A spar gauge is a simple piece of equipment, which anyone can make. However, its impact on the time it takes to make out a spar is huge, especially on a tapered spar, making it quick and easy. This is a video short, originally from the section 'Making wooden spars'.
The aim for this square piece of wood is to make it into a round mast. This is done by removing the 4 corners, resulting in 8 sides, and then removing those 8 corners and so on.
Each step brings it closer to a round shape.
The important outcome of this process is that all the sides' lengths are equal, this is where Pythagoras' theorem comes into play. Pythagoras' theorem states that in any right angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two sides that meet at a right angle. So the Pythagorean equation can be written:
a2 + b2 = c2
To create an octagon section from a square, it is necessary to plane or cut the 4 right angle triangles off. Due to this relationship, we can use Pythagoras outlined above to calculate the ratio between the sides of the triangle, square and the octagon.
From the above diagram, it is possible to see that side a and b are equal and side c is not only the hypotenuse of the triangle but also the sides of the octagon. This highlights the relationship between the sides and enables a spar gauge to be designed.
To find c, the equation can be rearranged to:
c = √( a2 + b2)
If you give a value of 1 to sides a and b (a and b are the same length as the corner angles are 45°, 90° and 45°), c can be calculated as being:
c = √( 12 + 12)
c = √( 1 + 1)
c = √2
c = 1.41
So the relationship between sides can be described by the ratio 1:1.41:1. If the spacing between the outer pins and inner scribes on a spar gauge uses this ratio, it will mark out the octagon within the 4-sided shape.
As long as the outer pins are pressed against the side of the mast, this ratio will be transferred to a tapered or straight mast as the spar gauge is drawn along the timber. Ideally the spar gauge needs to be at an angle of 45° to the mast, as a different angle will affect the ratio. For this reason you will require a different size spar gauge for different diameters of masts, however, the spar gauge will do a range of spar sizes within reason.
Once these corners have been removed to create an octagonal mast, it is necessary to remove these corners. It would be possible to make a spar gauge for this purpose, the ratio in this case would be 0.4005 : 0.199 : 0.4005 between the various components of the spar gauge.
Once you have made your spar gauge with its wooden or metal outer guide pins and the inner scribes (these could be pencils, metal spikes or even screws), you will be ready to mark up your spar.
The benefit of the gauge is that while the outer pins are pressed against the side of the mast, that ratio (1:1.41:1) will always happen and this is true for both tapered and straight masts. This removes any unnecessary calculations, marking outs, etc.
So place the spar gauge on the piece of wood, twist it so the guide pins have made contact with sides and draw it along making sure that the scribes (in this case screws) are marking the timber. To make the line easier to see, a pencil could be run down them. The lines give the edges of the corners which must be removed to make the octagonal shape required.
Measuring the distance from the edge to the line at different points along the mast demonstrates ratio at work. As the width changes due to the taper, the distance from the edge to the line also changes and a range of 14mm to 21mm was seen.
Rotate the mast and repeat the process for each side.