Hey guys, How do I find the radius of an arch if I have these measurements? Check out the picture.
thanx, Lou
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See the pic I have attached (same pic, but the jpeg is a smaller file). Line A-C is the radius of the circle. If you know the distance of the line A-B, then the line B-C can be found using BC(squared)=AC(squared)-AB(squared). Then you simply must subtract this number from the radius of the circle to find the radius of the arc (B-D).
I think that's right though it might not be the easiest way.
KJ
Using these points here, I think that the Michael Dresdner formula is right
From simple maths and the radius.jpg drawing given in post 2 to get distance AB, BD, etc..., my (literally) back of the envelope calculations give:
radius = (distance BD)/2 + (distance AB x 2) x (distance AB x 2) / (8 x distance BD)
This works accurately. I checked it on a CAD program for two different random settings. Bang on the number within their limits of error, more than accurate enough for this purpose. In any case, I'd trust the maths over the rounding in the CAD program that produced the incredibly minor discrepancy in the values (which was less than half a thou over 3 inches - not an issue unless it's a nuclear part or rocket science.)
Cheers,
eddie
Edited 2/6/2006 4:11 am by eddiefromAustralia
Hi,
check this site...you will have your anwser.
pierre
http://www.woodworkersjournal.com/ezine/images/header.gif
Your link doesn't take us to whatever you are trying to show us. I am interested in this.
Thanks,
Alan - planesaw
Hi, I mess up in my previous reply
the anwser that follows is ok and I got it form Woodworker's Ezine
pierre
Q: How do I calculate the radius of a curve that will fit a particular height and width?
Michael Dresdner: The formula is r = (c2+4h2)/(8h) where r is the radius, c is the length of the cord, (the width across the terminating ends of the curve) and h is the height from the center of the cord to the top of the curve.
Try this (filling in the knowns - rise and radius):
Gary
gwwoodworking.com
I would like to build an island countertop approx. 3ft. x 5ft. wood African mahogany
2.75" wide strips x1.5"thick can you give me advice on how you would build it, and what is the proper way to finish it?
Woodenhead,
I'd probably edge join the mahogany with a double row of biscuits and Titebond II or III glue. If available, I'd use vertical grain mahogany, for stability. And finishing depends on where it goes, how you use it, and what you want it to look like. I don't know if African mahogany or Khaya is food safe, so I'd look into that before considering a typical butcher block oil finish. If it'll be subjected to water, then an appropriate oil base finish will be a must. If it'll reside outside, then I'd coat it with a high quality marine varnish.
Say, wasn't this thread about math - figuring out the length of a circle's chord when Loucarabasi knew the radius and rise? Unless no one here has MS Excel, I can't understand why no one tried my spreadsheet to come up with the answer. Did I need to put in more directions for its use? Gary
gwwoodworking.com
Hi Gary, thanks you for your professional advice, you do beautiful work. I love wooden boats and i also love the Great state of Maine. visit http://homepage.mac.com/walterc530
Woodenhead,
You're welcome, and thanks for the compliments - I don't deserve them. Are you a carver? Have you been to that Long Island School? While editing FWW, I visited Ian Agrell, who's now in the Bay Area - see him at http://www.agrellcarving.com/school/ian/.Gary
gwwoodworking.com
Hi Gary , Yes i am a woodcarver and that is my school. My associate is a professional carver from Ukraine where he trained in all aspects of classical woodcarving, his name is Ruslan .We hope to introduce other aspects woodworking in to our program.
If you'll tell me the two distances, I'll send you a drawing with the arc radius. I just draw it up in AutoCad and use the properties function to tell me the radius.
Dave, I'll get the numbers today for you,
-Lou
To add to the list of tips and methods, here's a couple more.
I don't have a handy sketch to upload for this second method, but to find the radius draw a circle and then draw two chords anywhere on diferent parts of the circumference. Find the centre point of the two chords between where they touch the circle circumference. Then erect a perpendicular from the centre of each chord towards the middle of the circle. Where these perpendiculars intersect is the circle centre.
The more chords you put in the more you can verify that you've found the centre, but if your drawing is accurate just two chords will do it. Slainte.
Richard Jones Furniture
Hi Richard,
I've just put together a training drawing for my yr10 class on exactly this method.
I'll scan it over the next couple of days and put it up so you've got the resource if you need it again.
Cheers,
eddie
Ed, any way of just plugging in the numbers on a construction master calculater?
Thanx, Lou
Hi Lou,
The maths can be done on any calculator.
I was referring to the graphical solution that Richard referred to as the training drawing. - When I get the chance, I'll scan and put up the training drawing.
Cheers,
eddie
thanks mate,
-Lou
Is it a bit like this Eddie?
View Image
And my first image with a formula attached was this one.
Ed, you can do the sums (if you really have to) with a piece of pencil and paper so long as you don't use those silly bloody inches and fractions for doing the job, ha, ha, although you could even work it out using those. An ordinary calculator will do the numbers easy enough if you switch to decimal inches. Slainte.
View ImageRichard Jones Furniture
HI Richard,
I'd say that most probably, we've drawn the same thing - the images didn't work but, broken links on the screen. If you email them to me I'll put them up for you.
Cheers,
eddie(who's hoping that the new updated website fixes this problem for you)
It's this one Eddie. I thought I'd got the linking thing sorted from my imgae hosting site, but apparently not. Slainte.
Richard Jones Furniture
Maybe this will be of some help.
http://ca.geocities.com/web_sketches/circle_calculators/circle_radii/circle_radii.html
You can also find the radius with just a compass and straightedge. Set the compass to some nominal radius and strike an arc from each point where the chord intersects the circle, to both sides of the point. Connect the points where your new arcs intersect the circle with the straightedge and find the perpendicular. Extend the perpendiculars and you will find the circle's radius at the point where the perpendiculars intersect.
A formula was published in Woodwork Mag. Oct. 04.
s= the span of the arc, h= height of the center point of the arc.
s squared divided by 8h, that added to h divided by 2.
Tom
Heres the deal guys, Finding radius for dummys. Lets pretend I'm 8 yrs old. How would you explain this to me. Just tell me what measurments to take and how to punch the numbers in and what order. head injury left my memory a little off, I tend to struggle with some things, sorry
LMC
I thought I'd already put up a formula that is quite easy to work through without a scientific calculator here, http://forums.taunton.com/fw-knots/messages?msg=33840.10
You just need to break the formula into four simple sums and note the results before putting the final division calculation through.
For instance (A/2) ² (the first part of the formula) can be done thus if A = 84. 84/2 = 42 X 42 = 1764.
If B has a rise 30 then 30² is entered 30 X 30 = 900.
Add 1764 and 900 = 2664-- (you can use the M+ function on the calculator to add the result of the first two sums.)
The divider is 2B. Enter 30 X 2 = 60.
The final sum is 2664/60 = 44.4, the radius.
Er, and don't use fractions. Use metric or decimal inches. Slainte.Richard Jones Furniture
Lou,
I'm working at home today - give me the length of the chord (distance between both points of contact with the circle) and the height.
I'll do the calc and give you the radius.
Best regards,
eddie
okay - if you're using a construction master calculator the sequence is easy- I just had to show one of my project managers today....
Assuming your drawing had a straight line that was 32" long, and was 2" high at the centre...
the height of the triangle (2") is the RISE; half of the horizontal line (16") is the RUN.
press PITCH (7.125016deg)
with me so far? Okay then multiply that number X 2 (14.25003) press PITCH (degree sign should show up and says PITCH)
then use 16" as the RISE, and press DIAG (65inches)
That's your Radius. If I could post a picture I'd show you how it works, but that is how it works.
In essence- the angle from one end of the chord to the radius passing through the centreline of the chord is 2x the angle from the end of the chord to the top of the rise of the bisecting radius. Always. Works like crap on paper, but works like a charm with a Construction Master calculator that does rise/run calculations. Otherwise you need to go with SINE/COS/TAN calculations.
The older I get, the better I was....
Edited 2/8/2006 9:19 pm ET by papanick
lou
I see you have been given much good advice already. I find the easy way for me is this formula: 1/2 the chord squared plus the rise squared divided by 2 times the rise = radius. No fancy sines, tangents, square roots etc. just plain multiplication and division. Can be done even with a graphite filled calculator. ;o)
Example; Chord (distance from side to side of arc) is 30" so 1/2 of 30 = 15. 15 times 15 (1/2 chord squared) = 225. Rise (height of arc) is 8" so 8 x 8 (rise squared) = 64. 225 plus 64 = 289. 289 divided by 16 (two times the rise) = 18.0625 (18 and a sixteenth inch) is the radius.
This is the same formula given in some of the other posts but I hope this puts it in simpler language. I double checked these numbers with autocad just to make sure my memory wasn't playing tricks. Just plug in your own numbers and you should have an accurate answer.
RichThe Professional Termite
Before I posted to this, I wanted to check to see if anyone had the answer.
To all: Tom is right. This is the correct formula. Of course, mathematically speaking, there are several ways to skin this cat, but this formula gets the accurate result.
Jeff
I was never good a Math so I'd put a nail someplace and get some good string and 'see'.. Move the nail till it fits!
Sorry I had to.. Use to do that making replacements for OLD doors... In OLD houses...
EDIT:
I just saw Richards post!
For instance (A/2) ² (the first part of the formula) can be done thus if A = 84. 84/2 = 42 X 42 = 1764. If B has a rise 30 then 30² is entered 30 X 30 = 900. Add 1764 and 900 = 2664-- (you can use the M+ function on the calculator to add the result of the first two sums.) The divider is 2B. Enter 30 X 2 = 60. The final sum is 2664/60 = 44.4, the radius.
Rick.. You my old math teacher? I liked ya but NEVER understood ya!
Edited 2/8/2006 8:14 pm by WillGeorge
Or you could just draw it in a CAD program and let the computer figure it out.
Trevor
I think the point was that he didn't have access to AutoCad (or any other Cad), except maybe for NapkinCad or the infamous 2x6OnJobSiteCad.
Mind you- with all the helpful people here you really just need to post the question and the dimensions; within 5 minutes everyone will give you the answer!
The older I get, the better I was....
Check out this website. http://mathforum.org/dr.math/faq/faq.formulas.html
You should be able to find whatever formula your looking for.
This might be a bit easier than trying to type out all of the con and sin signs
http://www.flextrim.com/radcalc.asp
Just type in the width of the radius you're trying to achieve and the height of the chord.
Here is another site.
http://www.woodweb.com/knowledge_base/Radius_of_Convex_Wall.html
Woodwrkr,
Fantastic. I have been waiting throughout this discussion for someone to link us to the "right" spots.
Thanks,
Alan - planesaw
No problem Alan.
I have found it to be useful myself.
I thought about helping out others by posting how to figure the tallest cabinet you can put into a room knowing either the width, depth, both, and tip it up so it doesn't hit the ceiling. It took me a long time to figure it out and at about 3 in the morning I finally got it.
Interested? You can do it all by calculator in about 3 mins or less.
Sure. But isn't it the longest diagonal of the piece, depending on which way you want to tilt it?
Alan - planesaw
Yes, but there is a mathmatical way of figuring it out without laying it out on a board.
Lets say you have a ceiling height of 96". You want the bookcases to go to the ceiling and make them as tall as possible without hitting the ceiling when you tip them up.
By doing this math, it will tell you the minimum size molding you can put on top of your cabinet without reducing the height to acccept a bigger crown, etc.
It's the same thing as the A^+ B^ = C^ ^= Squared
But to do this, you have to do it in the reverse.
C^-B^= A^
C= Ceiling height you have
B= the smaller of the two dimensions, either your width or depth. "Go with whichever one can't change or is more important that it doesn't change.
A= the tallest cabinet you can put into that room with it just scraping the ceiling. "This figuring we live in a perfect world and every wall and ceiling and floor are perfect, so keep that in mind.
C= 96 so you take 96x96= 9216
B= 12 so you take 12x12= 144
A= 9216-144= 9072
Now to find the cross dimension or in other words the tallest cabinet you can make for that height ceiling, now hit the square rt button and you'll get
95.247047198325261258058167131013 or 95.24" or close enough to 95-1/4"
This also works well when buying furniture from a store. I have found it to work well when you're putting one cabinet into a niche that lets say is only 4' wide and you want to know how wide you can make the cabinet so it can turn and not hit the side walls. Obviously you could make the cabinet in two pieces and be fine, but if it needs to be one piece, it will work well.
Hope this helps.
Edited 3/5/2006 3:24 pm ET by Woodwrkr
Edited 3/5/2006 3:25 pm ET by Woodwrkr
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