# Hydrostatic calculations of boats and yachts

**Hydrostatic calculations of boats and yachts**

Hydrostatic calculations are an indispensable step in the design and construction of boats and yachts. Not only do they ensure the proper stability and safety of vessels, but they also affect their efficiency and performance during sailing. In this article, we will discuss the basic principles, methods and tools used in hydrostatic calculations, including their importance for the design of vessels.

**Why is hydrostatic calculation important? **

Hydrostatic calculations are important to determine whether a vessel will stay in a safe position on the water and whether it will easily return to an upright position in the event of a roll. In the calculations, we will get detailed information about the waterline (where it is located), displacement (how many kg it is able to displace), and stability of sailing (righting moment, i.e. what values of righting forces act at what angle of tilt). Hydrostatic calculations are essential in the design of boats and yachts so that the vessel sails steadily and safely returns to an upright position.

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**What are the basic steps of hydrostatic calculations?**

1) Determination of the main dimensions of the vessel,

2) Creation of a geometrical model, a numerical model of the hull,

3) Determination of design conditions: Determination of draught, displacement, center of gravity,

4) Hydrostatic calculations

5) Results of hydrostatic calculations:

– curve of the straightening arms,

– center of buoyancy,

– rolling,

– hull geometry coefficients.

Calculations can be performed for different load conditions by changing the draught, displacement, heel, trim of the boat, etc.

Regulations, including harmonized standard 12217, specify for which load conditions such calculations should be performed.

**On the basis of which standards are hydrostatic calculations of yachts in the European Union performed? **

All vessels entering the European Union must comply with the provisions of Directive 2013/53/EU (ex 94/25/EC) on recreational craft (RCD).

With regard to stability, vessels shall comply with the requirements of the following standards harmonized with the above-mentioned Directive:

ISO 12217-1: Small craft- Stability and buoyancy assessment and categorization Part 1: Non-sailing boats of hull length greater than or equal to 6 m

ISO 12217-2: Small craft- Stability and buoyancy assessment and categorization Part 2: Sailing boats of hull length greater than or equal to 6 m

ISO 12217-3: Small craft- Stability and buoyancy assessment and categorization Part 3: Boats of hull length less than 6 m

**What parameters are taken into account when carrying out hydrostatic calculations for boats? **

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Parameters for hydrostatic calculations:

– Lmax – maximum length,

– L_{wl}– length on the waterline,

– B_{max} – maximum beam,

– B_{wl} – beam at the waterline,

– V_{D} – displacement,

– Dmax – lateral height, vertical distance measured from the upper edge of the keel to the lower surface of the upper deck at the side,

– F – freeboard,

– T- draught, the distance measured vertically in the middle of the length of the boat from the structural plane of the waterline to the bottom plating,

– v- speed,

These markings are in accordance with ISO 8666.

**How to calculate boat displacement and why is it a key parameter in design?**

To calculate displacemenet, we need values such as:

– the volume of the solid displaced by the vessel,

– density of the liquid,

After multiplying the volume by the density, we get the weight of the liquid, i.e. the buoyancy force. Such calculations are usually performed by computer in programs such as Orca 3D or Maxsurf, which gives very accurate results and information about the position of the swimming waterline at a given displacement and the position of the center of buoyancy.

The displacement is responsible for keeping the vessel afloat, it must be selected appropriately for the weight of the vessel. If the displacement is too low, the vessel will offer much more resistance. It will move “suboptimally”.

As a result, it will burn much more fuel than a properly designed boat. With too much buoyancy, the vessel loses stability, there is a much greater chance of capsizing the yacht at high speed. In less extreme conditions, and with slower yachts, this will be reflected in the large heel of the yacht.

**What are the differences between hydrostatic calculations for vessels of different designs, such as sailboats, monohulls or catamarans? **

The calculations in both cases are prepared similarly. The biggest difference will be the parameter of the yacht’s righting arm when heaving. The graphs of arm force values differ significantly from each other. With a catamaran, the graph of forces will increase significantly to a maximum of 45 degrees, after this angle of tilt the values will decrease just as quickly. In the case of monohull yachts, much higher Righting lever values can be achieved, even some ocean-going vessels do not have negative Righting lever values.

**What are the methods for measuring and evaluating the stability of a boat using hydrostatic calculations? **

Measurement methods:

- The Archimedes method – which states “the weight of a yacht submerged in a liquid is equal to the weight of the liquid displaced by the yacht”. The buoyancy measurement allows you to determine the buoyancy forces and allows you to calculate the center of gravity of the yacht.
- Hull shape – getting stability with the help of shape. It is a procedure in which, with the help of the shape, we can obtain greater buoyancy in the place of our choice.
- Roll method – consists in controlled rolling of the vessel, and at the same time determining the forces of the Righting lever and the center of gravity.

Computer programs for hydrostatic calculations – software such as Maxsurf or Orca3D allow you to make complex hydrostatic calculations. The software allows for comprehensive yacht optimization.

Calculations and tests are performed according to ISO 12217.

**What factors affect the accuracy of hydrostatic calculations for boats and yachts? **

- Accuracy of the model – the hull model must be accurately reproduced during the production of the yacht, the lower the accuracy in geometry, the greater the differences in the accuracy of calculations.
- Accurate measurements and outputs – major structural dimensions should be precisely measured. Even small errors affect the accuracy of the results.
- Different conditions – the yacht should be tested under different conditions and loads to have a complete picture of the yacht’s behavior.
- Knowledge of boundary conditions – the accuracy of calculations depends on the selected boundary conditions such as the position of the center of gravity, the position of the center of buoyancy, etc.
- Experimental results – after comparing the hydrostatic results calculated in the software with the results of the tested yacht in the water basin, it will differ from each other.
- Software – in each software the calculations are different from each other, the results are often very similar to each other, but the final result is rarely the same. Therefore, it is important to use the latest software on the market, which will allow you to get a result that is close to the real thing.

**What are the consequences of improper hydrostatic calculations for the design and safety of vessels? **

- Low vessel stability – Miscalculations can cause the extension arm to shrink, resulting in greater boat roll and the risk of tipping over.
- Incorrect position of the center of gravity – may affect the accuracy of hydrostatic calculations, the moment of the straightening Righting lever, which will affect the stability of the vessel.
- Problems with carrying capacity – with improper hydrostatic calculations, the carrying capacity of the vessel may be underestimated, the yacht will not be able to carry the appropriate load.
- Problems with sailing – improper calculations expose the yacht to greater resistance, along with the resistance, structural stresses also increase, which may risk damage to the vessel.
- Safety – with incorrect calculations, the risk of safety of the yacht and the crew itself increases. Improper stability of the yacht can lead to accidents.
- Regulations – Improper hydrostatic calculations can lead to non-compliance with marine or inland safety regulations. Vessels must meet certain standards and requirements, and their design must comply with international standards.

**What tools and software are used to perform hydrostatic calculations for boats and yachts, and what are their advantages and limitations? **

Specialized software is used to carry out hydrostatic calculations, which helps to test the yacht in different conditions and under different loads. Examples of proven, specialized software for hydrostatic calculations are:

- Maxsurf – one of the most popular programs for yacht design, the program provides comprehensive tools for the design and hydrostatic analysis of vessels. It offers various modules like Modeler, Stability, Resistance that support different aspects of design. The limitation is the high cost of licensing and the level of complexity that experienced people can meet.
- Orca3D – an overlay (plug-in) for Rhinoceros, which is a 3D modeling tool. Orca3D has a good tool for hydrostatics and drag analysis. The limitation of the program is that it does not have dedicated hydrostatic calculations, you need to have additional plug-ins.

**Who can perform hydrostatic calculations?**

In Poland, there are no regulations that define the rights of persons performing hydrostatic calculations. Theoretically, there are no legal requirements, but in practice you should contact a person or company specializing in calculations that is able to carry out the process and evaluate the results, because in the process of obtaining CE certification, the calculations must be approved by a notified body.

In addition, it is very important to have access to specialized programs, such as Orca 3D or Maxsurf, which will guarantee high accuracy.

Intuition Yachts provides a team of educated ocean engineering engineers with many years of experience in designing boats. We work with specialized Orca 3D and Maxsurf programs supporting design. We operate on the basis of ISO 12217 standards, which is necessary for the designed unit to be CE certified and marketed in the European Union.

Feel free to contact us!

Authors:

Cyprian Błaszczyk

Marta Zawadzka