1. Motion equations

 

For surge, sway, and yaw,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Abkowitz (1966) mathematical modeling

 

Taylor Series Expansion with following assumptions,

   

Then,

 

Simplified derivative notation of SNAME (1952)

and so on, which are so-called 'Hydrodynamic derivatives' or the 'Maneuvering Coefficients'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. PMM Test

• Special cases of the mathematic model:

Static drift:
Pure sway:
Pure yaw:
Yaw and drift:

 

 

1) Motions:

	Surge	Sway	Yaw
Static drift	0		0
Pure sway	0		0
Pure yaw	0	0
Yaw and drift	0

 

 

 

 

 

 

 

 

 

 

 

2) Mathematic models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3) Mathematic models in a harmonics form (Dynamic tests)

Pure sway:

where

Pure yaw:

where

Yaw and drift:

where