CALCULATOR AND DERIVATION OF FORMULA AND TABLES FOR CROWN MOLDING AND MANSARD ROOF ANGLES 1999 June 15 2000 February 16 Rev B www.issi1.com/corwin/angles.txt www.issi1.com/corwin/crown.html mansard angles: each side angle in slant v1 = (cos(slant),0,sin(slant)) v2 = (0,cos(slant),sin(slant)) dot(v1,v2) = (sin(slant))**2 cos(2*bevel) = sin(slant)**2 bevel = 0.5*arccos(sin(slant)**2) edge = cross(v1,v2) = i j k cos 0 sin 0 cos sin =(-cos*sin,-cos*sin,cos*cos) uedge = edge/ (2*cos**2*sin**2+cos**4)**0.5 uedge = edge/ ((cos**2)(2*sin**2+cos**2))**0.5 uedge = edge/ (cos(sin**2+1)**0.5) cos(rake) = dot(uedge,-j) = cos*sin/(cos (1+sin**2)**0.5) = sin/(1+sin**2)**0.5) = sin(slant)/(1+sin(slant)**2)**0.5) pi/2-miter slant sin(slant) sin(slant)**2 rake bevel 0 0 0 90 45 10 0.1736 0.0302 80.1489 44.1360 10.1559 80 44.1092 10.7669 0.1868 79.4183 44 15 pi/12 0.2588 0.0670 75.4892 43.0795 20 0.1170 70.5004 41.6411 22.5 pi/8 0.3827 70.5004 40.7895 30 pi/6 0.5 0.25 63.4349 37.76 cube-octahedron: 35.2644 0.5774 60 35.2644 45 0.707 0.5 54.7356 30 36 pi/5 59.5536 34.8941 38 58.3810 33.8629 40.0604 57.2349 32.7651 40.0604 pi/2-32.7651 pi/2-57.2349 45 pi/4 0.707 0.5 54.7356 30 51.8273 0.7862 51.8273 25.9136 60 pi/3 67.3806 arctan(16/7) 47.5054 15.7808 75 45.9930 10.5453 80 45.4385 7.0530 90 pi/2 1 1 45 0 crown: 37.9769 58.3942 33.875 38 58.3810 33.8629 pi/2-31.625 58.375 a common pitch: arctan 7/16 = 23.6294 bend at peak 47.2588 16/7 67.3806 sin(38) = .61566148 cos sin = .48514786 cos(38) = .78801075 sin**2 = .37903905 cos**2 = .62096095 v1 = (cos(slant),0,sin(slant)) v2 = (cos(slant)cos(corner),cos(slant)sin(corner),sin(slant)) dot(v1,v2)= cos(corner)(cos(slant))**2+(sin(slant))**2 = cos(2*bevel) 0.62096095 cos(corner) + 0.37903905 = cos(2*bevel) edge = (-cos(slant)sin(slant)sin(corner), cos(slant)sin(slant)(cos(corner)-1) , (cos(slant)**2)*sin(corner)) edge = (-0.48514786 sin(corner), (cos(corner) - 1)0.48514786 , .62096095 sin(corner)) crown: 38 slant corner pi/2-miter bevel -90 121.6190 -33.8629 -75 115.2867 -28.8629 -60 109.5679 -23.2040 -45 104.3064 -17.5512 -30 99.3675 -11.7682 -15 - 5.9037 0 90 0 15 85.3661 5.9037 30 80.6325 11.7682 45 75.6936 17.5512 60 70.4321 23.2040 75 64.7133 28.6665 90 outside 58.3810 33.8629 from top undercut front from square cc: webeditor@taunton.com Are these tables published anywhere? Would any additional tables be useful? Would diagrams or illustrations be useful? Interpolation should be good to 0.5; are more points needed? email: billc@issi1.com Please inform me if additional angles in the above table would be useful; would a calculator or graphs be useful? given the rake = pi/2 - miter angle and bevel angle the formulas for the wall angle and slant or slope angle calculated cos(slant) = 2*cos(bevel)*sin(bevel)*(cos(rake)*sin(rake)*sin(rake)+ sin(rake)*sin(rake)*sin(rake)) cos(pi-wall) = sin(rake)*sin(rake) + cos(rake)*cos(rake)*(sin(bevel)*sin(bevel) - cos(bevel)*cos(bevel)) There is a calculator at http://www.issi1.com/corwin/crown.html ref: www.byeless.com www.issi1.com/corwin/crown.html www.issi1.com/corwin/unit_v.txt www.issi1.com/corwin/angles.txt tables: http://www.scrollsaw.com/miter.htm mouse trap: http://www.deltawoodworking.com/entry-4-projecthelp.html bibliography: http://www.detnews.com/news/metlife/9702/19/02190011.htm Tajiama Woodworker's Warehouse 800 818 8652 Tool Crib 800 358 3096 http://www.detnews.com/gadget http://www.uwec.edu/Academic/Geography/Ivogler/w367/parts/p213.htm mansard gambrel Mussell, Barry D. Roof Framer's Bible http://www.taunton.com/features/fh/techniques/15bible.htm Stockbridge GA 770 389 1703 MEI Publishing http://www.taunton.com/features/fh/techniques/16stairs.htm webeditor@taunton.com http://www.taunton.com/features/fh/tools/1threenewsaws.htm longitudinal and/or arched trusses for attic space: http://www.taunton.com/features/fh/design/8roof.htm cc: chubbys@earthlink.net lank hill@webtv.net klhaney@aol.com kblevins@pcn.com cherb@mail.csrlink.net rebecca.schindler@mckesson.com dncdurham@uswest.com mbruno@lehman.com eloyman@earthlink.net demjer@erols.com kbrunton@garlic.com workbench@workbenchmag.com abobos@tribune.com pepi@clark.net Lavatot@ndu.edu 3teddys@gte.net comet@acninc.net webworks@wwforum.com www.bobvila.com/ab.htm www.hgtv.com/hometalk/buildpostit.html RDobsevage@taunton.com Knots, Fine Woodworking's Fine HomeBuilding www.taunton.com:8090/WebX?128@129.4B16a51magB^4@.ee6e8b8 miter = arctan(width/(hypotenuse*tan(wallangle/2))) bevel = arcsin((height*cos(wallangle/2))/hypotenuse) FHB #68 July '91 p79,81 miter = arctan(A/(C*tan(F/2))) bevel = arcsin((D*cos(F/2))/C) where A is wall-ceiling corner to top edge distance B is bevel angle for 90 corner C sqrt(A**2+B**2) D is wall-ceiling corner to lower edge distance F angle of corner www.taunton.com:8090/WebX?@@.ee665a1 smessenger@taunton.com www.developer.com/directoies/pager/dir.javascript.jsutil.calculators.html --------------------------------------------------------------------- calculator example http://www.aurora.rg.iupui.edu/~schadow/units/ http://www.ur.ru/~sg/transl transl@sg.ur.ru