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hydrodynamic derivatives specifically developed for barge-ship forms, although, for the preliminary
design stage analysis, the present results are very satisfactory.

6 STABILITY ANALYSIS IN THE OFFLOADING OPERATION
The stability analysis for the offloading operation with a FPSO (L = 320 m, B = 52 m, H = 21 m,
A = 300 kton) , converted from a VLCC to operate in a water depth of 780 meters, connected to a 130
kton shuttle is performed for different incidence angles of the current with magnitude of 2.0 knots. The
mooring system consists of ten lines in the forebody and eight lines in the aftbody with symmetry in
relation to the longitudinal plane in a DICAS configuration. Figure 4a presents the real part of the
twelve eigenvalues as functions of the incidence angle of the current. It can be observed that the real
parts of the six eigenvalues associated to the FPSO are negative for most of the current incidence
angles. The presence of the shuttle introduces an unstable behavior to the system. It should be
emphasized that the shuttle has a stable behavior around the equilibria when connected to a single
point mooring. In order to extend the stability analysis; a time domain simulation is carried out for the
FPSO-Shuttle configuration with a current coming from astern. The results are presented in figures 4b.

FPSGShutUe System
Cumnt coming from astern

+ 3rd complex pail
7th eigenvalue
-+ 8th eigenvalue
+ 9th eigenvalue
'10th eigenvalue
2 I a. .. ..* .=-a* -...- ~ eigenvalue
:
+ 11th eigenvalue
- -2.00
. I -12th
-3.00 i 1 T ---I -200.0
0.00 1.57 3.14 4.71 6.28 -200.0 -100.0 0.0 100.0 200.0 300.0
Incidence angle of the current Surge motion (m)
Figure 4: a) Eigenvalues of the system and I Sway versus Surge motion
As observed in figure 4b, the system is unstable. The instability is more related to the shuttle, while the
FPSO shows an almost stable behavior. These results are in agreement with the stability analysis.
Although the FPSO execute small excursions, they are large enough to stimulate the unstable behavior
of the shuttle.

In field operation it is common to use a tug to assist the offloading procedure. In this case the tug can
be used as a stabilizer device. For the case simulated above a tension equal to 65 tonf was applied to a
200 meters long cable connected to the stern of the shuttle ship, provided by the tug. The stability
analysis shows that the system is stable around the equilibria, since none of the eigenvalues have
positive real part (real part of the eigenvalues: -0.4087, -0.4087, - 0.2463, -0.2463, -0.3535, -0.3535,
-0.3691, -0.3691, -0.5025, -0.5025, -0.03024,O.O). The time domain simulation also confirms this.

Acknowledgements
The authors thank ANP (Brazilian National Petroleum Agency) and CNPq (Brazilian National Agency
for Research and Technological Development) for the support to this work.