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Thread: Laying Out an Ellipse

  1. #1
    Join Date
    Feb 2008
    Vernon, WI

    Laying Out an Ellipse

    As many of you know, I built that crib a few months ago and on the front gate of it I layed out half of an ellipse. I showed how I did it with a little trick I learned using a string and a few quick moves. It seems that a few of you were pretty interested in how it was done. Well, I was pondering the new section on the forum entitled "Tips and Tutorials" and thought ALRIGHT! Time for me to share. Everyone on this site has helped me out and shown much encouragement. So I thought to myself "hey it's the least I could do" and share the little bit of knowledge I have up in that wandering mind of mine.

    An Ellipse, by definition, is a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal. It is a conic section formed by the intersection of a right circular cone by a plane that cuts the axis and the surface of the cone. Typical equation: (x2/a2) + (y2/b2) = 1. If a = b the ellipse is a circle.

    An Ellipse is often confused with an Arc, which is any section of the circumference of a circle, obviously having the same radius throughout. An Arc can be layed out in many ways with the simplest using just a tape measurer, or object with a designated length, a pencil, and a stationary pivot point. An Arc can also be layed out free-handed by using maybe some 1/4" masonite and a couple of nails to hold it in the desired shape. A true Ellipse cannot be done in this fashion. There are 3 different ways I was taught to lay out a true Ellipse and all you need to know is how wide and how tall you want the shape to be. I will share them Note: none of these pictures will be exactly to scale!

    The first, I have already shown on this forum, but I will try to explain it better here. This way is the easiest and probably the fastest.

    Method 1:

    First, you will need to draw out a Major Axis. Then determine how long you want your Ellipse to be and mark it out with points A and B. For this example, let's make that 40". Now you will need to mark out the center of AB, which will be 20". After you determine how wide you want your Ellipse to be, take half of your total width and mark it off as point C, drawing a line perpendicular off the center of AB. Example - if you want the total width of your Ellipse to be 24" then mark point C at 12" since we will only be laying out half the Ellipse right now.

    Attachment 29312

    Now take half of AB (20") and swing it from point C until it intersects with AB on both the left and right side. You can do this simply with a tape measure and pencil. We will call these new marks D and E.

    Attachment 29294

    Points C, D, and E are where you need to put screws (or nails). The screw or nail in point C is temporary, but since it requires you to put a hole in your workpiece, I always make sure that the edge of the screw is just inside my mark. Otherwise if you center the screw on your mark by the time you remove it and cut your shape out you'll have a hole half the diameter of whatever screw you used and that would not look pretty Along with a MS paint photo, I've given a real example. Since this is only half an ellipse, my major axis is the edge of the board so I obviously can't put a screw in points D and E. So all I did was clamp a piece of scrap on each side so I could run a screw in there. The only advantage to screws instead of nails is they are easier to remove without damaging the workpiece. And the advantage of nails to screws is that the sharp edges of the screws might shear the string, but no big deal use whichever u please.

    Now take a string and tie it to either screw D or E, NOT C'll be taking it out in a minute. The thinner the string the better, but nothing too weak so maybe like a thin nylon line if you have it would probably work best. After you tie it to either D or E, just wrap it around all 3 screws to make a complete triangle and tie it off again to the screw you ended on, which will be the one you started with The green represents the string. Make sure you stretch it as tight as you can amongst the 3 screws...

    Attachment 29295
    Attachment 29296

    Now remove the screw or nail in point C, keeping screws D and E in the wood with the string attached. Now just grab your pencil and push outward with it against the top half of your string that's attached and it will naturally guide it into an ellipse as you swing it left and right until it lands exactly on your original marks A and B You now have half of an ellipse! To make a full Ellipse just simply use the lower half of the string, keeping it attached to D and E, to make a perfect mirror image

    Attachment 29297

    Give it a whirl, they're pretty fun to make and once you get the hang of it you can whip them out in no time. Let me know if you have any questions on that I hope I explained it well enough. One thing to note with using this method, and you will notice this if you make a few different sized Ellipses, is that the wider your Ellipse is, the easier it is to swing your pencil over on points A and B. If you have a narrow Ellipse (like my real-life example above), it will be harder to swing over the nail or screw and get it to land exactly on A and B because it is so tight and one side of the string will have a little knot in the way, BUT it is very possible, just needs some practice!

    Method 2:

    Here again you'll have to lay out a Major Axis and mark out points A and B, which will determine the total length of your Ellipse. Also, at center point of AB, draw a line perpendicular to AB, marking points C and D to determine half of the width of your Ellipse. Next, draw a perfectly square box around points ABCD and lable the top left-hand corner E. In this example, I'm only going to lay out 1/4 of the Ellipse, but don't get worried, you will understand how to do the rest yourself

    Attachment 29298

    Now is the hardest part of this method and it involves math, but it's not too difficult. Take AE and ED and divide both of them by the same equal number. The number needs to be even, I don't know why it does, but that's just what I was told when I was taught the method Make sure that you divide each line by the same number also. You will notice because AE and ED are different lengths but you're dividing by the same number, you will obviously have larger gaps between the marks of ED compared to AE.

    In the example I divided by 10. Starting with point A you need to work towards E. Let's say AE is 20" long, divided by 10 marks = 2". So starting with A, move 2" up the line and mark off "1". 2 more inches and mark off mark "2"... and so on until you reach point E. Point E is also mark 10.

    Let's call line ED 40". 40" divided by 10 marks = 4". So starting with point E you want to work your way towards point D, marking off every 4" and labelling it the correct number. Mark 10 will share Point D also.

    Note: Points A and E are NOT included into being marks "1"

    Attachment 29305

    Now it gets real simple Just simply take a straight edge and connect the matching numbers. 1 with 1 will make a line, 2 with 2, and so on...

    Attachment 29306
    Attachment 29307

    ...until you get them all and you've created part of your Ellipse!...

    Attachment 29308

    Complete the whole Ellipse in the same fashion. Just make sure you start from the Major Axis (AB) and work your way out to the corners, then from the corners work your way in towards the center. There is a way to make this even nicer, and that is to divide by a higher even number. If you divide by oh say 20 instead of 10, you will have more marks and it will be a smoother flowing shape. Hope you enjoy!

    Method 3: continued on another post (no more picture room)...

  2. #2
    Join Date
    Feb 2008
    Vernon, WI
    Method 3:

    This method is called “Quartering the Rise” and is fairly simple, but it’s more time consuming than the other 2 methods, and to be as precise it requires some effort. Note: this will also not be exactly to scale!

    Again, like the other methods, the first thing you need to do is lay out a Major Axis and points A and B determining your total length. Also lay out points C and D determining half of your total width. In this example we will say CD is 20”. Next, connect AD and mark off the center of this line and call that point E.

    Attachment 29309

    Now draw a line perpendicular off of point E, making it ¼ the length of CD (20”). Mark this point F and you now have EF which is 5”. Connect AF and FD.

    Attachment 29310

    Now find center points of AF and FD, and mark them points G and H. Measure perpendicular off G and H, ¼ the length of the previous rise (EF 5”), getting 1 ¼”. Mark these points I and J.

    Attachment 29311

    …Continue using this “quartering the rise” method until you reach small enough numbers and you will notice your Ellipse taking shape. This is obviously the longest method of doing this, but it will work if you ever feel like giving it a try.

    Thanks for letting me share everyone. And thanks for looking! Let me know if you have any problems with the pictures, or any questions at all and I will be happy to clarify. Hope you enjoy

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