Replies

1. 
   VaTom | Jul 06, 2003 02:33am | #1

   Hi fatdiesel,

   Geometry was never my long suit but here goes... 

   You want a radius, or a circle ellipse?  Unless a = b in an ellipse, it's not  a circle.

   I've built more than a few curved windows.  One builder commonly wanted a 3 part window where the top line was an arc of a circle.  Not particularly complicated but without full-size drawings, it's easy to get the dimensions off a little and end up with a lumpy line.

   My windows here are the ellipse you are apparently wanting to avoid, a portion of an oval.  There's really nothing impractical about them that I know of.  To my eye, much more graceful.

   The "golden ratio" I assume is the golden section or golden mean.  The lesser is to the greater as the greater is to the sum of both, often rounded off as 2 to 1, even though that's not quite right (1.000 to .618).  This is what guided my decisions about height to width ratios.

   Are we on the same page?

   If you want a radius, just pick the portion of a circle you find pleasing.  I have no idea what Pella does.  Are you planning windows to build? Or a building that will need windows? 

   If you're wanting to build windows (or doors) and have several alike to build, I'd strongly recommend bent laminations.  Once the form is constructed you can really crank them out, and it doesn't care if it's an arc of a circle or something more complex.  I have 19 here, used 3 different forms.  Remind me to tell you how you use one bending form for both the frame and the stop (different radii) unless you've visualized it already.  My doors follow the same thinking, including my door-in-a-door where the outer door is 6+' x 8+' (think horseshoe) and the inner door is 4' x 7+' which holds a standard sliding door glass panel.

   Yeah, I had fun!  And NOBODY asks which home center they came from.  I did get wrong information about using "exterior" hardboard.  Gotta re-skin them.  This time it'll be in copper. 

   PAHS Designer/Builder- Bury it!

2. 
   Piffin | Jul 06, 2003 03:52am | #2

   If you want a steady radius, a Fibrionellian formula is out for you. It defines an ellipse but is not difficult to layout at all. I could do a sketch if you want. Give me trhe dimensions you are working within. It'll be a fun exercise.

   .

   Excellence is its own reward!

1. 
   Fat_Man_C | Jul 06, 2003 04:57pm | #3

   I am building houses and want a pleasing arch.  For example, say I have a 72" wide window and want an arch that looks appropriate (more like perfect), how high would the apex be.  The reason that I say a true ellipse formula would be impractical is that I would have to explain it to too many subs, etc (self included ha).  Where as a section of a circle would have a true radius.  The reason I mentioned the golden section is that a 72" wide window would not have the same apex (height) as a 36" wide unit.  I hope this gives a little more clarification.  I will use it for front porch "dog houses," windows, interior arches, etc.

   Thanks

1. 
   Piffin | Jul 06, 2003 05:30pm | #4

   It gets a littel more complicated for dormers because you are designing a whole face with all proportions interlinked there, and as you mentioned, applying these ratios perfectly to one portion of the whole will result in varying results according to base width indiuvidually. You certainly don't want twenty differnt finished window heights on the same house. A couple will look good and the rest will look like they came form a yard sale.

   As far as making it easy for average crews to understand and layout....

   I'll try to do a drawing that will employ some generalities and be workable with a framing square. Hold on....

   Excellence is its own reward!

2. 
   Piffin | Jul 06, 2003 07:02pm | #5

   OK

   Mathematically speaking, you build a spiralling curve with consistantly adding squares sized equal to the sum of the previous sides. so that 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, etc.

   geometrically speaking, you can draw triangles with a rise over run having the same proportions with the square; 5/8, 8/13, 13/21 etc.

   The easy layout with square is to draw a 13/21 and then run a diagonal line running across the end points. This will be at about 31.62°

   Now you can find the right proportion at any point along the line using the square and intersects.

   You can do it with a calculator too using the ratio 1.612. That tells me that for a six foot wide window the height should be 9'8-1/8" and the arched top works on a radius of 3'8-5/8". Choose the plain jane arch segment (Lavender colour) and it is easier to layout but just doesn't look as good. I prefer the elipse segment ( red colour) based on a minor axis of the same dimension to give the final shape shown (in blue) at the right.

   I hope this is more clear than mud. It's harder to explain in text than to do it in person.

   .

   Excellence is its own reward!

1. 
   GoldenWreckedAngle | Jul 08, 2003 01:44am | #8

   Well done Piffin!

   It won't get the arch set the way you described with the Fibbonaci series but one other simple method for deriving a "golden rectangle" is to start with a square, set the point of your compass at the mid-point of one of the sides and set the width to draw an arc from one of the two opposite corners down perpendicular to the side where your compass point is set. Extend the line of that side over until it intersects the arc and you have the side of the "golden rectangle" that corresponds to the square.

   If this doesn't make sense I will try to illustrate it graphically.Kevin Halliburton

   "I believe that architecture is a pragmatic art. To become art it must be built on a foundation of necessity."  - I.M. Pei -

1. 
   jonblakemore | Jul 08, 2003 02:47am | #9

   Could you spoil me with a graphical explanation? 

   Jon Blakemore

2. 
   Piffin | Jul 08, 2003 04:59am | #10

   thanks for that tip, tho I think you're right about applying it to window arches. It might work in some places if you took half the width of an openning to be the side of a square, an bisected that side to find the center of a spring arch.

   Here's what I think you were saying. I'll do another to illustrate what I think I'm saying.

   Excellence is its own reward!

   
3. 
   GoldenWreckedAngle | Jul 08, 2003 06:51am | #12

   Precisely! Thank you.Kevin Halliburton

   "I believe that architecture is a pragmatic art. To become art it must be built on a foundation of necessity."  - I.M. Pei -

4. 
   Piffin | Jul 08, 2003 05:04am | #11

   Actually, it might just work OK in a lot of places for a standard formula. It approaches a lot of cathedral work in proportion. Here's the graphic, and a photo of an arch I've built that happens to have the same shape. It was in a house where I was trying to find a common height and spring point fopr arches of three different widths..

   Excellence is its own reward!

   
3. 
   Danusan11 | Jul 07, 2003 02:48am | #6

   A trick I have used in field without aid of calc. and formulas is to find center point much the same way Piff shows in example. measure off horiz. line and center point equa; distances and project plumb line up pick a number for vertical distance, which is slightly shorter than center line and tick with pencil.

   do this along horiz. line both ways equal distances out from center pt. equal distances up each distance up a little less each time.

   this is strickely a eyeball thing, I then use 1/2" plastic water line to bend and trace tick marks. When I determine a arc that I like I pencil in hard and cut. Granted its a crude way of doing it but it works for me and takes a lot of the brain wracking out.

   
   

   ---

   Edited 7/6/2003 8:07:28 PM ET by DANUSAN11

1. 
   FrankB89 | Jul 07, 2003 03:20am | #7

   That's actually a variation of a method boatbuilders use (or used to use) to lay out the crown on a foredeck.

   Most of those old-timers couldn't read or write, but, by marking out as you describe and using a batten (thin, clear piece of wood a little over length...I've used 1/4" X 3/4" cedar canoe strips with good success), most any curve can be acquired.