Question:

After a SOLVE command, why is the delta weight not zero and why does it change when I give another SOLVE command? The ship is displacing about 13300 tons and the delta ranges from about 0.5 to about 2.0 tons.

Answer:

The changes in delta weight are due to the iterative process used in solving for equilibrium. The process stops when the deltas get below a tolerance, and the tolerance is based on the size of the ship. Due to the discrete nature of the model representation as well as the digital representation of numbers in the computer, it is not always possible to solve exactly. The program balances accuracy against speed, and selects an error tolerance which is well below the modeling errors. In this case, a delta weight of 2 tons is about 0.01% of the displacement which is much less than the 0.3% error margin generally considered good accuracy in ship stability work. On this vessel there would be more than 2 tons error in displacement for a 1mm error in draft readings.

The fact that the delta changes every time you give the solve command is due to the different initial conditions. The steps taken by the solver depend on how far away from the solution it is initially and the derivative values it may have retained from the previous solving operation. We could have written the program so that it always showed zero delta when the actual delta was within tolerance. We felt it was better to let the user see what the actual delta is.