Q: What does the message "*** WARNING: Negative On Diagonal Of Damping" mean?
REV 5.10

A: It means you have negative values in either your damping values and/or your added mass values resulting from the hydrodynamic pressure computation. We discovered users were not checking their added mass and damping output, so we added this warning message. This can be caused by a bad or strange hull definition, close proximity to the bottom, or irregular frequencies.

What we mean by "bad" hull definitions are those that do not have enough detail in areas of the vessel with a change of shape, such as the bow or stern. Often, adding more planes or panels in these areas can make the problem go away. Another good check would be to square off the ends of the vessel, and see if the warning is still reported. With 3D Diffraction, adding panels is automatic by using “&PARAMETER -M_DIST”. We have seen good results with a monohull model of 500 to 1000 panels. Some vessel shapes may require up to 6000 panels, but much more than this takes too long to compute. The optimal aspect ratio for diffraction panels is 1 to 1, meaning a square, but rectangular panels are acceptable. The program will create triangular panels when needed to avoid warped panels. The user can control the resulting mesh by careful selection of the points used to define the planes.

Strange hull shapes can include floating jetty type structures that look like an upside down "T" in cross section. Here you have a horizontal vessel surface in close proximity to the water surface, and this can cause negative added mass. In this case, the negative values and resulting motions are probably real, but thorough checking is advised. If you get the warning with both Strip Theory and 3D Diffraction, this increases the chances the answers are real.

Negative damping can also occur when the keel of the vessel is close to the seafloor. In this case, the water under the keel gets "pushed" against the bottom, and this "hydraulic spring" effect is captured in MOSES as negative damping.

Occasionally, negative damping is caused by irregular frequencies, a numerical phenomenon where the computational algorithm breaks down at particular frequencies. In essence, these are the natural frequencies at which water would slosh inside the vessel. Numerics being what it is, the problem being solved becomes "ill conditioned" in the neighborhood of these frequencies.

The onset of irregular frequencies depends on draft, length, and beam, but for a 400 X 100 foot barge it is around 3.5 seconds. For H851, is it about 6.5 seconds. More panels make the ill conditioning better. Therefore, before you can declare you are subjected to irregular frequencies, you need to fine tune and check your model carefully. If the negative damping occurs at only one or two periods where you know there is little or no spectral energy, these periods can be safely deleted from the computed periods list. Another option is to remove the offending periods from the “G_PRESSURE” command, but use them on the RAO command. MOSES will interpolate or extrapolate results for the removed periods.

Many research papers have been written concerning this topic. One of the more useful ones is "On the Significance of Negative Added Mass", by T. Vinje, presented at the Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague, March 19-23, 1989.