Finding the area of the waterplane at the design water line?

It has been awhile since I've been on the forums as I've been busy with other things. I've been taking hydrostatic courses on naval design and I have learned quite a bit about displacement and stability, but it hasn't taught me how to find the water area. I either missed it or it's missing for the lesson. I was wondering if anyone could point me in the right direction or help me out with this equation and has a recommended marine software modeling program for me to practice with. Thank you!.

 

You pull it off the lines plan (or have the software calculate it from the lines plan). So you understand how to calculate the displacement up to a given waterplane using a lines plan? (i.e. use Simpsons Rule on the section areas?). The water plane area is just the same only you use the half-breadths at each station at the waterplane you are interested in. The same spreadsheet (and the method was standardized on paper spreadsheets early 20th century, BuShips actually had pre-printed ones) will also allow you to calculate center of waterplane area and waterplane inertia. It really hasn't changed much in the last 100 years, and all a computer does is handle the tedious slicing of the lines plan and simple math calculations much faster. You really shouldn't just jump straight to a computer program until you understand the meanings of the sheer amount of data that it will spit out.
That handles the actual calculation, but I'm not sure if your question doesn't also include how to decide on and set the design waterline. That is a much more convoluted discussion centered around how you develop a lines plan in the first place.

 

I suppose you have a body lines plan. Then :
1.- Calculate the hydrostatic values for several drafts between the baseline and the main deck. (any architecture naval software)
2.- Calculate the weight of the structure, and its center of gravity, for which you need to have made, by the method that you like the most, an estimate of the ship's scantlings.
3.- Add all the other existing weights on board, with their centers of gravity. (spreadsheet)
4.- Calculate the total weight and the CoG, "G".
5.- Check at what value of the draft you get an offset (see point 1) equal to this total weight.
6.- The hydrostatic values calculated in point 1 will give you, for the previous draft, the float with all its parameters, area, geometric center of the water plane, etc.
7. Among other values of point 1 you will have obtained the longitudinal position of the center of buoyancy, "B". For the boat to float with zero trim, the longitudinal position of "B" and "G" must coincide. They will not coincide (it would be a miracle) so you will have to vary the position of some weights until you get it. If there is no way to get it, you will have to change the position of "B", based on changing the shapes of the ship.

P.S. : I forgot to warn you to make sure that the CoG of the boat is in the longitudinal plane, so there is no initial list.

 

Hmmmm it seems I have still have a lot to learn. Just cause I'm curious, you're saying the LCB and the LCG are not typically aligned in design longitudinally is possible to get them to align horizontally perfectly? I guess that sorta explains the forward upward list I see on some power boats with LCG more towards the stern of the vessel and the LCB more towards the aft. And no I do not have a lines drawing yet. I thought this was something I needed to know before drawing a design, so seeing as I'm just getting my feet wet in this area are there any good resources anyone has on designing ships in general?. And thank you both TANSL AND Jerhardiman for your input

 

There are several books out there, but for ships in general the classic is Hydrodynamics in Ship Design. The book actually leads you a complete ship design. A bit dated (i.e. BPC), but you still have to do everything in there in sequence.
Your question comes up every years or so, either ships or boats, so a general overview of design and lines development is given here: Lines Plan

 

What course are you currently doing CMW?
And are you mainly interested in the design of big ships, or small craft?

If big ships, then Principles of Naval Architecture (published by SNAME) is very well regarded.
Books, Proceedings & CDs - SNAME Main Site https://www.sname.org/pubs/books

If small craft, then the venerable Skene's Elements of Yacht Design is still very relevant today -
https://www.amazon.com/Skenes-Elements-Yacht-Design-Eighth/dp/0396079687#ace-g0160871354

If you would like a more 'modern' book, then Principles of Yacht Design is good -
https://www.amazon.com/Principles-Yacht-Design-Lars-Larsson-ebook/dp/B00H878Q54/

If you missed a lesson on Simpson's Rules, have a look at this link.
https://academicscience.co.in/admin/resources/project/paper/f201702151487147028.pdf
Rather than simply asking a computer program to do everything for you, it is well worthwhile to work though some typical examples longhand with a calculator in order to get a better appreciation of what it is all about.

 

Appreciate it mate, I'm more interested the design of smaller boats, yachts, ships. I'm not looking to design the next cruise liner, and would love to learn the math by hand, if at all possible as most courses keep saying let the computer handle it.

 

Righty ho - for small craft, this little book also comes well recommeded.
https://www.amazon.com/How-Design-Boat-John-Teale/dp/157409050X/

I have a paperback version of Teach Yourself Naval Architecture, which I bought 40 years ago - however even the cheapest second hand copies are now ludicruously expensive.
https://www.amazon.com/Naval-architecture-Teach-yourself-books/dp/B0007JFETG/

 

you were not kidding heh heh, 900$ for the book yikes. And I appreciate everyone's responses here, I do have a few pieces of literature here and might have personal library once I'm finished. I'll look into everything here and see what i come to.

 

Yup... i ahve that one took...got it in a 2nd hand book shop in Southampton when a student. So mine is rather old too..!

BUT... there is now an updated version of the book. It has a blue cover and in SI units too. As an old colleague (well this was few years ago he joined us from Uni) had one and showed it to me.
But i've never seen one on Amazon though..

 

There is also the Introduction to Naval Architecture.
This is E.Tuppers half way house between the teach yourself and his Basic Ship Theory books.

https://www.amazon.com/Introduction...al architecture&qid=1586998958&s=books&sr=1-2

You can find this online for free these days too

 

Print the plan, cut out the waterplane with scissors, weigh it on a jeweller's scale, then weigh a sheet of the paper you used, the rest of the calculation is easy !

 

My 2nd book is Naval Architecture for Non Naval Architects by Harry Benford. A book for someone who is on the outside looking in but doesn't like to get his feet wet. My first book is the Principles of Naval architecture, single volume edition. It was my first book and after 3 months into it, I didn't know if I will sink or swim.

 

I assume the jeweler's scale would be sufficiently accurate, and the paper is essentially uniform in density. Regarding the rest of the calculation, measure the area of the sheet and for convenience weigh the sheet before you cut out the waterplane, then weigh the waterplane. Divide the weight of the cut out weight by the weight of the total sheet then multiply this by the area of the sheet resulting in the area of the cut out. Then divide the length of the actual waterplane by the cut out length and square the number (as the beam increases by the same proportion), and then multiply the cut area by this squared number and that is the area of the waterplane on the boat. If this is not clear let me know and I can send a sample calculation.

Now the step beyond determining the waterplane area, determining the LCF; if you fold the cutout longitudinally, taking care to keep the folds perpendicular to the vertical station lines, and then balance it on a sharp device such as a pencil and marking it, you now have the longitudinal location of the center of flotation (LCF).

One of my mentors always invoked the KISS principle (Keep It Simple Stupid) and it has served me well. It also keeps you in touch with the theory and methodology that I often forget when I use a piece of software developed by a third party, and often in programming something, assumptions have to be made, and it is always nice to know what they are, in the event my application isn't typical.

While the developments in computer software have provided our profession with a tremendous amount of speed and the ability to undertake complex calculations which were either not technically within our grasp, or were not cost effective, there are some disadvantages, primarily distancing ourselves from the methodology and assumptions involved.

Do we need to be reminded of "garbage in, garbage out"!

 

I have a planimeter which is great for finding areas. They are cheap now. However, there are a lot of computer programs available that will calculate the area too.