# Maths and Ship Design

Discussion in 'Boat Design' started by Furkan, Nov 23, 2020.

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### FurkanJunior Member

Hello all,

I'm quite new in this forum and saw somebody was asking about how ship design and maths were related. So, this thread will be about how and why we use maths in ship design as well as asking for your own ideas and knowledge on how it's used.

So, What I will tell you is;

- Volumes and areas of sections and hulls are calculated by integrals or numerical calculations.
- Simpson integral and method of trapeze highly used for the stability and strength of ships calculations.
- You need to have a good command of understanding for geometrical shapes and their variations.
- Physics knowledge is more frequently required for ships. (Pressure, the flow of fluids, hull resistance and hydrodynamics.)
- All coefficients can be calculated with four processes. (+,-*,/)

Furkan

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### gonzoSenior Member

I think that if you calculated your volumes and areas by integration, it may not be necessary to resort to Simpson's rule.

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### TANSLSenior Member

Simpson´s rule is an, approximate, integration procedure.

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### Will GilmoreSenior Member

To calculate using integration, you need a curve that follows a known formula or all of it is an approximation. A Reimann Sum also works, with enough sections.

-Will (Dragonfly)

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### TANSLSenior Member

Normally, in the calculations of naval architecture, the equation of that curve, or of the hull surfaces, is not known so there is no choice but to resort to approximate methods. Even the most sophisticated CAD / CAM programs use approximate methods.

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### gonzoSenior Member

There are two ways to integrate it easily. One is to enter the data in a program like excel and get a curve of best fit. The other is to use a mechanical integrator, which can be bought used for very cheap. Both methods are simpler and faster than rectangles or other summation methods.

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### Eric ruttanSenior Member

Um, would not it be better to understand the inaccuracies?

Like, do the volume of a stack of simple sections smaller then the vol, and one larger. What is the diff, as A function of the volume.

If it is within 1%, does it matter?

There is also a way to find the error of an integration.

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### Mr EfficiencySenior Member

The most important number in design is the one preceded by this sign: (\$)

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### Will GilmoreSenior Member

I am not a naval architect, but I have done some engineering as a furniture and manufacturing design engineer and I love boat design. A good grasp of ratios around balance for buoyancy and trim, leverage for heeling over righting moment, being able to add up forces for pulley block ratios, understanding material strengths versus tension under varying loads with and without elasticity, all have a fundamental mathematical element. Rules of thumb work for much of the design demands until an architect wants to experiment and push into untried territory, use new technology or construction methods.

With the growing application of foiled hulls, for example, knowing the driving force, friction, balance and lift forces generated, are vital to a successful design. Math is necessary.

Then, there are electrical systems and power plants and their transmission to drive force. There's range and capacity, displacement empty, displacement loaded and effects of heeling on hull characteristics.

Don't forget cost analysis or material needs. If you're in business, there's more math that may seem mundane, but needs to be done, never the less.

It is possible to design a good boat without using much math, but not while competing in the commercial, experimental, or racing world.

-Will (Dragonfly)

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### Eric ruttanSenior Member

Spoken like someone whos livelyhood is effected by said \$.

A 'known truth' is the designer can easily write '±0.0001', and have no idea regarding the need for the level of accuracy, nor the cost. The quickest way to bankrupt a project is to allow a designer this freedom.

Low levels of precision are cheap, and higher levels are exponentially more expensive to execute, but very cheap to write on paper or a screen.
Math is important. But understanding that the math is simply a way to discuss parts of the project abstractly. Care must be taken to not confuse that abstraction with reality.

Also, regarding the OP's suggestion 'All coefficients can be calculated with four processes. (+,-*,/)'

I think coefficients are derived many ways, including calculus. Many can be utilized by arithmetics, but not all arithmetics are appropriate to apply to coefficients. Like algebra, it can be easy to make an error.

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### Will GilmoreSenior Member

True.

You really only need the one '+', but that can be a lot of work. Symbolically working out repetitive processes is one of the great achievements of Humanity.

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### HowlandwoodworksMember

Furkan,
You might want to start here:
THE DESIGN RATIOS
A Naval Architect's Dozen (or thereabouts)
A primer on some basic principles of naval architecture for small crafts
Home https://www.ericwsponberg.com/

His primer has been a valuable tool for many.

I can't say enough good things about the participant's here. They are top drawer, having share their knowledge freely and have been much help to me as a novice and my project.
Best of luck with all of your endeavours.

Last edited: Nov 25, 2020
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### IkeSenior Member

back in 1965 (before I signed up for the Coast Guard) I worked at Lockheed Shipbuilding (now defunct) in the Naval Architecture Section. All I did was math, Calculation of wieghts, CGs, moments, volumes and more. This was before desk top computers and even handheld calculators. It was tedious but extremely important. Get it wrong and the ship would list to one side or the other, tank would not hold as much as they were supposed to and at launch the ship could turn turtle and really piss everyone off at they guy who did the calculations (no that didn't happen). But it was a good lesson in the importance of math in ship and boat design. Made max use of Simpsons Rule, never used integration. Later (4 years later) went back to work there and now they had an IBM main frame to do more accurate calculations, but I still had to feed it the data. I assume the computer was using some sort of integration.

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### gonzoSenior Member

That is not true. Whoever requests the design will specify constraints and requirements. Some of those will be regulated by laws or organizations. In fact, many projects go bankrupt because the owner keeps on making changes and trying to micromanage instead of listening to the designer.

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### Eric ruttanSenior Member

It is true. You did not address the point.You created a strawman.
If someone is changing the design, how is that not the designer by another name?

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