I’ve been watching lots of videos about making cardboard furniture, with an eye to using recycled cardboard from the neighborhood to make some furniture. There are many different techniques: gluing in ribs with hot glue, laminating multiple layers with PVA glue thinned with a bit of water (unaccountably always with the flutes in the same direction), cutting matching notches to slide pieces together at right angles, using single-linerboard corrugated (usually used for packing) to run around curved contours, paper tape like you use on the back of pictures to hang to cover up joints, découpage with glossy magazine paper to add surface strength and a flat surface for painting, etc.
One point frequently made in the videos is that corrugated cardboard is much easier to crease parallel to the flutes; so, for example, if a shelf is supported at the ends and loaded in the middle, the flutes need to run lengthwise to prevent it from creasing and failing.
I just did a quick test with Mina and a pizza box we were discarding. 16 layers of the one-ply corrugated cardboard of the pizza box were sufficient to resist her strongest efforts to break the beam by pressing down on it in the middle, supported near the ends by my hands; but 8 layers were not. The beam was about 40 mm wide and about 300 mm long, and the flutes ran lengthwise. In the end she was only able to “break” the 8 layers by virtue of twisting the beam in the middle, at which point it failed by creasing — decreasing the beam’s moment of inertia by bringing its surfaces close together. The pizza box is about 2 mm thick, but this was probably not very significant in this test.
This suggests that maybe to resist her weight with only one layer, such a rectangular beam that’s protected from twisting might need to be four times as wide, perhaps 160 mm wide. The U-shaped bend used by the Chairigami chairs to support body weight could perhaps use 110 mm of depth of “web” on each side; if it were notched to 55 mm depth to match a 55 mm notch on a vertical support, that might be adequate. To reduce crushing at the point of contact at the bottoms of the notches, the tab cut out to make the notch could be folded over rather than cut off, thus increasing the contact area and making it not be entirely edge.
Four of the eight corrugated-cardboard boxes I have handy here, left over from Mina’s move, are about 4 mm thick, 1300 mm in circumference, and 360 mm in height (and of course the flutes run heightwise), plus another 170 mm of top flap and 170 mm of bottom flap. The other four are apparently the same thickness but somewhat smaller. They have all suffered some minimal damage from the moving process. Since this is Argentina, not the US, they don’t have edge-crush-test or bursting test ratings printed on the cardboard.
(This works out to 1300 mm × (360 + 170 + 170) mm × 4 = 3.6 m² of cardboard in the large boxes and perhaps another half of that in the small ones, for a total of 5.4 m².)
We’re seated on some 250-mm-seat-height chairs that we both agree are a bit too low for comfort; their seats are about 550 mm square, which for her is a bit too wide, and for me is a bit too narrow. The kitchen chairs, which are maybe a bit too tall, are about 450 mm tall and a somewhat uncomfortably small 350 mm wide. So something like the 360-mm height of the boxes could maybe work well.
If I try to support this body’s weight (110 kg?) on a 48 mm × 140 mm section of folded cardboard strip from one of these boxes, it barely crushes; at 64 mm thick it had no trouble. This suggests an edge crush pressure of between 120 and 160 kPa or, in medieval units, 17 to 23 psi. So the 8 mm square sections of folded tab I was thinking to use to support notch bottoms will safely hold 8 N, or only about 800 grams of weight. But that’s okay, because the majority of the weight will be borne on the edges of the “legs”, not the notch bottoms.
A normal singlewall corrugated cardboard box in the US is rated for 32_lbs/inch edge crush test, in medieval units. If it’s 4 mm thick, that’s 1400 kPa, about ten times the number I got from this test. This makes me think that probably my test is unreliable because I am pretty sure this cardboard is more than 10% of the strength of normal cardboard.
I’ll take the geometric mean of these numbers, 400 kPa, or 1.6 kN/m.
Suppose we need to support 200 kg over 300 mm of seat length, front to back. (The whole seat might be 550 mm long, but maybe the weight is not evenly distributed; and maybe I’m sitting down on it hard.) Each 4-mm-thick “leg” provides 480 N of crush strength over that distance.
So we need about four “legs” per person.
The Chairigami dude arranges this by using two double-layer legs (that is, with three layers of linerboard separated by two layers of flutes, rather than two layers of linerboard separated by a single layer of flutes). But if I space the four legs evenly instead, I can shorten the unsupported span length of the seat between legs (to 550 mm ÷ 4 = 138 mm), and avoid having to laboriously laminate layers of cardboard with glue.
Earlier I suggested that a 300-mm unsupported span might require 110 mm of “web” depth supporting the seat to keep it from collapsing. This shorter span might require only 50 mm, and thus only 25 mm of notch depth.
I can do an initial test with “legs” much shorter than the 360-mm height of the desired final product, since the initial objective is crush testing. The seat flutes need to run at right angles to the legs, so I’ll probably have to make the seat out of two overlapped pieces to get to the full 550-mm width, since 360 mm is the longest transversely-uncreased flute length I have available; each overlapped piece will have a “top” that is 550 mm long, plus 50 mm of “web” on each side with four 25-mm-deep folded-tab notches in it, which fit into matching notches on the legs. The legs are, say, 650 mm in the cross-flute direction, and 100 mm in the along-flutes direction, and each one has two 25-mm notches on its top, 550 mm apart. Probably I’ll need some kind of additional lateral stabilizer to keep the legs from all bending to one side or the other; a single deeper notch in the bottom of each, perhaps 30 mm, can allow the insertion of a single 100-mm-long, 550-mm-wide stabilizer with four 70-mm-deep notches.
A very crude ASCII-art drawing:
Top view leg
legs ____
| | | | | _| ___________________
| | | | | | -=-| | |_| |_| |_| |_| |
+-+-+-+ stabilizer | -| | s | |
| | | | |_ | | e | |
| | | | stabilizer =- | | | a | |
|- | | t | |
| _| | | _ _ _ _ |
(nothing to scale) | | -=-| |_|_|_|_|_|_|_|_|_|
| -|
|__|
Probably I should assemble a paper model first at about 10:1 scale, then assemble that out of cardboard.
If that doesn’t turn up any unexpected problems, a full-height stool is probably next (with a bit of under-kick, rather than vertical leg edges), then something with a back. The full-height stool will use four 360 mm × 650 mm legs, a 550 mm × 360 mm stabilizer, and two 360 mm × 650 mm seat scales (perhaps reused from the initial test), for a total of 1.6 m².
If that works out well, I’ll know enough to figure out how to scale up to a couch with a back.
I assembled a 10:1 paper scale model of the full-size stool (except that the paper is about 0.1 mm rather than 0.4 mm as it would need to be). I learned a number of things.
Making the seat out of two overlapped 36-mm pieces led to a notch only 1.6 mm away from the edge of each, which made it unnecessarily weak and hard to assemble. Moving the two center legs toward the middle would solve this problem.
The “web” flaps at the ends of the seat were short enough at 5 mm that they were hard to assemble. Making them 10 mm or 20 mm (100 mm or 200 mm in full scale) would be a lot better. An unappreciated factor was that those 2.5 mm (25 mm in full scale) notches are the only thing resisting forward-and-back movement of the legs under the influence of bending of the stabilizer or twisting of the seat around the vertical axis relative to the floor.
The Chairigami chairs bend the seat over the corner of the support and insert its support web into a slanted notch in the front of the vertical support. I probably need to do this in order for the seat not to be extremely uncomfortable for your legs hanging over the front. They also divide the seat into two or more seat sections bent into independent webs.
Another few things occurred to me, though, when looking at the model.
First, maybe the “crush” part is only relevant at the very top and bottom of each leg, in which case maybe I can get double strength by just folding the top and bottom of the leg over so that there’s a short width of double cardboard along the top and bottom edges. The middle of the leg would still have to support the compression without crumpling, but that might be a less demanding task. This might allow the stool to be strong enough with just a single pair of legs rather than two pairs of legs. As an extra bonus, Mina’s cardboard already has two transverse creases 360 mm apart.
(I’m not sure crushing failure actually works like that, but it seems like it would be worth a try.)
Second, instead of cutting apart the cardboard to make two separate legs, I can perhaps just give it two bends, U-style, to make a pair of legs with a web between them at one end, maybe the back. The web serves part of the purpose of the center stabilizer, but mostly the idea is that making two creases is easier than making one cut. (And if the legs don’t have to be parallel, you can make it one crease rather than two, bending it V-style rathe than U-style.) Taking this to the extreme, you could serpentine a long piece of cardboard back and forth in this way, but I don’t think the cardboard I have is long enough for that.
Third, though perhaps mutually exclusive with the fold-over-the-top idea, the seat can be contoured by making the tops of the legs curved rather than flat. This would also add extra bending strength to the seat in the direction parallel to the curvature, at least once you press the seat cardboard down into the curves by sitting on it.
Fourth, if the notches are too deep, everything is fine because the bottom surfaces sit on the flat floor and are brought into alignment even if the notch bottoms don’t meet; but if they’re not deep enough, the cardboard tears. Conclusion: plan to cut them too deep. It might be possible to improve the crushing thing a bit by expanding out each notch into a triangle at the bottom and folding it over, but probably at a heavy cost to other aspects of structural strength.
There was also a slight design-for-assembly problem, in that each of the two seat halves was almost symmetrical and could be glommed onto the legs in a number of different places and in two different orientations. Making the front and back web flaps obviously different lengths would help with reducing the ambiguity.
This was a sufficiently fruitful exercise that I think I should increase the number of prototypes to include a 5:1 cardboard model as well.
I don’t have a CNC cardboard-cutting machine, or in fact even an X-Acto knife and cutting mat, so I cut the paper model by sharpening a steel kitchen knife tip and cutting on a kitchen cutting board. While this did work, it required me to lay out the design beforehand, using a pencil, adding a substantial fraction of a millimeter of error, and I probably added another couple of millimeters of error with the knife.
Mina has an inkjet printer which I think can do 600 dpi on A4-size paper. That’s 42-micron resolution. We can print out designs on this paper and paste it onto the cardboard, then cut and crease the cardboard by hand, following the printed lines.
The cardboard is, however, substantially larger than the paper, and we can’t print the paper all the way to the edge (“full-bleed”). So we will probably have to print out multiple sheets of paper, cut full-bleed pieces out of them (in what need not be a particularly precise fashion), and paste them in an overlapping shingled pattern onto the cardboard. An A4 paper is 2⁻⁴ m², so each square meter of cardboard might require between 16 and 32 printed sheets; the stool above might be about 30. This may be more trouble than it's worth for such a simple design.
Laser-cutting might be a good option, though.