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[m2] 3.4357 CB [-] 0.651 DP [m] 0.150 Z [no. of blades] 5 P/D0.7 [-] 1.300 The considered experimental test conditions cover a set of tests, which are representative for a 1st quadrant 4 DOF PMM test and which can be used for assessment of the experimental uncertainty for representative conditions. The PMM testing technique enables various test conditions to be studied inpidually. The conditions, which are considered in this work, are “static rudder”, “static drift”, “static drift and rudder”, “static heel” “static heel and drift”, “pure sway”, “pure yaw” “yaw and rudder”, “yaw and drift” and “yaw and heel”. In the static test the model is towed in the same steady condition through the tank. The other tests are dynamic, i.e. the model is oscillating harmonically. In the present paper focus is placed on 3 DOF simulations, which means that only a subset of the conditions is covered, leaving all quantities related to heel and roll out. The contents of the considered test tests can be summarized as follows: 29th Symposium on Naval Hydrodynamics Gothenburg, Sweden, 26-31 August 2012 “Static rudder”: The model travels straight ahead through the tank with the rudder in a given angle δ. “Static drift”: The model travels through the tank in oblique flow due to a given drift angle β. “Static drift and rudder”: Same as “Static drift” but the rudder is deflected. “Pure sway”: The model travels through the tank on straight ahead course while it is oscillated from side to side. With u, v and r being the surge velocity, the sway velocity and the yaw rate in the ships local coordinate system, the pure sway motion can also be expressed in terms of the velocities, i.e. u=Uc (carriage speed), r=0 and v oscillates harmonically. “Pure yaw”: The model travels through the tank while it performs a pure yaw motion, where it is forced to follow the tangent of the oscillating path. In terms of velocities this means that v=0, while r and u oscillate harmonically. u oscillates, since the carriage speed in the present set-up is constant. “Yaw and rudder”: Same as “Pure yaw” but the rudder is deflected. “Yaw and drift”: The model travels through the tank, while it performs a pure yaw motion as described in “Pure yaw”. However, a fixed and preset drift angle is overlaid on the motion in order to obtain a drift angle relative to the tangent of the oscillating path. In terms of velocities this means that v≠0, but constant, while r and u oscillate harmonically. For all of the above conditions, the tests were conducted according to FORCE’s standard PMM testing procedures. This means that the model was constrained in all degrees of freedom except for heave and pitch to account for dynamic sinkage and trim. The PMM setup is shown in Figure 1. During the test the model is equipped with propeller and rudder. The propeller RPMs are kept constant at the model’s self propulsion point. The model is shown in Figure 2 and Figure 3, where the sand strips used for turbulence stimulation can also be seen. The PMM test program is carried out for speeds down to 0.35U0 corresponding to a Froude number of 0.091. The test program carried out including the repeat tests for the uncertainty assessment are shown in Table 2. During the test the instantaneous operatingconditions for the ship like speeds, positions etc. aremeasured together with the resultant forces. All forcesare measured in a coordinate system following the ship,meaning that X-components act in the longitudinaldirection of the ship (positive forward) and Y-components perpendicular to this direction (positivestarboard). The yaw moment is taken with respect tothe mid-ship position at ܮ/2. All hydrodynamicforces and moments presented in the present work arenon-dimensionalized by the data reduction equationsshown below. It should be mentioned that for the staticconditions, the hydro dynamic forces and moments areequal to the measured quantities, i.e. (6) ܺᇱ, ܻԢ and ܰԢ are the longitudinal force, the transverse force and the yaw moment, respectively. ߩ is the water density. ܷൌ √ݑଶ ݒଶ is the ship speed, where u and v are the surge and sway velocities respectively. r is the yaw rate. Finally, the dots above the velocity quantities indicate the corresponding accelerations. See Figure 4. ܶ and ܮ are the mean draft and the length between perpendiculars. ܯ and ܫ are the mass and moment of inertia of the model, i.e. of the model itself, the gauges and the ballast weights. ܺீ and ܻீ are the X- and Y-distances from the center of gravity of the model to the point, which the model rotates around. A part of the experimental work also covered assessment of the experimental uncertainty. Following the approach in ITTC 1999a and b and Simonsen 2004 the uncertainty assessment, which covers both precision and bias limits, is based on the data reduction equations for the forces and moments listed above. The uncertainties are expressed as 2 2 2' ' 'X X X P B U (7) 2 2 2' ' 'Y Y YP B U (8) 2 2 2' ' 'N N N P B U (9) B and P are the bias (systematic errors) and precision (random errors) limits, respectively. The bias contributions are found by sensitivity analysis of the data reduction equations and error estimates related to the inpidual components of the measurement system, The bias limits are assessed based on a study of the measuring system. According to ITTC 1999a they can be estimated on the basis of JiJiJi kik k i i i r B B B11112 2 22 (10) where ߠ is the influence coefficient defined by iiXr (11) ܤ is the bias limits in ܺ and ܤ is the correlated bias limits in ܺ and ܺ . Lk i ik B B B1) ( ) ( (12) where ܮ is the number of correlated bias error sources that are common for measurement of variables ܺ and ܺ. The bias error for each variable in the data reduction equation may consist of a number of bias errors, so in order to calculate the combined bias error the root-sum-square is used Jkk i iB B12 2) ( (13) ݅ is the number of the considered variable in the data reduction equation. The precision limits are assessed through repeated tests, which are built into the test program. The model has not been dismounted from the carriage during the test, so in order to “disturb” the system the repeat tests has been mixed with the other test configurations. According to ITTC 1999a the precision limit is estimated from MSP rr2