THE GEOMETRY OF SHEET METAL WORK

FOR STUDENTS AND CRAFTSMEN

BY

A. DICKASON C.G.LA., A.C.T. (BlRM.)

POST SECONDARY CORRADINU c..QMPLEX

U8RARY

:2 b G PAOLA

l'lTMAN

CONTENTS PREJ'A.OB

CHAP1'ER 1 CLASSIJ'IO,,-TlON OB' OJ:OM%TlUCAL J'ORIIIS

Th_ object of .urf_ devtolopment.-Otuliflcation of gooDl(ltrical forma-Method. of eurl"_ deve1opment: The racli&1 lin. method; The pantJ1elline method; Triangulation

FIRST COURSE

CHAPTER 2 'fHE RADUL LINE ){ETHOD •

Development by radi&l lin_Th. right. oonic fruatum-True lengtt.--Tb.e right cone out obliquely-The rigM cone out by • curved or IUlJ{Ular aurfllO&-Conieal jug t.o~Fancy crani.ter im­Th. pyramid out. obliquely-The oval-Complex oonical ~ Oval oonieaI pan

CHAPTER 3 THI!: PAIU.LLlI:L LINE METtlOD

Elbowa-Square pipe elbow-Cylindrieal !,lip" elbow-Double retum elbow_Double oft.'"" .lbow-Tee jom~ a.nd branch_ Right.~led t.ee--Oblique ~Rilbt and oblique oylind.~ Right orimder cut obliquely-Obli"ue oylinder-ObHque cylindrical "Y" pl ___ Right eylindrieal "Y' pi---suboontrary IIOOtion-An oblique connecting pipe-Lot.ter.b4Ml1r. bond-Elbow guaeet p~An open ohute-Moulding: curbe Md gutte~Wbeel.areh "...1

CHAPTER 4 THE KETHOD O. TRlANGULA.TlON •

Golden rule of triangulation-Dividing the .urlaoe int.o triang'­Pat.t.eml d .... wn to ecaJe-Variet,. of treatment.-Tra.n.formen between two pal'ILllel pltw_TwiIJt.ed aquare trantfonner-A aqllAf'll comer bend-Twisted recta.ngular duct--8qWU"ll·to-cirole.trant­former-Method of numbering the poinw-Ofl_oentre recta.ngle-to­circle tral18former-The grouping of limilariti----Oval.to-cirole tranefonner-Semieirole·to_eirole tral18formM'-Rect&ngIe, eemi. eircle.to-circle tranaformer-Fund&meDtaI prineip'-Hood with corner radii-Plant work

1

7

40

viii CONTENTS

SECOND COURSE

CHAPTER 5 TBE RADUL LINE XETHOD

The oblique cone--The .uboontrary 8&ltion-Oblique cone devel­oped-Oblique cone fruatum-Applicationa of the oblique cone-A Imoke hood-A &ht.ail no~de--A hip bath- True l~ha of the oblique cone--Hood for boiling kettle-An oblique comcal hopper

CHAPTER 6 THE PARALLEL LINE METHOD

Right_lUlgled t.ee of unequ.! diameter pi~blique tee, off-('Jlm.t"' -Right-Mgled t.ee, off.centre-Auxiliary projection-Double projection-Oblique cylindrical hoppen-Downspout heoda­Roof finial_Problemt of the common centntJ .phe",

CHAPTER 7 TRI.ANOULATION •

Adaptability of triangulation-Rectangle_to_cirde tran.former witb circle inclinod-Rectangle-to-citcle tl'lUllforzn&r with rectangle inolined-Projact.ed view_Transformer connection to long rect.angular hole--Tra.nlifonner segment--Stove chimney con· nection-8tove chimney, olf·centr&-Stove elbo'l'O' connecLion­Hoppera .,..ith kinked ,id_Feed hopper to elevat.or boo~Delivery chute from elev .. tor head

THIRD COURSE

CHAPTER 8 THE JLADIAL LINE METHOD •

Conical ventilator bMe--Rectan.gula.r pipe on conio b&M---Skill in pattem_drafting-Conieal .pout on cylindric .. , body---Conical connection on angular corner-Branch piec.o. in pipe work_T'Wo_ wII-y conicII-I branch pi_Multiple corneal branch piece

CHAPTER 9 THIl: PA..RALLRL LINE METHOD

Connection to lohner-back-Branch on four·piece lohllter·back­Cleaning out .tump on .. 10hllter_back_Lohllter.ba.clt bra.nch­AUl:iliary projactio_RectAngular branch on cylindrical pi~ ero. pi.,. which p-.rtWly intel'l&Ct-An oblique eylindrieaf chute -Orn .. mental bowl.. and vl!l-8Olt---Segmt.a1 roae bowl---8egme.ot.a1 vue-Further problem. of the central Iphere--Triple inte_tion developed-An off-centre funnel

97

113

136

151

CHAPTER 10

TR I A~GOLATIO~ .

Ov.l·te.pered connoo~ion to cylinder-Corner w.ll hopper-The egg.,haped oval-Outlet connection to tanlr.-An important prin· ciple-Triangulating. lmooth lurface--Tl1U18former on I'OC)f apell:­Two .... y breech.,. pi_Four·way breechea pi_Tho junction pieC'e_1'wo._y junction pi_Str8igh~back.ed junction-Three unitol in one-Square.to-eirele two.way junction-Three.w.y junct.ion. rectangle to circle

FOURTH COURSE

CHAPTER 11 .METHOD OB CU'ITING PLANES

Varying line of inteneetion-Classification of method_Method of cutting pl&nall---Conical bNe of an air filter-Cone and cylinder t.angcntiaJ interMCtion-A ,hon-elu mllthod_lfethoo. of general application-Cono and Iphere intereection--Oblique conical hOl'per on 'pherical dome--Int.ereection of two right conoa--Simi· Ia.ntiea of mllthod-Conical,pout on & oonical body-An alternative method-Tallboy tranafonner interaected. by eylindrical pipe­Cylinder penetrating tranaformer at an angle--Intenect,en of tallboy tl'aWlfonnllr and right con--oblique conical hood inter. IMCting wtnicai 8ue--Obliquo cono int.ereecting a right cone-­Oblique conic 8OCliona-EJliptieal cro8I·liIICtion

CHAPrER 12 BRANCH AND JUNCTION PLECES

Breech.,. piece of unequal diameter.-Four ... ay breech.,. of wlequal branch_A four. wily junction pi_A three .... y junction trnnsfonner

CHAPTER 13

THE TAPERED LOBSTER· BACK

Tapered lobater.back from oblique cone-Tapered lobster·back from right cone-Tapered lobster. back by common central lphere. -Lobllter.back developed by triangulation

CHAPl'ER 14 UNUSUA.L PIlOBLEKS

An off-oentre oblique conical broochllll pi_An oblique conical hopper-CompleJ: double tranllfortner-Pitfalia in trilWgulation­Special type hood connection-Co&1 hod "nd petrol mo&IW1I top-­Conical hopper corner

;,

175

202

236

248

259

, COKTDT8

FIFTH COURSE CHAPTER 15

DOUBLE PROJX01'lON . Double projection applied to pipe int.er'll«ltion-A ahorter method­Mol'EI projeet.io_A difficult "Y" pi_The work Ihortened­Elbow connection to rectangular pipe-An off·lI6t pipe connection -An off.oentre pipe on oblique oone

CHAPTER 16 TWISTED SURFACES

S'II'a.n.neck trantition p~ between pa""l1(11 planeIJ-Tra.naitioD piece betwoen p lane. at right allgl_Elbow tl'1Ulllition pi_ between angular planee--Spiral finial-Lobtlt.er.bllCk Ipiral­Spiral blad_Flat.-bottmned Ipiral chute

277

TNDF.X . 323

INDEX AlA filter, coruc.l bMe or. 207 AlWlma~ive method, 224 Apparent ,wiBt«I. aurlace, 299 Auxiliary projection, 101 . 120, 167

BoWLS and Va&Q$, ornamental, 163 Dranch on four-pioee lobater-back,

I" __ pillOOll in pipe work, 145, 236 Breech_ pieco!, four-way, 190 ____ , - - of unequal dia-

mete..., 239 ____ of unequal di .. rneWl .... 237 __ --, two-way, 187

CAN.t. boat cabin, 1l1.O\'1I chimney. 123 GeMra! sphere_ further problerru; of,

lOO Chute from elev .... to r head, 134 Chu~ with aides kinkod. 134 C1aaeilieation of form, 2 __ of methods. 203 C1eaning.out atump on lob.ter-back, .. , eoal hod. 271 Common central .phere. 109 ____ -- appliod to \.apered

lobllt.er-ba.ck, 254 Comploll' double tramformer, 265 Complicated drawinge. 136 Cone and cylinder , tan~ntial inter.

MICtion, 207 __ -.nd .pMI'II, intef'IeCtion, 213 Conic IIe(ltioI1ll, 204 Conieal b_ of an air filter, 207 __ branch piece. multiple. 148 ____ --, two-way, U 6

oonnection on duct eomef, 144 hopper corner, 214 jug loOp!!. 14 ptw, complex, 21 __ .oval.23 _pout on angular corner, 144 __ on cylindrical body, 1(3 ventilator baae, 138

Connection to lobllt.er-back, 161 Corner bond, aqwu-e, 68 __ wa.ll hopper, 177 ero.. pi~ ",hich partially intenect,

'" Curbll,46

Cutting plane., method of, 202 20 .. Cylinder and t.a.llboy tranlf"rmflr

intersection, 22.6 -- penotrating trantformor _t an

IU"Igle, 228 Cylindrical clmw, oblique, 162 -- pipe elbow, 26

DlSl'LA05D apex, ' '', 16 Double ofbet elbow, 28

projection, 104, 277 -- applied to pipe

tion, 278 return elbow, 27 t~former, complex,

DoWllIpout heads, 107

EOO_SILI.I'JCD oval, 179 E lbow, 24 -- gusaet pieooll, 41

'"

-- tran.eition piece between angu-'-r plan .. , 304

Eleva.tor hoppers with kin1r:ec:I .idllll, 131

Elliptico.l cnMlll-lI6Ction, oblique cone, '3<

F.NCY canillter :ids, 14 Feed hopper to elevator boot, 132 Finial, Ipiral, 308 Finiala, fOOl, 109 Fieht6i1 no~zle, 86 Flat-bottomed Ipirsl chute, 319 }o"our_way breechell of unequal di ...

metenl,239 -- -- piece, 190 __ junction piece. 242 Fl"Ulltum, oblique oone, 81 }-unda.mantal principles, 72 Funnel, oft'-oentre, 172

G ••• tove oonnect ion, 123 Golden rule of t.riangulatiOD. 49, 82 Grouping of limilari!.ioa, 86 GUMlt piece, elbow, 41 Gutt.enl, 411

Hu bath, 88 Hood oon.noction, lpeci.l type, 270 -- for boiling kett.le, 92 - - with oorner radii , 74 Hoppen with kinkad _idea, 131

323

•

324 TU OEOlUTRY O. SUET METAL WORK

IIII'OITANT principle, 184 Int.erooctioD, oone and cylinder, 201 _ _ , oblique con~ and righ~ cone, 232 _ _ , -_ -- and sphore, 216 __ , -- conical hood and vertical

flue, 231 --, right. oone and sphere, 213 --, tnuaformer .... d cylinder, 225 __ , __ and right cone, 228 __ , two right (lOOM, 217 Interaootiona, problema of, 202 Intricate pattern developm.mt.ll, 136

JUNCTION piece, 192 --,lour.way,242 __ , straight backed, 196 __ , three·way. rectangle-to·

circle,200 --, two· .. ay.aq\l&l'e·t.o-eirele,

'98 tnuaformer, three.way. 245

Kun.s in hoppen and chut.e6, 131

Lunc of inte~tiOll. varying, 203 Lobster·back bend, 38 --, cleanill$-out 't\lfTlp on, 154 __ , connection 1.0, 161 - -, four.F.>ece. branch on, 15" -- apira. 311 --, t&pered, by triangulation, 266 --, --, from oblique con~, 248

MrrHOO of cutting planes, 202, 204 __ , aimilaritte. of, 221 Met.hO<b, c_ification of, 203 -- of general applicatKm, 212 More projections, 282 Moulding, 45 __ I5eCtion •• 107 Multiple branch pi_. conical. 148

Nol.:ZI..l':. f1ahtail. 86 Numbering the poio"'. method of. 63

OBLIQlTI: cone. applications of. 82 ____ defined, 8, 79

develop&d. 80 frwltwn.8I intc.ll'llflCtiog figh~ cone,

'" __ • true len&'tM, 90 conic 'flCtion. 233

__ conical breeches. off-centre, 2~9 --, two_way. 1"6

____ hopper, 9", 262

Oblique conical hopper on spherical dome, 215

connecting pipe, 37 cylinder defined. 32 cylindrical chute, 43. 162 -- hopoera. 106 __ "y t. pieoe, 35 tee,30 --, off-a)ntre_ 98

Off-centre pipe on oblique cone. 294 Off_loOt pipe connection, 200 Ornamental 00"']' &lid vaaOll, 163 Oval conical pari. 23 -- connection to cylind6r, 175 --.oorl8truction of. 18 --. egg·shaped, 179 Oval_tn-cirdQ tranafomwr. 67

PAJI..u.t..E1. Line Method. 6, 151 rattern-drafting •• kill in, 142 Pattol'TUl drewn to lleale, 52 Petrol IIlOOBure top, 271 Pip6 oonnootion, oft·set, 200 -- on oblique oone, off·CIOnt .... , 29~ Pitfalls in triangulation, 267 Plant work, 7~ Prillm.2 Proiect«!. vi6 ...... 119 Projection. aUlriliary, 101 Pyramid. 2 -- cut obliquoly, 17

RADlAL Line Method, I'i Real twiBtOO. eurfaoe. 299 HectangI6-to-cirde transfor-rrMlr, 61,

114,11 7 Rectangle. eemicirele·to-cirele tr&08-

fOr-rrMlf. 71 Rect&ngular branch on cylindrical

pipe. 157 -- duct. tW'8tOO., 59 Hight_angled tee. equal d iameton, 2\J -- --, oft-centre, 101 Right oone cut obliquely, 1I

-- d6fined, 8. 79 _ _ intereecte<:l by oblique

cone. 232 conOll, intc.lreeclinn of two. 217 oonic ffWItum. 10 cylinder defined. 32 cyJindric.u .. Y" piece. 36

Roof fini.us, 109 __ ventilator blUlO, 186 RoIlO bowl, I!6gmentai, 164

S<J~ pan. "6 __ • patterns dnwn Lo • .5!:

OiDEX 326

SegrntlQlal mouldings, 163 -_ "'" bowl, 164 -_ vue, 167 Semicitcl"·I.O-eirele trtLIl.'lfonner, 60 Shoe-Ih_ped funnela, 106 Sho",·eu~ method, 211 Short radiu, 49 Similatitie.. grouping of, 66 __ of methods, 221 Skill in pattem.dr"fting, 142 Smoke hood, 82 Smooth eurfaee, triangulat.od, 184 Special type hood connection, 270 Spherical dome and oblique conical

hopper, 215 Spi,..t bJadea, 316 -- chute, 6at_bottomod, 319 -- finial, 308 -- lobeter.ba.ck. 311 Spout f!"Om rni""r outlet, 43 Square comer bend, 58 __ pipe elbow, 25 Squnl'&.l.O.eil'de trnnllfonner, 61 ___ two_way junction, 198 S~ve chimney connoction, 123 __ --, off·(:<lntre, 127 __ elbow connection, 127 Straight-bReked junction, 196 Suboontro.ry aec~ion, 36, 19, 234 Surface. dhiding into triAnglet. 00 Swan.neck tl'lUlllition piOOll, 300

TALLBOY tl'1l.lWfonner. 5 1 -_ --- and cylinder, intenec­

tion, 225 Tlmgttntial int.eraection of cone and

cylinder, 207 Tapered lobllter-blL<:k by common

wntra! Bphere, 204 -- --- by triangulation, 266 ____ from oblique cone, 248 -_ - __ froID right cone, 252 Tee joint. Imd branc~, 28 Th~-w.y junction, rectangle to

c ircle, 200 _ _ __ tnLTlllfonn~r_ 2~5

Tr'&naformer,2 and cylinder, penetration .t

Imgle, 228 -- Imd right cone interaection, 228 -- on roof ape", 186 --, oVII.I-to-circle, 67 --, rectangle, eemicircle_to_cirole,

71 --, rectangle.to_cirole, 64 -- -.egment, 123 --, &6micirole-t.o.circle, 69 --, 8quare_to_cirde, 61 --, aqua", twisted, 56 Tr..naformers between parallel plene..

" Tr..naition piece between engular plane., 30~

-- -- -- parallel plan.,., 300 -- -- -- plan.,. IU right

.ngle., 302 Triangulating a Bmooth aurface, 18' Triangulation, 11, ~9 --, adaptability of, 113 --, golden rule of, ~9 --, pitfllollo! in, 267 Triple interaection developed, 170 True lengtM on the oblique cone, 90 Twisted rect&ngul&r duct. 69 -- IUrfaCllll, 299 Two-w.y breechee piece, 187 -- conical brunch piece, 1'6 -- junction piece, 192

UNUeUll. problem_, 259

VARIETY of treatment, 63 Varying line of intersection, 203 Vaae, eogmental, 167 Va.see IlIld bowlo!, ornamental, 163 Ventilator bMe, conical, 136

\V"'TEROfO-C4N" roee, 8 Wheel_arch panel, " Wheelbarrow body, 17

"Y" 1'111:CI:, a difficult problem_ 283