Saturday, August 7, 2010

Fan of the Fan (III)

Continuing on now with a look at fan raftering, Japanese style. I mentioned in previous installments (1, and 2) in this thread some of the difficulties inherent in determining the radiating pattern of the rafters. It is a challenge to satisfy aesthetics when it comes to exposed rafters, which can be seen both from directly below, and from out in the yard/street, where the exposed rafter tips provide a pattern. While human estimations for distance are often poor without some point of reference, humans tend to be quite good at spotting irregularities in things that form rhythmical patterns. Both from below, where one can observe the pattern of the wedge-like spaces between individual rafters, and from afar, where the rhythm of the rafter tips is presented, there is an opportunity to observe and compare - and blunder, when it comes to the carpentry.

In a previous post I illustrated why it is mathematically impossible to satisfy both conditions in the case of the fan rafters. One cannot have both an even rafter tip spacing at the eave edge and have even-shaped triangular spaces between rafters. So, the alternative is to come up with some method which tries to find some sweet spot between demands, or finds an alternative arrangement to a regular spacing pattern which will also prove pleasing.

Today I want to look at the first of several methods used historically in Japan to find a solution to the fan raftering conundrum. Sometime later in this series I will also take a look at a Chinese traditional approach to the same issue to see how it compares.

Right then - this first method proceeds on the basis of trying to find a middle ground between the circle and the square. Here's how it works - first we draw out hip corner plan, a regular one with the hip aligned at 45˚:

I've labeled the corners 'A', 'B', and 'C' in the above drawing, with 'C' being the turning point for our fan rafter sweep.

Next comes the part where we try to relate the circle to the square by swinging an arc, length AC, across the 45˚ sweep, giving point 'D':

Then we take distance B~D along the hip plan and divide it in half, finding the midpoint between the circle and square, so to speak. This new point we label 'E', and then we connect a straight line over to 'E' from 'A':

Next, the line from 'A' to 'E' is divided evenly into the number of rafters we want to have, which in this case is eight rafters. Dividing a line into any number of segments is easy with a framing square.

Then rafter lines are run from the fan's origin point 'B' down to each division of line 'A~E' and extended out to the bottom of the triangle:

The bottom of the triangle, line 'A~B' is our eave edge of course.

So, with the drawing method complete we have what looks to be a fairly tidy looking arrangement. I will now examine in more detail how the spacings along the eave edge compare to one another, using some basic math to calculate the interval at the rafter tips:

Please click on the picture for a clearer view. As you can see, the spacing starts out adjacent to the common rafter (line 'A~B', which equals '10' in length) with 1.0868, then grows steadily:

1.1281...1.17184...1.2181...1.2672...1.3193...1.3747... and 1.4337 adjacent to the hip line. That seems like a workable arrangement, with a fairly gradual increase between rafters starting with 0.0413 between the first two and ending with an 0.059 spacing between the last one and the hip.

Now we turn to look at how the pattern of wedge segments look - the view presented when looking up at the rafters from below (I've swung around the view in the picture to look at the triangle from the origin end of the fan):

Here we see a pattern of angles that starts out along line 'A~C' (on the right side) with around 6.20˚. Then the next wedge climbs to 6.28˚, before falling at the next segment to 6.22˚. From there the pattern continues, with a drop in angular values between segments:

6.22˚...6.02˚...5.70˚...5.30˚...4.86˚... and 4.42˚.

I have rounded up the values from the drawing, in case that is causing anyone confusion.

In summary then, this first method has produced a pattern of rafter tips which gradually climb in space between themselves as the sweep proceeds from common over to the hip, and a pattern of angular spaces between the rafters which climbs briefly then falls in amount with each successive rafter over. It seems the patterns conflict with one another. It's not the cleanest solution, but it is considerably better than the option of either dividing the 45˚ sweep into regular increments (thus leaving the tip spacing poor) or vice-versa, spacing the rafter tips evenly and ending up with a higgledy-piggledy arrangement of spaces between rafters.

In the next post in this thread I'll take a look at another traditional solution to the fan rafter spacing problem and see what eventuates.

Thanks for your visit to the Carpentry Way today. --> go to post IV

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