$\_iKga|VpRpiFD1small{diameterD2L1KR3(KL2R5QL2AR2R1R4SlantlengthsaaTANC1C2 C3:C4XthetaH1RH2arcso ircumferencesircumferences.radusingFcLCL1CL2theta1theta2sCL1fullcircumferencesatthetwoendsends.C1L2C2R3C1R3bycross multiplyingR6V sm0 TAPERBLR.BAS (Peter Dawes, 19-06-03)#lJM! @ Vm####.##" \e V :m? D1=small end diameter: D2=large end diameter: L1= axial length"m L2= slant length.m9 C1= small end circumference; C2=large end circumference."m( R3= small end arc 'construction' radiusm+ R4= large end arc radius. "m0 Figure 2 shows the boiler rolled into its cone.m; Figure 1 shows the wrapper unrolled out into a flat sheet."m" Derivation of the formula for R3:m@ theta=C1/R3: theta also=C2/R4 but R4=R3+L2 so substitute for R4m C1/R3=C2/(R3+L2)"m4 C1(R3+L2) = C2R3 ----------------cross multiplying.m C1R3+C1L2=C2R3"m- C1L2=C2R3-C1R3 ------------------rearranging"mA R3(C2-C1)=C1L2 ------------------swapping sides & extracting R3."m. R3=C1L2/(C2-C1) -----------------evaluate R3.m9 Theta can now be found by using the values for R3 and C1"m; __________________________________________________________"m* Enter small, large diameter, axial length a |  ad   |d   V ap  V |p , C1,2=full circumferences at the two ends.$ Arc len = R*theta so R=arc/theta. d v wnd vO "% From Figure 2 using Pythagoras. p wn $% R3,4=Radii for those arc lengths.    > Calculate deviation of the arc from a straight-line chord -I = Ht of arc above its chord= R-SQR(R^2-(CH^2)/4)'where CH = chord len..G Also, length of a chord which subtends an angle theta at a radius of R, equals 2*R*sin(theta/2)dd p d Mp Q) Chord length for small endod p d Mp X) "  "  " large end. d v Qd vndwOw $'distance of chord to arc small end d v Xd vndwOw ' "  "  " "  large end d Mp  d Mp  - Results #-m Small end diam=" am: Large end diam=" |m: Axial length=" m Slant length = " \ m Included angle theta=" m radians or " \ :pm degrees."m R3=  \ m: R4= " \ m% Small and large end circumferences= " \ m% Small and large end Chord lengths = " \ Q Xm2 Distances of chord from arc, small & large ends = \ m Special offsets R5, R6 =  \  - End of TAPERBLR.BAS - ;