If the arch rises 6″ over 42″ what is ?
What is the length of the radius if the arch has a height of 6″ in a 42″ opening. I would appreciated the equations as well as the answer. tahnks, patrick.
What is the length of the radius if the arch has a height of 6″ in a 42″ opening. I would appreciated the equations as well as the answer. tahnks, patrick.
Fine Homebuilding is excited to be the official media partner of the 2024 Building Science Symposium series! This event offers builders, tradesmen, architects, designers and suppliers to discuss topics ranging…
"I have learned so much thanks to the searchable articles on the FHB website. I can confidently say that I expect to be a life-long subscriber." - M.K.
Get home building tips, offers, and expert advice in your inbox
Fine Homebuilding
Get home building tips, offers, and expert advice in your inbox
© 2024 Active Interest Media. All rights reserved.
Get home building tips, offers, and expert advice in your inbox
Become a member and get instant access to thousands of videos, how-tos, tool reviews, and design features.
Start Your Free TrialStart your subscription today and save up to 81%
SubscribeGet complete site access to expert advice, how-to videos, Code Check, and more, plus the print magazine.
Already a member? Log in
Replies
segement of a circle?
"A wrongdoer is often a man who has left something undone, not always one who has done something."--Marcus Aurelius
I realize it's a segment of a circle I just don"t remember the math.
Why do you need math to figure this out?
On the subfloor of the house pull 42" off a butt seam and make a mark.
Then mark your 6" height at 21".
Nail a board to the floor and keep swinging the arch until you hit all three points.
Don't ask a mathematician why he needs math.
I used to snap lines to make triangles that intersected to find the radius. You start by making a t and then connecting the rise and run points diagonally. Then you make a line perpindicular to the diagonals in the center and where these intersect the center line, you measure down to that point and it's your radius. I used to use the CMIII and that's when started using a shortcut from that. On the 42" opening and 6" rise, you would use half the opening for the run, 21 and a 6 inch rise. Then hit pitch and write this # down. You divide the diagonal in half then hit = rise. Enter the pitch again and it will give you the diagonal, which is the radius.I think that's right, The came out with the new CM about a year after I figured that out and included the shortcut.
it's good to know the math...what if he was dealing with 42'?
"On the subfloor of the house pull 42" off a butt seam and make a mark.
Then mark your 6" height at 21".
Nail a board to the floor and keep swinging the arch until you hit all three points."
also I believe there's a little more to it than that. 2' board or 4'? maybe 21" or 42" I'm just picking numbers here, and so would he.
I've done what you describe, but use a tape measure and work my way down from parallel to the bottom chord until I hit the 3 points. I think that is essentially what you were getting at, because once you nail a random length board and you start to swing that will only give you one random radius. you have to change the pivot point as well as the length of board.
someone described similar method but working off of lines perpendicular to segmented diagonals, which when crossed gets the starting point for your pivot...which you simply measure and that's your radius. that would speed things up real quick.
but knowing the math is a good thing.
Edited 11/18/2006 9:08 am ET by alrightythen
I know math is a good thing to know.
One length board is needed, if the points don't all hit move the pivot as needed. Pretty easy.
The board could be 12' for that fact. You may only use 3' of it though.
Just grab a 1x off the ground, swing it roughly without nailing it down to get a rough spot, then nail it down and swing it until you hit the points.
I am giving advice for an easy way, not knowing what the OP knows. Perpindicular and diagonals to the circumference of and unknown cube may confuse the guy. :)
I knew what you were getting at, cuz I've done it before. but someone not knowing the dynamics of working with arcs I think would get lost without knowing the exrta info that you just added. as well that it is important that your centre pivot for you radius be perpendicualr to the bottom chord, otherwise you can get way off.
I prefer to work with tapes same ay that you use the stick but one is able to read the difference in lenghs to the different points and adjust accordingly.
maybe I am missing something with the stick. if you have 12 foot stick. and it runs obviously "through" all points ( stick being longer than required) at what point to you know that the stick is at an equal distance to each point? are you eyeballing an equal distance then when you think it's close making a mark on the stick to confirm that the 3 points line up precisely? try it with a tape next time, same idea, but the tape already has marks, then when you are close set your nail and hook over that to pivot. you can even draw off the tape by notching your pencil into the tape. ( great for large radius when long sticks hard to find.)
Edited 11/18/2006 9:06 pm ET by alrightythen
I have tried it with a tape measure, to much play.
hmmmm...well more than one way to skin a cat, and to each his own, I guess.
No, it really was a question. And what I meant by asking was do you really want it to be an exact segment of a circle, or would an elipse or oval fit the desired outcome better? I dunno, sometimes huge radius arches with short spans look under-emphasized. Just thinking while typing...don't mind me.-dukeDCG Your Neighbor's Contractor LLC
"A wrongdoer is often a man who has left something undone, not always one who has done something."--Marcus Aurelius
I have been pondering over this for years.
Never took the time to figure it out mathematically on the construction master. Will now
Thanx, Lou
Thanks to everyone, gr. 10 was awhile ago, and awhile to go before my son get's there. patrick.
your radius is 39 3/4" and the arc length is 44 1/4"
>> What is the length of the radius if the arch has a height of 6" in a 42" opening. <<
Patrick,
There are many ways to figure it out. Here are a couple.
1) (WidthX²/ 8xHeight) + (Height/2) = Radius
(42x²/8x6) + (6/2) = 39-3/4" = (Radius)
2) (1/2 WidthX² / Height + Height) / 2 = (Radius)
(21x² / 6 + 6) / 2 = 39-3/4" = (Radius)
Or Construction Master Calculator.
42" [Run]
6" [Rise]
[Conv] [Diag] = 39-3/4" = (Radius)
Joe Carola
Edited 11/11/2006 8:43 pm ET by Framer
The answer to your question is really quite simple if you understand geometry, or ask a 10th grader, anyway I'll give it a shot it's been a while. Suppose you have a segment of a circle, bounded by an arc of the circle and the chord subtending it. Let the length of the arc be s, the length of the chord be c, the radius of the circle be r, the distance from the midpoint of the chord to the midpoint of the arc be h (the height), the measure in radians of the central angle subtending the arc be theta (where 0 ¡Ü theta ¡Ü ), the distance from the midpoint of the chord to the center of the circle (the apothem) be d, and the area be K. Therefore You know c and h. Then
r = (c2+4h2)/(8h),
theta = 2 arcsin(c/[2r]),
s = r theta,
d = r - h,
K = r2[theta-sin(theta)]/2.
Trig and calc. did pay off see that all those years it was useful for something.
First off ---- who let the cougs in here anyways
OK I have a better calc somewhere--- can't find it at the moment but here is one for your problem.
http://ca.geocities.com/web_sketches/calculators/SAGITTA.html
“It so happens that everything that is stupid is not unconstitutional.” —Supreme Court Justice Antonin Scalia
patrickpatrick
This will give you an easy way to construct the arc with a set of trammel points.
The perpendicular bisectors of all chords of a circle will intersect in the center of the circle.
1. Draw chord AB 42"
2. With trammel points, swing arcs (with a radius longer than 21") from points A and B, and where arcs intersect, draw perpendicular bisector through chord AB
3. On perpendicular bisector, measure up 6'' from chord AB and mark point C.
4. Draw chords, AC and CB
5. Draw perpendicular bisector for either chord AC or chord CB
6. Intersection of perpendicular bisectors will be center of circle
oldfred
Edited 11/13/2006 9:05 am ET by oldfred
Edited 11/13/2006 10:02 pm ET by oldfred
Circular Arch Calculator: Scroll down the page for the math and diagram.
The link to the calculator posted by plumbbill works from the length of the curve of the arch (not the height) and the arch width. I didn't include the math on that page because the algorithms were something wicked. I had a bitch of a time coming up with the code for that sucker.
Joe Bartok
Edited 11/13/2006 5:12 pm ET by JoeBartok
I use my CAD program, Turbocad.
Just curious, are you sure it's a true circular arch you want and not an elipse?
As a third way to do it, what are called spiral curves at each end which fair into a circular radius in the center portion (I think this is actually an elipse as well, but I'm no geometry major). This is what most highway curves are. ;-)
"Let's get crack-a-lackin" --- Adam Carolla
An arch following the curve of an ellipse? In that case ...
Elliptic Arch Calculator: You decide what value to assign to the major or minor axis.
Elliptic Arch Calculator given two Arch Dimensions
Ellipse Axes Calculator: given two points on the Ellipse
The theory is given further down the pages.
Or ... how about some other conic sections like a parabola or an hyperbola?Joe Bartok
Some more Circular Arch Layout MathJoe Bartok
Use geometry and the Pythagorean Theorem. X*X + Y*Y = R*R
PlaneWood by Mike_in_Katy (maker of fine sawdust!)PlaneWood
To make the arch here is no need for math or to know what the radius is.
Lets call the 6 inch rise point A. Lets call the points that make up the 42 inch span B and C.
Put nails at points B and C. At mid span (21 inches) measure up 6 inches and put in another nail.
Get 2 pieces of one-by a 4 to 6 inches longer than the distance between A to B or A to C. Lay the one-bys so their ends run past points B and C. Lay their other ends so they cross at point A and nail or screw them together. Put a pencil in the crux of the one-bys where they cross at point A. Now ride the nails with the one-by to point B and then to point C while holding the pencil where the one-bys cross.
That will give you your arc.
I'm all for simple and thats about as simple as it gets.
Mike Merisko
http://www.sawkerfs.com
"I'm all for simple and thats about as simple as it gets."
huh?
maybe I have to watch you do it, but I got lost somewhere.
Mike,Are you talking about this? Hope the pictures expalin it. I did this last winter just as an experiement and it works perfect.Still faster using math though and figuring out the radius in about 5 seconds wityh a calculator and scribing without making up that jig. That jig would be good on a big arc.Joe Carola
Hello Joe,Thats exactly it. If you don't have a clculator handy or not enough room to swing an arc its just another way to get where your going.Mike Merisko
http://www.sawkerfs.com