Getting Geeky with Wood Properties

Last Friday, I left you hanging with this little chart:


It’s a rough workup of some wood strength data that I’ve been gathering and analyzing, since it has become clear that I’ll have to make some deviations from accepted practice in the wood selection for my Windsor chairs. Of particular concern is finding a suitable substitute for the leg stock. Tradition dictates (and modern makers all seem to be in agreement) that the premier wood for Windsor chair legs is sugar maple.

They have a strong argument – sugar maple compares favorably among native timbers for its strength characteristics. This is important, because the most highly regarded Windsors – both today and in the past – feature legs and posts turned to diminutive dimensions that simply wouldn’t hold up in a lesser wood. However, a look at some strength tables clearly demonstrates that, while sugar maple is certainly no slouch, it’s not at the top of the pack, either.

Terry Kelly
Sugar maple is used for the delicate turnings. Notice the dramatic curves and the diminutive dimensions of the coves. A strong wood is required to stand up to the abuse that a chair faces. Photo Credit: Terry Kelly

Let’s consider two different measures of wood strength: modulus of elasticity (MOE) and modulus of rupture (MOR). MOE can be referred to as “stiffness”. It’s a fairly straightforward measurement that simply asks: How much force is required to bend a clear section of wood of specific dimensions by a certain amount? In other words, imagine holding a popsicle stick; how much force does it take for you to bend it by 1/4″? This will be determined by the stiffness, or MOE, of the wood.

MOR can be understood as “breaking strength”. The question it asks is: How much force is required to bend a clear section of wood of specific dimensions to its breaking point? Going back to the popsicle stick, we’re simply asking how much force it will require for you to break it in your hands.

There are many more measures of strength, but these are two of the most commonly used and easily understood. There is a definite correlation between MOE and MOR. Woods that have a high stiffness also tend to have a high breaking strength. However, there are some deviations from this general rule that we’ll find to be important. Also, both measurements are correlated with density – the denser the wood, the more likely it is to be stiff and strong. Ideally, however, we would like to build with the lightest possible wood that will provide appropriate strength. No use making our chairs heavier than they need to be, right?

Alright, that’s enough of the backstory. Let’s have a look at some juicy graphs. There’s a lot going on here, so I’ll try to walk you through (please note that you can click on the graphs for a larger version). The top graph plots MOE (stiffness) against density*. Each dot represents a single tree species. As you move from right to left, density increases, and stiffness increases as you move from bottom to top.

Wood Stiffness

Wow, lots of trees here. In the version below, I’ve highlighted some species that are at least as stiff as hard maple.Stiffer WoodFirst off, there are some obvious surprises (even to me, and I have a Master’s degree in wood properties). Look at Douglas-fir and the yellow pines: lighter and stiffer than sugar maple. So should we Southerners be building our chairs out of longleaf pine? Well, not so much, as we’ll see when we examine the MOR graphs. I was also surprised to see sweet birch and yellow birch perform so well. Same density as hard maple, greater stiffness. These species pretty much overlap the same range as sugar maple, so it doesn’t help me out, but it begs the question: Why aren’t these birches regarded as highly as sugar maple? (Do keep in mind that these two are head and shoulders above all other birches – don’t try turning Windsor legs out of paper birch or river birch or you’ll be sorely disappointed).

There are some less surprising candidates as well. Hickory is off the charts, head and shoulders above most of the crowd. Oak of many different species (both white and red) aren’t too far behind. However, notice how variable the oaks are. Some of them actually rate pretty poorly. And poor bur oak – the density of sugar maple with the stiffness of black willow – yikes! I almost wonder if that’s a data error or just a poorly selected test sample. Black locust fits in somewhere amongst the hickories and oaks.

Now, oak and hickory and locust are all perfectly nice woods, but they do have one common shortcoming: they are all ring-porous. That is, they all have alternating layers of big-pored wood and small-pored wood that correspond to the growing seasons. What we want for a spindle turning is a nice even-grained, diffuse-porous wood (maple and birch are common examples). Because of the evenness of their texture, diffuse-porous woods tend to be less likely to splinter while turning, so they can hold crisp beads and fillets and be polished to a smoother surface straight from the tool. To be precise, hickory is actually a semi-ring-porous wood, meaning that it fits somewhere in between oak and maple – and it would probably be a perfectly fine wood to use in a pinch – but I’ve turned enough of it to know that it’s no joy to turn, unlike maple.

So what is left?

Well, there are two interesting candidates remaining. Live oak is one. I know, I just got done saying that oak is a ring-porous wood, unsuitable for the crisp details of a baluster leg. There is one exception to that rule, and it’s live oak. Live oak is not a wood that woodworkers run into frequently, so it would be easy to overlook the fact that it falls into its own category, separate from red and white oak. It’s stronger than most any oak, but that strength comes with a lot of extra weight and hardness. It is not an easy wood to work. But it’s also a diffuse-porous hardwood, and it’s the most common tree on the island where I live. Very interesting. There are some problems as well, though. Live oak is a nightmare to split. And it has very prominent rays that might cause problems with chipping when turning. It seems to be worth a try, though.

Live oak end grain
This live oak is diffuse-porous – it doesn’t have the bold annual rings of red or white oak. However, notice the prominent rays (those white streaky-thingies). Those might cause some problems when turning (click to zoom in).

Finally, the most interesting candidate of all: Persimmon. It’s stiffer and harder than sugar maple. It’s diffuse-porous (okay, some references will call it semi-ring-porous, but the pores are not as big and prominent as, say, hickory). And I know from experience that it splits easily and turns beautifully. Seriously, it takes a world-class polish straight from the tool. Turn it once, and you’ll never forget how well it works. I daresay that persimmon might be the silver bullet – the one wood that we Southerners have that could surpass sugar maple in every measurable characteristic (except density, but I think that’s a minor issue; it certainly won’t affect appearance). The only problem: it’s not the most common tree to find in the dimensions needed for Windsor chair legs. Oh, I’ve seen it 4′ in diameter and 120′ tall, with nary a branch for the first 70′. But that is the exception, rather than the rule. I’m going to give it a go at some point, though. Mark my words. And if I still have any readers at that point, you’ll be the first to know how it turns out.

Alright, stiffness isn’t the only trait we’re interested in. No, we don’t want our chair legs to flex excessively, but the more critical virtue is making sure that the suckers don’t break. That’s where breaking strength (MOR) comes in.

Wood Strength

One thing I notice right away is that the relationship between density and breaking strength (R2 = 0.80) is much tighter than the relationship between density and stiffness (R2 = 0.52). Also, notice that the softwoods (southern yellow pine and Douglas-fir) that seemed so impressive on the stiffness scale have dipped into mediocrity on the breaking strength scale. Add to that the fact that softwoods don’t turn worth a crap, and you have your answer as to why we don’t use conifers for chair legs.

Stronger Wood

Beyond that, the placement of the species has changed very little. The hickories are still the leaders of the pack. Black locust, black and yellow birch, persimmon, and live oak are still sitting above sugar maple in breaking strength. The red and white oaks don’t seem to perform quite as well as they did in the stiffness test, but the change is minor. So whatever conclusions we drew from our examination of MOE would seem to hold true when we consider MOR.

Wow. I hope this post hasn’t turned out too dry, but I fear that it has. Density, stiffness, porosity…these aren’t usually the things that gets a woodworker’s blood pumping. We like pretty colors and striking grain patterns. Most craftsman-made furniture tends to be over-engineered to such a degree that it makes nary a difference whether we choose pignut hickory or eastern redcedar to built that blanket chest or dining table. It just has to look good!

Windsor chairs are different. The grain needs to be straight and plain and boring. Straight grain means ultimate strength. The shapes – rather than bold wood color or showy grain – provide the visual interest. And the dimensions are pushed to the extreme, so the wood (and the joints) must accommodate. You will be need to be equal parts craftsman and engineer – and I don’t know if you’ve noticed, but that suits me just fine.

*All data for this series was adapted from this US Forest Service Publication. Density, MOE, and MOR measurements were all taken at 12% moisture content. I will be posting a link to the raw data that I pulled from the publication, as well as the graphs included in the article, in the form of an Microsoft Excel file.

UPDATE: The wood property data and the primary source have been added to “Wood Properties Resources” in the menu bar at the top of the page.

How to Calculate the Radius of a Circumscribed Circle of an Equilateral Triangle with Side Length (x) and Why You Should Care.

So, do I win the award the award for the most objectionable blog post title ever?

What? There’s no award? What a waste.

Well, anyway, one of my dear readers (and you are dear, trust me, I can count you on my fingers and toes) asked me about how I located the peg holes on the underside of the top of my sassafras kitchen table (from this post). The intuitive way would be to flip the table upside-down and set the base on top, then push it around until the distance from the point atop the legs to the nearest edge of the tabletop is equivalent for each leg.

The tops of the legs form an equilateral triangle. Your mission, should you choose to accept it, is to mark the corners of a congruent triangle that is precisely centered on the underside of the tabletop.

That would work, I suppose, but it would be finicky and prone to error. As my reader surmised, there is indeed an easier, more precise, more elegant way. First, we just need to envision that the top corners of the three legs form an equilateral triangle. The length of the sides is easy enough to measure. In this case, it was 28.75″ precisely.

Let’s call the length of the side (x). If you recall from high school geometry, there is a fixed relationship between the length of the sides of an equilateral triangle and the radius of a circle – we’ll refer to the radius as (y) – that passes through all three corners (i.e., a circumscribed circle).

That relationship is: y = x (√3) ÷ 3

circle 001
Mmm…numbers. For the record: No, I didn’t remember this formula. I had to look it up.

So, we just plug in 28.75 for (x) and we get 16.598820…Let’s call it 16.6″. I don’t have a ruler that’s marked in tenths of an inch, so I just used 16 38/64 (16.594″). I adjusted my trammel to the radius and scribed a circle on the on the underside of the table (you can see it on the picture above).

Okay, now we have a circle of the proper radius that is perfectly concentric to the edge of the table, but we still need to accurately locate the three corners of the triangle. Well, that’s dead-simple now that we have a trammel set to the radius. Just pick a point on the perimeter and start “walking” the trammel around the perimeter, making a mark at each intersection. You should end up at the same point that you started at (or very close to it) with six equally spaced marks around the circumference of the circle, forming a perfect hexagon. Drill a hole in every other point, and there you have your perfect equilateral triangle.

Mathematical constants are fun and useful!

So there you have it. Hopefully I made the process tolerably clear – it took far longer to write about it than it did to actually complete it.