El Faro Stablity

#82

Departure GM was 4.5 feet (1.3 meters) min required was 3.7 feet ( 1.1 meter)

From NTSB

Shoreside loading personnel and deck officers with experience on El Faro told
investigators that a 0.5-foot GM margin was added to the vessel’s required GM at sailing
(3.655 feet). 166 GM margin is not a statutory requirement. The CargoMax printout from
September 29 gave a sailing GM of 4.854 feet, corrected for free surface effect to 4.455 feet fordeparture. (Free surface effect is a reduction in a vessel’s stability caused by liquids moving about freely in a tank or hold.) The corrected GM was thus 0.8 foot above the required GM and 0.3 for more than the owner-applied GM margin of 0.5 foot.

#84

⠀⠀⠀ ⠀⠀⠀ image ⠀⠀IMG_2672
The second formula is for shifting a weight (w) over a certain distance (d), thus we can say:

PAH = w x d or 6358 = w x d If we shift a weight of 500 ton transversely on the center line of the deck over a distance of 12.72 m we comply with the equation.

⠀⠀⠀⠀⠀_2686

If we rework the formula a little bit and use the above figures then:

tan θ = w x d/W x GM = 500 x 12.72/38490 x 1.3 = 0.127 The list angle θ = 7.24°

To bring the ship at an angle of 14° then a weight of 981 ton has to be shifted over a distance of 12.72 m. The permanent list of 2° requires a weight of 137 tons to be shifted over the same distance.

#85

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ IMG_2699

KB and BM depend on the geometrical form of a ship and that complicates things a bit. For an ordinary ship the KB may be found fairly accurately by Simpson’s Rule, a numerical method and a way to approximate integrals without having to deal with lots of narrow rectangles. However, I will keep it simple and use the following formula:
‌ ‍ ‎ ‏ ‌ ‍ ‎ ‏ ‌ ‍ ‎ ‏ ‌ ‍ ‎ ‏ ‌ ‍ ‎ ‏ ‌ ‍ ‎ ‏ ⠀⠀⠀⠀⠀⠀⠀⠀. IMG_2694

In the formula Cw = 0.7 en Cb = 0.62 and then BM = 5.61 m which means that KB = 13.59 - 5.61 m = 7.98 m

The green numbers in the picture are verified numbers taken from the NTSB investigation report. The red numbers indicate that these are not exact verified data. I was not able to find these numbers in the different reports, hence this exercise.