Engineering Staked Furniture

After reading the Anarchist’s Design Book, I decided to make a three-legged stool as my first piece of staked furniture.  I made a quick sketch of the stool and a model to help guide my leg angles and placements.  Based on the model, I found a leg angle of 21 degrees to look nice, to me at least.

I’m an engineer and the things that I wondered was how much does the angle change the loads on the legs and how close was I to the failure point of the leg.  I googled around a little and didn’t find any clear guidance on the analysis of the legs of a chair, so I decided to go ahead and do it myself.

Like all good engineering problems, you start with a free-body-diagram (FBD).  This drawing catalogs all the forces acting on the leg and serves as the roadmap for an analysis. The thing we are most interested in is the moment at the point the legleg_forces enters into the seat M_s.  We need to make some assumptions to figure this out.  The first assumption is that the force on the leg due to the person sitting on it is distributed evenly.  That means

F_s = \frac{W}{N}

or the weight of the person W is divided by the number of legs N. We also assume that the friction between the leg and the floor is zero, so f_f=0 in the FBD to the left.  Now we can sum up the forces and solve for the moments which gives us

 M_s = \frac{W}{N}\left(\frac{h}{\cos\theta}\right)\sin\theta

F_f = F_s = \frac{W}{N}

This means that the moment at the leg mortise varies in a mostly linear way as the angle of the leg changes, assuming that the seat height remains fixed.  The graph below demonstrates that relationship.

force_angle
Moment at the seat for h=19 in.

While this is important, what we are really after is the stress in the leg.  Stress is simply the force in the leg divided by the cross-sectional area of the leg.  It is important because we can compare the calculated stress level to measurements made on representative wood specimens.  If our stresses in the leg are below the measured maximum stresses in the samples, then we can be sure that the leg won’t fail. Assuming our force analysis is correct.  When we do the stress analysis we get the following relationship, where \sigma is the stress in the leg

 \sigma_{tensile} = \frac{W}{N}\left(\frac{2h}{\pi r^3}\tan\theta-\frac{1}{\pi r^2}\cos\theta\right)

For the equation above, I’ve made the assumption that the leg is circular at the mortise, which is a pretty good assumption. When we do the same study as in the plot above and ask what the stress in the leg is for a given angle and a fixed seat height we get

stress_angle
Stress at the leg mortise for h=19 in, r=1.125 in

From this plot I can see that my leg stress is approximately 1700 psi.  That’s actually not much and when you compare that stress level to measured failure stresses in typical leg woods we see that we have a lot of leeway

Species Modulus of Rupture (psi)
White Oak 18,400
Red Oak 18,100
Ash 15,000
Hard Maple 15,800
Hickory 20,200

Most of these woods have failure stresses 10 times higher than the stresses we see in the legs.  This is great and likely contributes to the longevity of the samples that Chris talks about in the book.

The next question is leg length.  I am currently making a stool that is about normal seat height, but will be making a counter height stool (23/24 inches) as the next one.  Modeling that seat gave me a leg angle of 17 degrees, which also happens to be the angle Mike Dunbar suggests in his stool article here.  The plot below shows the leg stresses for a range of seat heights from 17 to 27 inches for that 17 degree leg angle

seat_height
Mortise stress for a 17 degree leg that is 1.125 in in diameter.

Again, the results are good. For a standard 1.125 inch diameter mortise, the stresses are about 2000 psi. That gives me lots of head room without changing any of the mortise dimensions. If you want some more details about how I got these equations, check out this little document I put together chair_forces.

DISCLAIMER – this is a pretty “back of the envelope” calc and may have some errors. Use at you own risk.

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The Anxiety of Tool Care

Many of the tools I own and use are more than twice as old as I am. This actually produces a sense of anxiety about how I treat the tools and how well I care for them.  When you become, essentially, a keeper of the tool for the next generation, your relationship to these things change.  This bleeds over into my other, less provenanced, tools as well.

Take my set of 1990’s marples chisels for example. These were the bad-ass Dodge Stratus of the time and the entry-level chisel of every woodworker I know. And they’re still great. But my dog got ahold of the 3/4 chisel while I was sharpening one day and chewed the end. Thankfully no one was hurt, but the handle was mangled.

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Did this change how this chisels worked? No way. But it changed how I felt about it.  The handle stared back at me from my tool chest and kept saying “fix me.”  So I finally did.  I have made one chisel handle replacement before for a long paring chisel that was just a simple hexagon.  For this handle,  I decided to make a modified london pattern handle .  There are a number of tutorials on making these handles on the wb (see here, here, and here, for example).

The basic procedure is pretty simple.  Take a block of wood, ash in my case, and plane (or saw) into an octagon.  Chuck this into a lathe and turn the curvy parts.  Drill a tang hole and pound the handle home.  For this handle I picked up a ferrule from Ron Bontz at Bontz Saw Works because they are nice looking and I wanted something other than the copper pipe cutoffs that are the standard for the typical handle replacement.
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I am pretty happy with how it turned out.  The handle is a little tilted, but I was happy with the outcome from me free-handing it with the tange hole. When you put the handle on, try to line up one of the flats of the octagon with the plane of the blade.  It makes it easier to register when you pick it up.   I finished it with a little shellac and it’s now ready for another 20 years of work.

Jig Saw or how I stopped worrying and learned to love the reciprocation

The first, and only, experience I had with jig saws was using my dad’s vintage craftsman. 

Wholesale stolen from ebay.

It looked pretty much like the one above, but it had the additional “feature” of being able to “steer” the blade via a twisty handle at the top. It was loud, vibrated, and had the cut accuracy of the average user of public restrooms.  I hated using it. 

Fast forward 25 years and I was staring down needing to cut out a 12″ circle from 3″ thick poplar for my first staked furniture build.  I don’t have a capable bandsaw so my choices were rigging something up with a router or cutting it with a coping saw.  Neither was a great option for me (i have router phobia). 

I was wandering through the big box store and they happened to have a Bosch jigsaw on discount. Two minutes of in-store tool review searching and I picked up the JS470E and took it home. It stated on the box that it had 4″ hardwood cutting capacity, so I hoped that a a 33(.3333333…)% overcapacity would mean that it would actually work. I thought that I could at least get it close and then clean it up. It worked ao much better than I had expected. 


The saw easily handled the poplar and left a clean (and square) cut. Took less than 10 mins to zip out the blank above and that included clanping and unclamping from the workbench.  Technology has most certainly advanced in the last few years. 

Don’t fear freehanding a circle too. Draw your line and just cut. You can always fair it out with a plane and spokeshave later. Even with a bandsaw you’ll have to do something to clean up the saw marks. And your circle diesn’t have to be perfect, just good enough to fool the eye.  

Twisting in the Wind

The space between projects is always an interesting one. There’s a sense of disorientation, for me at least, and a little bit of loss.  When you’ve been focused on the provess and goal for a long time, being without that focus can be disorienting. Since finishing  the nail cabinet, I decided to work on some essential hand woodworking layout and reference tools to fill the gap between larger projects.  The first up was a short straight edge from a scrap of maple I had lying around from my moxon vise build. I decided to make a couple of thumbnail ends and an ogee-like shape at the top for a finger hold. 


I cut these with a coping saw and then used a couple of rasps to clean up the shape.  I have a nicholson rat-tail and a Narex half-round. Both of which work fine and aren’t that expensive. I did further cleanup with some metal files.  The endgrain of this maple responded really well to the file.  Since this straightedge is only 1/4 inch wide you would think a 1/2 chisel would be enough to clean up the long sides. However, I had the best luck with my 2 in wide chisel. I think it let me feel if I was tilting and it also let me skew cut along the length.  

After the profile was shaped, I cut a finger recess with a gouge.  This worked OK, but it wasn’t very straight or even.  I used a curved scraper to straigten and smooth the groove. This was super critical because I couldn’t cut the groove with the gouge without tearing out. Curved scrapers are awesome and can be made from straight scapers with some judicious grinding. 


The next item was some winding sticks. I made these from quartersawn sapele that I picked up at woodcraft.  Not a cheap way to do it, but I wanted some dark wood.   The sticks are frequently triangle shaped because, I think, they are cut from one piece of wood.  That’s how sellers approached his. My wood wasn’t thick enough to do that, so I cut it in half and the ripped the angle. 


I cleaned up the cut on my sticking board, which let me run an angled jointer over this thin stick of wood.  If you haven’t made a sticking board, do it. It’s an incredibly useful piece of kit.  

Then came the inlay of a couple of lighter wood strips. I chose some quartersawn maple for a  nice understated ray fleck.  I defined the inlay recess with marking knives and a cutting gauge and then cleaned out the recess with a sharp chisel. A small router plane might have helped a lot here.  At least made the process faster.  

The inlay material was again cut from the moxon leftovers and then planed down to about 3/32 or so just using my smoothing plane and the bench stop. It was kinda scary planing at the toothed hook with a very thin piece, but as long as you press down hard before planing forward the part stays put. I then glued it into the 1/16 in-deep inlay recess and planed it flush with my block plane after the glue dried. 


There are some gaps, but overall I am pretty stoked with my first inlay attempt. One down side was that the sapele warped a little after gluing. I think the water in the glue caused this and I am hoping it will die down over time. The warp is along the length and doesn’t appear to impair use. Just looks bad. 

This was a lot of fun and a nice exercise in precision planing. Highly recommended. 

Stock Photos

If you asked someone what was is most fun part of woodworking, prepping stock is generally not everyone’s first choice.  While I wouldn’t sign up for a full week of prepping stick with handtools, I’ve found that I actually enjoy establishing a true edge and face.  I don’t have a jointer, so I have to do all the flattening by hand.  There is something satisfying about being able to run your square down an edge and have it all line up.  Makes you feel like you’ve accomplished something significant.

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I still use my dewalt surface planer to do a lot of thicknessing, but you have to establish a flat face for the planer to work properly.  Like all things in handwork, the stock prepping process is so much easier if your tools are sharp.  Especially in hardwoods.  You can usually muscle through pine.

If prepping your stock by hand seems scary, check out this video that popular woodworking recently posted.  It’s a great step by step for getting it done. Not a huge fan of the intro soundtrack on this video….

The Bay

I have had a reasonable amout of success purchasing tools on ebay. While nothing beats getting to pick up a tool and look it over, being picky online can net you some pretty sweet tools. There will be misfires though. The starrett no92 in the picture below is a notable example. 

Starrett 92 on the left and its cheaper cousin the stanley 58 on the right.

I clearly saw that the spring on the micro adjust was missing, but I thought I could fix that easily. So I picked it up for just over $40.00 shipped.  What I didn’t see was that the quadrant rod was bent and the rod clamp had been seriously distorted. So now I own a nice-ish looking, non-locking compass/paperweight. 

So how do you avoid this? One way is to arm yourself with knowldege. Look at vintage catalogs so you know what parts should be there. There are a couple of sites with freely available scanned catalogs. The Alaskan Woodworker and Blackburn Tools both host many scans from the Rose Tool archive that is now gone from the web. Grab the catalog you want and learn what you’re looking for. This is most useful for planes and other complex tools.  Then arm yourself with a tolerance for dissappointment. You are going to buy some clunkers. Get used to it. 

If the thought of buying trash is distressing to you, then stick to the online sites devoted to user grade tools.  Hyperkitten Tools and Patrick Leach at The Superior Toolworks are two that I buy from and I have never been disappointed by either. 

Here are some other strategies that I have found helpful. If you want a desirable tool, look around at competing manufactuers. The stanley 58 above has 80% of the functionality as the Starrett 92, while routinely selling on ebay for 1/3 the cost.  If a company still makes the tool, it can be cheaper new than used, sometimes. This is particularly true of Starrett and Lie Nielsen. I have seen used versions of normal production tools of both manufacturers go for crazy high prices. Finally, if you see a tool that is going for way less than normal, chances are that there is something wrong with it and the more experienced buyers are staying away. Exceptions to rule include situations with mispellings and clear mislabelings.  

Burnish this

Last year sometime, James posted a review of a birdcage awl by Chris Black on his blog The Daily Skep. I wasn’t in the market for an awl at that point, but Chris makes several other tools and sells rehabbed old user tools as well.  If you’re in the market for something, check out what he has on craigslist.

While I didn’t need an awl, I did need a burnisher.  Craig has some nice ones that use a hardened M2 tool steel bar.  A quick hop over to the AZO Materials website, which is a great place if you ever need some quick and dirty material properties, told me that the bar should be close to 60 HRC in hardness.  That’s pretty hard.  So I ordered one.

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It’s a great looking tool.  The handle is nicely turned and the ferrule is the right size to balance the transition. So, instead of using it, I went right to the lab and put it into a hardness tester to see if the hardness was what it was promised to be.

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The hardness of this burnisher was 61.1 HRC.  That’s hard and should be able to turn a hook on almost anything.  No where near as hard as carbide (90 ish HRC), but more than enough to do the trick.  I’ve used it now to sharpen a few scrapers and it just works.  If you have some sort of crazy hard scraper it might not work, but the old bahco and the two cherries card scrapers I have turn a hook right away.  So if you need a burnisher, you would be hard pressed to go wrong with one from Chris.  Get it here.

As a postscript, I do not suggest hardness testing your burnisher.  The diamond indenter leaves a little raised ridge around the indent that can cause trouble when you’re burnishing. I had to sand it smooth after testing.