Tuesday, December 31, 2013

Can't See the Forest for the Trees (IV)

In the previous post in this series I looked at the outcomes of sawing a log through-and through in three different orientations:
  1. No adjustment for log taper (cuts A, B, and C)
  2. Ajust taper so pith of log is aligned to the cut (cuts A', B', and C')
  3. Adjust taper so bark side of log is aligned to cut (cuts A", B", and C")
I used the term 'cutting to the inside' in regards to cuts which followed the alignment of the pith, and 'cutting to the outside'  for cutting aligned to the outside surface of the log.

Cutting through and through to produce dimensional lumber involves a slabbing cut and then an edging cut. For methods (1) and (2) above, the edging cuts were made in alignment to the pith, while for method (3), in keeping with the logic of the log alignment in that case, the edging cuts were made parallel to the bark side of the planks.

An analysis of the three methods showed that whether taking slices from the log to produce boards which were flatsawn, riftsawn, or quartersawn, cuts made in alignment to the bark, sawn to the outside, generally resulted in boards with straighter grain. The difference was most pronounced with the flatsawn boards and least with the quartersawn boards.

A reader pointed out in one of the subsequent comments which I received, "I would think board C' would have the least grain runout, because you are taking it from the halfway down portion of the log. When you "saw to the inside" it seems you will have best grain alignment with a shim that sets the pith level to the mill bed.". I made a reply or two to that comment and then thought it was worth a more thorough explanation at the start of this post.

Here we have the log shimmed so that the pith is perfectly parallel to the deck of the mill, and therefore to the run of the cut:

The desired quartersawn board's cut lines are indicated by the lines marked on the log.

Now we'll remove the rest of the log and consider only the board slabbed out by those two cuts:

Now, if we execute the edging cuts so that they are aligned to the outside of the log, cutting to obtain a pair of wide quartersawn planks, we would obtain the following:

Tossing aside the trimmed bark side (mostly sapwood) and the tapered center boards with pith, and voila!, here are our two absolutely perfect straight-grained boards:

The result is perfect, however, this perfection is coming about largely by looking at the situation purely academically.

Getting to that desired board in the first place has its own set of difficulties. If it were the only board we cared about, and considered the rest of the log as waste, that would be one thing, however that's not a common scenario. The common scenario is to convert as much of the log as possible into usable timber.

If we went directly to the upper surface of that quartersawn board with our first cut, we would have a situation like this:

That can present a problem, as the massive offcut on top is difficult to maneuver, and it has to be removed before we make the next cut. In any case, in making the cut so far into the log there is a chance of the log pinching the blade, especially with longer logs, so extra steps to wedge the kerf of the log open may be necessary. Removing the massive offcut from the log deck would also incur the strong possibility that the setting of the lower portion of the log would be disturbed, requiring re-adjustments, and such a large offcut, if it were to be dropped or tipped off without care, poses a hazard to both sawyer and mill. Plus, when done dealing with our quartersawn board and the rest of the log below, the half-log must be reloaded onto the mill, which is hardly what one would think of when trying to be efficient.

More likely, if the sawing were to be executed through and though so as to obtain planks, the boards would be taken as so many layers to be sliced off, one by one, proceeding from the outside of the trunk until we reached our desired quartersawn board near the log center. However, given the fact that we have shimmed the log to the pith, all those other boards we slab off, to one extent or another, would suffer from having grain run out, as noted in the previous post. So, to produce one super high quality board, we produce an inferior grade for the rest of the material. This might be an acceptable trade off for some, but it cannot be said to be a great return on the volume of wood we have to work with overall, to obtain one excellent board and have the rest be also-rans.

Another aspect worth mentioning is that of the edging. Larger mill operations will have dedicated edging saws, the boards slabbed off the log on the main mill and then transported, often by conveyor, to the edging saw. Some edging saws cut one edge at a time, however more efficiency is gained by the use of gang rip saws and the like to edge-cut several boards at once from each slab. In such a circumstance, it is less likely that the edging cuts on the slabs will be done in a fastidious manner, for each board produced. In fact, since the mantra of maximum conversion for economic reasons seems to be the main concern, you will often see lumber produced by such mills incorporating a good portion of the sapwood and the piece with the pith is kept and turned into yet another 2x4 or 2x6. A trip to your local lumber yard will confirm this.

If the mill operation is smaller, then the edging cuts are typically going to be done on the sawmill deck by the same saw, or they are not done at all and what is produced are waney boards.

If the edging is done on the mill deck, it is not done like this:

Obviously, a tall board like this would not be very stable during cutting, and it would be tedious to make it plumb and fixed firmly prior to cutting - some additional material would be needed to stiffen the board. It is not efficient to edge one board at a time generally. More typically, one would gang several boards together, and edge them as a group, and in such circumstances it is unlikely that the edging cuts on any one board in the gang are going to be in the optimal grain alignment for that board. Plus, slabbing the boards off, then reloading them on the mill to edge them is inefficient and most folks would prefer to handle the heavy green boards as little as possible if they had the choice to do so.

If the goal is to produce boards cut on on all four sides from a log, it is more sensible to turn the log into a cant, slabbing off the sapwood on four faces, and then re-saw the squared up cant into boards.

Here's a case where aligning the log so that the pith is parallel to the cut and the mill deck makes good sense - the boxed-heart timber:

In larger timbers, the slabbed offcuts may have enough volume to yield an additional board or two, but for the purposes of illustration, those steps have been ignored here.

In carpentry employing large timbers, the use of boxed heart material is fairly common. One issue with boxed heart timber is that that they are difficult to dry by conventional methods, and when they do dry, the outside dries ahead of the interior of the timber, which introduces considerable stresses. The way the timber resolves these stresses is to crack on the outside faces. If the timber has been processed into a component in a joined timber frame of some sort, and has squared housing and notches cut into the faces, then it is likely that the drying stresses will most readily propagate cracks from the corners of those housings and notches, as such 'geometric discontinuities' are stress risers

"Geometric discontinuities cause an object to experience a local increase in the intensity of a stress field. Examples of shapes that cause these concentrations are cracks, sharp corners, holes, and changes in the cross-sectional area of the object."

Cracks running through joinery can considerably weaken integrity of those structural connections, and the cracking and general distortion that results as the timber dries from the outside in may be considered a negative from an aesthetic perspective. If the presence of a heavy timber in an architectural space is considered as a show of integrity and strength, then the presence of cracks through such material, just like cracks through concrete, connotes very much the opposite I do believe.

An excellent solution to the problem of boxed heart timbers is to kerf the timber along one face, a saw cut taken down to the pith of the timber:

The kerf allows some air circulation to the interior of the timber, and as the timber dries and stresses intensify on the outside of the stick, the kerf acts as a relief mechanism. The integrity of the timber is little affected by the cut. As the timber dries, the kerf opens up into a wedge shape. This process can be assisted slightly by placing wedges along the kerf and driving them down as the kerf widens over time, but not pounded in so hard that they cause the timber to crack at the bottom of the kerf!

Once the kerfed timber has dried to the desired point, it will no longer be square in section, so it will need to be jointed and planed back to square and straight:

Then the timber can be placed in the building, the kerfed face oriented where possible away from sight, buried in a wall, or the like. If the timber is visible on all four faces, and boxed heart material is the only available option, then the wedge-like opening formed by kerfing and drying can be filled with a patch fairly seamlessly. Here's one such example:

 If the boxed heart cant is to be re-sawn further, it is simply laid flat upon the mill deck and sawn up as desired, keeping in mind that most of the boards produced will not have a perfectly straight run of grain:

Since the production of a boxed-heart cant in which all faces are aligned to the pith does not yield boards with especially straight grain, another method might perhaps be superior. We'll look at some other options next time.

Thanks for coming by the Carpentry Way, and all the best for 2014!

Tuesday, December 24, 2013

Sidling up to Sideboards (2)

This thread is a continuation of the 'Mizuya' Series, an exploration of kitchen sideboard design (see here). That series of posts started in October 2012. Geez, has it been that long?!

After working up a design over several months, a design which took many of its cues from Japanese traditional kitchen storage furniture, I came to a point where the design I had produced wasn't quite making sense for the context in which it would be placed. In the final post in that series, entitled "Mizuya 12: Total Makeover?" I came to conclude that a two-piece stacked cabinet made more sense than a single monolithic one, that I didn't want a frame which sat upon a sill with either unit, and, due to factors which associate to making a piece out of hardwood rather than softwood (as is the case with many Japanese furniture pieces), etc., many elements could be slimmed down. In short, the whole design needed a revamp.

The previous post in this follow up, entitled Sidling up to Sideboards, was published way back in September of this year. I had gone back to the (CAD) drawing board, and after a few readjustments, I had brought the design to this rough point:

Not sure about the tripled sliding doors in the upper unit - requires a very wide track for starters, and that ripples down to posts sizing and on out.

I then decided to take a look down the path of making one or both of the cabinets splayed, following a train of thought inspired by some classic Chinese cabinets of a two-piece tapered form. After a few hours, I arrived at this point with the design:

While I liked some aspects of the revamp, there seemed to be no shortage of drawbacks to this rendering. Do you hear the sound of wheels slipping in the mud? The cabinet is going to be placed into a corner of sorts, an 18" recess along a wall, and thus the tapered form leaves a tapered gap along one side - I'm not wild about that for starters. The table top of the lower unit ends up with limited functionality as there is not much access to the surface, while the upper cabinet has significant side volumes which are not well accessed from the doors at front. Putting doors onto the flanking portions didn't seem like an attractive solution. It still seems too tall and 'looms', despite the tapering form.

Put it this way: the design wasn't working on a number of fronts. So I decided to take a step back and let my thoughts gel a bit, and see if any new inspirations came along.

That was perhaps an overly optimistic hope on my part, as not much 'gelling' went on in succeeding months, unless one considers the cement-like progress with the design. Things sat. And sat some more, and a little despair even crept in, as I started to wonder with each tentative re-engagement if I would ever come to a design that I was happy with. I felt stuck with where things were with the design, and it wasn't a simple case of paralysis by analysis. I couldn't see a clear path forward.

This 'stuckness' has happened before, and the thing here is that there is no client pressure here, as this piece is for my house and if it gets built this month or six months from now is really immaterial. There's no rush, or need to feel impatient - and yet at times I did indeed feel impatient.

I think the great thing about CAD design, as compared to pencil and paper is that it is comparatively easy to tweak or even completely revamp a design, whether at a general or detail level. The investment in time is not tied to a physical artifact as it is with pencil and paper. I tend to think that once a design has been carefully sketched with ruler, compass and pen on a surface, be it paper or hardboard, at full scale or otherwise, a certain inertia sets in in terms of making changes to that design. Erasing lines over and over can make a mess of things, and thus a certain reluctance to make changes to the design may occur. I know it did for me when I used to make my drawings on paper or MDF, doorskin, etc.. In one sense this is good, as you have to make more of an initial commitment to what you draw, but in another I think it really limits how far one may choose to explore a design. Also, there is the limitation of considering a design purely from parallel projection elevation views, as few people are going to take the trouble of manually drawing perspective views of their piece. a few will make cardboard or other mock ups of their piece to explore its physical volume and presence a bit, but again, this describes a minority of cases I think. And again, with physical mock-ups, a certain inertia sets in once you have made the thing, a certain reluctance to make it all over again or tear it half apart and remake pieces.

Sometimes a person can have a flash of insight and see the whole design and then sketch it out and it is 'there', shaken out, as it were, from the coat sleeve. I've had that happen personally on several occasions. Other times though, the design direction is not so clearly envisioned from the outset, and a certain exploration needs to take place, and it is there that CAD is a real asset.

I find with CAD drawing this inertia/reluctance to make changes to what has already been drawn largely disappears. You can keep your design as is to one side and explore various avenues with certain components and then reintegrate them afterward. Moving a line or a surface is a matter of a mouse click and not careful erasing. There's less 'commitment', and with that a greater freedom, which, however can also lead to bouts of wandering about somewhat aimlessly searching for the result which you seek. The freedom to make changes as you please can lead to option paralysis.

At last though, wheels began turning again. I think it was handling the large planks of quartersawn bubinga that I have during the recent construction of a new wood rack which got me looking at things from different angles. I would like to make the entire sideboard out of quartersawn bubinga, which, while not as loud a material as flatsawn or curly bubinga, is still fairly dramatic and powerful, rich and beautiful. I realized that making the cabinet with simpler lines and fewer details allowed the wood to speak a bit more - well, at least with less competition.

Back to the drawing board, and I chose to discard the tapered leg piece. I revisited the last step before that, found I liked a lot of aspects to the lower cabinet. It was the upper cabinet really which was the tough nut to crack. I gave a lot of thought to how my wife and i would use the cabinet and whart sort of things we would put in it. for one thing, unlike some families, we don't own a large collection of special Chinaware that might be nice to display, nor is is likely we ever will. I wanted something a bit more utilitarian and yet with some allowance to display something nice, like a vase, flower arrangement, moon rock, what have you. Some aspect of the idea of the tokonoma, where a seasonal motif is displayed and changed out from time to time is appealing to me, but I wanted this to be a minor aspect to the cabinet. Really, it is a large box to store stuff related to dining.

Also, I took into consideration some of the other pieces in the space, which included a tsuitate (Japanese room partition) and vanity I had built. I wanted some points of aesthetic tie-in with those pieces. Sketching and head scratching ensued....

Here's where I'm at now with the design:

I wanted to retain the shippō-gumi lattice pattern, and decided that one pair of sliding doors was enough of a statement in that regard. The lower doors will be hinged. The glue-less and fastener-free drawer design is retained. The overall height of the piece has dropped be nearly a foot, and the space above the lower unit's table top has increased to make it more useable. I have made the left side of the upper cabinet a display space, and may put a small shelf in there, or maybe not. The door and drawer hardware is absent in the above rendering.

The lower unit's tabletop will have a raised bead all around which will allow the feet of the upper cabinet to nest, a feature I came across on some Chinese 2-piece cabinets. Here's my version, viewed at one corner:

I've come up with a new way - well, new to me anyhow - of connecting the breadboard ends to the table top. Actually, there will be a lot of entertaining joinery, much of which will be demountable.

Many details remain to be resolved, and I am already sure I will be making some changes to the form of the aprons which run under the main carcases, top and bottom. The lower doors will likely have a rounded inner arris - there are lots of minor things to figure out yet. These details I will resolve when I redraw the entire piece. At this stage the sketch is the equivalent of a mockup only, and some of the dimensions in the sketch, from frequent cutting and pasting from one drawing to the next, seem to have lost tolerances. That's a SketchUp thing. So, I'll start again from the ground up, wringing out the joinery and profile details from stick to stick.

I'm feeling good about the design overall, and happily my wife is too! I have the 'energy' back and look forward to refining the design. I'm planning to commence the build in the next 3~4 weeks, and will of course photo-document that process here in case anyone is interested.

Thanks for coming by the Carpentry Way, and comments most welcome. And by the way, all the best to you and yours over the holiday period!! On to post 3

Monday, December 16, 2013

The Tale of the Hammer

Some form of striking tool is common, I would imagine, to every carpentry tradition on the planet. In Japan of course various versions, tiny to huge, see wide use. Recently I was reading some Japanese material on hammers and became curious about some of the kanji (Sino-Japanese characters) used to describe the tools.
There are a few different words used to mean 'hammer' in Japanese. One is kana-zuchi (金槌), which transliterates as metal () hammer ().

Here's a picture from the Takenaka Tool Museum showing some examples of kanazuchi:

Funny enough, just as a hammer with a metal head doesn't float in water, the term kanazuchi is also used as a euphemism for a person who can't swim. Do we have a single word in English to describe that? The term kana-zuchi refers most aptly to a metal-headed hammer., while ki-zuchi (木槌), are 'wooden' () mallets () . The english word 'hammer' has also entered the Japanese lexicon, transliterated as ハンマー , read directly as "hanma-"

The other common Japanese term for hammer is gennō, which may be written in two different ways:




You will notice that the first character in either version, gen (), is the same, and it is only the second character which varies. The character for gen stems from a pictograph which shows the tip of a twisted thread stretched between and linking two points

Compare the likeness of the character () to the above and I think you'll see some resemblance.

This character gen () is meant to describe something so slender as to be barely perceptible, which leads to its primary modern meanings of 'mysterious' and 'obscure'. I began pondering how this kanji relates to something so seemingly mundane as a hammer? And with that, I went down what for me was an interesting trail.

The second character of gennō, as shown above, is either '' or ''.  My research has revealed that the first pairing, '玄翁', is the correct one. The latter character of the pair we see, '', meaning 'ability', is kind of a stand-in, nothing more, technically the wrong character. Believe me, misspellings or at least varied use of terms are nothing at all unusual to find in Japanese carpentry books. So, we can ignore that one.

What does '' mean then? Well, I like to use the dissection method here: This character combines  an upper part, '公' meaning open (space), and a lower part, '', meaning feather or (bird) wing. Put them together and you get open spaces between the feathers, a reference to an old bird. An old bird, is in turn a euphemism for old man

I guess the term old bird gets used in English to describe certain elderly people, but more usually old women it would seem. So it's not all that unusual an appellation really, having wide cross-cultural use I would suspect.

So, it would appear that the characters for hammer, gennō, 玄翁, combine to mean mysterious old man


I found this piece of information puzzling and surprising, and I was struck too that I hadn't noticed this before. Maybe it's nothing, but sometimes the most ordinary sort of things can contain neat little mysteries, either one stops to observe for a moment, or one happens upon by luck.

I dug a little further, given the enticement of the connection between 'mysterious old man' and hammer? There's no obvious connection coming to mind. 

As it turns out, the term gennō (玄翁) traces to a Muromachi Period (1337 to 1573) collection of Japanese prose called the Otogizōshi. This collection of some 350 pieces of narrative prose, many by authors unknown, forms a portion of the Japanese medieval literary heritage, somewhat akin, quite possibly, to Chaucer's work The Canterbury Tales in English.

Many of the tales in the Otogizōshi relate stories of mythological figures, and one of those is the story of Tamamo no Mae (玉藻の前). Tamamo no Mae is the name of a courtesan who served in the court of Emperor Konoe, the 76th Emperor of Japan. He reigned from 1142~1155. In some versions, she served in the court of his father Emperor Toba, a few years earlier. Here is Tamamo no Mae's depiction in a woodblock print from the late great Yoshitoshi's work New Forms of Thirty-Six Ghosts:

As the woodblock print collection title suggests she is some form of ghost. There was something a little different about Tamamo no Mae. She was beautiful, always smelled wonderful, and curiously her clothes were never wrinkled or dirty. No only was she physically beautiful, but she was infinitely knowledgeable on all subjects, despite the fact that she looked only about 20 years of age. She was respected and adored by one and all in the court, and the emperor and many around him fell in love with her.

Tamamo no Mae gained her name from an incident in late summer:
Sometime around September 20, there was a performance of poetry and music at the Seiryoden, the serene, cool chamber. The Emperor took her along and they sat within the bamboo blinds. Just at that moment, a strong wind rushed through, blowing out the fire of the lanterns, and the room was plunged into darkness. Yet in an instant, there seemed to be light emanating from Tamamo-no-mae's body. Surprised, the honorable ministers looked around and realized that the light was spilling from within the bamboo blinds that surrounded her. The light was like the morning sun.
        Ignoring the music, the Emperor declared in response to the minister's enquiries, "She is quite a mystery. There is no doubt that she is the embodiment of the Buddha and the Bodhisattva." When the bamboo blinds were raised, it became brighter than noon even though it was darkest night. The light was just like a glowing bulb, and that is how she came to be known as Tamamo-no-mae.
Her name literally means in front (前) of the jeweled (玉) algae (藻). Hmm. What do you make of that name? I can't say that I fully understand what the author of the tale is getting at here with the naming of this beautiful courtesan as a form of algae, or somehow like algae in some way. I can't say whether awareness of algae was a form of common knowledge at the time. Does it perhaps suggest a pearl before swine sort of thing?

I looked into the algae piece a little further. Searching under that kanji  (藻), I found images of a type of algae that does have white pearl-like flowers, that do seem to be glowing a bit, like jewels:

It appears she's named after a beautiful plant - fair enough.

Back to the story...

Shortly after the incident, the emperor fell ill, and became precipitously sicker by the day. He tried medical doctors first and they could not cure him. Then priests, fortune tellers and astrologers were consulted, to no avail. His condition worsened. Then a fortune teller named Yasunari told the emperor that the cause of his illness was in fact Tamamo no Mae. This information was revealed by Yasunari somewhat apprehensively, as he knew how close the Emperor was to Tamamo no Mae, and how much he liked her. Might be risky to share the bad news. Pressed for more information to substantiate his claims, the fortune teller revealed that Tamamo no Mae was actually a 100 year-old fox in disguise - a fox that was really 42' tall no less(!). In some stories she has two tails, in others nine tails.

Here's a look at one painting depicting the pursuit of Tamamo no Mae, the fox god, by the two warriors and their entourages, and we see that the fox god has two tails:

As the story continues, Tamamo no Mae disappeared shortly after the revelations as to her true identity emerged. They dispatched two of the Emperor's best warriors to track down and kill the fox god, as she was the cause of the illness. The thought was that despite Tamamo no Mae's superhuman abilities, they might have a chance against her using arrows. After many days, and several narrow misses, they had tracked the wily fox down to the Nasuno Plain. Seven more days of fruitless searching ensued. Then one of the warriors, Miura-nosuke, took a 20 minute nap, and had a dream in which Tamamo no Mae appeared to him and said he would kill her tomorrow, and asked him to please spare her life. In his dream, Miura-nosuke stood firm and said he would show her no mercy. The next morning, Miura-nosuke and his compatriot finally ran down the fox, shot her with an arrow and killed her.

It is here that the accounts diverge as to what happens next....

In one account, the fox's corpse is taken back to the capital, and later a re-enactment of the fox hunt was performed in front of the Emperor in the exact spot where the kill occurred. End of story.

In the other account , which I happen to be more interested in talking about, and from which I'll quote. This clipping from an 1875 Japan Weekly Mail gives account of the legend:

So, the stone is cleaved away to reveal the true essence within - that's the core meaning of the word for hammer in Japanese, gennō? Hmm.

In the account about the name origins from the Takenaka tool museum website,

"Once upon a time, in a place called Nasuno in the ancient country of Musashi, there was a monstrous stone that would force birds to fall from the sky and animals to die when touched. A monk called Gennō decided to put an end to this, and uttering the mantra, he stroke down onto the stone with a large sledge hammer breaking it into pieces. Since then the sledge hammer came to be called gennō"
Again, the hammer is a force for good. It resolves problems. And that it does, in truth. It can also, in the wrong hands, make a mess of things, let's acknowledge that as well.

The Zen Shin Sect priest named Gennō (玄翁), mentioned above is the 'mysterious old man' we talked about earlier. That guy smashing the rock with a metal hammer to reveal the, er, 'foxy lady' within? The tool called 'gennō' is named after the big hammer the priest was using and it was also the name of that priest.

Interesting to say the least. Makes the tool religiously blessed and pure from the outset, a tool for good. It's certainly a colorful term, and I wonder how many Japanese carpenters are aware of this story about one of the most fundamental tools in their set? Whether they know or not doesn't really matter, obviously, but it is interesting to ponder.

Well, I've rattled on long enough for now. I hope the investigation of the 'mysterious old man' was worth a look. Thanks for coming by the Carpentry Way.

Tuesday, December 10, 2013

Can't See the Forest for the Trees (III)

In the previous post I delved into the topic of log scaling to a certain extent, and now want to move on to look at the sawing process. Just as there are various ways to scale a log and compute the volume and/or board footage, there are various ways to saw up a log, and pros and cons for each. Again, I don't speak as a professional sawyer, so my knowledge is limited in that respect. Still, nearly every woodworking project involves sawing material at some step, and having some grasp about how a log is cut translates into better understanding and planning when assessing a board to be cut.

I'm going to assume the log we will deal with is a tapered, truncated cone, or frustum. The  model tree is 48" at the base and reaches 100' high. This is the sort of taper one might see with a cedar tree. Other trees are less tapered, but using a stronger taper shows the results of the cuts more clearly, I think, so that's the direction from which I'll proceed.

I drew a tapered cross section, made it into a cone, and then chopped the bottom 10' off:

The resulting cut log tapers uniformly 2.4" each side, over 10' length, working out to about 1.15˚ per side:

I don't think there is anything especially unusual about this section of log, save for its large size and geometric perfection.

There are various saws with which we might slice up such a log, and we could make the cuts in a horizontal orientation or a vertical one. There are bandsaws that cut each of those directions, or angles in between for that matter. Sans power, there is pit sawing, where the cuts are made using a long handsaw, either by one person alone, or two working in tandem, top dog and under dog fashion, or two working separately:

Or one could sit by the side of the log and rip it horizontally as well.

So, for purposes here,  I'll simply assume the cutting will occur horizontally, the sort of thing that could happen on a Woodmizer or chainsaw-based portable mill, bearing in mind that the various ways of cutting we'll look at could equally be done on a machine which saws vertically.

Speaking of the various ways of cutting up a log, there are many, and most methods developed revolve around maximizing yield. we're going to considerably simplify matters though, and ignore yield altogether, focusing in on cutting the same log in three different ways, the aim being to cut three different boards. Those boards are, specifically, flatsawn, riftsawn, and quartersawn.

In cutting method one, we take the log section we have, and rest it on the deck of the mill 'as is'. This is an exotic softwood, heh-heh, having alternating green and white growth rings.

The three cuts we looks are are labeled on the end of the log, as A (flatsawn), B (riftsawn) and C (quartersawn):

In cutting method one, no compensation is made for the taper of the log. The log lays on the mill cross members 'as is'. The whole log, relative to its pith, is tilted down 1.15˚.

In the above view, the narrow end of the log is facing us, as this is the end at which cutting is always originated, proceeding down the tree trunk to the butt, for obvious reasons.

For board A, we would make a preliminary slabbing cut then follow it up with a second slabbing cut 2" lower, which would produce a waney board like this:

The 'cathedral' pattern on the face of the board is probably what most people think of when they think of 'wood grain'.

That 2' slab is then edged, the cuts run in alignment to the pith of the log, and a 2"x12" board is produced. I'm choosing this size of board for illustrative purposes - a wide board shows the grain patterns that result from sawing more obviously than does a narrow board.

We can execute a similar set of cuts for the other two boards,  B and C, slabbing and edging, until we have produced the desired three sticks, A, B, and C:

Let's set those 2x12s aside for the moment and start all over again from the beginning with the log. This time we will make some adjustment for the log taper, such that the very center of the tree, the pith, is aligned to our cut direction. The pith is therefore horizontal. We can call this 'sawing to the inside' of the log. Some sawmills have built-in devices to raise or lower one end of a log, and if we were cutting a long log we would need to look at supporting the log at intermediate points as well so as to maintain a straight section throughout.

Again, we see the three cuts we are after, which I will label A', B', and C':

Note the presence of a shimming board under the narrow end, roughly a 2"x4". To keep the pith of the log level with the sawmill deck, the log is tilted up 1.15˚.

We take the three cuts as before, slabbing and edging, the edging being done in alignment to the pith. That leaves three boards, A', B', and C':

We'll set those aside and start again.

The last cutting alignment we'll look at also has an adjustment for taper. This time though, instead of shimming the log so that the pith of the log is parallel to the cutline, we shim up the narrow end a bit more so that the top of of the log is parallel to the cut line, i.e., horizontal. Our three boards are now A", B", and C":

As you can see, the shim used is much thicker than when we cut in alignment to the pith, twice as thick to be precise, a 4"x4". Now the lower surface of the log is tilted up 2.3˚ relative to the deck of the mill.

Previously, we cut to the 'inside' - now we are going to cut to the 'outside' of the log.

The three boards are produced once again, labeled A", B", and C":

Now we have produced boards which are flatsawn (A, A', and A"), riftsawn (B, B', and B"), and quartersawn (C, C', and C"), we can compare them to see how the run of the grain compares. First, we look at the A set, flatsawn:

As you can see, the log sawn without regard to taper produces a flatsawn board with considerable grain run out, and numerous cathedrals on the tangential faces. Here's another view of the same three boards so you can see the run of the grain along the board edges, along with the pith-facing portion of the board:

Again, the log sawn without attending to taper produces the board with the most angling of the grain. The board sawn so along the pith line, A', exhibits less grain run out, while the board sawn to the outside of the trunk, A", exhibits virtually no grain run out. The alignment of the grain perfectly along the long axis of the stick makes the board sawn to the outside of the tree, A", the strongest of the three were they to be used as posts. If the above sticks were to be used as beams, again A", with the grain running straight down the stick, should bend the most evenly and predictably of the three I would think.

The other two methods of sawing, A' and A, produce some amount of grain slope on the faces of the sticks. While the end grain view of the three sticks is very similar, you can clearly see the degree to which the grain runs at a slope along the sticks by comparing the narrow edges of the boards.

The B set of sticks were all sawn in a rift grain orientation when viewing the end grain. Let's see how they compare:

Again, the sticks sawn with accommodation to taper, B' (to the 'inside') and B" (sawn parallel to the 'outside' of the log), show the least amount of grain slope, with B" showing the least amount of grain slope of the two.

Here's another view of the B set:

Finally we can compare the sticks which were quartersawn, C set:

Here, given that the grain runs 90˚ radially, the effect of sawing for taper (or not) is minimized, however it is still clear the sawing to the outside of the trunk, as in C", produces the least grain slope of the three cuts.

Another view:

We'll look more at 'sawing to the outside' in a subsequent post.  There are various reasons why we might want straight grained timber as a result of sawing practice - better strength, which is as critical in a dining table as it is in a building column, is one important reason, and unless sloping grain is desired as an aesthetic, conveys the line of a frame more clearly than does sloping grain, which, if extreme enough, 'fights' the lines of the piece.

Thanks for coming by the Carpentry Way.

Tuesday, December 3, 2013

Can't See the Forest for the Trees (II)

I'm not a logger or a sawyer, so I can't speak exactly from those perspectives. I have logged and I have sawn logs many times in my life, not enough to be any sort of expert in either matter, but I'll offer what I can on the subject.

Let's say you find some logs, like what you see, and you want to buy them. Or, perhaps you have some logs and want to sell them. What if you wanted to sell logs internationally? How is the price to be negotiated?  By number of logs? By length, by width, by volume? By the amount of usable timber or by the total volume of the log including bark? Or without bark?

Saw logs are conventionally sold on a 'cubic meter' volumetric basis, and this has been the case since the late 18th century.

You would think that a 'cubic meter' - 1m. wide x 1m. deep x 1m. tall  -would itself be a fairly well-defined and universally agreed sort of thing, but it is not so when it comes to logs. A cubic meter here is not the same as a cubic meter there.

It boils down to the one question: how do you measure a log?

What comes into consideration though, before the matter of measuring of volume, is the assumption as to which geometric shape the log conforms as we calculate volume based on a geometric form. The candidates are:

  1. Cylinder

      2. Cone

    3. Paraboloid

'Paraboloid' itself can be considered a simplification. We might also assume the tree trunk has varied forms according to which section of the trunk is considered:

Those seem to be the choices in front of us. Notice in all four that the base or horizontal plane cutting through the geometric form is a circle. Any horizontal plane cutting through the log would also render a circle. Trouble is, trees are rarely, if ever, perfectly circular in cross-section, and some are a good deal non-circular. We could have added in an illustration of a cone with an elliptical base, for example. Not that any tree has a perfectly elliptical cross section mind you!

No tree trunk is a pure cylinder, however old Sitka Spruce trees do look a lot like gigantic pencils in the forest and the logs therefore come very close to cylinders. Some trees are much more tapered in form, like a cone. Cedar trees come to mind. Some tree trunks taper evenly, others stay fairly cylindrical and then taper radically at the crown portion. Some trees flare strongly at the butt, others not so much.

Between the forms of a cone and a parabola, neither is an absolute ringer for any tree I've come across, however the cone is certainly a simpler form upon which to base calculations. Assuming a conical shape for a log was the standard way to do things way back in 1765, as noted by Oettelt in Germany.

Assuming that a log is a section of a cone is a simplistic one, however the fact is that no tree truly conforms to any geometric form, not precisely at least. So we proceed from a simplistic assumption and nothing more, simplicity taken as a virtue over ultimate accuracy. Refining the accuracy of the measurement is seen to be more expense in term of the time involved than is realized as a benefit resulting from the extra effort. Relative accuracy, therefore, is what is sought, and that is simply the maximum accuracy that is profitable and possible to obtain in practice.

Right, given that, we can at least start from the basis of assuming each log is a portion of a cone, and calculate volume from there, yes? The formula for determining the volume of a cone is easy to remember, it seems to me, IF you find the formula for the volume of a cylinder easy to remember. How's that for a bit of, er, circular reasoning?

The volume of a cylinder is that of the base circle (π r2) times the height (h):

A cone is simply 1/3 the volume of a cylinder, or 13 π r2h:

An easy way to think about how a cone and a cylinder relate to one another is to imagine a pair of paper drinking cups, one a cone and one a cylinder. Both have the same total height, and the same cicular base. If we filled the conical cup with water or salt, say, and poured it out into the cylindrical cup, it would fill that cup 1/3 of the way:

One can see thereby the vastly different estimate of volume one would obtain whether one were to consider a log as a cylinder or a cone.

One niggling point though in regards to cones: when we are looking to buy logs, we're not typically looking for the pointy end of the stick (i.e., a pointed cone), as that is the end with all the branches. That bit is perhaps best left behind in the forest. We are looking instead at a section of the trunk, which is a truncation of a cone. Another name for a truncated cone is 'frustum' cone, a frustum being that portion of the cone laying between the two parallel planes cutting it:

The word frustum comes from Latin and means 'piece', or 'crumb'.

Now, the formula for a frustum of a cone is a little bit trickier than the formula for the volume of a cone. A simple way to do it, if you had both portions of the original cone before truncation, would be to perform two separate calculations, one for the entire uncut cone, and a second for the piece which was lopped off on top. Subtract the volume from that upper piece from the total and you will find the volume for the frustum. That's an inefficient way to do things, and it is also the case that when looking at a log you only have the frustum to consider. So we need a formula just for that portion:
The volume of a frustum of any cone is equal to one-third of the product of the altitude and the sum of the upper base, the lower base, and the mean proportional between the two bases.
Put into mathematical language, the above sentence becomes:

The uppercase 'R' in the formula denotes the radius for the base of the frustum, and the lowercase 'r' is the radius of the upper cutting plane. The area of the base is given by π R2 while the area of the upper plane is π r2 - you can see those formulas as part of the larger formula above. The piece under the square root symbol in the formula above, “√ π R2( π r2)” is the "mean proportional between the two bases". The 'mean proportional' of two different quantities, let's call them a and b, is a quantity r such that a is to r, as r is to b (a:r = r:b). for instance, the mean proportional between 2 and 18 would be 6 (as 2:6 = 6:18). The Golden mean, 1:1.6180339, is a particularly famous proportional, known to many readers I’m sure.

Consider then that the formula (a:r = r:b) can be simplified algebraically to r2 = ab. Solving for r, we get: r = √ab, and that is the core idea of the portion of the formula above we see as π R2 wh(π r2 wh). Of course, when we see a formula in which we take a square root of an entity that is squared, in effect we cancel out both the square root and the squares, as √62 wh = 6. Therefore, π R2 wh(π r2 wh) becomes simply πRr. We thereby produce this formula:

This formula can then be cleaned up a bit by extracting π out from the parentheses:

Well, not quite so easy to remember as the formula for the volume of a regular cone, but it does fall short of what one would call a complex formula. The math geeks out there will possibly be yawning at this point.

So, let's say we have a log, and it measures 300 centimeters long, has a butt end of 100 centimeter diameter (R of 50 cm), and a skinny end of 80 cm diameter (r of 40cm). By the above formula we would write:

V = ⅓ π ((502 wh+ 402 wh + (50 x 40)) x 300

That gives us:

V = ⅓ π (2500 + 1600 + 2000) x 300

Simplifying to:

V = ⅓ π (6100) x 300

Pi (π) equals 3.14159 or thereabouts. To complete the solution, we obtain:

V = ⅓ (3.14159 x 6100) x 300
V = ⅓ (5,749,109.7)
V = 1,916,369.9

The answer, since we reckoned the problem in centimeters, is in cubic centimeters. Logs are sold on a cubic meter basis, and 1 meter is 100 cm. Therefore, 1 cubic meter (1 m³) equals (100 cm/m)³ = 100³ cm³ = 1,000,000 cm³. We therefore divide the above obtained value in cubic centimeters, 1,916,369.9 by 1,000,000, to obtain the volume in cubic meters: 1.916.

Keep in mind that when we performed the above calculation we were working with nice round numbers, however lengths and diameters of actual logs are more often given with nominal or rounded forms, possibly in 2-foot length multiples, for instance, or the calculated answer may also be rounded, the 1.916 above being rounded to 2 cubic meters.

If you measured the log in inches or feet, it is much the same process, however at the end one would need to convert over to cubic meters from cubic feet or inches. One cubic meter equals 35.315 cubic feet. The conversion is simple enough: take the volume in cubic feet and divide by 35.315 to obtain cubic meters. If working from cubic inches, divide by 61024 to obtain cubic meters.

If only things were so simple as plugging data into a formula, but the situation turns out to be very much different in the world of log scaling today. Because taking a simple mathematical calculation of a log to obtain volume does not give us the actual likely amount of convertible timber, does it? Logs vary, and in some species by quite an amount. Between species it becomes more varied yet. Some trees, for instance, have thin bark while others have thick bark. In the US, log volume excludes the bark but in other countries the bark is incorporated in the calculation. Some tree trunks contain enormous amounts of sapwood with little commercial value (Gabon ebony would be a good example). American Black Walnut is a tree which also has a hefty band of sapwood, however the case is different from the ebony as the wood can be steamed so as to homogenize the color of the sapwood with the heartwood. Young trees have a higher proportion of juvenile wood than do old growth trees. Some species are prone to defects of various kinds, or have characteristic areas of rot, also limiting the amount of convertible timber. Some logs are almost exclusively converted into veneer, while others are nearly always sawn for timber. And on it goes. Log scaling is simply the process for estimating the weight or volume of a log while allowing for features that reduce product recovery.

One could come up with different scaling methods to calculate the useable extractable volume of timber from a log on a species by species basis, however it is fortunate that things haven't gotten quite that fractionated - but it is close. Welcome to the world of log scaling, where complexity, as they say, rules.

In reckoning log volume, some systems average the log end areas, while others average the log end diameters. Some assume different geometric shapes for the log. Here are 7 basic systems, with the actual formulas left out:
  1. Smalian (assumes a parabolic log shape, and is the standard log rule (in metric form) in British Columbia and the basis of the Interagency Cubic Foot scaling System)
  2. Bruce's Butt Log (as Smalian's formula assumes a paraboloid shape, it tends to overestimate volume of butt logs. David Bruce came up with his rule in 1982 to adjust for the butt portion of the tree trunk)
  3. Huber (this formula assumes the average cross section area is found at the midpoint of the log, an assumption which is not always true of course)
  4. Sorenson (derived from the Huber formula and assumes a taper of 1 inch per 10 feet of log length. The taper assumption is not always correct however)
  5. Newton (the most accurate, requiring measurement of both end diameters of the log as well as the midpoint diameter, however this measuring is more time consuming to execute)
  6. Subneloid (similar to the Smalian, however configured so as to allow a multiplication by 12 to obtain the board foot measure, becoming the "Brererton Log Foot Scale")
  7. Two-end Conic (assumes the log shape is a cone, and is the basis of the "Northwest Cubic Foot Log scaling Rule")
There is also the Hoppus rule, derived in Britain. It is the most widespread system internationally; assumes an assumption about processing loss. Sometimes called the "quarter girth formula", it considers the volume of a log in cubic meters to be:

V = (C/4)2 wh x L/10,000

Where, V is volume, C is log circumference in centimeters and L is the log length in meters. The result obtained by this formula can be compared to the math formula for volume we worked earlier, using the same numbers. We would have to pick a circumference though, so I'll average the small end (r = 40cm) and the large end (R=50cm) to obtain a radius of 45cm. Radius converts to circumference as 2πr, so a 45cm radius gives a circumference of π90, or 282.743...

Plug that into the formula and let's see what we get:

V = (282.743 / 4)2 wh x 3/10,000

V =  4996.48722805 x 3/10,000

V = 1.49894616842 cubic meters

Compared to the strict mathematical estimate for cubic volume, the Hoppus rule gives a volume which accounts, on average, for about 78.5% of the cubic volume of the log-  the other 21.5% is lost as edgings, sawdust, and slabbed offcuts. Another name for the cubic volume measure obtained by the Hoppus rule is the Francon Cubic Meter, so as to distinguish it from the solid cubic meter.

As mentioned above, there is the Interagency Cubic foot System, developed in the US in 1991. This takes the Smalian formula and applies it to any log segment of 20' or less. If the log is longer than 20', then it is divided into segments and the taper of each segment is estimated as the difference between diameters at each end. This method aims to reduce the bias which results from the Smalian formula otherwise, which assumes a log to be a paraboloid. As you can see from the 4th picture in the series of geometric forms of logs shown above, the log usually does not conform perfectly to the paraboloid form.

That is an overview of the situation in western countries, however other places have different log rules yet. For instance there are four different log rules used in Japan (these rules are also used in Korea):

  1. Japanese Agricultural Standard (JAS): the log diameter is measured at the small end only, and taken in two axes, which are averaged, towards obtaining what is called a 'scaling diameter' (D). The scaling diameter (D) receives adjustments which are done using a table. Scaling length (L) is in 20cm intervals. Volume = D2 whL / 10,000 if L is ≤ 6meters. If L is ≥ 6 meters, then the formula becomes V= [D -INT(L) -4) / 2 ]2 wh x L/10,000. "INT(L)" is the length of the log rounded down to the nearest meter, and the expression INT(L) -4) / 2 is a taper adjustment of 1cm per meter of length. This formula views a log as a square cant with a side equal to the scaling diameter.
  2. Revised JAS: modifies the formula for logs 6 meters and longer with a factor to adjust the original taper assumption.
  3. South Sea Log Scale (SSL): also known as the Brererton. Measure the long and the short axis of each log end and round them down to the nearest 2cm (i.e., 77.1 cm becomes rounded to 76 cm). then average the two rounded measures to the nearest whole centimeter. This gives the 'D' (diameter) value. Volume = 0.7854 D2 whL /10,000. This formula is the metric equivalent of the Subneloid formula described in the earlier table.This formula is typically applied to hardwood logs from tropical Asian sources.
  4. Hiragoku or Heiseki scale: Uses the same procedure for finding the 'D' measure as the SSL method above. Volume = D2 whL /10,000. This method considers the log as being a square cant with each side equal to the recorded small end diameter, and there is no adjustment for taper.
In fact, in Japan the traditional measure of log volume has not been the cubic meter until recently. Much the same as Japanese carpentry, which is done to the measurement system of Shakkan-hō using shaku 尺 (30.3030cm) sun 寸 (3.0303cm) and bu 分 (3.0303mm), logs are reckoned by koku 石, a unit of volume equal to 10 cubic shaku. A koku was originally defined as a quantity of rice, supposedly equal to the amount required to feed one person for a year. The unit for koku, 石, is in fact the same character as is used for stone - if you find this confusing, welcome to the world of Kanji. For internal purposes, I would suspect a lot of log scaling in Japan is done on the basis of koku, however when importing or exporting, the koku value needs to be converted to cubic meters, one koku equals 0.2782 m³ (9.826 cubic ft.).

Indonesia, Malaysia and the Phillipines often use the SSL system, however there are regional variations in how dimeters are taken and recorded which lead to variances.

British Columbia, larger than many countries, has its own log rule system, the 'BC Metric Scale' which is the metric form of Smalian's formula. Here it is: V = (r12wh + r22 wh) L 0.0001570976, where r1 and r2 denote the top and bottom radii, rounded to the nearest even number, and L is the length in meters recorded to the nearest 0.2m, with the convention that exact odd numbers are rounded down (i.e., 13.5m becomes 13.4m).

Let's see how the BC Metric Scale compares to our previous reckonings using a 3m log, 40 cm radius at the skinny end and 50 cm radius at the fat end:

V = (402wh + 502 wh) 3 x  0.0001570976

V =  (4100) 3 x  0.0001570976

V = 1.93230048 cubic meters.

This formula lead to an answer in which the volume of wood was slightly greater than for the geometric form of the frustum of a cone, which is not surprising since the Smalian method presupposes the log is a paraboloid. 

Chile uses the JAS method. Russia uses a system called GOST 2708-75, which has similarities to the JAS and Hiragoku systems, and to the Huber formula. New Zealand has its own systems, one for logs used domestically, and three other systems specially for logs exported to other Countries. For export to Japan they use a system which is an Imperial form (that is, in feet and inches) of the metric Hoppus formula described above. Or they will use the JAS system. For logs exports to China, likely to be the bulk of business these days, the William Klemme system is used, which calculates the volume a if a log were a simple cylinder.

In practice, a given location and a given mill will likely be using one scaling system all the time, so once a log scaler is familiar with the particular scaling system, it is fairly straightforward process. When international trade gets factored in, the picture can be a good deal more complex and buyer beware. Those selling logs may well have incentive to use systems which tend to bump up the apparent net volume of timber converted.

This post has been but an overview of the fairly convoluted world of log scaling. Not wishing to write a book on the topic myself, certain details have been omitted or simplified in the interest of brevity. There is plenty of reading to be found online in regards to log scaling, and I recommend interested readers have a look around.

Next post in this series will be a look at board foot measures for lumber and we'll find that the picture there is no tidier than the ones for cubic volume measure. Stay tuned, and thanks for visiting.