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!