Let a catenary be embedded in a cartesian plane so that the 𝑦-axis passes through the lowest point of the catenary. (The word catenary comes from the Latin word catena meaning chain).
To offset the lowest point to (0, 0), then a formula could be:
y = a*cosh(x/a) - a
for a pipe laying down seabed.
a = BLT (t) / sw (t/m)
laying angle = pi/2 - asin (BLT/(y*sw+BLT))
top tension = BLT / cos (laying angle)
Catenary length * sw = top tension * sin (laying angle) = sqrt (top tension ** 2 - BLT ** 2)
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