Experimental tests and numerical calculations of replenishment at sea
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- Institutt for marin teknikk 
Experimental tests and numerical calculations of replenishment at sea operations for two Fridtjof Nansenclass frigates have been performed. A Fridtjof Nansen-class frigate has been model with the use of empirical formulas for the hull, propeller and rudder properties. The hull is based on hull description from a VERES model. Turning circle and zigzag maneuvers have been performed with a maneuvering simulation program from the work of Skejic (2008). The results of these numerical maneuvering tests with the model does not correspond entirely with the results from model tests and full scale test of the ship class. The reason for this might be due to the hull description the model is based on, which lacks the appendices and has been manipulated to fit the program. But the differences in results are in an order of magnitude such that it is possible use the model for the further calculations. Full scale tests were performed with two Fridtjof Nansen-class frigates. Measurements of position, rudder angles, course, heading and other parameters was done with on board equipment from both ships. The most distinctive result is the oscillations of the rudder angles of the approaching ship. This effect is most evident in the wake of the other ship, but carries on during the replenishment as well. The effect was seen on both ships when being in the wake of the other. The effect of these oscillations might lead to a reduction in the rudder lift. Which means there is little effect of the rudder oscillations. When using these rudder angles in a simulation of the maneuvering, we get a course close to the one being measured. Due to these oscillations it is hard to get some comparable rudder data from the replenishment maneuver. The positioning measurements for the RAS maneuver from GPS is not accurate, and other methods for measuring the transverse distance should be used in addition to the GPS. Numerical calculations have been performed with the simulation program from the work of Skejic (2008). Two Fridtjof Nansen-class frigates have been modeled in the program and various runs have been performed. First in calm water conditions to see the effect without the disturbance of waves. For replenishment maneuvers at transverse distances according to the given procedures, that is between 30 and 50 meters, only small rudder angles are needed to account for the sway force and yaw moment due the presence of the other ship. Both the rudder angle and the drift angle are less than 1o . With other external loads, like waves, wind current, working on the ships during the maneuver, the interaction forces would be difficult to distinguish from the others. We see that the approaching speed is of significance, especially when the delivering ship is relatively small compared with the receiving ship. A larger ship will get little effect of presence of a smaller approaching vessel. From the sensitivity analysis we see a strong dependency on the thrust deduction factor, in addition to the location of the COG. When including waves in the calculations, we see that the waves makes an equally large contribution on the ships as the presence of an other, at transverse distance of 45 meters and 55 meters.