I have a question for all of the math guys here.
Thanks in advance for your help.
A few months ago we were trimming a house with custom moldings. We
had several arched top windows that needed trim to match. These
windows had a top section that was arched and the arch was really just
a part of a true circle but less than a half circle. In other words
if you knew the radius you could make the trim piece to match.
Now, I've done a lot of these and I normally mark a plumb line in the
center of the window and use a stick long enough to move up and down
the line and change the length until my stick follows the window.
This gives me the radius and I'm good to go.
In this case, since the moldings were to match, the millwork sent out
the sales guy and he got out his tape and measured the length across
the arch (where the arch hit the vertical sides) then measured the
distance from that line up plumb in the center of the window which
would be the highest point of the arch. He wrote down the
measurements and left. My partner and I both had this look on our
faces that said "I'll believe it when I see it!". A few days later
(very much to our surprise) the trim pieces arrived and were correct.
My question is how the hell did he do that?
Does anyone know what formula might be used to find the radius when
you only have the two measurements mentioned above?
I have two arched windows to trim in the house we're currently
working on.
Window A arch length 57 1/2" rise 10 7/8"
Window B arch length 53 1/2" rise 9 1/2"
My preliminary stick method on window A is 43 3/8" radius
and surprisingly window B is about the same.
If anyone could post a formula for me I would appreciate it very much.
If not, I'll just keep poking a stick at it.:-)
Thanks.
Mike O.
On Thu, 14 Jul 2005 18:27:24 -0500, "Swingman" <[email protected]> wrote:
>> If anyone could post a formula for me I would appreciate it very much.
>> If not, I'll just keep poking a stick at it.:-)
>
>IIRC:
>
> r = (c² / 8h) + (h / 2)
>
>Where c = the chord (your "Length" above) and h= height (your "rise" above)
>
>My brain is too tired to attempt to prove it at the moment ... try it and
>see if it comes close to your expectations. if it is wrong, rest assured it
>will be well pointed out, ad infinitum. :(
It worked great! My stick was only off by 1/16!
I also went to DJ's site and plugged in the numbers and everything
matched.
Thank you very much and thanks to everyone else who answered!
BTW, now I just feel like a dumb ass! ;-)
Mike O.
"Mike O." <[email protected]> wrote
> the sales guy and he got out his tape and measured the length across
> the arch (where the arch hit the vertical sides) then measured the
> distance from that line up plumb in the center of the window which
> would be the highest point of the arch. He wrote down the
> measurements and left.
It might be useful to know that he first measured the chord of the arc and
then the sagitta.
Jeff G
--
Jeff Gorman, West Yorkshire, UK
email : Username is amgron
ISP is clara.co.uk
www.amgron.clara.net
I used to be able to do all the geometry and trig stuff in my head.
Since using CAD I can't do any of it anymore but I can solve even more
complex problems without even thinking about it. I recall when I was
just a pup and I solved some nasty hip and valley bracing intersections
in about an hour using CAD. It took the seasoned checker 2 days, he
built a cardboard model of some parts and still couldn't get every
dimension. However, he signed off on the few he couldn't prove because
he couldn't find even one error in the ones he could prove.
This was for fabricated steel that was fab'd in California and shipped
to Hawaii for installation on the roof of a high rise. It all fit.
Chris Melanson wrote:
> Hope this helps
> a: 43 7/16
> b: 42 13/16
> CAD works great for things like this if you need any other help just ask.
>
> Chris Melanson
> BLH Millwork LTD.
>
> "Mike O." <[email protected]> wrote in message
> news:[email protected]...
>
>>I have a question for all of the math guys here.
>>Thanks in advance for your help.
>>
>>A few months ago we were trimming a house with custom moldings. We
>>had several arched top windows that needed trim to match. These
>>windows had a top section that was arched and the arch was really just
>>a part of a true circle but less than a half circle. In other words
>>if you knew the radius you could make the trim piece to match.
>>Now, I've done a lot of these and I normally mark a plumb line in the
>>center of the window and use a stick long enough to move up and down
>>the line and change the length until my stick follows the window.
>>This gives me the radius and I'm good to go.
>>In this case, since the moldings were to match, the millwork sent out
>>the sales guy and he got out his tape and measured the length across
>>the arch (where the arch hit the vertical sides) then measured the
>>distance from that line up plumb in the center of the window which
>>would be the highest point of the arch. He wrote down the
>>measurements and left. My partner and I both had this look on our
>>faces that said "I'll believe it when I see it!". A few days later
>>(very much to our surprise) the trim pieces arrived and were correct.
>>
>>My question is how the hell did he do that?
>>Does anyone know what formula might be used to find the radius when
>>you only have the two measurements mentioned above?
>>
>>I have two arched windows to trim in the house we're currently
>>working on.
>>Window A arch length 57 1/2" rise 10 7/8"
>>Window B arch length 53 1/2" rise 9 1/2"
>>
>>My preliminary stick method on window A is 43 3/8" radius
>>and surprisingly window B is about the same.
>>
>>If anyone could post a formula for me I would appreciate it very much.
>>If not, I'll just keep poking a stick at it.:-)
>>
>>Thanks.
>>
>>Mike O.
>
>
>
This one is used to find radius in just such a manner in traffic
accident investigation.
C squared M
___________ + ________
8 * M 2
Where "C" is chord meaning you measure between two points on the curve.
"M" is middle ordinate which is the distance between the middle of the
chord and the end which is the same distance in which your two chord
points meet. With those two variables, you can determine the radius.
Don
"Mike O." wrote in message
> I have two arched windows to trim in the house we're currently
> working on.
> Window A arch length 57 1/2" rise 10 7/8"
> Window B arch length 53 1/2" rise 9 1/2"
>
> My preliminary stick method on window A is 43 3/8" radius
> and surprisingly window B is about the same.
>
> If anyone could post a formula for me I would appreciate it very much.
> If not, I'll just keep poking a stick at it.:-)
IIRC:
r = (c² / 8h) + (h / 2)
Where c = the chord (your "Length" above) and h= height (your "rise" above)
My brain is too tired to attempt to prove it at the moment ... try it and
see if it comes close to your expectations. if it is wrong, rest assured it
will be well pointed out, ad infinitum. :(
--
www.e-woodshop.net
Last update: 7/12/05
Leon wrote:
>
> "Mike O." <[email protected]> wrote in message
> news:[email protected]...
> >I have a question for all of the math guys here.
> > Thanks in advance for your help.
> >
> > A few months ago we were trimming a house with custom moldings. We
> > had several arched top windows that needed trim to match. These
> > windows had a top section that was arched and the arch was really just
> > a part of a true circle but less than a half circle. In other words
> > if you knew the radius you could make the trim piece to match.
> > Now, I've done a lot of these and I normally mark a plumb line in the
> > center of the window and use a stick long enough to move up and down
> > the line and change the length until my stick follows the window.
> > This gives me the radius and I'm good to go.
> > In this case, since the moldings were to match, the millwork sent out
> > the sales guy and he got out his tape and measured the length across
> > the arch (where the arch hit the vertical sides) then measured the
> > distance from that line up plumb in the center of the window which
> > would be the highest point of the arch. He wrote down the
> > measurements and left. My partner and I both had this look on our
> > faces that said "I'll believe it when I see it!". A few days later
> > (very much to our surprise) the trim pieces arrived and were correct.
> >
> > My question is how the hell did he do that?
>
> If you have the width of the opening and the distance from the top of the
> arc down to where the arc stops you can use a CAD program to determine the
> radius. I suspect that is what he did.
Probably not... :)
See other posts for what he "probably" did.
Leon wrote:
>
> "Duane Bozarth" <[email protected]> wrote in message
> news:[email protected]...
> > Leon wrote:
>
> >
> > Probably not... :)
> >
> > See other posts for what he "probably" did.
>
> I do them that way.
Sorry, after posting I regretted what was probably to much of a
knee-jerk reaction...
W/ so many automated millwork shops these days and the plethora of CAD
designers, it is quite probable a custom mill shop <did> do it that
way...
"Edwin Pawlowski" <[email protected]> wrote in message
news:U9%[email protected]...
>
> "Lowell Holmes" <[email protected]> wrote in message
>>
>> The Smoleys post was made with tongue in cheek. Smoleys are not used much
>> any more.
>
> You should be ashamed of yourself. The Smoley family will starve to death
> because people use cheap $5 made in China calculators from Wal Mart rather
> than look up the figures in the book for $90. It will be a sad day when
> there are no more Smoley tables.
When I first was introduced to Smoleys (1957), there were only mechanical
calculators, Monroe and Marchant comes to mind. They cost hundreds of
dollars and of course the big advantage they had was extracting square
roots.
A slide rule or Smoleys was the state of the art in trig calculations.
Initially, I had no use for the segmental tables, but that soon changed. I
never heard of a sagitta until yesterday. I suppose an old dog can learn new
tricks.
Being comfortable with trig, finding a radius is no problem with a $5
calculator. :-)
I do know a fabrication shop that still uses Smoleys, just like I know
woodworkers that use hand tools.
On Thu, 14 Jul 2005 23:57:06 GMT, "Leon"
<[email protected]> wrote:
>> My question is how the hell did he do that?
>
>If you have the width of the opening and the distance from the top of the
>arc down to where the arc stops you can use a CAD program to determine the
>radius. I suspect that is what he did.
Yes, it can be done that way:
1. Draw the chord.
2. Draw the height from chord center.
3. Join the height top point to the chord ends.
4. Draw the perpendicular bisectors of those two smaller chords.
Where they meet will be the circle center. Dimension the radius from
there to a chord end point.
Hope this helps
a: 43 7/16
b: 42 13/16
CAD works great for things like this if you need any other help just ask.
Chris Melanson
BLH Millwork LTD.
"Mike O." <[email protected]> wrote in message
news:[email protected]...
>I have a question for all of the math guys here.
> Thanks in advance for your help.
>
> A few months ago we were trimming a house with custom moldings. We
> had several arched top windows that needed trim to match. These
> windows had a top section that was arched and the arch was really just
> a part of a true circle but less than a half circle. In other words
> if you knew the radius you could make the trim piece to match.
> Now, I've done a lot of these and I normally mark a plumb line in the
> center of the window and use a stick long enough to move up and down
> the line and change the length until my stick follows the window.
> This gives me the radius and I'm good to go.
> In this case, since the moldings were to match, the millwork sent out
> the sales guy and he got out his tape and measured the length across
> the arch (where the arch hit the vertical sides) then measured the
> distance from that line up plumb in the center of the window which
> would be the highest point of the arch. He wrote down the
> measurements and left. My partner and I both had this look on our
> faces that said "I'll believe it when I see it!". A few days later
> (very much to our surprise) the trim pieces arrived and were correct.
>
> My question is how the hell did he do that?
> Does anyone know what formula might be used to find the radius when
> you only have the two measurements mentioned above?
>
> I have two arched windows to trim in the house we're currently
> working on.
> Window A arch length 57 1/2" rise 10 7/8"
> Window B arch length 53 1/2" rise 9 1/2"
>
> My preliminary stick method on window A is 43 3/8" radius
> and surprisingly window B is about the same.
>
> If anyone could post a formula for me I would appreciate it very much.
> If not, I'll just keep poking a stick at it.:-)
>
> Thanks.
>
> Mike O.
"Guess who" <[email protected]> wrote in message
news:[email protected]...
> On Thu, 14 Jul 2005 23:57:06 GMT, "Leon"
> <[email protected]> wrote:
>
>>> My question is how the hell did he do that?
>>
>>If you have the width of the opening and the distance from the top of the
>>arc down to where the arc stops you can use a CAD program to determine the
>>radius. I suspect that is what he did.
>
> Yes, it can be done that way:
>
> 1. Draw the chord.
> 2. Draw the height from chord center.
> 3. Join the height top point to the chord ends.
> 4. Draw the perpendicular bisectors of those two smaller chords.
>
> Where they meet will be the circle center. Dimension the radius from
> there to a chord end point.
With AutoCAD the radius dimension tool will show the radius.
Simply draw a line the width of the window. From the midpoint draw a
perpendicular line the height of the arc. Then draw an arc through all 3
points and use the radius dimension tool to show the radius of the arc.
Swingman (in [email protected]) said:
| r = (c2 / 8h) + (h / 2)
|
| Where c = the chord (your "Length" above) and h= height (your
| "rise" above)
|
| My brain is too tired to attempt to prove it at the moment ... try
| it and see if it comes close to your expectations. if it is wrong,
| rest assured it will be well pointed out, ad infinitum. :(
Check the link below. Works for both coves and arches.
--
Morris Dovey
DeSoto Solar
DeSoto, Iowa USA
http://www.iedu.com/DeSoto/CNC/cove_geom.html
"Jeff Gorman" <[email protected]> wrote in message
news:[email protected]...
>
>>snip
>
> It might be useful to know that he first measured the chord of the arc and
> then the sagitta.
>
> Jeff G
What in blazes is the sagitta?
I suppose you fellows have never heard of a Smoleys book of tables. :-)
"Duane Bozarth" <[email protected]> wrote in message
news:[email protected]...
> Leon wrote:
>
> Probably not... :)
>
> See other posts for what he "probably" did.
I do them that way.
[email protected] wrote:
> On Thu, 14 Jul 2005 18:00:25 -0500, Mike O. <[email protected]> wrote:
>
>>I have a question for all of the math guys here.
>>Thanks in advance for your help.
>>
>>A few months ago we were trimming a house with custom moldings. We
>>had several arched top windows that needed trim to match. These
>>windows had a top section that was arched and the arch was really just
>>a part of a true circle but less than a half circle. In other words
>>if you knew the radius you could make the trim piece to match.
>>Now, I've done a lot of these and I normally mark a plumb line in the
>>center of the window and use a stick long enough to move up and down
>>the line and change the length until my stick follows the window.
>>This gives me the radius and I'm good to go.
>>In this case, since the moldings were to match, the millwork sent out
>>the sales guy and he got out his tape and measured the length across
>>the arch (where the arch hit the vertical sides) then measured the
>>distance from that line up plumb in the center of the window which
>>would be the highest point of the arch. He wrote down the
>>measurements and left. My partner and I both had this look on our
>>faces that said "I'll believe it when I see it!". A few days later
>>(very much to our surprise) the trim pieces arrived and were correct.
>>
>>My question is how the hell did he do that?
>>Does anyone know what formula might be used to find the radius when
>>you only have the two measurements mentioned above?
>>
>>I have two arched windows to trim in the house we're currently
>>working on.
>>Window A arch length 57 1/2" rise 10 7/8"
>>Window B arch length 53 1/2" rise 9 1/2"
>>
>>My preliminary stick method on window A is 43 3/8" radius
>>and surprisingly window B is about the same.
>>
>>If anyone could post a formula for me I would appreciate it very much.
>>If not, I'll just keep poking a stick at it.:-)
>>
>>Thanks.
>>
>>Mike O.
>
>
> how he did it, I bet is he got a measurement close enough to pick the
> arch out of the seven or whatever number they make. in other words, it
> wasn't an exact measurement....
I believe the formula is as follows:
Let a = half the arch length
Let b = rise
then radius = (a*a + b*b)/(2*b)
where * means multiply.
In your two examples above I get 43.44" and 42.21" respectively.
It took Pythgoras and a bit of manipulation.
Best regards,
Jack Fearnley
"Guess who" wrote in message
> Are my messages not getting through? I'd like to know, since there
> are other problems [replies with no sign of the original message] and
> I need to speak to my ISP aobut that.
You forgot this is Usenet, where you post first, read and understand (maybe)
later (but only after the pissing contest), and there are on average 62
replies with the same answer/solution?
Actually, it may take a while to get some of the messages to all the nntp
servers in the world, so if you wait a day/week/month/year, you'll often see
someone chime in again the next day/week/month/year.
... and some even get lost. Go figure.
--
www.e-woodshop.net
Last update: 7/12/05
"Lowell Holmes" <[email protected]> wrote in message
>
> The Smoleys post was made with tongue in cheek. Smoleys are not used much
> any more.
You should be ashamed of yourself. The Smoley family will starve to death
because people use cheap $5 made in China calculators from Wal Mart rather
than look up the figures in the book for $90. It will be a sad day when
there are no more Smoley tables.
I have to agree with Leon. He probably used a cad program, though it
certainly doesn't have to be done that way. Most anyplace that build
anything these days uses cad. Work like this generally go through the
planner, or programmer if done on a CNC, and that would be the cad man. If
he had it, no reason he wouldn't use it.
"Leon" <[email protected]> wrote in message
news:[email protected]...
>
> "Duane Bozarth" <[email protected]> wrote in message
> news:[email protected]...
> > Leon wrote:
>
> >
> > Probably not... :)
> >
> > See other posts for what he "probably" did.
>
> I do them that way.
>
>
Another even easier mode is do use the three points on the circle to draw a
circle using CAD and measure the radius.
Walt Cheever
"Mike O." <[email protected]> wrote in message
news:[email protected]...
>I have a question for all of the math guys here.
> Thanks in advance for your help.
>
> A few months ago we were trimming a house with custom moldings. We
> had several arched top windows that needed trim to match. These
> windows had a top section that was arched and the arch was really just
> a part of a true circle but less than a half circle. In other words
> if you knew the radius you could make the trim piece to match.
> Now, I've done a lot of these and I normally mark a plumb line in the
> center of the window and use a stick long enough to move up and down
> the line and change the length until my stick follows the window.
> This gives me the radius and I'm good to go.
> In this case, since the moldings were to match, the millwork sent out
> the sales guy and he got out his tape and measured the length across
> the arch (where the arch hit the vertical sides) then measured the
> distance from that line up plumb in the center of the window which
> would be the highest point of the arch. He wrote down the
> measurements and left. My partner and I both had this look on our
> faces that said "I'll believe it when I see it!". A few days later
> (very much to our surprise) the trim pieces arrived and were correct.
>
> My question is how the hell did he do that?
> Does anyone know what formula might be used to find the radius when
> you only have the two measurements mentioned above?
>
> I have two arched windows to trim in the house we're currently
> working on.
> Window A arch length 57 1/2" rise 10 7/8"
> Window B arch length 53 1/2" rise 9 1/2"
>
> My preliminary stick method on window A is 43 3/8" radius
> and surprisingly window B is about the same.
>
> If anyone could post a formula for me I would appreciate it very much.
> If not, I'll just keep poking a stick at it.:-)
>
> Thanks.
>
> Mike O.
On Fri, 15 Jul 2005 03:57:57 GMT, "Leon"
<[email protected]> wrote:
>>"Guess who" <[email protected]> wrote in message
>With AutoCAD the radius dimension tool will show the radius.
>Simply draw a line the width of the window. From the midpoint draw a
>perpendicular line the height of the arc. Then draw an arc through all 3
>points and use the radius dimension tool to show the radius of the arc.
Sigh. Yes, you can do that too. :-)
[using an older version of DeltaCad]
"Guess who" <[email protected]> wrote in message
news:[email protected]...
> On Fri, 15 Jul 2005 12:20:57 GMT, "Lowell Holmes" <[email protected]>
> wrote:
>
>snip>
>>I suppose you fellows have never heard of a Smoleys book of tables. :-)
>>
>
> I'd rather have the formula and a calculator. Much easier to carry
> around, and easy to use with practice.
I agree, I use a calculator or AutoCad when I need the sagitta (:-)
I might even lay it out if the radius is small.
The Smoleys post was made with tongue in cheek. Smoleys are not used much
any more.
On Thu, 14 Jul 2005 18:00:25 -0500, Mike O. <[email protected]> wrote:
>I have a question for all of the math guys here.
>Thanks in advance for your help.
>
>A few months ago we were trimming a house with custom moldings. We
>had several arched top windows that needed trim to match. These
>windows had a top section that was arched and the arch was really just
>a part of a true circle but less than a half circle. In other words
>if you knew the radius you could make the trim piece to match.
>Now, I've done a lot of these and I normally mark a plumb line in the
>center of the window and use a stick long enough to move up and down
>the line and change the length until my stick follows the window.
>This gives me the radius and I'm good to go.
>In this case, since the moldings were to match, the millwork sent out
>the sales guy and he got out his tape and measured the length across
>the arch (where the arch hit the vertical sides) then measured the
>distance from that line up plumb in the center of the window which
>would be the highest point of the arch. He wrote down the
>measurements and left. My partner and I both had this look on our
>faces that said "I'll believe it when I see it!". A few days later
>(very much to our surprise) the trim pieces arrived and were correct.
>
>My question is how the hell did he do that?
>Does anyone know what formula might be used to find the radius when
>you only have the two measurements mentioned above?
>
>I have two arched windows to trim in the house we're currently
>working on.
>Window A arch length 57 1/2" rise 10 7/8"
>Window B arch length 53 1/2" rise 9 1/2"
>
>My preliminary stick method on window A is 43 3/8" radius
>and surprisingly window B is about the same.
>
>If anyone could post a formula for me I would appreciate it very much.
>If not, I'll just keep poking a stick at it.:-)
>
>Thanks.
>
>Mike O.
how he did it, I bet is he got a measurement close enough to pick the
arch out of the seven or whatever number they make. in other words, it
wasn't an exact measurement....
On Fri, 15 Jul 2005 08:45:26 -0500, "Swingman" <[email protected]> wrote:
Thanks for the info. At least that one got there. :-0
I'm more interested in the fact that I'll often see replies to
apparently recent issues, but not the original. I'll sort it out.
Thanks again.
>You forgot this is Usenet, where you post first, read and understand (maybe)
>later (but only after the pissing contest), and there are on average 62
>replies with the same answer/solution?
On Fri, 15 Jul 2005 12:20:57 GMT, "Lowell Holmes" <[email protected]>
wrote:
>What in blazes is the sagitta?
Are my messages not getting through? I'd like to know, since there
are other problems [replies with no sign of the original message] and
I need to speak to my ISP aobut that.
The "saggita" is the vertical distance from the chord center to the
arc. There's a reason Latin was used, and it's political as well as a
bit snobbish, and a long story. It's just another word.
>I suppose you fellows have never heard of a Smoleys book of tables. :-)
>
I'd rather have the formula and a calculator. Much easier to carry
around, and easy to use with practice.
"Mike O." <[email protected]> wrote in message
news:[email protected]...
>I have a question for all of the math guys here.
> Thanks in advance for your help.
>
> A few months ago we were trimming a house with custom moldings. We
> had several arched top windows that needed trim to match. These
> windows had a top section that was arched and the arch was really just
> a part of a true circle but less than a half circle. In other words
> if you knew the radius you could make the trim piece to match.
> Now, I've done a lot of these and I normally mark a plumb line in the
> center of the window and use a stick long enough to move up and down
> the line and change the length until my stick follows the window.
> This gives me the radius and I'm good to go.
> In this case, since the moldings were to match, the millwork sent out
> the sales guy and he got out his tape and measured the length across
> the arch (where the arch hit the vertical sides) then measured the
> distance from that line up plumb in the center of the window which
> would be the highest point of the arch. He wrote down the
> measurements and left. My partner and I both had this look on our
> faces that said "I'll believe it when I see it!". A few days later
> (very much to our surprise) the trim pieces arrived and were correct.
>
> My question is how the hell did he do that?
If you have the width of the opening and the distance from the top of the
arc down to where the arc stops you can use a CAD program to determine the
radius. I suspect that is what he did.
On 15 Jul 2005 10:07:22 -0700, "SonomaProducts.com" <[email protected]>
wrote:
>I used to be able to do all the geometry and trig stuff in my head.
>Since using CAD I can't do any of it anymore but I can solve even more
>complex problems without even thinking about it. I recall when I was
>just a pup and I solved some nasty hip and valley bracing intersections
>in about an hour using CAD. It took the seasoned checker 2 days, he
>built a cardboard model of some parts and still couldn't get every
>dimension. However, he signed off on the few he couldn't prove because
>he couldn't find even one error in the ones he could prove.
>
>This was for fabricated steel that was fab'd in California and shipped
>to Hawaii for installation on the roof of a high rise. It all fit.
As usual, anything works well in the right hands. My older brother
[rest his soul] became wealthy as a consultant correcting structural
steel drawings done by young engineers using CAD. I don't know if he
could turn on a computer. His background was the old trade
school/steel works apprencticeship /drafting office; a good solid on
the ground foundation then the theory. Also, he wasn't afraid of the
fudge factor, instinctively knowing the limitations from his
background.
When he got really stuck, and needed more advanced math or
verification, he used me. Remember, I said *he* was the one who got
rich. His last job involved deciding whether a bent piece at the NY
site was supposed to be that shape. He said I saved him hours and
hours of work when I showed it was from his dimensions. I taught
math, and can still teach *all* high school math without a computer.
They're useful, and I sue one all the time, but base knowledge, not
the tool, is the key. That's why I'm here. There are some people
with some excellent down-to-earth useful advice willing to share, and
I like to listen in.
On Thu, 14 Jul 2005 18:27:24 -0500, "Swingman" <[email protected]> wrote:
> r = (c² / 8h) + (h / 2)
It's right. I used "c" for semi-chord; you use it for the entire
chord length. I use one fraction, you separate it into two.
Otherwise it's the same end result.
>Where c = the chord (your "Length" above) and h= height (your "rise" above)
>
>My brain is too tired to attempt to prove it at the moment
Radius = "R", semi-chord = "c". By difference the other side of a
right triangle from chord to center = "R - h".
By Pythagoras... R^2 = (R-h)^2 + c^2
Expand and simplify for "R" in terms of "c" and "h".
On 14 Jul 2005 20:48:04 -0400, DJ Delorie <[email protected]> wrote:
>Mike O. <[email protected]> writes:
>> Does anyone know what formula might be used to find the radius when
>> you only have the two measurements mentioned above?
>
>That, and a form to do the math for you...
>
>http://www.delorie.com/wood/chord-radius.html
Just added to favorites!
My very scientific stick was only off by 1/16". :-)
Thank you!
Mike O.
On Fri, 15 Jul 2005 07:32:53 +0100, "Jeff Gorman"
<[email protected]> wrote:
>
>"Mike O." <[email protected]> wrote
>
>> the sales guy and he got out his tape and measured the length across
>> the arch (where the arch hit the vertical sides) then measured the
>> distance from that line up plumb in the center of the window which
>> would be the highest point of the arch
That's what he said.
>It might be useful to know that he first measured the chord of the arc and
>then the sagitta.
That's what I said, and is what he said, which was clear enough.
On Thu, 14 Jul 2005 18:00:25 -0500, Mike O. <[email protected]> wrote:
>In this case, since the moldings were to match, the millwork sent out
>the sales guy and he got out his tape and measured the length across
>the arch (where the arch hit the vertical sides) then measured the
>distance from that line up plumb in the center of the window which
>would be the highest point of the arch. He wrote down the
>measurements and left. My partner and I both had this look on our
>faces that said "I'll believe it when I see it!". A few days later
>(very much to our surprise) the trim pieces arrived and were correct.
>
>My question is how the hell did he do that?
Pythagoras [and a little algebra]. End result:
Distance across chord = "2c", height from chord to circle [called
"segment height" or "saggita"], = "h"
R = (h^2 + c^2)/(2h)
Mike O. <[email protected]> writes:
> Does anyone know what formula might be used to find the radius when
> you only have the two measurements mentioned above?
That, and a form to do the math for you...
http://www.delorie.com/wood/chord-radius.html