Boat Building Forum

Find advice on all aspects of building your own kayak, canoe or any lightweight boats

graphing Cartesian coordinates
By:Paul G. Jacobson
Date: 8/21/2003, 12:25 am
In Response To: S&G: Figure X Y coordinates ? *LINK* (Dustin Jones)

: I'm looking to build my first kayak . Ive got the lofting figured out for the
: panel offsets. But I just cant seem to figure out the Forms offsets . I
: understand that they are in XY coordinates . My problem is I'm not able to
: lay these out in a manor that I can use . Ive got some CNC back round and
: I'm not sure if this is hindering or helping me ... most likely not
: helping as I'm lost.
: Ive been searching for some time now and have yet to find the information I
: need . I'm even more confused by the negative numbers . I'm looking at the
: plans of the Guillemot here in the site .
: I know just simply buying another set of plans would solve everything except
: my satisfaction of doing the entire project from scratch designs.
: Ive got all the materials I need at my disposal and would like to get rolling
: as soon as possible. But alas I'm lost at XY..
: Any help you guys could offer is greatly welcomed.

Basic intro to graphing:
Take a sheet of paper and draw a vertical line roughly in the center of the page, going from top to bottom. We will all that your "Y" axis.

On the same page draw a horizontal line, roughly in the center of the page, going from left to right. We will call that your "X" axis.

If you have this rough sketch done properly your sheet of paper should be divided into approximate quarters by these two crossed lines.

The point where these two lines cross is called your "origin". For all intents and purposes you can think of this point as being the same as zero.

If you move along the horizontal line from the origin ( where the lines cross) and to your right you are moving in a "positive" direction. You can use a ruler to measure your distance from that origin point and with a pencil make a mark on the x axis. If you go to the left of the origin then you are graphing "negative" distances or lengths along the X axis.

In the same manner, if you measure above the horizontal line you are going into a positive area, and if you go below the line you are going into negative territory.

Since boat hulls have a lot of strange curves to them a designer will pick some reference point -- and it may be totally arbitrary (!) -- as the origin. Some like to use the waterline of the boat as the base line, or x axis. If you drew the boat on your graph paper then the part of the hull which were underwater would be indicated by negative numbers along the "Y" (vertical) axis.

Since many boats are built upside down, some designers pick an origin point which corresponds to the top of their strongback or work table. This way all the points are positive ( above the table) and easy to work on. After you make the forms you can double chek your work by measuring from the tabletop to a amrking on the form, and assure alignment.

Others pick origin points which will fall on ALL the forms, even if it makes little sense as a reference point later on. Here you just go with what you get.

By pasting on more sheets of paper, those lines you drew can extend up and down, or left or right for any distance you might wish. For most graphing projcts in school you can do a scale model and keep all the information on one sheet of typing paper, but for making a boat you will need a very long sheet of paper. With the data in Nick's table you an see that while some of the information leads you to draw things a little under the "X" axis, most of the information is plotted above that line, in positive territory. At thte same time, yu can see that he plots his information along the lenght of the lines of the boat, so the origin would go on your left side, and you would measure to the right of that for some 200 plus inches. That's a lot of pasted on sheets of paper. You might want to get a roll of butcher paper, or cheap wrapping paper. Small newspapers frequently sell the remnants of rolls of newsprint for $2 to $5 each. These usually give you many hundres of feet of paper for a dirt cheap price.

Some people don't even bother with paper, they just draw their lines on the floor of their shop, or directly on the plywood panels they plan to cut.

Nick's page shows two different tables, and if I count things correctly there is information there for creating ( by graphing) 12 different parts. these would be 10 building forms and 4 panels for the boat. You would actually cut two copies of each of these panels, giving you 8 long, skinny, pieces for the boat, which you would wire together. Yo mgiht not need to make any of the forms, or you could make two or three and use them to make sure that the boat was going together in the right shape.

So, let me describe how to make one of the boat panels, and one of the forms.

Looking at the list of numbers Nick has, it appears that he intends to cut all 4 panels from a piece of wood which is about 32 inches wide, and about 205.5 inches long -- or he wants to work with a sheet of paper which is at least that wide and long.

Either way, we start at the left side of the paper, draw our base line or x axis, and measure up from that for 24 inches. make a dot.

Now slide 6 inches to the right along the x axis and straight up from yo want to measure two distances: one is 22.56 inches, (make a dot) and then directly abov that, at a distane which is 24.19 inches above the baseline you make a second dot. A little subtraction here tells me that these dots are going to be 1.63 inches apart.

we slide to the right along the x-axis another few inches and now we are 12 inhes from the origin. Nick's hart shows that at this point we want to measure up 21.94 and 24.69 inches and make our dots at those points.

We continue along, measuring along the x axis until we come to the distance specified at the top of the column. Except towards the ends of the panels most of these marks are at intervals which are one foot apart ( 24, 36, 48, 60 inhes, etc.) For this panel we see that at a distance of 188.69 inches from the origin the panel ends. Both the top and bottom marks for this panel are in the same place, at a height of 22.63 inches.

Once you have all the dots drawn out, you need to get a long, thin strip of wood (this is called a spline) and lay it on your graph paper, bending it so that it touches all the bottom dots. Trace along this to connect the dots with a smooth, even curve. then use it to connect the top dots, and when you have drawn out this line you will have the outline drawn of the hull bottom panel (remember, you need two, and they should be mirror images of each other, so stack two sheets of your plywood with the good faces touching and cut them out at the same time. The reason you have the good faces touching is so that any splinters come on the "bad" side, where they will probably be hidden by the fillet, and glass tape which joins the panels.

as you wire together these panels you may question whether you have the corect shape. Let's graph one of the forms from the data in the bottom chart.

Note that one form is for the bow, and one form is for the stern. Other than that these forms fit 20 inches apart, with the first form sitting 20 inhes from the bow. For each form there are two colums of data giving the height and the width. Actually, after looking at these numbers it seems that they are for creating only HALF of the form. That is not a problem. The forms are symmetrical.

Let's graph the form whih is called "60". This will fit 60 inches from the bow. Nick has given names to the points. The popint called "Top" will be the center line of the dek on the finished boat. It is located diretly above the origin, so you measure zero inches to the right, and just measure straight up from the origin 7.97 inches. Te point he calls Deck is going to be along the seam in the two piece deck. Measure up 4.46 inches from your baseline, and go 8.61 inches to the right. Even though it is not on Nick's list, I want you to also make a mark which is 8.61 inches to the LEFT of your origin. Remeber, these numbers are for just the right 1/2 of a form. By opying the same distance, but in the other direction, we can plot BOTH sides of the form at the same time.

The next point is called "sheer". The sheer line on a kayak is where the deck meets the hull. On a canoe this would be the gunwale. You make your marks 1.62 inhes above the baseline of your graph, and 9.56 inches to the left and right of the center.

An aside: Based on these numbers I can see that at this point (60 inches, or 5 feet, from the bow, the boat should be 19.12 inches wide on the inside. The outside of the boat will be bigger by the thikness of the plywood used in the hull panels. If I was drawing a form for the widest part of the boat then I would be able to simply find the beam of the boat. Looking along the hart i see that the form at the 100 inch mark has a width of 10.55 inches at the sheer line, so I would guess the outside of the boat to be about 21.5 inches wide here, and that is probably the beam.

Bak to drawing our form. the next points are for the chine. This is where the side of the hull meets the bottom of the hull. The bottom of it will be underwater in most paddling situations, so looking at the numbers, i suspect that Nick has selected the designed water line (DWL) as his zero point when he made this chart. No worries. We go 1.94 inches down, under the x axis, and put our marks 8.95 inches to the right and left of the centerline.

The final number is for the keel, or the center line which will run the length of the hull. sine this is the center of the boat it should not be any surprise that it falls right on the enterline or "y" axis, and sine it is going to be under water, we mark it at 3.16 inches under the base line.

Now, connet these 8 dots using a stiff straight edge and you will get an irregular octagon which is the size and shape that yor boat should be at a distance 20 inches from the bow.

I hope this is of assistance to you. I realize i may be going into greater detail than you need, but I'm sure there are others who are not as experienced as you who will read this posting later -- so I'm writing for them, too.

Best of luck with your project.

PGJ

Messages In This Thread

S&G: Figure X Y coordinates ? *LINK*
Dustin Jones -- 8/20/2003, 9:00 pm
graphing Cartesian coordinates
Paul G. Jacobson -- 8/21/2003, 12:25 am
Re: graphing Cartesian coordinates
Dustin Jones -- 8/21/2003, 8:49 am
Re: S&G: Figure X Y coordinates ?
daren&karen -- 8/20/2003, 11:11 pm
Re: S&G: Figure X Y coordinates ?
Dustin Jones -- 8/21/2003, 8:28 am