood rules. The four scales are laser engraved on the rules, two on the front and two on the back, and include small holes at each numerical point designed to capture the points of a set of dividers. The stiffness of the hinge can be adjusted with the special tool that is supplied.
A 26 page instruction booklet (but no dividers) is also supplied, with additional instruction videos available on the company website. It is available from Lie-Nielsen Australia, for $319. I have already put my money down (paying full price), to endorse my opinion of its usefulness.
Review tool supplied by Lie-Nielsen Australia, www.lie-nielsen.com.au/Sector
Robert Howard is a woodworker and sculptor who lives in Brisbane. He teaches woodcarving classes from his studio.