Locking segment with logarithmic spiral surface

A method of designing a locking segment having a body comprising an upper surface defined by a logarithmic spiral for restraining a spigot of a first pipe to a bell of a second pipe, the bell having an inner surface oriented at a slope relative to an outer surface of the spigot when the spigot of the second pipe is inserted into the bell of the first pipe along a common longitudinal axis, the method comprising:

• providing a representation of the spigot of the first pipe inserted within the bell of the second pipe to a predetermined position at which the spigot is to be restrained,
• calculating a contact point between the upper surface of the locking segment and the inner surface of the bell based upon
• an angle θ between a first line on the outer surface of the spigot and the slope of the inner surface of the bell, wherein the first line originates from a reference point on the spigot's outer surface, and
• a range a of the logarithmic spiral as measured from the reference point,
• such that a second line connecting the reference point to the contact point proximately intersects a centroid of the body of the locking segment, and the upper surface of the locking segment is tangent to the inner surface of the bell at the contact point.