Numerical/mathematical methods for hullform lines to Modern Vessels

Good afternoon. I am new to this forum and a master's student in Naval and Ocean Engineering in Spain.

And I wanted to ask about modern mathematical models to generate the shapes of a ship since, in my studies, we only teach how to model through CAD programs such as MaxSurf or Rhinoceros, with parametric transformations and control point adjustments.

It is something that I would like to learn, apart from interacting with programs, to go deeper into how the shapes of a hull are really drawn, such as waterlines, buttocks and sections.
I only know David Taylor's mathematical model from the MNVDET website. I researched this model and, although it is effective, it is a somewhat outdated criteria.
I would like to know more models apart from the aforementioned Taylor. And how to find documents regarding them. Since I am not very convinced about playing with boat preforms in Maxsurf.

This question is motivated by curiosity and the desire to learn more about my studies, since what I am asking is not usually given in my educational center. I sincerely hope to be taught how ship hull forms are actually made.

Greetings and a good autumn from Spain.

 

Welcome to the forums Robert.

Yes there are many more model series than the original Taylor, generally every design firm or shipbuilder will have their own preferences.

Are you wanting to know how to design a hull from first principles or how it is normally done commercially?

I will tell you right up front there is no "magical" mathematical formula that will turn out the "perfect" hull form; and any CFD just integrates your (knowingly or unknowingly) selected biases. This is why most ship's underwater form is based on just a handful of model series. The percentage performance gain over the vessels operational lifetime is rarely worth the up-front design and build costs; more so if infrastructure (channel width or depth, lock size, etc.) is involved.

 

In addition to JEH's wise words above.

There are ostensibly two issues at play in your question.
1. How to create the lines, mathematically in a 3D environment.
2. Why have the shape it is and varying as such.

In no.1 it is maths that is used in "isolation" from the purpose of the Design.
In no.2 the absence of a systematic series to investigate, one is left with - creating the shape from ideas/thoughts/knowledge...etc.

Understanding Design (naval architecture) and how shapes influence the hydrodynamics of a hull's performance (speed and statical stability) are all integral with "the shape".

So are you more interested in defining shapes using mathematics in 3D, or, defining shapes for a purpose, which then uses mathematics to create it?

 

Good afternoon.

Answering your question: I want to define the shapes, with a hydrodynamic purpose (Speed and Resistance), and then use mathematics to create the 3D shapes.

Regards.

 

Today, extremely few hulls are designed solely for maximum speed or minimum resistance because the compromises of the other factors (seaworthiness, range, carrying capacity, arrangements, etc.) are so reduced as to make the vessel useless except for a very small niche (i.e the golf quandary...if the idea is to make the lowest strokes why hit the ball at all?).

If all you are looking for is to tie minimum resistance/maximum speed to a mathematical method of lines development and formulation; then Lamb's Hydrodynamics is a good place to start (actually.... it was the book where it all started in 1879). Otherwise, for overall hydrodynamics in the development of useful ship lines see SNAME's Hydrodynamics in Ship Design by Saunders. While there are newer texts, these two provide the firm foundation that almost all modern ship hydrodynamic development work is based on.

Additionally, you might want to investigate The Principles of Naval Architecture Series: The Geometry of Ships by John Letcher and the rest of his papers if you are interested in how to smoothly transform developed parent hull shapes into daughter hull forms by computational methods.

 

I design and build many types of boats without AutoCAD

And I'm the controlling information when I hire people that do AutoCAD
The AutoCAD projects are at my website Tyler ltd.com

 

Like the original poster, I'd like to experiment with generating hull lines mathematically. I've struggled to replicate the results shown via the spread sheets from http://www.mnvdet.com/Index.html.
Specifically, the polynomial section lines for the Taylor method. The coefficients presented don't seem to generate curves that are non-dimensional and I'm wondering how one would try to derive them?
I've checked all the publications I can find and while the derivations of the equation for SAC curves is well documented, I can't locate the same detail for the individual sections.
Would anyone have a reference to the original info from Rear Admiral Taylor?

 

I remember John Letcher saying how he designed a sailboat hull using parabolic curves for the waterlines, the curves were calculated with a hand cranked adding machine.

 

https://ia601406.us.archive.org/34/items/speedpowerofship00tayluoft/speedpowerofship00tayluoft.pdf

 

I just re-skimmed this classic and, unless I'm blind, there is nothing about the derivation of the 4th order polynomial that Taylor used for individual sections lines?

On this page in the MNVDET site these coefficients are given but, as I mentioned they don't seem to work and I'm not finding any further detail on their derivation :

"For the underwater hull sections RADM Taylor found that a single equation did not appear to be suitable for all possible sections so;

• • for sections with a sectional area less than about 0.75 he proposed a 4th order parabola

y = l x + ax^2 + bx^3 + cx^4
"
and

"Specifically, if;

• • y = the half-breadth at any waterline as a fraction of the value at the design waterline (ie y = 1 @ x = 1)
  • x = the distance above the keel as a fraction of draft (ie x = 1 @ the design waterline)
  • m = the local sectional area of the section in question
  • l = the recipricol of the deadrise angle for the section
  • f = the flare angle for the section

Then, for the 4th order parabola

• • a = 3/2 f - 9/2 l + 30 m - 12
  • b = -4 f + 6 l - 60 m + 28
  • c = 5/2 f - 5/2 l + 30 m + 15 "

When I work through examples in a Libre Office Calc spreadsheet, I get a curve that looks about right but, the Y values never range from 0 to 1 when X goes from 0 to 1 as expected.

Any pointers on how to make that work would be appreciated.

 

The volume of a body increases to the cube, and the surface to the square. Also, as a vessel gets larger the ratio of wave size to vessel size, wind spedd to vessel size, etc. decreases. The design should be dimensional. A 400 meter dinghy shape would make no sense.

 

Vague generalities aside, I'm not attempting to model a 400 meter dinghy and non-dimensionality is the whole point of the exercise. RADM Taylor was developing lines for 20 foot long towing tank testing models of a 533 foot long British Armored Cruiser. I'm trying to use the same equations to build hulls for Radio Controlled models, in popular scales (1/144, 1/96, 1/72, etc) , of warships from that era that look good and sail well. Any help would be greatly appreciated.

 

The basic laws of physics are not vague generalities, but constraints you can't avoid.

 

@xanthar, I hope the attached document is helpful. I've been using this procedure for many years and it gives excellent results.

 

true after65 years playing, sailing, helming, building,all I do is follow my gut feeling as to what will work