Long moorings (longer than water depth) with buoyancy should have the top float stay at the surface

[richardsc]

Illustrated with example:

library(mooring)
m <- mooring(anchor(depth=100), wire(length=200), float())
plot(knockdown(discretise(m), u=1))

^{Created on 2022-03-07 by the reprex package (v2.0.1)}

[dankelley]

Here, for my notes, is a sketch I have for how I think it will look, when I code this up. I won't bother explaining my notation, since it's just a GH equivalent to a scribble on a napkin.

[dankelley]

CR and I discussed this a few days ago. Handling this is a bit tricky, because the present solution method starts at the float, assumes that buoyancy matches the vertical component of the tension vector, etc. Then we write the equation for the float's horizontal force balance. We have 2 equations now, and can solve for 2 unknowns (the tension in the wire attached to the float, and the angle of that wire). We proceed downwards, element by element, with a similar approach (although for all elements other than the top float, we of course also have tension above, but we know that from the analysis of the element just above).

This model breaks down for a float at the surface, because the upward gravity force will depend on the volume fraction that is submerged. And that fraction will depend on the tension below. In other words, the present solution method fails in the case of the top float being in contact with air.

I have some ideas on how to proceed, but some experimentation will be required. Partly, they involve iteration, and that is on the cards as a higher priority than this.

For a memory jog, below is the blackboard that CR and I made in our meeting. It won't mean much except to us.