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Re: graphing Cartesian coordinates
By:Dustin Jones
Date: 8/21/2003, 8:49 am
In Response To: graphing Cartesian coordinates (Paul G. Jacobson)

: 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

I am beyond thankfully for you sharing this information with me and the others who will come with the same questions. You have spent the time to lay this out in a manner that really leaves no questions to be asked. As well as the time that it took to type it out in such a concise manner. This information will give me the ability to build a great many boats over the years.
This year Is my first year in a kayak ever and my first boat is a Necky Sky.
I put my 9 year old daughter in it and she took off and also found a new found love . I had made the decision to buy a nice touring boat this spring... I will now be building a nice touring boat this winter and launching it this spring.

Because of you and Daren as well as this board and Nicks Generosity I can now combine my two greatest loves Wood working and paddling together . Thank you greatly for going out of your way to help a fellow enthusiast out to such a degree. May the boat Fairy shine blue Sky's and pleasing water upon you and yours.

Dustin Jones Upstate Adirondacks of NY

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