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Old 01-02-2012, 12:18 AM   #1
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Gambrel math


Designing a gambrel roof using the 2 hexagon method always results in a ridge (peak) height equivalent to a half-pitch (12/12) roof. Rafter lengths equal span/2.732.

Kind of had an "aah-ha" moment, so thought I would share.

Anybody see any errors?

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Old 01-02-2012, 01:24 AM   #2
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Gambrel math


I prefer pictures.

Andy.

I could get more detailed but I am lazy when I am not paid.
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Old 01-02-2012, 07:38 AM   #3
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Gambrel math


Andy - I believe your picture is of an octagonal gambrel rather than a 2-hexagonal gambrel. Same result for height (if using full side lengths) but different rafter/span relationships.

Bad photo of a hexagonal gambrel.
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Old 01-02-2012, 08:23 AM   #4
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Worked for Wolfram Research at on time. Horrible company to work for but Mathematica is a stellar product. You might want to see if one of their online calculators would be helpful. If you are, or have a kid in school? Your college or university probably will let you have a disc and a site license of the whole thing for like $10---even if you are an English lit major or something. The manual, is essentially a book that goes for $65 in bookstores. You could also buy and license your own retail copy for around $1200 as I looked last.

There are specific add ons for doing things like construction calculations and so forth. They are not overpriced for what they do. Mathematica is worth every penny of what it costs by the way. And I do understand academic pricing and that the site license is expensive. Software people never catch on that it just looks bad to the average consumer to see $10 and $1200 in the same day, for the same product. Adobe is the most clueless I think. And Microsoft? My copy of the full office suite, for personal use but purchased with academic credentials, was under $80. Doesn't it retail for over $400 these days? Sublime to absurd.

And come on. The argument is for every retail or even personal academic priced piece of product sold, I and others have Chinese 3-year-olds in my spare room duplicating copies? What nonsense. And should I not find it insulting that software companies would assume I would steal and distribute their products? Sorry, I am into stealing trucks carrying pallets of cartoned Clorox!

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Old 01-02-2012, 08:54 AM   #5
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Quote:
Originally Posted by sdsester
Worked for Wolfram Research at on time. Horrible company to work for but Mathematica is a stellar product. You might want to see if one of their online calculators would be helpful. If you are, or have a kid in school? Your college or university probably will let you have a disc and a site license of the whole thing for like $10---even if you are an English lit major or something. The manual, is essentially a book that goes for $65 in bookstores. You could also buy and license your own retail copy for around $1200 as I looked last.

There are specific add ons for doing things like construction calculations and so forth. They are not overpriced for what they do. Mathematica is worth every penny of what it costs by the way. And I do understand academic pricing and that the site license is expensive. Software people never catch on that it just looks bad to the average consumer to see $10 and $1200 in the same day, for the same product. Adobe is the most clueless I think. And Microsoft? My copy of the full office suite, for personal use but purchased with academic credentials, was under $80. Doesn't it retail for over $400 these days? Sublime to absurd.

And come on. The argument is for every retail or even personal academic priced piece of product sold, I and others have Chinese 3-year-olds in my spare room duplicating copies? What nonsense. And should I not find it insulting that software companies would assume I would steal and distribute their products? Sorry, I am into stealing trucks carrying pallets of cartoned Clorox!
Ummm...ok. Don't forget the cost of a computer in your analysis.

The "ahh-ha" I had in the original post was derived from a plastic Chinese protractor, a 0.7 mechanical pencil, and a scrap piece of paper from an erroneous tax return from the past. Total cost...probably under $10. But then I posted my findings to this forum using an iPhone 4!! Insanity!

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Old 01-02-2012, 09:25 AM   #6
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Gambrel math


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Originally Posted by jlmran View Post
Ummm...ok. Don't forget the cost of a computer in your analysis.

The "ahh-ha" I had in the original post was derived from a plastic Chinese protractor, a 0.7 mechanical pencil, and a scrap piece of paper from an erroneous tax return from the past. Total cost...probably under $10. But then I posted my findings to this forum using an iPhone 4!! Insanity!
The guy has a computer or with protractor, mechanical pencil and let's not talk about tax returns right now oK? He tapped the internet.

Never trust fresh seafood or math calculations being sold from the back of a pickup with Oklahoma plates is what I was taught.

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Old 01-02-2012, 09:40 AM   #7
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Gambrel math


Based on my Chinese protractor and a table of natural sines, the rafter lengths for a full octagon gambrel should equal the span/2.1796. This differs from Andy's picture above (if I converted inches to decimals correctly), and I don't believe it is rounding error. Anybody know why?

Edit: think I found my mistake. Standby for an update.

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Old 01-02-2012, 11:52 AM   #8
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Gambrel math


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Originally Posted by jlmran View Post
Based on my Chinese protractor and a table of natural sines, the rafter lengths for a full octagon gambrel should equal the span/2.1796. This differs from Andy's picture above (if I converted inches to decimals correctly), and I don't believe it is rounding error. Anybody know why?

Edit: think I found my mistake. Standby for an update.
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Old 01-02-2012, 12:28 PM   #9
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Gambrel math


Andy was correct. For full octagon, rafter length=span/2.6132.

Now I've got to check my hexagon math.
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Old 01-02-2012, 12:40 PM   #10
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Gambrel math


Hexagon number is correct. I think the hexagon looks better.
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Old 01-02-2012, 03:48 PM   #11
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Gambrel math


Just realized that these numbers are not a constant. They only apply if the four roof planes are to have equal rafter lengths. Took me a while to realize that the slopes (pitches) can be maintained while at the same time manipulating their ratio to one another.
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Old 01-03-2012, 01:02 AM   #12
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Originally Posted by jlmran View Post
Just realized that these numbers are not a constant. They only apply if the four roof planes are to have equal rafter lengths. Took me a while to realize that the slopes (pitches) can be maintained while at the same time manipulating their ratio to one another.
When calculating relationships between lines, it is customary to assign the value of 1 (making it your unit) to the length of the principal line. By assigning, for example, the value of 1 to each of the legs of a right triangle, we come up with the value of the square root of two for its hypothenuse.

Both drawings in this thread start with a right triangle with both legs of unit length (that's why both have "inner" 12-in-12 rafters). When you say that "these numbers are not constant", what you've done is break that one-to-one relationship between the legs of the triangle.

What I'm trying to say is that the relationship between lines becomes more evident when you use unit lengths for the basic line or lines (in this case one or both legs of a right triangle, not the rafters).
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Old 01-03-2012, 03:46 AM   #13
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Originally Posted by jlmran View Post
The "ahh-ha" I had in the original post was derived from a plastic Chinese protractor, a 0.7 mechanical pencil, and a scrap piece of paper from an erroneous tax return from the past.
The basic tools for drafting are a straightedge and a compass.
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Old 01-03-2012, 01:59 PM   #14
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Gambrel math


I was simply trying to determine rafter lengths for a gambrel roof. This was the only solution I could determine without the use of anything more than a pocket calculator.
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Old 01-03-2012, 02:41 PM   #15
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Quote:
Originally Posted by jlmran View Post
I was simply trying to determine rafter lengths for a gambrel roof. This was the only solution I could determine without the use of anything more than a pocket calculator.
Each of the two rafters has a rise and a run; the rise of one rafter is the run of the other rafter, and viceversa. All of your dimensions depend on that right triangle with equal legs.

It sounded like you were enjoying yourself. If you want to have even more fun, try drawing it using only a straightedge and a compass.

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