Test case 3a.9: Pure yaw

Conditions

• Captive pure yaw motion in still water
• Fixed (Even keel)
• Without rudders
• With bilge keels

Pre scribed PMM motions:

• Sway motion:
• Sway velocity:
• Sway acceleration:
• Heading angle:
• Yaw rate:
• Yaw acceleration:

[-]	[-]	[m/s]	[rpm]	[m]	[deg]	[-]
0.280	4.643´10^6	1.531	8.0210	0.1636	10.2	0.30

Items and Remarks

Figure Number	Items	Remarks
Fig. 3a.9-1	Time history of non-dimensionalized longitudinal force ()	To be compared with experimental results download
Fig. 3a.9-2	Time history of non-dimensionalized transverse force ()	To be compared with experimental results download
Fig. 3a.9-3	Time history of non-dimensionalized yaw moment ()	To be compared with experimental results download
Fig. 3a.9-4	Damping parts of and vs.	To be compared with experimental results download
Fig. 3a.9-5	Inertial parts of and vs.	To be compared with experimental results download

• Coordinate system for comparision is ship-fixed at midship on the undisturbed waterplane.

• ,

where, is towing carriage speed, is the gravitational acceleration and is the kinematic viscosity of water.

• All quantities are non-dimensionalized with water density (), ship speed (), lateral underwater area (), and the length between perpendiculars ().

• From the Fourier series expansion of and ,

damping parts are

and inertial parts are

where,

• Non-dimensional yaw rate and accelerations: