1. Mount and Mount Conditions

1) Fix-mount and Fixed-model conditions

• Fix-mount constrains the model in all motions

• Model is assembled rigidly with the fix-mount and then ballasted:

  • to the static waterline position (FX₀: fixed even-keel condition)

  • to the dynamic sinkage (σ = 0.192 x 10^-2 L) and trim (τ = -0.136˚; bow down) corresponding to Fr  = 0.280 (FX_στ: fixed sunk and trimmed condition)

Fix-mount	Fixed-model

2) Free Mount

• Free-mount allows the model to move freely in heave, pitch, and/or roll motions.

• Model is connected to the free-mount with two types of joints using roller or spherical bearings.

• The roller bearing prevents and the spherical bearing allows the roll motion, respectively, while transmitting the heave and pitch motions of the model.

• Model is first ballasted to the static waterline and then connected to the free mount:

  • using the roller joint (FR_zθ; free to heave and pitch condition)

  • using the spherical joint (FR_zθf; free to heave, pitch, and roll condition)

Free-mount	Free-model

2. Effects of Motions on Forces and Moment

Define:

      (ratio to FX₀)

and

             (ratio to FR_zθ)

where, x₀, x_στ, x_zθ, and x_zθf can be any quantity from the FX₀, FX_στ, FR_zθ, and FR_zθf conditions, respectively.

1) Static drift test

Compared to FX₀ condition:

• The effect of fixed sinkage and trim (ξ_στ) is relatively small, about 3 ~ 7% increase of forces and moment.

• The effect of free heave and pitch motions (ξ_zθ) is relatively large, up to 33% increase of forces and moment.  In general ξ_zθ value increase with Fr and β.

• The effect of roll motion (ζ_f, i.e. ξ_zθ/ξ_zθf) is small, within 2 ~ 3% differences in forces and moment between the roll-fixed (FR_zθ) and -free (FR_zθf) conditions.

2) Dynamic tests

Compared to FX₀ condition:

• The effect of fixed sinkage and trim (ξ_στ) is fairly small; within about +10% change in the dominant harmonic amplitudes.

• The effect of free heave and pitch motions (ξ_zθ) is relatively large, up to 25% increase of the dominant harmonic amplitudes of forces and moment.

• The effect of roll motion (ζ_f, i.e. ξ_zθ/ξ_zθf) is small, about +1% difference of the dominant harmonic amplitudes between the roll-fixed (FR_zθ) and -free (FR_zθf) conditions.

• The effecte of heave, pitch, and roll motions on the phase angle of the dominant harmonic (φ_Y1 and φ_N1) are very small, typically within +2%.

3. Effect of Motions on Hydrodynamic Derivatives

Compared to FR_zθ condition:

• Linear (velocity) derivatives values from FX₀, FX_στ, and FR_zθf mount conditions are fairly similar, with differences within +10%.

• Non-linear, acceleration, and cross-coupled derivatives from the fix-mount conditions (FX₀ and FX_στ) values are usually smaller.

• Non-linear derivatives values for the roll-free condition (FR_zθf) do not show a clear trend.

• Acceleration and cross-coupled derivatives values for the roll-free condition (FR_zθf) are fairly similar.