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Michael Baglio
 
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Default Math help please, computing an arc and radius.

I'm trying to put a _very_ subtle curve on the bottom of some table
aprons. I've placed some nails in the apron templates at the
appropriate points and used a piece of 1/8th" thick wood to try to
draw a fair curve but, (whether I drink to much coffee or I'm just not
good at drawing), I'm not liking the resulting lines, so I'm hoping
I'll get more perfect results by using a (_very_) long trammel arm on
my router to do this.


The height of each arc will be 1/4" above the baseline of each apron.
The center point of the long aprons is 25-3/8ths from each end, and
for the short aprons the center is 9". Like I said, these are going
to be very subtle curves, but visually important and I want them
perfect. ;


How would I compute the radii of the circles I would need to give me
the arcs for each apron?

(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)

Michael "Shakey" Baglio
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Todd Fatheree
 
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"Michael Baglio" wrote in message
...
I'm trying to put a _very_ subtle curve on the bottom of some table
aprons. I've placed some nails in the apron templates at the
appropriate points and used a piece of 1/8th" thick wood to try to
draw a fair curve but, (whether I drink to much coffee or I'm just not
good at drawing), I'm not liking the resulting lines, so I'm hoping
I'll get more perfect results by using a (_very_) long trammel arm on
my router to do this.


The height of each arc will be 1/4" above the baseline of each apron.
The center point of the long aprons is 25-3/8ths from each end, and
for the short aprons the center is 9". Like I said, these are going
to be very subtle curves, but visually important and I want them
perfect. ;


How would I compute the radii of the circles I would need to give me
the arcs for each apron?

(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)

Michael "Shakey" Baglio


Assuming that the endpoints of the arcs are the ends of the aprons, you're
going to need a very long trammel, especially on the long ends. The radius
works out to about 100 ft. I'm sure I could calcuate it myself with enough
time, but that's why God invented AutoCAD. I've always had pretty good
results doing it the way you're doing by bending a strip of wood, so I'm not
sure I understand the problems you're having. With the small amount of
curvature, the difference between an arc of a circle vs. some other order
polynomial curve should be nearly insignificant and difficult if not
impossible to see by eye. Good luck finding something that works for you.

todd


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DJ Delorie
 
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Michael Baglio writes:
How would I compute the radii of the circles I would need to give me
the arcs for each apron?


http://www.delorie.com/wood/chord-radius.html

(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)


http://www.delorie.com/wood/camber.html
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Dan White
 
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"Michael Baglio" wrote in message
...

The height of each arc will be 1/4" above the baseline of each apron.
The center point of the long aprons is 25-3/8ths from each end, and
for the short aprons the center is 9". Like I said, these are going
to be very subtle curves, but visually important and I want them
perfect. ;


How would I compute the radii of the circles I would need to give me
the arcs for each apron?

This shows it mathematically (first equation, second diagram)
http://www.sli.unimelb.edu.au/planes...p12-04-06.html

The square of the distance from the center point to the end equals the
height of your arc times the rest of the diameter of the circle, or
(25.375)^2 = .25 x L. L is 2575.6 inches, which makes a diameter of 2575.8
inches and a radius of 107 feet!

dwhite



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Bill Rogers
 
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On Sun, 26 Sep 2004 13:48:59 GMT, Michael Baglio
wrote:

1. The math is done already by others. Your eyes will not be good
enough to see small differences over that distance, so forget
"perfect". I gave a method some time back for calculating heights to
the arc at various distances, but it was questioned as to the
usefulness. [I used to teach math, and was *very* good at it, so I
just ignored replies.]

2. Having calculated, and drawn, how will you cut it? You clearly
won't use a radius that large, so a router guide is out. I'd suggest
hand-planing down to near the line for the larger difference from
square, then sanding to the line.

Bill.

I'm trying to put a _very_ subtle curve on the bottom of some table
aprons.


The height of each arc will be 1/4" above the baseline of each apron.
The center point of the long aprons is 25-3/8ths from each end, and
for the short aprons the center is 9". Like I said, these are going
to be very subtle curves, but visually important and I want them
perfect. ;


How would I compute the radii of the circles I would need to give me
the arcs for each apron?

(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)

Michael "Shakey" Baglio




  #6   Report Post  
Tom Watson
 
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On Sun, 26 Sep 2004 13:48:59 GMT, Michael Baglio
wrote:

I'm trying to put a _very_ subtle curve on the bottom of some table
aprons. I've placed some nails in the apron templates at the
appropriate points and used a piece of 1/8th" thick wood to try to
draw a fair curve but, (whether I drink to much coffee or I'm just not
good at drawing), I'm not liking the resulting lines, so I'm hoping
I'll get more perfect results by using a (_very_) long trammel arm on
my router to do this.


The height of each arc will be 1/4" above the baseline of each apron.
The center point of the long aprons is 25-3/8ths from each end, and
for the short aprons the center is 9". Like I said, these are going
to be very subtle curves, but visually important and I want them
perfect. ;


How would I compute the radii of the circles I would need to give me
the arcs for each apron?

(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)

Michael "Shakey" Baglio



The fairing strip is the right idea, Mike but it needs to be thicker.
An eighth inch strip will kink at points where the grain rises to the
face.

Half inch ply or MDF works better but half inch solid stock can be
used if it is straight grained and quartersawn.

I would use this to describe the line and make a pencil line on the
template material, by clamping the straight piece onto the material
and clamping it with moderate pressure at the two outside points.
Then I would take a block and clamp it behind the center point of the
fairing strip.

Tap the block towards the strip until the curve looks good to your
eye. Although math is useful in cabinetmaking, the eye rules.

When you've struck a pencil line on your fair curve you should rough
cut the line to within an eighth inch or so of the finished line.
Then move your fairing strip back the distance that is described from
your router base to the edge of your trimming bit, trying to maintain
a measured distance from the faired curve at all points.

Now block your fairing strip at enough points that it can resist the
force of your pushing the router base against it to trim to the pencil
line. I use hotmelt glue but you could just pin it or screw it.

At this point you should have a template that can be used on multiple
pieces.

I have to say that I only use this method when I have to make a lot of
repetitive pieces. If I was only doing a few I would use the firing
strip to describe the line, cut close to the line, and clean it up
with any of a number of techniques/tools.


Regards,
Tom.

"People funny. Life a funny thing." Sonny Liston

Thomas J.Watson - Cabinetmaker (ret.)
tjwatson1ATcomcastDOTnet (real email)
http://home.comcast.net/~tjwatson1
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Tom Watson
 
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On Sun, 26 Sep 2004 16:23:22 -0400, Tom Watson
wrote:

Mostly a lot of confusing nonsense.

Mike:

I did such a bad job of describing it that I took some pix of the idea
and posted them on ABPW.

These in conjunction with my babbling should give you a sense of this.



Regards,
Tom.

"People funny. Life a funny thing." Sonny Liston

Thomas J.Watson - Cabinetmaker (ret.)
tjwatson1ATcomcastDOTnet (real email)
http://home.comcast.net/~tjwatson1
  #8   Report Post  
Michael Baglio
 
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On Sun, 26 Sep 2004 17:48:08 -0400, Tom Watson
wrote:
Mike:
I did such a bad job of describing it...


Uh-oh. I understood it immediately. ;

... that I took some pix of the idea
and posted them on ABPW.
These in conjunction with my babbling should give you a sense of this.


Yep. Got it.

Tom, Bill, Dan, Todd, et al., I want to thank you all for helping me
get through one of my "how could I be that dumb" days.

In the end, it was the strip of wood I was using that was too thin, so
Tom's suggestion of using a thicker piece of hardwood was spot on. (I
should be ashamed to admit this but, wtf, what I was using for a
"fairing strip" was a narrow piece of cheap-o HD 3/16ths (?) ply.
Maybe about the thickness of a couple of door skins. It _doesn't_
make a good fairing strip.)

Now, having said all that, I gotta tell ya that what I was mostly
thinking about all day as I was using the improved Watson-esque
fairing strip was...

....tying one end of a 107-foot piece of monofilament line to the
handle of my router and the other end to the truck antenna and backing
it up far enough to make the world's first "DeWalt-Tacoma Trammel from
Hell".

You can't imagine how much I'm just _dying_ to try that.

Thanks again, everyone.

Michael "Hey Alice! Watch THIS!!!" Baglio
  #9   Report Post  
Tom Watson
 
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On Mon, 27 Sep 2004 00:03:20 GMT, Michael Baglio
wrote:

...tying one end of a 107-foot piece of monofilament line to the
handle of my router and the other end to the truck antenna and backing
it up far enough to make the world's first "DeWalt-Tacoma Trammel from
Hell".

You can't imagine how much I'm just _dying_ to try that.


Damn Bubba, you go with that thought.

I want pix.




Regards,
Tom.

"People funny. Life a funny thing." Sonny Liston

Thomas J.Watson - Cabinetmaker (ret.)
tjwatson1ATcomcastDOTnet (real email)
http://home.comcast.net/~tjwatson1
  #10   Report Post  
Tom Watson
 
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On Sun, 26 Sep 2004 20:46:27 -0400, Tom Watson
wrote:

Damn Bubba, you go with that thought.


Uh, I meant "Damn, Bubba"

I didn't mean you was a "Damn Bubba".

I project manage a company that is out of NC and I wouldn't want them
to get the wrong impression.

They might fire me and make me get a real job again.


Regards,
Tom.

"People funny. Life a funny thing." Sonny Liston

Thomas J.Watson - Cabinetmaker (ret.)
tjwatson1ATcomcastDOTnet (real email)
http://home.comcast.net/~tjwatson1


  #11   Report Post  
Larry Jaques
 
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On Sun, 26 Sep 2004 20:46:27 -0400, Tom Watson
calmly ranted:

On Mon, 27 Sep 2004 00:03:20 GMT, Michael Baglio
wrote:

...tying one end of a 107-foot piece of monofilament line to the
handle of my router and the other end to the truck antenna and backing
it up far enough to make the world's first "DeWalt-Tacoma Trammel from
Hell".

You can't imagine how much I'm just _dying_ to try that.

Damn Bubba, you go with that thought.

I want pix.


Now just watch. Charlie "never the easy way" B. will
have done one 248' 11-29/64" by tomorrow night.

Yup, just watch.


----------------------------------------------------------------------
* Scattered Showers My Ass! * Insightful Advertising Copy
* --Noah * http://www.diversify.com
----------------------------------------------------------------------

  #12   Report Post  
Michael Baglio
 
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On Sun, 26 Sep 2004 21:37:24 -0700, Larry Jaques
wrote:

On Sun, 26 Sep 2004 20:46:27 -0400, Tom Watson
calmly ranted:

On Mon, 27 Sep 2004 00:03:20 GMT, Michael Baglio
wrote:

...tying one end of a 107-foot piece of monofilament line to the
handle of my router and the other end to the truck antenna and backing
it up far enough to make the world's first "DeWalt-Tacoma Trammel from
Hell".

You can't imagine how much I'm just _dying_ to try that.

Damn Bubba, you go with that thought.

I want pix.


Now just watch. Charlie "never the easy way" B. will
have done one 248' 11-29/64" by tomorrow night.

Yup, just watch.


Nah, he's probably busy hand-cutting the 700th dovetail for his
workbench drawers. ; Btw, I re-thought that whole
attach-the-fishing-line-to-the-pickup's-antenna-router-trammel thingy.
The fun kinda went out of it when I realized that Plamman probably
_has_ a hundred-foot trammel.

M--


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Jeff Gorman
 
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"Tom Watson" wrote

: The fairing strip is the right idea, Mike but it needs to be thicker.
: An eighth inch strip will kink at points where the grain rises to the
: face.

A tip for a really subtle curve, ie non-circular, is to taper the fairing
strip or reduce the thickness towards its centre.

Jeff G
--
Jeff Gorman, West Yorkshire, UK
Email: username is amgron
ISP is clara.co.uk
www.amgron.clara.net


  #14   Report Post  
Tom Watson
 
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On Mon, 27 Sep 2004 05:18:49 GMT, Michael Baglio
wrote:

The fun kinda went out of it when I realized that Plamman probably
_has_ a hundred-foot trammel.




:- :-0 :-o :-)




Regards,
Tom.

"People funny. Life a funny thing." Sonny Liston

Thomas J.Watson - Cabinetmaker (ret.)
tjwatson1ATcomcastDOTnet (real email)
http://home.comcast.net/~tjwatson1
  #15   Report Post  
Pat Barber
 
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Now you know why PC brought out that funky battery
powered router. Time to head to the deserted K-Mart
parking lot and get out the mono...

Michael Baglio wrote:

...tying one end of a 107-foot piece of monofilament line to the
handle of my router and the other end to the truck antenna and backing
it up far enough to make the world's first "DeWalt-Tacoma Trammel from
Hell".

You can't imagine how much I'm just _dying_ to try that.




  #16   Report Post  
Hylourgos
 
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Michael Baglio wrote in message . ..
snip
(Alternatively, is there another method that doesn't rely on how
steady my drawing hand is in order to do this?)

Michael "Shakey" Baglio


Hi Michael,

(I may be way off here--I'm not sure I know exactly what you're asking
or if I can accurately describe another suggestion after the
suggestions of so many others who know far more than I ever will, but
with those caveats projected...)

How about using that monofilament in a different way: connect it in
two places at the ends of your piece (the one you want to make into an
arc).

Since this is a table apron, you might measure equal distances from
the table to get consistent ends (of the arc).

Now mark the center of the apron, and run the monofilament across the
two end points so there's just enough slack to reach the edge of the
apron at the centerpoint.

[or put another way: take the slack out of the monofilament until you
reach the apron centerpoint mark.]

Now run a pencil along the monofilament. Shold produce a nice gentle
arc.

Step back and look at the arc to see if it looks right.

Cut.

Am I anywhere in the ballpark?
H
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Australopithecus scobis
 
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On Mon, 27 Sep 2004 12:57:02 -0700, Hylourgos wrote:

Now run a pencil along the monofilament. Shold produce a nice gentle
arc.


Nice idea. Ran to the shop and tried it, coupla nails & scrap. You don't
get repeatability with this; have to draw one apron piece and cut both
together. Had a spool of 10# laying around the shop; heavier might resist
the pencil better. The stuff stretches (the whole point), and how hard you
push against it changes the curve.

Definitely a technique for the eyeball-it folks. The analytical types
might want to stick to the other methods.

--
"Keep your ass behind you"

  #19   Report Post  
Bill Rogers
 
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On Mon, 27 Sep 2004 21:18:41 GMT, Michael Baglio
wrote:

Now run a pencil along the monofilament. Shold produce a nice gentle
arc.
Step back and look at the arc to see if it looks right.
Cut.
Am I anywhere in the ballpark?


I think that would produce section of an ellipse, rather than an arc
section of a (very large) circle, yes?


Yes, but you won't see the difference in this case. The "ellipsicity"
is so close to a circle that it's negligible.

Bill.

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Hylourgos
 
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Australopithecus scobis wrote in message ie...
On Mon, 27 Sep 2004 12:57:02 -0700, Hylourgos wrote:

Now run a pencil along the monofilament. Shold produce a nice gentle
arc.


Nice idea. Ran to the shop and tried it, coupla nails & scrap. You don't
get repeatability with this; have to draw one apron piece and cut both
together.


Well, you *could* make a template out of some thin material (e.g.,
hardboard) onto which you mount the mono.

Had a spool of 10# laying around the shop; heavier might resist
the pencil better. The stuff stretches (the whole point), and how hard you
push against it changes the curve.


Yea, I used mono above to continue the mono suggestion. But if I were
to do this I'd use thin wire cable--you could still use the fishing
wire, to keep that theme going....

Definitely a technique for the eyeball-it folks. The analytical types
might want to stick to the other methods.


It's no less analytical than using a jillion-foot circumference jig,
it just makes an elipsis rather than a circle (which, at this size, I
doubt the human eye could detect). Both methods are equally
geometrical, but one is distinctly easier than the other.

Archemideianly yours,
H


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