Multi Point Lifting Sling Vectors

My neighbor has a fishing boat and wants to add four lifting points so he can launch at a rather extreme harbor on the Oregon coast. Appropriate length slings are required to keep the boat level, considering that the center of gravity (CG) is aft of the boat’s mid point.

I got a solution for two lifting points first, then struggled to solve for three and four lifting points, all the while hoping for a generalized solution that eluded me. My four point solution works and the distance between each pair of lift points (2 forward and 2 aft) can be zero, effectively becoming a three point solution if you remember to double the load at the forward point.

One way to visualize the problem is to keep the CG at the origin with the “hook point” directly above it. The height of the hook point can represent the total boat weight. So the challenge then is to find the magnitude for each of the “sling vectors” such that when added together, they equal the Vector 2Pt from CG (origin) to hook point. (18.2 KB)

The “sling angles” should never be less than thirty degrees.

To avoid polluting anyone’s thought process, I won’t post my own solution now but this image (below) tells the story of what is expected. I believe the numbers are accurate. The vertical vector in the center is literally the sum of the four sling vectors shown. Changing the ‘weight’ slider doesn’t affect the image at all, only the values for “sling loads” and “shear loads”.

Besides, I failed to find a general solution for ‘N’ points at arbitrary locations, the ‘3 Pts Asym’ scenario in the stripped down model posted above. Either I have a mental block about this or it’s harder than it looks? (a matrix of vectors?)

The yellow points show where the slings intersect the gray bimini top (bad!) but that part is easy and irrelevant to the main issue of calculating the sling loads.

This (below) is a three point sling arrangement on a bigger boat. Notice that the forward lift point is on top of the pilot house, at a different height than the two lift points aft:

P.S. My mistake, this yellow boat is using four lifting points, not three. The forward points are just aft of the numbers on the pilot house.

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