1. Ship Computer Aided Design

2. Contents Upright Hydrostatic Analysis Introduction
Hydrostatic Calculations
Hydrostatic quantities in the curves of form
Curves of Form
Bonjean Curves

3. Introduction
Upright Hydrostatic Analysis is used to assess hydrostatic equilibrium & stability.
This analysis is used during loading & operation of the vessel.
In case of Grounding or Collision, hydrostatic properties maybe important in the success of salvage operations.

4. Hydrostatic Calculations
The input is in most cases a form of offsets on transverse stations.
Graphic views of the offsets are beneficial.
1. Longitudinal view: gives good indications of the quantity and quality of data.
2. Transverse view: good supplement to the longitudinal view.

5. Curves of Form
For a vessel that operates at a significant range of loadings (displacements), the hydrostatic properties must be presented for a range of flotation conditions.
It is customary to use vessel draft as the independent variable, and to tabulate properties at a reasonable number of draft values.
In the curves of form, the draft is the vertical axis (because draft is a vertical measurement), and dependent quantities are plotted horizontally.
A generic “scale of units” from 0 to 10 is used.

6. Curves of form for the ship

7. Hydrostatic quantities in the curves of form include:
• Displacement. • Longitudinal center of buoyancy. • Vertical center of buoyancy. • Waterplane area. • Longitudinal center of flotation. • Transverse metacentric height. • Longitudinal metacentric height. • Wetted surface area. • Form coefficients, e.g., block and prismatic coefficients.

8. Curves of Form

9. 1. Displacement “∆"
It is the weight of the water that a ship displaces when it is floating.
Molded displacement in salt water.
Total (gross) displacement in fresh water.
Total (gross) displacement in salt water.

10. 2. Longitudinal Center of Buoyancy “LCB”
“LCB” is the longitudinal distance from a point of reference (often midship) to the center of the displaced volume of water when the hull is not moving.

11. 3. Vertical Center of Buoyancy “VCB”
“VCB” is the vertical distance from a point of reference (often the baseline) to the center of the displaced volume of water when the hull is not moving.

12. 4. Water plane Area and Incremental Displacement
Its use is primarily to furnish a ready calculation of the incremental displacement due to a small additional immersion.

13. 5. Longitudinal Center of Flotation “LCF”
“LCF” is the longitudinal distance from a point of reference (often midships) to the center of the area of water plane when the hull is not moving.

14. 5. Transverse metacenter

15. dl/dϴ=ρg𝛻(Zmt-Zg).
(Zmt-Zg)=metacentric hight=GM.
Positive initial stability is desirable.
Too large an initial stability causes quick rolling response but uncomfortable and impediment ship operations.

16. Most cargo and passenger ships operate with GMT in range 0.5:1.5m.
Some times unconventional high speed boats don’t need positive initial stability it depends partially or completely on dynamic lift.
Sail boats need roll stability to counter heeling moments made by wind force on their sails.

17. 6. Longitudinal metacenter

18. dM/dɸ=ρg𝛻(Zml-Zg)=ΔGMl.
GMl is the longitudinal metacentric hieght.
Not large design issue.
Used operationally to predict the effect of :
a)longitudinal weight movement.
b)loading trim angle.
Moment change trim 1 cm.
MT1cm=ΔGMl/(100L).

19. 7. Wetted surface area
Is the total area of its outer surface in contact with the water.

20. Important for resistance , powering and speed prediction.
Indicates the antifouling required to coat this area up to water line.
WS =∬ 𝑔 𝑑𝑠𝑑𝑥=∬𝑠𝑒𝑐𝛽𝑑𝑠𝑑𝑥.
𝑔=𝑓 𝑦𝑥,𝑦𝑠;𝑧𝑥,𝑧𝑠 .
X=longitudinal ordinate.
S=arc length measured from CL at X.
𝛽 is the bevel angle for slender hull.

21. 𝑊𝑆≅∫𝐺 𝑥 𝑑𝑥
Where G(x) is wetted girth at station x.
Wetted surface area coefficient.
𝐶𝑤𝑠=𝑊𝑆/√𝛻𝐿
𝛻 is displacement volume.
L is length.

22. Bonjean curves
Bonjean curves are a graphical presentation of transverse section areas as function of draft.
Bonjean curves data:
𝑆 𝑥,𝑧 =2 𝑧 0 𝑦 𝑥,𝑧 𝑑𝑧
Where y is transverse offset.

23. Bonjean curves can be presented in two alternative formats:
(a) from a common vertical axis.

24. (b) From individual vertical axis (stations).

25. In manual hydrostatic calculations bonjean curves were useful for:
displacement.
LBC in trim condition.
damage stability.
volume and moment of volume for specific water line.
Today all previous calculations can be done by computers, Unless the bonjean curves were used internally by program.
However they remain requirement that naval architect must know.