This is really the only thing in carpentry that has given me an as yet to solve problem. How does one make a tangent scroll based on a hyperbolic spiral ? An equal angular or logrythmic spiral is easy to lay out. I’m fairly certain a center line through the scroll should meet at its apex at the same level as the handrail would be at that point from a side perspective. Now if only I could lay out a hyperbolic spiral to try it out. Why hyperbolic you ask ? It’s more gradual than an equal angular and would be easer to mate to an inside radius of a handrail. It also looks more elegant. I sure wish I knew how to use this computer so I could draw a picture and send it along
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It's only satisfying if you eat it.
What is the relationship of the tangents to one another?[email protected]
It's Never Too Late To Become What You Might Have Been
The rectangles have the length to width ratios of (1+51/2)/2--------------------------
It's only satisfying if you eat it.
PS.
I don't pretend to be master carpenter. Logarithms are basically useless in the field because there are too many variables.
I just happen to remember most things I've read, and where to find them on the internet.
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It's only satisfying if you eat it.
Edited 2/6/2006 7:16 pm ET by dustinf
Impressive yes! But not a Jedi yet.<g>
I just happen to remember most things I've read, and where to find them on the internet.
figures............;)[email protected]
It's Never Too Late To Become What You Might Have Been
I really need a lesson in math but it looks like the golden rule to me.
It is the golden rule.--------------------------
It's only satisfying if you eat it.
If I understand the question correctly I believe you've got it. The way you lay out that spiral is to start with a square, then draw an arc, with its center point at the mid point of an edge and a radius to one of the opposite corners. (see attached)
can't be right the radius increases exponentially I need to learn how to scan pictures scan them and post them I'm new to this toy. thanks for trying
Sorry, what I was showing you was not how to lay out the spiral, but how to get the Golden Rectangle you use to lay out the spiral pattern that dustinf showed you. See how the squares in his illustration form the Golden Rectangle that grows exponentially.
Each new arc section is enlarged by making the short side of the rectangle the same length as the long side of the previous rectangle. The spiral is created by drawing a square inside that rectangle using the short side measurement and striking an arc with three corners of the square. Now you know how to create the correctly proportioned rectangle to do what he showed you - no math required.
Another alternate way to get the Golden Rectangle without math is to use your carpenter's square to draw a line at a 31.7 degree angle, then draw a rectangle of any size with that line going through its opposing corners.
If you prefer the math, the ratio you need is .61804:1. If any of that isn't clear let me know and I will try to illustrate it better with a drawing.
Ok, never mind - I just re-read your original post and see that you you already know how to handle the child's play I just tossed ya and are looking for something else entirely. I kind of default to Golden Wrecked Angle mode - sorry.
Ah well, maybe someone else can use those tricks. Let me do a little head scratching and see if I can help you with your actual question.
You expresed it geometricly. The length of each radius is equall to the sum of the previous two lengths, as an algebraic formula.1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
13+8=21
21+13=34
34+21=55it's a beautifull thing
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Piffin
Thats whats refered to as Finbonacci's number.
Doug
Thanks - I knew, but could couldn't spell it that late at night and didn't have the energy to walk across the room to the bookcase.;)
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
Good example but you don't actually get to the Golden Ratio until you get several rabbit escapades into that sequence.
The Fibo-na-zi rabitt romp scenario is not so much the foundation of the Golden Ratio as it is another one of the billions of places it just sort of magically appears.
Shhhhh....Don't let the rabbit out of the hat!LOL
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
Sorry but thats an equalangular AKA logrythmic AKA pertaining to the golden rule. A hyperbolic spiral does not start in the centre withh an exponentially increasing angle from a centre. That allows you match the radius of the handrail withuot getting disy and making a massive scroll AKA going around to many times
That curve is derived from math developed by the Italian mathematician Fibonacci, and is seen in conch and nautilus shells, and a lot of other stuff from the sea.
Here is a cool site re Fibonacci numbers, with great graphics.
http://www.textism.com/bucket/fib.html
read the Golden Ratio by Mario Livio. Makes one realize the Universe is really a cool place to hang out in.
Dustin's sketch looks a little like an involute.
Don't know if this response is helpful in any way, but nobody has mentioned an involute, so I thought I'd chime in.
And I know pretty much nothing about building stairs like that.
Good luck.Pete Duffy, Handyman
This is strange I know I heard the term in math before but I cant find it in the dictionary,a book math from the beginning of numbers,or a book on algebra. Wait let me check volute. Right direction. A spiral or twisting form. Now get me from a 6 foot inside radius to a near centre with the surface of the scroll tangent to the centre
An involute is basically the path the point of a string would make as it's unwound from a cylinder.
That's about all I know about it. To apply it to stairs, well, good luck.
Sorry I'm not much help.
Pete Duffy, Handyman
Guess I'm no master (but I already knew that).
I guess I'll be watching this one for someone who speaks low level to translate for me.
I hope someone can help you with whatever the hell you're talking about.
Remodeling Contractor just on the other side of the Glass City
Check into a book by Dichristoforo ( sp?) "guide to stairs and tangential stair building" I have it buried somewhere around here, and am not sure of the exact title or spelling..but that'll get ya googleing close enough.
Spheramid Enterprises Architectural Woodworks
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This is what your talking about
http://www.woodworkerslibrary.com/search.php?substring=A+Simplified+Guide+to+Custom+Stairbuildi
Great book!
That's it THANKS. I haven't opened it in yrs. a VERY DEEP read.
Spheramid Enterprises Architectural Woodworks
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Thanks for the info. Think Ive seen it before. If I'm correct there wasn't the info on scrolls I needed. Some day it will all be clear to me then I will be master carpenter garybuilt mathematically enlightened one.
Ask Stan Foster.
[email protected]
It's Never Too Late To Become What You Might Have Been
On a re-read I think what you are looking for in layman's terms is how to lay out an Ionic volute. Here is a link to the method used by Vitruvius in his "Ten Books on Architecture."
http://www.nexusjournal.com/AndGal.html
Is that what you needed?
Vitruvius book III chapter V The Ionic Order. I think that may be hyperbolic but I'm not sure how he obtained it. I have the book on hand with illustrations. The Greek scrolls have parallel sides and don't look as elegant. go to http://-history.mcs.st-andrews.ac.uk/history/Curves/Hyperbolic.html problem is how to lay out. I even have the formula but no idea how to apply it
Yup - Pages 91-93 to be specific, at least in my copy.
I got a "page cannot be displayed" error on your link.
try just lookin up spirals. That info was from a sight from years ago the last time there was a computer in the house hold
I don't remember how to get the original circle but I've laid out similar progressive spirals by wrapping a string with pencil around a plywood circle and draw as you unwrap. I did some shingle patterns on restaurant walls back in the 70's. Not sure if that's what you're after........
Norse
That sounds more like an equal angular spiral (think counch shell). I'll dry to draw in your mind a hyperbola. Imagine a commet on its last odyssey. It comes in towards the sun on its elicitical path but this time the sun gravitational pull due to its nearness is going to spell doom. The commet makes it about 3/4 around the sun before making contact with the surface. Velocity verses gravity. Where the heck is Newton when ya need him? No wait you didn't start in the centre maybe it is a hyperbola but I want something that looks like the above. Thanks for trying.