Tow loading may be generated from motions, accelerations or RAO's. This post describes each method of generating inertia loading and some of the options that are available in Tow.

The motion data is entered as translational accelerations and rotational motions with an angle and period. This input is organized such that it is easy to enter data provided by other publications. For instance, DNVGL-ST-N001 (0030/ND) provides a table of motion criteria for based upon general vessel information:

Length (m) | Width (m) | L/B | Block Coeff | Period (s) | Roll (deg) | Pitch (deg) | Heave (g) |
---|---|---|---|---|---|---|---|

>140 | <30 | N/A | <0.9 | 10 | 20 | 10 | 0.2 |

>76 | >30 | N/A | <0.9 | 10 | 20 | 12.5 | 0.2 |

<=76 | <=23 | >=2.5 | <0.9 | 10 | 30 | 15 | 0.2 |

<=76 | <=23 | >=2.5 | <0.9 | 10 | 25 | 15 | 0.2 |

<=76 | <=23 | <2.5 | <0.9 | 10 | 30 | 30 | 0.2 |

<=76 | <=23 | <2.5 | <0.9 | 10 | 25 | 25 | 0.2 |

*note that these values are a sample of values provided and are not applicable to every possible case*

The DNV data referenced from the link above is intended to be used with the tow motions input line only when site specific data, such as that from physical model testing or computational analysis is not available.

SACS takes the motion data and converts it into angular accelerations using the following equations:

where

is the angular acceleration

is the roll/pitch angle

is the period

*note: angular frequency *

SACS provides five different ways to consider gravity which are input on column 77 of the MOTION line in the tow input file:

- Blank - Do not include the effects of gravity.
- G - Include gravity for surge, sway and heave.
- L - Include gravity for surge and sway only.
- H - Include gravity for surge, sway and heave and force heave to be vertical.
- V - Include gravity for surge and sway only and force heave to be vertical.

Consider a vessel with rotational motion , rotation period , translational acceleration and translation acceleration . The inertial loading for an element of mass at distance and angle from the center of motion would be calculated as follows:

Equivalent Lateral Forces

Force Due to Translational Acceleration

Force Due to Angular Acceleration

Force Due to Gravity (G or L options)

Force Due to Gravity (H or V options)

Equivalent Vertical Forces

Force Due to Translation Acceleration

Force Due to Angular Acceleration

Force Due to Gravity (G option)

Force Due to Gravity (L option)

Force Due to Gravity (H option)

Force Due to Gravity (V option)

The total force for a given element in a given direction would be the summation of the force components due to translation acceleration, angular acceleration and gravity component. Note that the force due to angular acceleration is the only component affected by the relative location of the center of motion.

The acceleration input is similar to the motions input except that the rotational motion data is entered as rotational accelerations. There are no gravity options on the acceleration input line so gravity accelerations must be entered as translational accelerations in addition to the surge and sway translational accelerations.

Since there are not gravity options, the calculation of inertial forces is simpler. Consider the same vessel with rotational acceleration , translational acceleration and translation acceleration . The inertial loading for an element of mass at distance and angle from the center of motion would be calculated as follows:

Equivalent Lateral Forces

Equivalent Vertical Forces

It should be noted that the user can manually calculate the equivalent accelerations of the motions input using the equations from the previous section and enter them as acceleration input. The user will get the same results from both analyses.

The attached example as a single mass of 10 kips which is located at joint 0266 (53ft,-3ft,28.533ft). The center of rotation is defined at (0,0,0) and the coordinate system has been rotated so that the longitudinal direction is X, the transverse direction is Y and the vertical direction is Z. Two motion cases are considered with each of the five gravity options.

SACS Example Model

Case | Roll Angle | Period | Pitch Angle | Period | Heave |
---|---|---|---|---|---|

P+H | 12.5 | 10 | 0.2 | ||

R+H | 20 | 10 | 0.2 |

*note: SACS motion load cases typically are labeled using rotational motion +/- heave. For example P+H would be Pitch + Heave and R-H would be Roll - Heave.*

The equivalent accelerations were calculated for each gravity option using the equations from the previous section.

Case |
Gravity Option |
X Acceleration [G] |
Y Acceleration [G] |
Z Acceleration [G] |
Rx Acceleration [Rad/Sec²] |
Ry Acceleration [Rad/Sec²] |
Z Acceleration [Rad/Sec²] |
---|---|---|---|---|---|---|---|

P+H | B | 0.2 | -8.60-2 | ||||

P+H | G | -0.2164 | 1.1763 | -8.60-2 | |||

P+H | L | -0.2164 | 0.1763 | -8.60-2 | |||

P+H | H | -0.2597 | 1.1716 | -8.60-2 | |||

P+H | V | -0.2597 | 0.1716 | -8.60-2 | |||

R+H | B | 0.2 | -0.138 | ||||

R+H | G | 0.3420 | 1.1402 | -0.138 | |||

R+H | L | 0.3420 | 0.1402 | -0.138 | |||

R+H | H | 0.4104 | 1.1280 | -0.138 | |||

R+H | V | 0.4104 | 0.1280 | -0.138 |

Note: The acceleration reported in the listing file of the attached sample is related to the center of motion of the vessel therefore the components of the rotational acceleration are not included in this report.

As an example, the R+H-G case equivalent accelerations will be calculated here:

After running the tow analysis the resulting inertial forces are reported for each load case:

Load Case | Fx | Fy | Fz |
---|---|---|---|

PH-B | -0.764 | -2.080 | |

PH-G | -2.928 | -11.843 | |

PH-L | -3.361 | -1.843 | |

PH-H | -2.928 | -11.796 | |

PH-V | -3.361 | -1.796 | |

PHBA | -0.763 | -2.080 | |

PHGA | -2.923 | -11.840 | |

PHLA | -2.923 | -1.184 | |

PHHA | -3.363 | -11.800 | |

PHVA | -3.363 | -1.800 | |

RH-B | 1.222 | -4.270 | |

RH-G | 4.642 | -13.667 | |

RH-L | 4.642 | -3.667 | |

RH-H | 5.326 | -13.546 | |

RH-V | 5.326 | -3.546 | |

RHBA | 1.222 | -4.273 | |

RHGA | 4.642 | -13.673 | |

RHLA | 4.642 | -3.673 | |

RHHA | 5.326 | -13.553 | |

RHVA | 5.326 | -3.553 |

*note: the load case naming is a bit different for this example. The load case PH-G indicates Motions P+H with gravity option G and PHGA is the equivalent Acceleration load case.*

The resulting loads are almost identical aside from small rounding errors.