Boxes made of corrugated cardboard are ubiquitous, Andrew Glassner s Notebook. Know When to Fold

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1 Andrew Glssner s Noteook Know When to Fold In the woods of Snoqulmie there s tle tht is told When the dy times re lmy nd the night strs turn old, Of er tht romed freely, mking mp sites wrek, hwrting trppers from Greely, New Orlens, nd Quee. il gl with red hir nd trined 3D rin Sid, I ll pture tht er in folded-up plne. She ut nd she sored, nd mde sight to ehold: An old sheet of ord tht ws redy to fold. When the jo ws omplete, she mde it from old fish. he er thought it smelled sweet: Les Poissons! rès delish! hen sproing, slip, nd slp! As quik s fox She flipped the lst flp, nd ught the er in the ox. hey set the er free, fr north in the wood, Where he let mpers e nd ne er gin te their food. he lesson we ve lerned is to question rute fore, And you ve no dout diserned tht somehow I hd to work in some sort of referene to this month s topi of rdord oxes, nd though this whole er story ws it implusile, it did the jo, though I did hve to streth just little, of ourse. Boxes mde of orrugted rdord re uiquitous, ut often overlooked. Some oxes re remrkle euse they re mde of single piee of rdord, whih is neither glued nor tped. Yet they re ple of gret strength, rigidity, nd longevity proteting frgile items during interntionl shipping or holding set of fvorite pens nd penils for mny yers. In this olumn I ll shre few ox designs nd tlk little out how I like to think out them. My gol is not so muh to present speifi oxes, ut to get your 3D visuliztion skills fired up. One you mke the models nd ply with them nd strt thinking out where the piees fold nd where the lernes should e, then you n strt seeing the entire shpe in your hed. he simple 2D lyout trnsforms into n imminent 3D ojet: the templte seems to wnt to jump up nd fold itself up into ox, nd you n see in your mind s eye just how lenly everything fits nd how strong nd stle the result will e. A long time go... A reltively reent invention, orrugted rdord egn life s something lled fluted medium. his is simply pper shped into n extruded sine wve, shown in Figure 1 (top). Fluted medium ws originlly used s swetnd in men s hts. I suspet tht this hd two dvntges. First, the rinkled pper ould flex little it, thus ensuring snug nd omfortle fit for slightly different hed shpes nd sizes. Seond, like frtl, this design inresed the ville surfe re so tht the ring ould sor more swet thn simple nd. In 1871, Alert L. Johnes reeived ptent on using fluted medium to protet ottles when they were shipped nd stored. One drwk to fluted medium t this point ws tht with enough pressure, it ould fltten out gin nd lose its shok-soring ilities. his hnged in 1874, when Oliver Long reeived ptent for gluing sheet of pperord to oth sides of the fluted medium, reting the orrugted rdord we know tody. he pper served to keep the fluted medium urved, mintining its ility to sor shok. Andrew Glssner Mirosoft Reserh 1 Mking orrugted rdord. Fluted medium (top). Singlefe orrugted ord (middle). Doule-fe or single-wll orrugted ord (ottom) /98/$ IEEE IEEE Computer Grphis nd Applitions 79

2 Andrew Glssner s Noteook 2 he geometry of flp of the hexgonl envelope. Equilterl tringle ABC sits next to tringle ADC. E is the enter of irle tht lies nywhere on the line joining A nd the isetor of side BC. When E is hosen, the rdius is determined y the distne to B (or C). he hevy line shows the flp. 3 he utter digrm for the hexgonl envelope. 4 he hexgonl envelope mde from mnil folder. C D ody we ll the originl fluted medium unlined. With pperord liner on one side (s in Figure 1) it s lled single-fe orrugted ord. he most ommon vriety is overed on oth sides (see Figure 1) nd lled doule-fe or single-wll orrugted ord. he ide of selling individul produts in their own pkge diretly to the individul me few yers lter. In 1879, Brooklyn printer nd pkging mteril mnufturer Roert Gir ws overseeing press run of seed pkets. One of the printing pltes ws pled on the press inorretly nd ended up sliing pkge. While looking t the ripped pkge, Gir hd the ide of repling the printing pltes with utting pltes nd the die-ut pkge ws orn. It first hit the shelves in 1896, when the Ntionl B A E Bisuit Compny strted selling Uneed Crkers in their own oxes (long with n inner sleeve to retrd spoiling). As little s 25 yers lter, the US lone hd hundreds of rdord-rton mnufturers. Designing rdord ox is not trivil work: it requires lning estheti demnds nd prtil effiieny. A designer needs to wield reltively smll set of design tehniques with the imgintion to ome up with n eonomil, prtil, nd ttrtive design. When designers wnt to show proposed ox to lient, they prepre utter digrm drwing of the unfolded ox s lyout showing where uts should e mde, piees punhed out, nd folds sored (long with the diretion of the fold). he onventions for these digrms re very muh like those in origmi (the rt of pper folding). A solid line indites ut, dotted line mens the piees on oth sides of the fold re pushed wy from you (reting mountin), nd line of lternting dshes nd dots mens the piees re folded up towrds you (reting vlley). From the utter digrm the designer mkes lnk, or plin rdord mok-up of the design. If the lient pproves, the rtwork is designed nd registered to the ox. he lnks re generlly reted in one of three wys. First, you n shpe piee of metl into the desired outline of the ox nd use it like ookie utter to stmp the ox from the rdord sheet. his is lled hollow die utting, whih mnufturers use exlusively for lels nd envelopes. Seond, you n shpe one or more metl steel rules into shpe nd then push them into preut grooves in piee of 3/4-inh plywood. his tehnique of steel-rule die utting n e used with oth flt nd ylindril presses. If the steel rule is lunted, then it n e used to press grooves nd therey sore folds. his is y fr the most ommon tehnique. A reent innovtion is lser utting. he dvntge here is effiieny nd ury, though it s used less often thn steel-rule die utting. One ut nd sored, the lnks re delivered to the lient in knok-down form, whih simply mens tht they re flt ut redy for ssemly. his involves folding nd perhps gluing, tping, nd dding extr piees suh s ruer nds or springs. When experimenting with designs (s opposed to mss produing them), I find tht metl strightedge nd X-Ato knife work fine for mking uts. You n use n empty llpoint pen for soring, ut e reful not to rip through the pperord. You n mke mny utter digrms with trditionl tools suh s strightedge, ruler, ompss, lipers, nd so on. I find tht lthough there s ertin estheti ppel to the pper-nd-penil route, I n work lot more quikly on the omputer using n off-the-shelf 2D drfting progrm. hen it s esy to mke design vrition, whih n e printed, ruer-emented to piee of mnil folder, nd then ut nd sored. One itertion of the loop from printing the digrm to holding the finl ox tkes only out 15 minutes for the oxes I desrie here. 80 Septemer/Otoer 1998

3 Hexgonl envelope Before we get into mjor 3D mentl-visul listhenis, let s wrm up with simple workout: flt hexgonl envelope. his is mde from light ord suh s mnil folder. Beuse this mteril is quite thin, you n pretty muh tret it s infinitely thin when designing the digrm nd things will still line up losely. his envelope should ontin something thin nd smll, suh s prty invittion, photogrph, or lueerry pnke. Figure 2 shows the geometry ehind one flp of the top of the envelope. Figure 3 shows the templte for the entire hexgonl envelope, nd Figure 4 shows the result. he top stys losed euse the urved it on the side of eh tringle holds down its neighor. Sine the lid is irulr, eh flp simultneously ontriutes oth to the tension pulling the envelope open nd to the mutul pressure keeping it losed. In Figure 5 I dded wlls to rete squt hexgonl ox, ut the priniple remins the sme. he tringulr flps tuk inside their neighor to prevent rks t the edges. You ould still use mnil folders for short ox, ut orrugted rdord would e etter for tll one. his is good ox for olletions of things suh s uttons, ruer nds, or stks of lueerry pnkes. Constrution tehniques Now we re redy to get into thiker, stronger mterils suh s orrugted rdord. I m not n expert in this sujet. I don t hve ny first-hnd knowledge of how these oxes re professionlly designed nd uilt. But from exmining lot of oxes nd plying with them, I ve reognized few tehniques tht pper over nd over. he desription of the oxes will e muh esier if I over these tehniques first. o see them, let s strt with simple ue. Figure 6 shows one of mny possile utter digrms for the six squre fes. o uild ue from this you ll need to tpe the edges, sine it n t hold together y itself. And even then it will e struturlly wek nd prone to woling nd rushing. For prtil use, you ll wnt to improve two things out this ue. First, it should e stronger, so nything pled inside (suh s rem puff) won t e squshed. Seond, it should e more rigid or stle, so tht it doesn t wole. hese two properties of strong ox re losely relted, ut efore pssing judgment on design, you should hek it for oth riteri. Let s now look t some tehniques for improving this simple ox. Flps nd loking One of the most elegnt nswers to oth strength nd rigidity is the use of flps. Flps n e used to rete wlls severl lyers thik, whih strengthens them. And the flps hold other flps in ple, keeping the struture in its designed shpe. You n use flps in ll sorts of wy to do these jos, ut they ll hve something in ommon: somewhere, something hs to lok into ple. Figure 7 shows one pproh using t nd hole: flp hs t t the end nd tht end goes into hole. he t doesn t ome out the other side it s only s long s the rdord is thik. he only pressure on the () () t is sidewys, whih pushes it ginst the side of the hole. he rest of the ox is usully rrnged to keep the t in the slot when the ox is losed. Figure 8 shows heper version of the sme devie, exept in this se you don t even mke the hole. he flp is shorter nd the t pushes ginst the ord where hole would e. If you mke the t slightly too () 5 he utter digrm for the hexgonl ox. 6 A uil ox. he utter digrm (left). Folding it up (middle). he resulting ox, whih will only hold together if tped or glued (right). 7 he t fits into the hole (left), ut doesn t extend out the other side (right). 8 he gry piee hs short t on the ottom, whih is rushed ginst the ottom wll. IEEE Computer Grphis nd Applitions 81

4 Andrew Glssner s Noteook 9 he t fits into the slot long the edge. 10 he lower lip of the slot (light gry) pinhes the t (drk gry), holding it seurely in ple. 11 he fold is modeled s though two seprte piees of rdord shred entered hinge. long to fit in the ox, you n jm the t down into the ord (it will rush little). he pressure will keep the t from sliding round. his is weker thn using slot, ut n e heper to mnufture (sine you don t hve to ut hole). You n mke this devie stronger on long edge y using severl ts side-y-side. Another useful devie keeps the ox shut. Figure 9 shows the ide: t on the front fe pushes into hole in the edge etween the top nd inside front fes. If the rdord is just little thiker thn the hole, it will e squeezed little y the ottom edge of the hole ginst the top. If the rdord s grin is prllel to the hole, then you n move the ottom piee into the dips of the inner orrugted lyer, s in Figure 10. his frition helps keep the t in ple nd keeps the top losed. A U-ut in the t retes the smller piee tht you grip to pull the lrger t out. As you ll see with the shoe ox elow, prtiulrly elegnt touh is tht the hole is ut so tht the top fe protrudes little forwrd (this gives you something to grip with your thum when pulling the top of the ox open). Prmeteriztion he rdord s thikness is impertive to the suess of ts. he t tehnique doesn t do you muh good with thin rd euse there s nothing for the t to push ginst. he size of ny loking devie (t or hole) needs to mth the rd s thikness. hus we re nturlly led to prmeterizing the templtes, whih is good ide nywy. All of the templte sizes should e with respet to the four numers tht desrie the ox. hese re length L, width W, depth D, nd thikness. I found it onvenient to define s onehlf the thikness of the ord, thus sheet of rdord hs thikness of 2. he ox s mesurements re with respet to its outermost dimensions, inluding the rdord s thikness. So if someone sys tht they hve hole in piee of onrete with dimensions L, W, nd D, then ox mde with those numers will fit in the hole extly. Nturlly, this isn t perfetly true in prtie. he ig question is wht hppens when the ord folds. I spent some time folding orrugted rdord nd wthing wht hppens nd me up with the model in Figure 11. Bsilly, I ssume tht the ord folds round hinge in the middle of the rd. he pper on the inside of the hinge ompresses, nd the pper on the outside strethes (I omitted the pper in this figure for lrity). his is oviously n pproximtion, ut it seems to fit wht I 12 A U-fold s prt of wrppedup tue (top). If the totl width is W, the distne etween fold lines for setion is W 2 (ottom). H W e d e d H 4 W 2 H 2 82 Septemer/Otoer 1998

5 see when I fold sheet. Plus, it mthes the wy most oxes seem to e ut when I open them up nd mesure the piees. Figure 12 shows how to nlyze U-fold (suh s t the ottom of ox). he rule of thum is tht t 90-degree fold, the folded rdord stiks out distne eyond the se (nd extends inwrds s well). So if the se is ment to e W units wide, the fold lines re drwn distne of W - 2 prt. When the ends re folded upwrds the distne stiking out on oth sides rings the totl width to W. his is why I use for the hlf thikness of the rdord nd 2 for the full thikness. Idioms We ve lredy seen one ommon feture of orrugted oxes: folds extend units over their se. Another ommon idiom is the 3D orner. he top left of Figure 13 shows the orner of ox, nd the top right shows how to nlyze the onstrution. Notie two fetures. First, the ottom of is ove the ottom of. his is euse folds round hinge AC nd will extend units ove the hinge line. hus must e ut short y units. Similrly, the side of must e wider thn so it n line up with. So extends eyond y units. he ottom left of Figure 13 shows how this looks in digrm. he little noth is hrteristi feture of mny orners. You n het sometimes nd leve the noth out. he sfest ple to do this is if one of the sides is flp nd not outside the ox. hen it will srunh up ginst the other piee, whih n provide it with little side-to-side strengthening. A C B 13 A orner fold. he orner of ox (top left). A lose-up of the fold (top right). he digrm for the orner (ottom left). A lose-up of the irled region in the digrm (ottom right). 14 A photo of lok ox. Lok ox Figure 14 shows wht I ll lok ox euse it loks up tight. I got this design from ox full of ooks tht I reently reeived in the mil. I knew it hd to e very relile if it ws going to rry suh preious rgo without dmge. I took the ox prt nd studied it, resulting in the digrm in Figure 15. I leled some spots in Figure 15 the other hlf of the digrm is symmetril (s suh templtes often re). he first trik is set up y the side flp f. When folded in, it provides nother lyer of thikness ginst wll h, strengthening it nd keeping it from moving. he pyoff omes with the flp mde of p nd r. On the outside, p pops up, whih is fine. hen the little it etween them rolls over the top nd r goes k down inside, loking into the se with t. his is huge win in stility nd strength. With this trik the designer qudrupled the thikness of the side wll, mking it strong nd stle. his tehnique lso dded stility to the front nd k sides s nd t, euse now they n t rotte round their hinges. As if this weren t enough, the top fits inside this thik wll nd dds fifth lyer. hen the front tuks into the front of the wll, reinforing the orner ginst dents while dding sixth lyer to the wll (though it only overs it of the wll). Hving the rel ox to work on helps enormously in figuring out the prmeteriztions nd hinge xes. I mde speil note of three interesting spots mrked s t f h p r 15 he digrm for the lok ox. IEEE Computer Grphis nd Applitions 83

6 Andrew Glssner s Noteook,, nd (enlrged in Figure 16). Note the extr lerne in the nothes of thikness in nd nd how the width of flp r is redued y 2 in. I originlly wrote few prgrphs to explin these detils, ut deided this is one se where experiene is worth thousnd explntions. I highly enourge you to uild this ox (or disssemle one like it) nd see for yourself why these little djustments ren t just useful, ut elegnt. Shoe ox I ought some new snekers lst week nd seleted one model in prtiulr euse they were tough nd strong. he mnufturer plyed off this reputtion y printing loks nd hins on the shoe ox nd dding ir holes, s though wht ws inside ws live nd so powerful it required tht kind of restrint to keep it ontined. Wow, tht s lot of promise for sneker. he pkge would e joke if it were mde of flimsy, thin ord. his shoe ox is solid nd ontriutes to the notion of something strong inside. I squeezed hrd on the wlls of this ox it didn t ukle or give. Figures 17 nd 18 show photo nd digrm of the shoe ox, respetively. his shoe ox s strength strts with medium-thikness ord (out 3 mm). It uses ouple of vritions on the lok ox trik. he side flps reinfore the se rther thn the sides, ut then other flps mke the side triple thik. he shoe ox lso hs t nd slot to keep the sndwih on the side together. he front flp doesn t tuk into the front s we sw efore. Insted, there s flp tht stiks into slot in the top front. his is very importnt. If this dditionl loking devie hd not een inluded, then the top would sty on only s frition fit, nd the dngerous snekers ould espe t ny time. Agin, I noted three interesting detils in the digrm nd enlrged them in Figure 19. If you uild the ox you my e s impressed s I ws with how the designer mde the right djustments in the right ples. 16 Close-ups of regions,, nd in Figure A photo of shoe ox. 18 he digrm for the shoe ox. Disply esel Figure 20 shows nie exmple of disply mde out of orrugted ord. his little disply esel is mde from single sheet, yet it provides stnd with thikness (for mny sheets of pper or thin produt), short se, nd solid, loking support. See Figure 21 for the digrm. CD-ROM pkge A lot of softwre is sold tody on CD-ROM. But CD- ROMs re pretty smll, nd I ve gotten the feeling tht mnufturers like to sell things in ig oxes it implies tht you re getting lot of stuff for your money. So they inlude some doumenttion, registrtion rd, nd perhps dvertisements for other produts. Now they hve the prolem of keeping the CD-ROM from flopping round in the muh lrger ox. ypilly designers rete right, eye-thing rdord sleeve round orrugted sheet tht rdles the CD-ROM nd keeps the doumenttion together. Figure 22 shows n exmple. Figure 23 shows the digrm. I inluded this exmple euse it s so elegnt. he CD is held sfely in the middle of the ox proteted nd uffered on ll sides nd the printed mterils re ll kept in their own omprtment. he down side of this design is tht it s wsteful the pkge ould e muh smller nd use less mteril. I m guessing tht mrketers nd retilers hve minimum-sized pkge in mind, lrge enough to ontin rresting grphis nd to suggest tht it s full of good stuff. Although the CD holds huge mount of dt, it s pretty smll. I presume tht igger ox mkes it look more impressive. Folding up I enourge you to uild the models, ply with the piees, nd try out vritions. Or disssemle some oxes on your own nd see how they re uilt. You n find some good dvie for mking oxes in Crd Engineering y In Honeyone (Outline Press, London, 1990). he hexgonl ox in this olumn ws tken from tht ook. Most of the history setion (exluding my onjetures) me from he Pkging Designer s 84 Septemer/Otoer 1998

7 19 Close-ups of regions,, nd in Figure A photo of n esel disply. 21 he digrm for the esel. 22 A photo of prtilly folded CD nd doumenttion holder. 23 he digrm for the CD nd doumenttion holder. Book of Ptterns y Lászlo Roth nd George L. Wyeng (Vn Nostrnd Reinhold, New York, 1991). I reommend strting out with thin rd for your designs until you get the hng of things it s esier to ut nd quiker to try to out new ides. hen you n go to doule-sided orrugted rdord for strutures with lot of strength, rigidity, nd durility. Lst-seond ddition: Box knowledge n hve gret prtil vlue. At Siggrph 98 in Orlndo, Florid just few weeks go, em Settle (Dvid Slesin, Mihel Cohen, nd me) won Siggrph Bowl III ( omputer grphis trivi ontest). We eh reeived first-ple prize of n insried Luxo desk lmp. One of us opened up our ox on the spot to dmire it, only to disover when putting it wy tht the lmps hd een retively pked in triky rdord oxes. Only through our knowledge of oxes nd pking tehniques were we le to sfely return the lmp to its originl ox nd ship it k to Wshington unhrmed (where it n now sheds its light of triumphnt vitory through the riny Settle dys nd nights). Reders my ontt Glssner t Mirosoft Reserh, e-mil glssner@mirosoft.om. IEEE Computer Grphis nd Applitions 85