Next, we’re going to label the units of the output figure to show millimetres. Still on the formatting menu we want to select ‘User-defined’ from the Category list, and enter “mm” to the ‘Format code’ (fig. 7). Any text that is entered between inverted commas (“ ”) will appear after any data entered in the cell.

Fig.7
 

This is the re-formatted cell E9 in the spreadsheet. The result of the calculation is displayed to one decimal place and labelled with millimetres (fig. 8)

Fig.8
 

Now we’re going to take what we’ve learned so far and apply it to making a spreadsheet to work out mast tapers.

Using the spreadsheet to work out mast tapers
Depending on the vessel and period, masts and yards were tapered according to formulae. Steel’s The Elements and Practice of Rigging and Seamanship Vol. 1 has tables of data showing the measurements worked out for various diameters of mast. This reference work can be found online at http://www.hnsa.org/doc/steel/index.htm

The length of mast determines its diameter at the partners (where the mast is at it greatest diameter as it passes through the upper deck). The diameter of the mast at the partners determines the diameters at the various quarters, the head and the heel.

From Steel The Elements and Practice of Rigging and Seamanship Vol. 1 p39
The diameters in proportion to the length, in the royal navy, are as follow: viz.
The main and foremasts of ships of 100 to 64 guns inclusive, are one inch in diameter at the partners to every yard in length. Ships of 50 to 32 guns inclusive, 9/10 of an inch to every yard in length. And ships of 28 guns and under, 7/8 a of an inch to every yard in the length.
The main-mast of brigs to be one inch to every yard in length, and the foremast 9/10 of the diameter of the main-mast.

The following table is from Steel The Elements and Practice of Rigging and Seamanship Vol. 1 p42

So, knowing the diameter of the mast at the partners, we can get the spreadsheet to work out the various diameters throughout the length of the mast. Note that there are fore and aft, and athwartships dimensions for the heads, which were wider athwartships (6/7 of the diameter at the partners) than they were fore and aft (3/4 of the diameter at the partners).

Okay – lets get this information into a spreadsheet. I’ve set mine up as shown in fig. 9. By now, you should be able to work out the formulae to enter into the relevant cells. I’ve listed them next to the example spreadsheet for the work-shy. I’ve also highlighted the cells that require input in green.

Fig.9

Next, consider that we need three masts. All of the cells can be copied to another part of the spreadsheet without worrying about the formulae we’ve entered. The cells named in the formulae are automatically updated to the new locations. We need to copy the table we’ve made twice, for the foremast and the mizzen. Simply highlight the areas to be copied (click and drag), copy (control C), click the top left cell of the area where they are to be pasted, and paste (control V).

We know the diameters of the masts at the partners from the data in Steel (p49), and these can be entered into the relevant green cells. Of course, Steel provides us with the various diameters of the masts too, but the spreadsheet automatically converts these to millimetres and at the required scale (fig. 10)

Fig.10
 

Some of the data in this spreadsheet are redundant – for example, the scale has been entered three times, and the diameter of the mast in millimetres before scaling isn’t a required measurement for the model. It can, however, be useful to include such results in the design of your spreadsheet as it makes it easier to troubleshoot. I also think it’s good practice not to have long formulae, for the same reason.

It’s possible, given the way mast and yard dimensions are calculated, to design a spreadsheet that will produce all the required mast and yard dimensions upon entering very few figures.

Steel (p39) …
The length of the lower deck and extreme breadth being added together, the half is the length of the main-mast.
If we know the length of the mainmast, then …
Fore-mast, 8/9 of the main-mast.
Mizen-mast, 6/7 of the main-mast.
If we know the mast lengths, then ….
Main-yard, 8/9 of the main-mast.
Fore-yard, 7/8 of the main-yard.
Etc, etc

So, if anyone is feeling inspired …

To download this article in PDF format, click HERE
 

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