Category Archives: Joinery Etude

Hopper Joinery

The hopper is an old form you can still see all the time in things like wheel barrows and baby’s cribs, sloped sides meeting in compound miters. Although initially intimidating, learning to determine the cut angles for butt or mitre joints is as simple as drawing a few lines with a carpenters square, opening up a whole exciting world of non-orthogonal intersecting surfaces.  Learning hopper joinery is step number one towards Japanese roof carpentry, heady stuff indeed!

Although there are western methods for deriving these cut angles, I learned it first from Chris Hall’s second volume of carpentry drawing books. They’re only available as an e-book and not cheap, but its still cheaper and faster than learning Japanese. He kind of bludgeons you (in a good way) with numerous methods of understanding this stuff, from a basic trigonometric understanding to developed drawing to my favorite and the dead simple approach with the sashigane.

Since I want to keep this simple and don’t want to rip off Hall’s hard work in teaching this stuff I’ll omit the Japanese names for the various parts of the unit triangle.  Also of import is that this method only works for regular slope, regular plan. Which is to say, the splay is the same on all four sides and they meet at ninety degrees in plan view.

Slope is expressed most commonly as a ratio, here 4/10. I apologize for the crappy surface of my work beam, the rest of it was scraped clean, but I didn’t want to erase the unit triangle until work was complete. Hopefully its clear though that I used the square to draw a triangle with right angle sides of four and ten, with the edge of the beam forming the hypotenuse. The short segment of the triangle gives the bottom bevel angle of your hopper. From there a line is extended up square to the hypotenuse and meeting at the right angle . The length of this segment that divides the unit triangle gives the face cut angle, 3.75/10. Further, the hypotenuse is now divided by this line into two segments, a short and a long. The long segment gives the edge mitre angle 9.375/10 if you want a hopper to join with 45 degree corners in plan view, and the short segment gives the butt mitre angle of 1.5/10.

I’m using butt joints, so just as I drew the original 4/10 triangle, the square is used to lay out a line on my beam for the edge butt angle and the face cut angle, and then transferred to a bevel gauge.

Its handy to have a couple of bevel gauges, each one set to the needed angles.

Apparently Shinwa makes a western framing square in stainless steel, couldn’t resist! It has the normal rafter tables and brace length table, but no Essex board foot scale. I don’t think I’ll miss that one though, never having used it.

Rather counter-intuitively, for a hopper with butted edges, the inside length is longer than the outside, which you have to watch out for when marking the edge angle.

Once you know which side of the board faces inward on the hopper you can mark the bottom bevel.

These hoppers are a real pain in the ass to nail together without some kind of joinery, so I decided to cut a simple dado. For marking the width of that dado you need to use the length of the cut line along the edge, not the thickness of the board. Its a slight difference at 4/10.

I’m using my double bladed marking knife for illustrative purposes. Marking with ink is easy on the eyes if slightly less accurate than a knife line, but my joinery was tight in any case.


With the layout almost complete I started by beveling the bottom of the hopper sides so that they will sit flat. Beveling the bottom also removes the need to cut an annoying barb where the bottom edges of the sides meet, as well as making it easier to cut a bottom panel groove with hand tools.


With the bottoms beveled I finished marking the joinery. You know something is going right if your lines meet square across the beveled bottom edge.

Cutting the dado’s with dozuki and a piece of kumiko as a guide fence to my cut line. I start the saw with a stroke or two to get a kerf all the way across the cut, then take the guide away and angle the saw. Its good practice for dozuki technique. To keep the saw from jumping the kerf you have to saw flat.

Ahhh! So much easier to assemble with a little joinery, even if this thing is getting nailed together with pneumatics.

Once the sides were together I lopped the upper corners off. The angle for that cut is a further segment of the unit triangle, important when you want to cut mortise and tenon, but for a simple hopper like this I just flush sawed using the edge of the side as a guide.

I didn’t use a bottom panel groove, just beveled the edges to fit in the hopper a little above the bottom. Surely this is not as strong as nailing the bottom on to, well, the bottom, but it looks nicer to me.

If you want to make a strong nailed box or hopper its worth studying the prototypical Japanese style crate, this one’s for my drafting tools.

So there it is! Basic hoppers are not at all intimidating once you give it a try, and you will be on the road to some really awesome woodworking possibilities once you step outside the world of square boxes. I’d really like to make a rocking crib one day that uses a hopper and splayed legs!

X Marks the Spot


For the past day or two I took on the challenge of drafting a carpentry drawing exercise of Bruno Sutter’s, a compagnon, detailed by Chris Hall on his blog, in a series titles X Marks the Spot.

Its basically one of those great blog series of Hall’s that seem irreducibly complex even after reading through several times, but there had to be a reason for him to present the material. As it turns out, its not terrible compared to a Mazerolle sawhorse, and teaches many important descriptive geometry concepts for a relative neophyte such as myself.

Its not worthwhile to rehash the how-to of this endeavor, Hall does a very thorough job himself. What I do want to get across is the importance of actually doing the drawing work if you want to understand how this works. I’ve made inroads with using Google Sketchup for drafting, as well as by hand, and have things I like about both.

  1. Sketchup is free, fast, and accurate (with the exception of certain functions regarding curves and circles), but doesn’t work without a computer.
  2. Hand drafting was the only option until a generation ago, and our carpentry forbearers managed much masterful work. That said, its easy to accumulate small errors in accuracy even working full scale, such as when projecting a line long distance from the edge of a footprint. While you can draft with not much more than paper, pencil, straightedge, and compass, you’ll definitely find it more manageable with stuff like a T-square, parallel rule, drafting triangles, protractor, scale ruler, and a range of hardness in pencils or line weight of pen.


For this exercise I decided to work it out on paper, best to be familiar with both ways of working, you never know when the zombie apocalypse will take out computer functions…


My drawing, mostly completed. Notice how hard it is to see? That’s because I’m using a very hard sharp pencil for accuracy, with the paper taped down nice and flat to the edges of the drafting board.


The basic sequence of the drawing consists of starting with a plan view of the two crossing sticks, using the cross section to find the footprint via folding down the elevation view, and then finding where the planes of each of the faces on one stick intersect the other. By unwrapping the stick like a cardboard box layed flat the lines of intersection can be transferred, and each of the faces shown as if you were looking at them directly.IMAG2226

The drawing is to scale for the size of the pieces I wanted to use, one inch square in cross section and a little over a foot long. The advantage of drawing to scale is that the pieces can be place on the drawing and marked directly. Pretty neat, no?


The last step of actually figuring out what bit of wood to remove presented the greatest difficulty. Hall says that you basically have to ‘intuit’ from the planes of intersection what represents the actual cut lines. My spatial skills are not quite there yet, so I made the miter cuts at the end of the sticks and held them close together in their correct orientations until I could see where one piece fit through the other and shade in between the lines.


On the unflolded view of the drawing the planes of each of the faces of the opposing piece are marked in blue and red, with the resulting space that needs to be cut out shaded in green. Not exactly jumping out to you that these are the cut line for one square piece of wood fitting through another, but that’s what happens with stuff at slope and differing angles to plan.


Cutout was a petite masterclass in cutting angles. I basically cut all the lines I could with a ryoba saw, and then went in with a fret saw for the bottom line that can’t be reached with a normal saw. Paring a bit with a chisel and voila! Not a piston fit, but at least it shows that I understood the drawing exercise. I had to draw this whole thing twice because I noticed my first drawing wasn’t accurate enough, lines that should have been parallel were not, and the cuts would have been all fucked up as a result.

If I wanted to do really accurate work? Computer drafting is the answer.

Splay Legged Stool

Like, say, a splay legged stool? Yup! I figured out the kinks on this one too, but it deserves much discussion of its own, so I’ll save it for next time.

Keyed Sliding Dovetail


Well well well, have a look inside the mystery joint from yesterday, sans shachi-sen. Look familiar? I’ve seen this joinery used to great effect by Chris Hall in numerous furniture pieces now (as well as larger structures like a gate), connecting things like table leg rails to the top frame above it. I found it to be quite a challenge! But, seeing as this is the way that I want to hold fast together the matched wooden straightedges for the study group meetup today, I thought it was high time to give it a go.


The pieces to be joined are marked together with marking knife  for the two mortises, ensuring that they will match up when the dovetail keys are installed.


The proportions of the dovetail are largely determined by the width of the chisels that will be used, adjusting the taper of the dovetail key is done by changing the mortise depth.


A lot of the accuracy of the method that I use depends upon accurate depth to the mortise. Perhaps a more forgiving method would employ scribing the dovetail key to the slot that is cut. I layed out half of the dovetail key to make sure the proportions look good, and then made a small depth gauge to match.


The bottom of the dovetail key is 1/2″, the top 1/4″, each slot is the same length at 3/4″. The bit that the dovetail key slides into starts as a 1/4″ wide mortise.


And then the sides are flared out to meet the bottom, forming the dovetail slot. The back of these small sliding dovetails was very tight, I found myself needing a small fishtail chisel, unfortunately I don’t have one that small, so I resorted to a small 1/8″ detail chisel to clean the end grain corners as the cheeks of the dovetail slot were pared.


My dovetail keys, both slightly over sized in every dimension. I made a small saw cut to define the depth of the waist.


And then started splitting off the waste by paring top to bottom.


Now a bit more accurate chisel work to make sure my surfaces are flat. I was pleased not to need a clamp to work these small pieces, though my fingers were at times in danger of poking with the chisel.


The wedge was first fitted to the 1/2″ dimension of the mortise, undergoing a bit of adjustment here and there. By and large most of the fitting took place on the dovetail slot, especially paring in the back corners where I tended to leave too much wood.

I had to push down on the dovetail key pretty hard as I tapped it in with my hammer. I imagine a longer dovetail key would be easier in some respects to install without blowing out the face grain of the mortises. Tricky to fit these! Always a puzzle to figure out where the surfaces are proud.


Each side of the dovetail key was individually fitted to its respective slot, so everything had to be labeled or its a fools progress. With the dovetail keys tapped home the plugs can be planed to fit from the same stock the keys are made of.


I screwed the surface quality of the inside face by sawing too close while making the plug flush. Its always some stupid little error committed after jumping the more difficult hurdles, but that is why this is a practice attempt, I’ll be more mindful in the future. Which is to say, cut proud of the surface and pare with a chisel. Make your mama proud of your work!


And how about we throw a locking wedge in there for full effect. This would be the full expression of the joinery application, and is what I plan to use to join the carcass to the bottom skirt of the cabinet piece I’m working on. I eyeballed the taper and transferred marks across the top of one piece, though the marks could also be brought across the interior surfaces once the pieces are separated.


Definitely locked together, and easily demountable. Is it worth it to join pieces together this way as opposed to screws which are cheap and easily employed? I don’t know, but it sure is fun! You have to do work that you are satisfied with, and I for one will always seek to improve my technique.

Layout for Simple Japanese Hip Roof

Hello! Tonight we go further down the rabbit hole that is Japanese hip roof joinery. Where might it lead? To building of course! I’m not sitting here in my shop obsessively building joinery models as an attempt at some kind of mental masturbatory self indulgence. This is about a little corner of structure, a fundamental of human existence. It is then, as they say, an existential topic to speak of timber joinery.

I think most peoples experience with structure has been entirely sub-optimal. Except, maybe if you’ve lived on a boat. But for most of us we don’t even know what we’re missing. If you have the misfortune to live less than a comfortable first world existence then necessity becomes the drive that creates the idea of a better circumstance, and often a better structure.

Tonight I had the good fortune to speak with Mark Grable for a bit on the telephone, I found it galvanizing. You have to understand the potential out there for people that are willing to get shit done. How bad do you want it, how badly? Now go find out.

So, to get back to the topic at hand, I’m giving it another try with the simple Japanese hip roof model. This is walking step by step towards structure by understanding one small piece of it at a time.


We have our two keta beams joined together with a wedged mortise and tenon. By the way, my model is about half scale to what is listed in the book. My keta measure 60mm by 80mm. I feel awkward trying to explain this because my own understanding is so rudimentary, but here goes.

You can see that the layout starts quite simply with the hip centerline drawn on the top surface of the joined beams. Then the width of the hip rafter can be added in parallel to the centerline. Lucky for me this is a normal hip roof, symmetrical between the wall edges at 45 degrees.


Next I added the lines parallel to the top centerlines that represent  the top and bottom edge of the common rafter notches. Because there is a jack rafter projecting out from the end of the centerline of either beam the kogaeri line must extend into the layout for the hip rafter notch.  Then the cut lines for the rafter notches can fall in place. It does make things look a bit crowded in there.

I remember the first time I looked at these hip roof models and the layout for it. Mush! Unless your a genius its hard to work out what’s going on. Give things a name, order appears, and structure commences.


From there we can draw a series of lines perpendicular to the hip rafter, they all seem to have their own names too. You can see I’ve made a nice little series of squares by intersecting at the centerlines of the keta. There’s almost a hip rafter notch, but I’ll have to do a bit of layout on the hip rafter to find out where to place one of the cut lines on the keta.


I started the hip rafter layout with the middle honchu line. Where as the common pitch of the roof (rise/run) is 5/10, the hip rafter uses its own pitch, 5/14.14, based on the relationship of the normal hip rafter being the hypoteneuse of a right triangle whose two sides are equal.

With our hip rafter pitch we can mark both a level line and a plumb line. In this case I saved myself some time by grabbing the plumb line with my bevel gauge and referencing to the edge and not the centerline. In practice I wonder if that would be possible. This whole endeavor does seem to depend on quite carefully dimensioned and squared material. I wonder what acceptable tolerances are for beam cross section and squareness?


I made a mistake yesterday in the spacing of these lines, because I was measuring along the edge of the hip rafter and converting the distance between lines on the keta mathematically to the distance along the hip edge. I cut that out entirely this time, measuring equal distances along the level line of the hip rafter run.


I used the same method to transfer the distance to the back face of the keta beams. The distance between nyuchu line and the back face of the keta beam is equal to the distance between honchu line and the tip of the notch on the back. This ensures that we get a triangle that will be 45 degrees to plan when the hip rafter is at the proper slope. Remember how those three intersecting lines helped form a series of squares on the keta? Now they’re a bit stretched out on the bottom of the hip rafter.


Next I added the level baseline that intersects with the bottom rafter line and nyuchu. Because the baseline for this model is above the keta centerline 5mm I had to mark a line below the baseline that represents the top of the keta beams. This new line, “top of keta” extends to a new point where it hits the bottom of rafter line.


Last for the hip rafter was marking the front of the notch where it intersects with the side of the keta beam.


I’ve drawn some stars to help point out the new line derived from the hip rafter that is the start of the notch on the keta. All that was left from there was dropping the hip rafter notch lines down the side of the keta beam to the correct depth. I made a mistake there yesterday, hit the wrong numbers in the calculator or something. So I decided to get the numbers both mathematically and graphically.


This time apparently I did things okay. It wasn’t a perfect fit, but most of my marks lined up pretty well.


Pretty cool looking!


I did make one mistake, my jack rafters are not meeting the hip rafter in plane, but that was another simple mistake with how I marked the depth of the jack rafter line on the hip rafter, and I’m getting too tired to explain it properly. Sebastian and I will be cutting a slightly more complicated model next week some time, we’ll try to explain it together and I look forward to continue exploring this aspect of house joinery. Its quite challenging, but fun!

Hip Roof Model Fail


From “Wood Joints in Classical  Japanese Architecture” we have this wonderful little hip roof model, of the intersection between the wall sill plates, or keta, and the hip rafter/adjoining jack rafters. The model has a pitch of 5/10. So, how the hell to go about building this thing? Its a murky depth to probe at first. There’s something really important about having the pieces in your hand as you mark for cuts, looking at the orientation. I’m also working (almost) entirely in metric, the time saved converting decimals to inches is appreciated. I still want a sashigane with square root scale, even if it means working in shaku.


Ahh, the good old compound miter for the jack rafter. Top face marked 45 degrees to plan, side faces marked with common rafter 5/10 pitch using the carpenters square. Bread and butter stuff if you’re cutting a stick framed roof.


The top edge of the hip rafter is beveled to stay in the plane of the roof, and the jack rafter has to meet that plane evenly. So how do you find the angle for beveling the top of the hip rafter? It gets more interesting than that, there’s a common “pivot point”, or toge that represents where the bottom face of the rafter meets the base line of the top of the sill plate. Usually it would seem toge is often an imaginary point a little above the center line of the keta beams. It matters because the joinery has to be cut on the hip rafter such that the top planes that form the roof slope lie in the same plane as the common rafters, there’s a relationship there that is not immediately clear how to apply in layout for the cutting of the joint.

For the purposes of my model I made toge 5mm above the centerline.


The sashigane is the most important tool in this awesome adventure. Can you say, hip rafter pitch?


Finding the bevel angle for the top of the hip rafter involved measuring along a  level line on the side face representing the 5/14.14 pitch for a distance half the width of the hip rafter.


The same use of the sashigane gives the plumb line as well, along which you can measure the distance to the bottom line of the jack rafters. I realized at this point that I made my hip rafter too deep, not sure about the proper proportioning yet.


On the keta, we have the center line above which is our imaginary pivot point. Based on the common rise/run of 5/10 I know that the bottom of the jack rafters will contact the top of the beam 10mm away from the center line. On the side face of the beam we have the all important kuchiwaki line, representing the bottom of the jack rafter notch.


“The Complete Japanese Joinery” was my main reference for understanding the process of layout. But I’ve already made a terminal error in my marking here, not to be found until I started cutting.


The downward slope of the jack rafter notching continues from the kuchiwaki line where it intersects the perpendicular keta beam. From there I measured up to find the slope cut on the nose of the beam. I couldn’t tell from the model if it was supposed to be flush with the top of the beam or slightly below.


At least I did a bang on job with the wedged tenon. This is the first time I’ve tried the technique of drilling small stress relief holes at the bottom of the saw kerfs on the tenon.


It should have been a simple matter to measure the notch depth, somehow it became way lower on the left side and I didn’t notice the twist until I started chiseling out the waste.


My second and more serious error was in the joinery for the hip rafter. The cuts on the side were properly marked at 5/14.14 pitch, but the spacing between marks for the bottom I multiplied from the keta beam using the square root of two, effectively marking for a 10/10 pitch roof…


At least I’ve reached an understanding of my mistakes, and know how to mark correctly for the next try. But that is for tomorrow, all this thinking of angles and hypotenuse makes for a night dreaming of triangles.