Alpha k = K(k) E(k) Force = F Force = F Gap Gap Bow Max stress deg Sin(Alpha/2) Pounds Newtons Opening = 2a Opening = 2a Depth = d psi Notes Inches Meters in. 0 =SIN(A5/2*PI()/180) 1.5708 1.5708 =$M$11*$M$14*$C5*$C5/36 =E5*4.4482 =$M$6*(2*$D5/$C5-1) =G5*0.0254 =$M$6*$B5/$C5 =$E5*$I5/$M$17/4.4482 Spring made of steel 2 =SIN(A6/2*PI()/180) 1.5709 1.5707 =$M$11*$M$14*$C6*$C6/36 =E6*4.4482 =$M$6*(2*$D6/$C6-1) =G6*0.0254 =$M$6*$B6/$C6 =$E6*$I6/$M$17/4.4482 L = 12 in 4 =SIN(A7/2*PI()/180) 1.5713 1.5703 =$M$11*$M$14*$C7*$C7/36 =E7*4.4482 =$M$6*(2*$D7/$C7-1) =G7*0.0254 =$M$6*$B7/$C7 =$E7*$I7/$M$17/4.4482 W = 3.5 in 6 =SIN(A8/2*PI()/180) 1.5719 1.5697 =$M$11*$M$14*$C8*$C8/36 =E8*4.4482 =$M$6*(2*$D8/$C8-1) =G8*0.0254 =$M$6*$B8/$C8 =$E8*$I8/$M$17/4.4482 T = 0.018 in 8 =SIN(A9/2*PI()/180) 1.5727 1.5689 =$M$11*$M$14*$C9*$C9/36 =E9*4.4482 =$M$6*(2*$D9/$C9-1) =G9*0.0254 =$M$6*$B9/$C9 =$E9*$I9/$M$17/4.4482 10 =SIN(A10/2*PI()/180) 1.5738 1.5678 =$M$11*$M$14*$C10*$C10/36 =E10*4.4482 =$M$6*(2*$D10/$C10-1) =G10*0.0254 =$M$6*$B10/$C10 =$E10*$I10/$M$17/4.4482 Modulus of elasticity (steel) 12 =SIN(A11/2*PI()/180) 1.5751 1.5665 =$M$11*$M$14*$C11*$C11/36 =E11*4.4482 =$M$6*(2*$D11/$C11-1) =G11*0.0254 =$M$6*$B11/$C11 =$E11*$I11/$M$17/4.4482 E = 29000000 lb/in2 14 =SIN(A12/2*PI()/180) 1.5767 1.5649 =$M$11*$M$14*$C12*$C12/36 =E12*4.4482 =$M$6*(2*$D12/$C12-1) =G12*0.0254 =$M$6*$B12/$C12 =$E12*$I12/$M$17/4.4482 16 =SIN(A13/2*PI()/180) 1.5785 1.5632 =$M$11*$M$14*$C13*$C13/36 =E13*4.4482 =$M$6*(2*$D13/$C13-1) =G13*0.0254 =$M$6*$B13/$C13 =$E13*$I13/$M$17/4.4482 Section Moment of inertia 18 =SIN(A14/2*PI()/180) 1.5805 1.5611 =$M$11*$M$14*$C14*$C14/36 =E14*4.4482 =$M$6*(2*$D14/$C14-1) =G14*0.0254 =$M$6*$B14/$C14 =$E14*$I14/$M$17/4.4482 I = T3 W / 12 = =$M$8*$M$8*$M$8*$M$7/12 in4 20 =SIN(A15/2*PI()/180) 1.5828 1.5589 =$M$11*$M$14*$C15*$C15/36 =E15*4.4482 =$M$6*(2*$D15/$C15-1) =G15*0.0254 =$M$6*$B15/$C15 =$E15*$I15/$M$17/4.4482 22 =SIN(A16/2*PI()/180) 1.5854 1.5564 =$M$11*$M$14*$C16*$C16/36 =E16*4.4482 =$M$6*(2*$D16/$C16-1) =G16*0.0254 =$M$6*$B16/$C16 =$E16*$I16/$M$17/4.4482 Section Modulus 24 =SIN(A17/2*PI()/180) 1.5882 1.5537 =$M$11*$M$14*$C17*$C17/36 =E17*4.4482 =$M$6*(2*$D17/$C17-1) =G17*0.0254 =$M$6*$B17/$C17 =$E17*$I17/$M$17/4.4482 Z = T2 W / 6 = =$M$8*$M$8*$M$7/6 in3 26 =SIN(A18/2*PI()/180) 1.5913 1.5507 =$M$11*$M$14*$C18*$C18/36 =E18*4.4482 =$M$6*(2*$D18/$C18-1) =G18*0.0254 =$M$6*$B18/$C18 =$E18*$I18/$M$17/4.4482 28 =SIN(A19/2*PI()/180) 1.5946 1.5476 =$M$11*$M$14*$C19*$C19/36 =E19*4.4482 =$M$6*(2*$D19/$C19-1) =G19*0.0254 =$M$6*$B19/$C19 =$E19*$I19/$M$17/4.4482 K(k) is the complete Elliptic Integral 30 =SIN(A20/2*PI()/180) 1.5981 1.5442 =$M$11*$M$14*$C20*$C20/36 =E20*4.4482 =$M$6*(2*$D20/$C20-1) =G20*0.0254 =$M$6*$B20/$C20 =$E20*$I20/$M$17/4.4482 of the first kind. 32 =SIN(A21/2*PI()/180) 1.602 1.5405 =$M$11*$M$14*$C21*$C21/36 =E21*4.4482 =$M$6*(2*$D21/$C21-1) =G21*0.0254 =$M$6*$B21/$C21 =$E21*$I21/$M$17/4.4482 34 =SIN(A22/2*PI()/180) 1.6061 1.5367 =$M$11*$M$14*$C22*$C22/36 =E22*4.4482 =$M$6*(2*$D22/$C22-1) =G22*0.0254 =$M$6*$B22/$C22 =$E22*$I22/$M$17/4.4482 E(k) is the complete Elliptic Integral 36 =SIN(A23/2*PI()/180) 1.6105 1.5326 =$M$11*$M$14*$C23*$C23/36 =E23*4.4482 =$M$6*(2*$D23/$C23-1) =G23*0.0254 =$M$6*$B23/$C23 =$E23*$I23/$M$17/4.4482 of the second kind. 38 =SIN(A24/2*PI()/180) 1.6151 1.5283 =$M$11*$M$14*$C24*$C24/36 =E24*4.4482 =$M$6*(2*$D24/$C24-1) =G24*0.0254 =$M$6*$B24/$C24 =$E24*$I24/$M$17/4.4482 40 =SIN(A25/2*PI()/180) 1.62 1.5238 =$M$11*$M$14*$C25*$C25/36 =E25*4.4482 =$M$6*(2*$D25/$C25-1) =G25*0.0254 =$M$6*$B25/$C25 =$E25*$I25/$M$17/4.4482 E(k) and K(k) values obtained from 42 =SIN(A26/2*PI()/180) 1.6252 1.5191 =$M$11*$M$14*$C26*$C26/36 =E26*4.4482 =$M$6*(2*$D26/$C26-1) =G26*0.0254 =$M$6*$B26/$C26 =$E26*$I26/$M$17/4.4482 " ""C.R.C. Standard Math Tables"", 11th ed." 44 =SIN(A27/2*PI()/180) 1.6307 1.5141 =$M$11*$M$14*$C27*$C27/36 =E27*4.4482 =$M$6*(2*$D27/$C27-1) =G27*0.0254 =$M$6*$B27/$C27 =$E27*$I27/$M$17/4.4482 46 =SIN(A28/2*PI()/180) 1.6365 1.509 =$M$11*$M$14*$C28*$C28/36 =E28*4.4482 =$M$6*(2*$D28/$C28-1) =G28*0.0254 =$M$6*$B28/$C28 =$E28*$I28/$M$17/4.4482 Parameter Alpha is the angle made 48 =SIN(A29/2*PI()/180) 1.6426 1.5037 =$M$11*$M$14*$C29*$C29/36 =E29*4.4482 =$M$6*(2*$D29/$C29-1) =G29*0.0254 =$M$6*$B29/$C29 =$E29*$I29/$M$17/4.4482 by each end of the spring with the 50 =SIN(A30/2*PI()/180) 1.649 1.4981 =$M$11*$M$14*$C30*$C30/36 =E30*4.4482 =$M$6*(2*$D30/$C30-1) =G30*0.0254 =$M$6*$B30/$C30 =$E30*$I30/$M$17/4.4482 original plane of the spring. 52 =SIN(A31/2*PI()/180) 1.6557 1.4924 =$M$11*$M$14*$C31*$C31/36 =E31*4.4482 =$M$6*(2*$D31/$C31-1) =G31*0.0254 =$M$6*$B31/$C31 =$E31*$I31/$M$17/4.4482 54 =SIN(A32/2*PI()/180) 1.6627 1.4864 =$M$11*$M$14*$C32*$C32/36 =E32*4.4482 =$M$6*(2*$D32/$C32-1) =G32*0.0254 =$M$6*$B32/$C32 =$E32*$I32/$M$17/4.4482 Force = E I K(k)2 / 36 lb. 56 =SIN(A33/2*PI()/180) 1.6701 1.4803 =$M$11*$M$14*$C33*$C33/36 =E33*4.4482 =$M$6*(2*$D33/$C33-1) =G33*0.0254 =$M$6*$B33/$C33 =$E33*$I33/$M$17/4.4482 Gap Length = L (2 E(k) / K(k) - 1) in. 58 =SIN(A34/2*PI()/180) 1.6777 1.474 =$M$11*$M$14*$C34*$C34/36 =E34*4.4482 =$M$6*(2*$D34/$C34-1) =G34*0.0254 =$M$6*$B34/$C34 =$E34*$I34/$M$17/4.4482 Bow Depth = L k / K(k) in. 60 =SIN(A35/2*PI()/180) 1.6858 1.4675 =$M$11*$M$14*$C35*$C35/36 =E35*4.4482 =$M$6*(2*$D35/$C35-1) =G35*0.0254 =$M$6*$B35/$C35 =$E35*$I35/$M$17/4.4482 Max Stress = F d / Z psi 62 =SIN(A36/2*PI()/180) 1.6941 1.4608 =$M$11*$M$14*$C36*$C36/36 =E36*4.4482 =$M$6*(2*$D36/$C36-1) =G36*0.0254 =$M$6*$B36/$C36 =$E36*$I36/$M$17/4.4482 64 =SIN(A37/2*PI()/180) 1.7028 1.4539 =$M$11*$M$14*$C37*$C37/36 =E37*4.4482 =$M$6*(2*$D37/$C37-1) =G37*0.0254 =$M$6*$B37/$C37 =$E37*$I37/$M$17/4.4482 Note: Parameters may be entered 66 =SIN(A38/2*PI()/180) 1.7119 1.4469 =$M$11*$M$14*$C38*$C38/36 =E38*4.4482 =$M$6*(2*$D38/$C38-1) =G38*0.0254 =$M$6*$B38/$C38 =$E38*$I38/$M$17/4.4482 " in cells M6, M7, M8 and M11" 68 =SIN(A39/2*PI()/180) 1.7214 1.4397 =$M$11*$M$14*$C39*$C39/36 =E39*4.4482 =$M$6*(2*$D39/$C39-1) =G39*0.0254 =$M$6*$B39/$C39 =$E39*$I39/$M$17/4.4482 70 =SIN(A40/2*PI()/180) 1.7312 1.4323 =$M$11*$M$14*$C40*$C40/36 =E40*4.4482 =$M$6*(2*$D40/$C40-1) =G40*0.0254 =$M$6*$B40/$C40 =$E40*$I40/$M$17/4.4482 72 =SIN(A41/2*PI()/180) 1.7415 1.4248 =$M$11*$M$14*$C41*$C41/36 =E41*4.4482 =$M$6*(2*$D41/$C41-1) =G41*0.0254 =$M$6*$B41/$C41 =$E41*$I41/$M$17/4.4482 74 =SIN(A42/2*PI()/180) 1.7522 1.4171 =$M$11*$M$14*$C42*$C42/36 =E42*4.4482 =$M$6*(2*$D42/$C42-1) =G42*0.0254 =$M$6*$B42/$C42 =$E42*$I42/$M$17/4.4482 76 =SIN(A43/2*PI()/180) 1.7633 1.4092 =$M$11*$M$14*$C43*$C43/36 =E43*4.4482 =$M$6*(2*$D43/$C43-1) =G43*0.0254 =$M$6*$B43/$C43 =$E43*$I43/$M$17/4.4482 78 =SIN(A44/2*PI()/180) 1.7748 1.4013 =$M$11*$M$14*$C44*$C44/36 =E44*4.4482 =$M$6*(2*$D44/$C44-1) =G44*0.0254 =$M$6*$B44/$C44 =$E44*$I44/$M$17/4.4482 80 =SIN(A45/2*PI()/180) 1.7868 1.3931 =$M$11*$M$14*$C45*$C45/36 =E45*4.4482 =$M$6*(2*$D45/$C45-1) =G45*0.0254 =$M$6*$B45/$C45 =$E45*$I45/$M$17/4.4482 82 =SIN(A46/2*PI()/180) 1.7992 1.3849 =$M$11*$M$14*$C46*$C46/36 =E46*4.4482 =$M$6*(2*$D46/$C46-1) =G46*0.0254 =$M$6*$B46/$C46 =$E46*$I46/$M$17/4.4482 84 =SIN(A47/2*PI()/180) 1.8122 1.3765 =$M$11*$M$14*$C47*$C47/36 =E47*4.4482 =$M$6*(2*$D47/$C47-1) =G47*0.0254 =$M$6*$B47/$C47 =$E47*$I47/$M$17/4.4482 86 =SIN(A48/2*PI()/180) 1.8256 1.368 =$M$11*$M$14*$C48*$C48/36 =E48*4.4482 =$M$6*(2*$D48/$C48-1) =G48*0.0254 =$M$6*$B48/$C48 =$E48*$I48/$M$17/4.4482 88 =SIN(A49/2*PI()/180) 1.8396 1.3594 =$M$11*$M$14*$C49*$C49/36 =E49*4.4482 =$M$6*(2*$D49/$C49-1) =G49*0.0254 =$M$6*$B49/$C49 =$E49*$I49/$M$17/4.4482 90 =SIN(A50/2*PI()/180) 1.8541 1.3506 =$M$11*$M$14*$C50*$C50/36 =E50*4.4482 =$M$6*(2*$D50/$C50-1) =G50*0.0254 =$M$6*$B50/$C50 =$E50*$I50/$M$17/4.4482 --- Sides bent parallel 92 =SIN(A51/2*PI()/180) 1.8691 1.3418 =$M$11*$M$14*$C51*$C51/36 =E51*4.4482 =$M$6*(2*$D51/$C51-1) =G51*0.0254 =$M$6*$B51/$C51 =$E51*$I51/$M$17/4.4482 94 =SIN(A52/2*PI()/180) 1.8848 1.3329 =$M$11*$M$14*$C52*$C52/36 =E52*4.4482 =$M$6*(2*$D52/$C52-1) =G52*0.0254 =$M$6*$B52/$C52 =$E52*$I52/$M$17/4.4482 96 =SIN(A53/2*PI()/180) 1.9011 1.3238 =$M$11*$M$14*$C53*$C53/36 =E53*4.4482 =$M$6*(2*$D53/$C53-1) =G53*0.0254 =$M$6*$B53/$C53 =$E53*$I53/$M$17/4.4482 --- STM-8 98 =SIN(A54/2*PI()/180) 1.918 1.3147 =$M$11*$M$14*$C54*$C54/36 =E54*4.4482 =$M$6*(2*$D54/$C54-1) =G54*0.0254 =$M$6*$B54/$C54 =$E54*$I54/$M$17/4.4482 operating point 100 =SIN(A55/2*PI()/180) 1.9356 1.3055 =$M$11*$M$14*$C55*$C55/36 =E55*4.4482 =$M$6*(2*$D55/$C55-1) =G55*0.0254 =$M$6*$B55/$C55 =$E55*$I55/$M$17/4.4482 102 =SIN(A56/2*PI()/180) 1.9539 1.2963 =$M$11*$M$14*$C56*$C56/36 =E56*4.4482 =$M$6*(2*$D56/$C56-1) =G56*0.0254 =$M$6*$B56/$C56 =$E56*$I56/$M$17/4.4482 104 =SIN(A57/2*PI()/180) 1.9729 1.287 =$M$11*$M$14*$C57*$C57/36 =E57*4.4482 =$M$6*(2*$D57/$C57-1) =G57*0.0254 =$M$6*$B57/$C57 =$E57*$I57/$M$17/4.4482 106 =SIN(A58/2*PI()/180) 1.9927 1.2776 =$M$11*$M$14*$C58*$C58/36 =E58*4.4482 =$M$6*(2*$D58/$C58-1) =G58*0.0254 =$M$6*$B58/$C58 =$E58*$I58/$M$17/4.4482 108 =SIN(A59/2*PI()/180) 2.0133 1.2681 =$M$11*$M$14*$C59*$C59/36 =E59*4.4482 =$M$6*(2*$D59/$C59-1) =G59*0.0254 =$M$6*$B59/$C59 =$E59*$I59/$M$17/4.4482 110 =SIN(A60/2*PI()/180) 2.0347 1.2587 =$M$11*$M$14*$C60*$C60/36 =E60*4.4482 =$M$6*(2*$D60/$C60-1) =G60*0.0254 =$M$6*$B60/$C60 =$E60*$I60/$M$17/4.4482 112 =SIN(A61/2*PI()/180) 2.0571 1.2492 =$M$11*$M$14*$C61*$C61/36 =E61*4.4482 =$M$6*(2*$D61/$C61-1) =G61*0.0254 =$M$6*$B61/$C61 =$E61*$I61/$M$17/4.4482 114 =SIN(A62/2*PI()/180) 2.0804 1.2397 =$M$11*$M$14*$C62*$C62/36 =E62*4.4482 =$M$6*(2*$D62/$C62-1) =G62*0.0254 =$M$6*$B62/$C62 =$E62*$I62/$M$17/4.4482 116 =SIN(A63/2*PI()/180) 2.1047 1.2301 =$M$11*$M$14*$C63*$C63/36 =E63*4.4482 =$M$6*(2*$D63/$C63-1) =G63*0.0254 =$M$6*$B63/$C63 =$E63*$I63/$M$17/4.4482 118 =SIN(A64/2*PI()/180) 2.13 1.2206 =$M$11*$M$14*$C64*$C64/36 =E64*4.4482 =$M$6*(2*$D64/$C64-1) =G64*0.0254 =$M$6*$B64/$C64 =$E64*$I64/$M$17/4.4482 120 =SIN(A65/2*PI()/180) 2.1565 1.2111 =$M$11*$M$14*$C65*$C65/36 =E65*4.4482 =$M$6*(2*$D65/$C65-1) =G65*0.0254 =$M$6*$B65/$C65 =$E65*$I65/$M$17/4.4482 122 =SIN(A66/2*PI()/180) 2.1842 1.2015 =$M$11*$M$14*$C66*$C66/36 =E66*4.4482 =$M$6*(2*$D66/$C66-1) =G66*0.0254 =$M$6*$B66/$C66 =$E66*$I66/$M$17/4.4482 124 =SIN(A67/2*PI()/180) 2.2132 1.192 =$M$11*$M$14*$C67*$C67/36 =E67*4.4482 =$M$6*(2*$D67/$C67-1) =G67*0.0254 =$M$6*$B67/$C67 =$E67*$I67/$M$17/4.4482 126 =SIN(A68/2*PI()/180) 2.2435 1.1826 =$M$11*$M$14*$C68*$C68/36 =E68*4.4482 =$M$6*(2*$D68/$C68-1) =G68*0.0254 =$M$6*$B68/$C68 =$E68*$I68/$M$17/4.4482 128 =SIN(A69/2*PI()/180) 2.2754 1.1732 =$M$11*$M$14*$C69*$C69/36 =E69*4.4482 =$M$6*(2*$D69/$C69-1) =G69*0.0254 =$M$6*$B69/$C69 =$E69*$I69/$M$17/4.4482 130 =SIN(A70/2*PI()/180) 2.3088 1.1638 =$M$11*$M$14*$C70*$C70/36 =E70*4.4482 =$M$6*(2*$D70/$C70-1) =G70*0.0254 =$M$6*$B70/$C70 =$E70*$I70/$M$17/4.4482 --- Ends almost touching 132 =SIN(A71/2*PI()/180) 2.3439 1.1545 =$M$11*$M$14*$C71*$C71/36 =E71*4.4482 =$M$6*(2*$D71/$C71-1) =G71*0.0254 Ends intersecting. 134 =SIN(A72/2*PI()/180) 2.3809 1.1453 =$M$11*$M$14*$C72*$C72/36 =E72*4.4482 =$M$6*(2*$D72/$C72-1) =G72*0.0254 Not physically realizable. 136 =SIN(A73/2*PI()/180) 2.4198 1.1362 =$M$11*$M$14*$C73*$C73/36 =E73*4.4482 =$M$6*(2*$D73/$C73-1) =G73*0.0254 138 =SIN(A74/2*PI()/180) 2.461 1.1272 =$M$11*$M$14*$C74*$C74/36 =E74*4.4482 =$M$6*(2*$D74/$C74-1) =G74*0.0254 140 =SIN(A75/2*PI()/180) 2.5046 1.1184 =$M$11*$M$14*$C75*$C75/36 =E75*4.4482 =$M$6*(2*$D75/$C75-1) =G75*0.0254 142 =SIN(A76/2*PI()/180) 2.5507 1.1096 =$M$11*$M$14*$C76*$C76/36 =E76*4.4482 =$M$6*(2*$D76/$C76-1) =G76*0.0254 144 =SIN(A77/2*PI()/180) 2.5998 1.1011 =$M$11*$M$14*$C77*$C77/36 =E77*4.4482 =$M$6*(2*$D77/$C77-1) =G77*0.0254 146 =SIN(A78/2*PI()/180) 2.6521 1.0927 =$M$11*$M$14*$C78*$C78/36 =E78*4.4482 =$M$6*(2*$D78/$C78-1) =G78*0.0254 148 =SIN(A79/2*PI()/180) 2.7081 1.0844 =$M$11*$M$14*$C79*$C79/36 =E79*4.4482 =$M$6*(2*$D79/$C79-1) =G79*0.0254 150 =SIN(A80/2*PI()/180) 2.7681 1.0764 =$M$11*$M$14*$C80*$C80/36 =E80*4.4482 =$M$6*(2*$D80/$C80-1) =G80*0.0254 152 =SIN(A81/2*PI()/180) 2.8327 1.0686 =$M$11*$M$14*$C81*$C81/36 =E81*4.4482 =$M$6*(2*$D81/$C81-1) =G81*0.0254 154 =SIN(A82/2*PI()/180) 2.9026 1.0611 =$M$11*$M$14*$C82*$C82/36 =E82*4.4482 =$M$6*(2*$D82/$C82-1) =G82*0.0254 156 =SIN(A83/2*PI()/180) 2.9786 1.0538 =$M$11*$M$14*$C83*$C83/36 =E83*4.4482 =$M$6*(2*$D83/$C83-1) =G83*0.0254 158 =SIN(A84/2*PI()/180) 3.0617 1.0468 =$M$11*$M$14*$C84*$C84/36 =E84*4.4482 =$M$6*(2*$D84/$C84-1) =G84*0.0254 160 =SIN(A85/2*PI()/180) 3.1534 1.0401 =$M$11*$M$14*$C85*$C85/36 =E85*4.4482 =$M$6*(2*$D85/$C85-1) =G85*0.0254 162 =SIN(A86/2*PI()/180) 3.2553 1.0338 =$M$11*$M$14*$C86*$C86/36 =E86*4.4482 =$M$6*(2*$D86/$C86-1) =G86*0.0254 164 =SIN(A87/2*PI()/180) 3.3699 1.0278 =$M$11*$M$14*$C87*$C87/36 =E87*4.4482 =$M$6*(2*$D87/$C87-1) =G87*0.0254 Brett Nordgren 166 =SIN(A88/2*PI()/180) 3.5004 1.0223 =$M$11*$M$14*$C88*$C88/36 =E88*4.4482 =$M$6*(2*$D88/$C88-1) =G88*0.0254 http://bnordgren.org/contactB.html 168 =SIN(A89/2*PI()/180) 3.6519 1.0172 =$M$11*$M$14*$C89*$C89/36 =E89*4.4482 =$M$6*(2*$D89/$C89-1) =G89*0.0254 "October 14, 1998" 170 =SIN(A90/2*PI()/180) 3.8317 1.0127 =$M$11*$M$14*$C90*$C90/36 =E90*4.4482 =$M$6*(2*$D90/$C90-1) =G90*0.0254 172 =SIN(A91/2*PI()/180) 4.053 1.0086 =$M$11*$M$14*$C91*$C91/36 =E91*4.4482 =$M$6*(2*$D91/$C91-1) =G91*0.0254 This analysis is largely based on a 174 =SIN(A92/2*PI()/180) 4.339 1.0053 =$M$11*$M$14*$C92*$C92/36 =E92*4.4482 =$M$6*(2*$D92/$C92-1) =G92*0.0254 discussion of the Elastica curve on p. 138 176 =SIN(A93/2*PI()/180) 4.743 1.0026 =$M$11*$M$14*$C93*$C93/36 =E93*4.4482 =$M$6*(2*$D93/$C93-1) =G93*0.0254 "of Reddick & Miller - ""Advanced " 178 =SIN(A94/2*PI()/180) 5.435 1.0008 =$M$11*$M$14*$C94*$C94/36 =E94*4.4482 =$M$6*(2*$D94/$C94-1) =G94*0.0254 "Mathematics for Engineers"" - 2nd Edition" 180 =SIN(A95/2*PI()/180) inf. 1 inf. inf. n/a n/a "New York, John Wiley & Sons, 1938"