Discussion:
Geometry question.
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Neil Green
2007-04-15 08:20:01 UTC
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I need to make some curved rafters for a verandah
roof.
The common rafters will be 1500mm when measured in a
straight line from the end points with a curve of
100mm, that is, the mid point of the curve will be
100mm from a straight line drawn from end to end, and
the curve will be part of a circle.
I need to know the curve for the rafters at each
corner of the verandah which are at 45deg.
The length is obviously 1500mm x sqrt2, but is the
curve 100mm x sqrt2?
I hope I've made it clear, and thanks in advance for
any help.
Neil.
Ken Pledger
2007-04-17 01:50:24 UTC
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Post by Neil Green
I need to make some curved rafters for a verandah
roof.
The common rafters will be 1500mm when measured in a
straight line from the end points with a curve of
100mm, that is, the mid point of the curve will be
100mm from a straight line drawn from end to end, and
the curve will be part of a circle.
O.K. That much is clear. You could use the technical terms "arc"
(shortened from the Latin word for "bow"), "chord" (from Greek, but
related to the English "cord" meaning a string), and "sagitta" (the
Latin word for "arrow"). A diagram makes the reasons for those names
pretty obvious.

You chord is 1500 mm and your sagitta is 100 mm. Those are enough
to calculate the radius of the circle, which I make 2862.5 mm. (If you
want the formula for that, just ask.)
Post by Neil Green
I need to know the curve for the rafters at each
corner of the verandah which are at 45deg.
The length is obviously 1500mm x sqrt2, but is the
curve 100mm x sqrt2? ....
That's more obscure. Also, I didn't follow your words "the common
rafters" above. Will you have rafters from left to right, from front to
back, and diagonally as well? Also, your mentioning sqrt(2) suggests
that viewed from above your verandah roof will be square, not just any
old rectangle. I know it's hard without a diagram, but could you
explain in a bit more detail?

Ken Pledger.
Neil Green
2007-04-17 04:38:06 UTC
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Post by Neil Green
I need to make some curved rafters for a verandah
roof.
The common rafters will be 1500mm when measured in
a
straight line from the end points with a curve of
100mm, that is, the mid point of the curve will be
100mm from a straight line drawn from end to end,
and
the curve will be part of a circle.
O.K. That much is clear. You could use the
technical terms "arc"
(shortened from the Latin word for "bow"), "chord"
(from Greek, but
related to the English "cord" meaning a string), and
"sagitta" (the
Latin word for "arrow"). A diagram makes the
reasons for those names
pretty obvious.
You chord is 1500 mm and your sagitta is 100
mm. Those are enough
to calculate the radius of the circle, which I make
2862.5 mm. (If you
want the formula for that, just ask.)
Post by Neil Green
I need to know the curve for the rafters at each
corner of the verandah which are at 45deg.
The length is obviously 1500mm x sqrt2, but is the
curve 100mm x sqrt2? ....
That's more obscure. Also, I didn't follow
your words "the common
rafters" above. Will you have rafters from left to
right, from front to
back, and diagonally as well? Also, your mentioning
sqrt(2) suggests
that viewed from above your verandah roof will be
square, not just any
old rectangle. I know it's hard without a diagram,
but could you
explain in a bit more detail?
Ken Pledger.
Thanks Ken.
By common rafters I mean those that run at 90deg from
the building, although there will also be one common
rafter at each end against the building.
The verandah roof will be rectangular, 4900 long by
1500 wide approximately, which in plan view can be
divided into two 1500 x 1500 squares at each corner
and a rectangle of 1900 x 1500.
The rafters I need to calculate run diagonally across
each corner to each corner point and need to be such
that the roof is in a plane, both across the front and
towards the building at each corner.
The arc of these rafters needs to be different to the
common rafters but I'm not sure how to get to it.
These rafters will span 1500(Common rafter) x sqrt2.
If this isn't clear can I email you a diagram?
Thanks again
Neil.

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