**Making the Most of It:**

Maurice Tebbutt and Keith Drew talk us through the maths and making of a segmented bowl.

A ‘surprise package’ arrived in the post. Given its size – about 20 x 15 x 5cm, it seemed surprisingly heavy and inspection showed that it was a block of something like teak (*Tectonia grandis*) or oak (*Quercus robur*). The letter inside the package revealed that it was a gift from a friend, who lives on the Falkland Islands and knew of my interest in woodturning. She indicated that the timber was not just ‘any old block of wood’, but a part of an old sailing ship, called the *Vicar of Bray*, which had been rotting away there, more or less steadily, aided by the frequent storms to which the Falklands are subject, until she finally disappeared in 2015.

A bit of internet research showed that the ship was launched in 1841 and had plied her trade for some time in various parts of the world including involvement in the ‘Gold Rush’ before foundering on the Falklands

in about the 1880s. All of this reinforced my intrigue with the block of wood and I resolved to try to do something with it in keeping with its venerable history. Here is the original block that was contaminated with tar and showing signs of rot, which was not altogether surprising for timber which was about 170 years old and had potentially spent much of that time in salt water.

I thought that a 150mm shallow dish or even a plaque didn’t fit the bill and also involved turning away and losing a substantial part of the timber in the block. Ideally what I wanted was to preserve as much of the block as possible; to find some means of ‘bulking it up’ and also present it attractively. Eventually it occurred to me that segmenting could meet my requirements. It can, and often does, involve combinations of a number of different colours of timber, hence meeting the ‘attractiveness’ requirement, while coincidentally achieving the desired bulking up. This would seem to solve the problem, except that I had little idea how to do it. Fortunately, there are a number of members of my woodturning club, Worcestershire Woodturners, who are skilled in the techniques required, one of whom is Keith Drew.

**Plans, equipment and materials**

**Tools
**• Bandsaw

• Hotmelt glue gun

• Adhesive

• Bowl gauge

• Scraper

• Clamping system

**Materials**

• Contrasting timber to the block

• Plywood

**The maths**

The main characteristic of Keith’s suggested bowl design was a simple shape, which led to ease of construction while also minimising the wastage of material. The diagram also shows that the circular edges of the slices are at 45° to the horizontal (and vertical, of course!). It may also be apparent that the combination of the thickness of the slices and the angle of cut (in this example 45°) means that the rings can be cut in succession from one board, and that they will sit on top of each other to form the shape shown. This unusual method of constructing the bowl opened the way to being able to determine whether it would be feasible to construct the bowl from the block of wood which we had available. The greatest volume of available timber, which we can call ‘A’, was 20 x 15 x 5cm or 1500 cubic centimetres. So, A = 1500.

We decided to make the initial board, i.e. the top of the bowl, about 20cm square. Making a board t cm thick would require 20 x 20 x t cubic centimetres of timber. We called this ‘R’, so R = 20 x 20 x t. If we assumed that we would just use the timber from the block and could perform the redistribution without any waste, the two volumes would be the same. i.e. R = A or 1500 = 20 x 20 x t (1) and t = 15/4 or 3.75cm.

So, if our assumptions were correct then the task would be eminently feasible, producing an initial board, and hence also the subsequent layers, almost 4cm thick. However, we knew that the whole of this volume would not be available for one of two possible reasons; either because of wastage during the conversion process, which would happen in any case, or because of the effect of the rot on the block.

The direct effect and indirect effect of the rot in our block meant that only about one third of the original block (which we can call the ‘conversion fraction’) would be available for use, this would give a volume of A/3 or about 500 cubic cm. Equation (1) now becomes 500 = 20 x 20 x t (2) So t = 500/400cm, or about 1.3cm).

So, if it turns out that only a third of the block is usable, it would be possible to produce a board with a reasonable thickness, so that the whole fabrication process would be feasible. However, it will be clear that this is not the whole ‘story’ since the ‘contrast’ timber, which we have ignored so far, would also contribute to the amount of available timber, and we did not have a reliable method of determining the conversion fraction.

Although this may appear to be very complicated, Keith’s solution was eminently simple – basically to start at the end!

He decided that he wanted the ‘bowl’ to be about 20cm square (as quoted in the calculation above) and to sit about 9cm high. It was to consist of the top, together with four supporting layers (five in all), which are cut in succession it from it so each layer would be 9/5 or 1.8cm thick. It will be clear that the bowl is constructed mainly from rings of timber, with a circular base and a topsquare with a circular hole.

**Top tip: When laminating and using various types of adhesives, you may find that placing a thin sheet of plastic or shrink wrap underneath will help minimise the risk of any excess adhesive squeeze out bonding to other hard surfaces on which your laminations sit. **