Fan of the Fan (IV)

Last time we looked at one method the Japanese use in traditional carpentry practice to space fan rafters. That method involves taking the run length and swinging it over to the hypotenuse length, after which the difference between those two lengths is divided and a new line snapped across. The aim was to split the difference between the extremes of spacing associating to both ends of the fan spectrum, moving from the common length to the hip length. The result of that method was that the spaces between rafter centerlines at the eave edge climbed steadily as the fan swung over to the hip, while the angular value of the wedge spaces between rafters climbed for a rafter or two, then fell off steadily. That method did not result in perfection, so we will consider other approaches to see if something better can be found.

Today we look at another traditional Japanese method which is fairly similar to that first one in that the difference between the extremes, namely the run of the hip rafter and the run of the common, will be related.

Here's our starting point, triangle a-b-c, 45˚ in plan:


Previously we swung the run length over to the hip run; in this case we do the opposite and will swing the hip length over to the common, creating point D:


In the previous method we then divided the difference in the two lengths in half - here we will not. A line is simply snapped across from B to D, forming, incidentally, a 22.5˚ angle to the eave line AB:


The triangle formed, B~C~D, is an isosceles ('iso-' means equal, and '~sceles' means scale). Notice that as with our previous method, we have also divided our new line segment, B~D, into eight equal divisions.

Next we extend rafter centerlines from the origin to the eave, passing though our line division marks:


Right, there we have the method for fanning the rafters along eave edge A~B.

Now let's see in depth what result devolves. First we will look at how the angular divisions work out. If we divide 45˚ into 8 even units, we obtain 5.625˚ as mean, or 'ideal'. Here's what we have produced with this second method in comparison:


Clicking on the image will make it more easily readable. The angular pattern is this, moving from common over to hip:

5.2421˚ - 5.5570˚ - 5.7888˚ - 5.9121˚ - 5.9121˚ - 5.7888˚ - 5.5570˚ - and 5.2421˚

This pattern grows steadily to the middle pair of rafters in the set, then falls steadily, in mirror image. Considering the 'ideal' of 5.625˚ as a mountain peak, say, we have climbed up to, slightly surpassed, and then dropped down around that mark. Not the smoothest pattern - the rafter angulation appears slightly congested at each end of the range.

Let's take a look now at the rafter tip spacing. If you divided the eave edge, a length of 10 in the drawing, into 8 equal parts, you would have rafters spaced 1.25 units apart as an 'ideal'. The result of this second method produces the following however:


Similar to the first method seen in the previous post, the arrangement of rafter tip spacing is on a gradually ascending order. That's not too bad. Like the first method we looked at, this one produces a decent pattern at the eave edge, however the arrangement of the angular spaces, such as would be seen viewing the fan rafters from below, is not so sweet. It seems like the perfect arrangement still eludes us. In the next post in this thread I'll take a look at a third Japanese traditional method for arranging fan rafters, one of the most popular, to see what it offers.

Thanks for dropping by the Carpentry Way today my friends. --> go to post V