5.1.1 As
                                 an alternative to the formula in Pt  5, Ch  11,  4.1 Minimum thickness 4.1.1,
                                 for Class 3 vessels only, the minimum thickness, t, of
                                 a torispherical unstayed end dished from plate and having pressure
                                 on the concave or convex side is to be determined by the following
                                 formula:
                                 
                              
                              
                              
                              
                              
                              
                                 
                                    where
                                    
                                       | 
                                                
                                             t, p, and R
                                             i
                                             
                                                
                                                
                                              | 
                                       = | 
                                        are as defined in Pt  5, Ch  11,  1.2 Definition of symbols
                                              | 
                                    
                                    
                                       | 
                                                
                                             C
                                              | 
                                       = | 
                                       2,57
                                             for ends concave to pressure | 
                                    
                                    
                                       | 
                                                 | 
                                       = | 
                                       1,65 for ends convex
                                             to pressure | 
                                    
                                    
                                       | 
                                                
                                             S
                                              | 
                                       = | 
                                       specified
                                             minimum tensile strength of plate, in N/mm2, which should
                                             be not less than 410 N/mm2.
                                              | 
                                    
                                 
                               
                              
                              
                            
                           
                           
                           
                              
                              
                              5.1.2 The
                                 inside radius of curvature, R
                                 i, of the end
                                 plate is to be not greater than the external diameter of the cylinder
                                 to which it is attached.
                                 
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              5.1.3 The
                                 inside knuckle radius, r
                                 i, of the arc joining
                                 the cylindrical flange to the spherical surface of the end is to be
                                 not less than four times the thickness of the end plate, and in no
                                 case less than 65 mm.
                                 
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              5.1.4 Ends
                                 convex to pressure are not to be used for vessels exceeding 610 mm
                                 internal diameter.
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              5.1.5 Where
                                 the end is provided with a flanged manhole, the thickness of the end,
                                 in mm, determined by Pt  5, Ch  11,  5.1 Minimum thickness 5.1.1,
                                 is to be increased by 3 mm, and the total depth, H, of
                                 the manhole flange, measured from the outer surface of the plate on
                                 the minor axis, is to be not less than :
                                 
                              
                              
                              
                              
                              
                              
                                 
                                    where
                                    
                                       | 
                                                
                                             t
                                             1
                                              | 
                                       = | 
                                       required thickness of the plate, in mm | 
                                    
                                    
                                       | 
                                                
                                             H
                                              | 
                                       = | 
                                       depth
                                             of flange, in mm | 
                                    
                                    
                                       | 
                                                
                                             W
                                              | 
                                       = | 
                                       minor
                                             axis of the manhole, in mm. |