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On page 115 in the Guilmartin's Book "Galleons and Galleys", it is described that "-----; no small matter with a gun weighting 7,000 pounds mounted on the bow of a hull displacing 170 tons, figures representative of mid sixteenth-century Venetian triremes. Shipwrights compensated for the weight by designing hulls that were fuller at the bow and finer at the stern, giving the underwater lines a graceful , fish-like shape."

I am interested in this description. So, I try to calculate the trim of the galleys.

When all of the guns move from the center to the bow, the waterline rotates around the y-axis at the center of flotation "F" as shown in the figure.

The metacenter M is the pivot point of the entire body for small angles of rotation around y-axis. The distance between the metacenter and the center of buoyancy B or B' is as follows.

x=0 is at the center of flotation "F"

On the otherhand, the distance between the center of gravity G and G' is as follows.

Since rotation angle is small, following equations are derived.

Therefore, trim

Generally, we can assume

Therefore

The center of flotation "F" is the geometric center of the waterplane area. Therefore, xc is obtained by following equation.

I assumed that the displacement =170 tons and the weight of the guns

waterplane shape (y-axis is enlarged) | BM | t | tf | xc |

60.3 m | 18.7 cm | 9.3 cm | 0m | |

100.9 m | 11.2 cm | 5.2 cm | 1.28 m | |

114.7 m | 9.8 cm | 4.6 cm | 1.43 m | |

128.6 m | 8.8 cm | 4.4 cm | 0 m | |

54.3 m | 11.7 cm | 5.9 cm | 0 m | |

16.1 m | 17.6 cm | 8.8 cm | 0 m | |

22.5 m | 28.2 cm | 14.1 cm | 0 m | |

8.9 m | 31.8 cm | 15.9 cm | 0 m |

BM : Distance between the metacenter and the center of buoyancy

t : trim

tf : Bow sinking depth from the initial waterline plane

xc : Distance between the center of flotation "F" and the center of the body

But we can see a tendency that the shape with a fat bow and a slim stern reduces trim.

Since the freeboard of the galley was very narrow, the several centimeters improvement of the trim mght be very important.

Therefore, I think this calculation supports Professor Guilmartin's description.

Reference:

1) "Ship Hydrostatics, Equilibrium and Stabilty: Basics".

2)Correspondence study course of ship building (in Japanese)

3)2.9.3 Longitudinal Center of Floatation (LCF)