I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

On 4/15/2013 9:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

http://www.mathopenref.com/arcradius.html

On 4/15/2013 9:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

http://www.handymath.com/cgi-bin/rad2.cgi?submit=Entry

http://www.ehow.com/how_7846775_radius-arc.html

http://mathcentral.uregina.ca/QQ/dat...leberger1.html

http://www.woodweb.com/knowledge_bas...of_an_arc.html

On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry




R=226" according to Sketchup.

On 4/15/2013 11:38 AM, Leon wrote:
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry




R=226" according to Sketchup.

Trigonometry concurs.

http://www.flickr.com/photos/gdguari...ream/lightbox/

Thanks to the O.P. for a pleasant lunchtime puzzle.

On 4/15/2013 1:41 PM, Greg Guarino wrote:
On 4/15/2013 11:38 AM, Leon wrote:
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry




R=226" according to Sketchup.

Trigonometry concurs.

http://www.flickr.com/photos/gdguari...ream/lightbox/

Thanks to the O.P. for a pleasant lunchtime puzzle.

It was more fun to try to work it out for myself, but I just looked it
up and there is (of course) a more direct way to find it.

Radius = H/2 + W^2/8H

Where H = the height of the arc (2")
and W= the width of the base (60")

In our example that's:

2/2 + 60^2/8(2)= 1 + 3600/16 = 1 + 225 = 226

Greg Guarino wrote:
On 4/15/2013 11:38 AM, Leon wrote:
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry




R=226" according to Sketchup.

Trigonometry concurs.

http://www.flickr.com/photos/gdguari...ream/lightbox/


Thanks to the O.P. for a pleasant lunchtime puzzle.


Greg, We both drew the same picture. How much math background do you
have (if you don't mind me asking)?

Bill

On 4/15/2013 3:26 PM, Bill wrote:
Greg Guarino wrote:
On 4/15/2013 11:38 AM, Leon wrote:
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry




R=226" according to Sketchup.

Trigonometry concurs.

http://www.flickr.com/photos/gdguari...ream/lightbox/


Thanks to the O.P. for a pleasant lunchtime puzzle.


Greg, We both drew the same picture. How much math background do you
have (if you don't mind me asking)?

Bill

Nothing too advanced. Algebra, geometry and trig in high school, a
little calculus in college. That would all have been in the '70s.

"Greg Guarino" wrote in message ...

On 4/15/2013 3:26 PM, Bill wrote:

Greg, We both drew the same picture. How much math background do you
have (if you don't mind me asking)?

Bill

Nothing too advanced. Algebra, geometry and trig in high school, a
little calculus in college. That would all have been in the '70s.

Here's where my kids would ask "1870s or 1970s?" ;~)

John
....of about the same vintage

"Leon" wrote in message
news
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are
5 feet apart and the depth of the arc at the center point is 2 inches.
What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial
and error, oui?

Larry




R=226" according to Sketchup.
================================================== =========================
My calculator says that your program is right.

On 4/16/2013 7:57 PM, CW wrote:


"Leon" wrote in message
news
On 4/15/2013 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry




R=226" according to Sketchup.
================================================== =========================
My calculator says that your program is right.


I'm glad you were able to verify the accuracy of your calculator. ;~)

On 4/15/13 10:14 AM, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Larry


According to those cool calculators, 18'10".


--

-MIKE-

"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com

---remove "DOT" ^^^^ to reply

Hah! Now all I need to do is figure out how to draw an arc with an 18 foot radius :-) I have a couple of ideas and will post pix of the process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to trial and error, oui?



Larry

On Mon, 15 Apr 2013 09:10:54 -0700, Gramp's shop wrote:

Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

Bend a piece of thin cutoff around the points?

--
When fascism comes to America, it will be wrapped in the flag and
carrying a cross.

On 4/15/2013 12:43 PM, Larry Blanchard wrote:
On Mon, 15 Apr 2013 09:10:54 -0700, Gramp's shop wrote:

Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

Bend a piece of thin cutoff around the points?

My sense of the physics involved tells me that that method will not
produce an arc of a circle. Will it matter? Might the resultant curve be
subtly nicer than a circular arc? That's up to the designer.

My plan exactly, Larry. I'm going to start with drilling screws into the waste side of the end points and the top of the arc, attach a thin strip of one-by with spring clamps and then add a couple of screws/clamps along the arc.

The other Larry

On Monday, April 15, 2013 11:43:27 AM UTC-5, Larry Blanchard wrote:
On Mon, 15 Apr 2013 09:10:54 -0700, Gramp's shop wrote:



Hah! Now all I need to do is figure out how to draw an arc with an 18

foot radius :-) I have a couple of ideas and will post pix of the

process.



Bend a piece of thin cutoff around the points?



--

When fascism comes to America, it will be wrapped in the flag and

carrying a cross.

"Larry Blanchard" wrote in message ...

On Mon, 15 Apr 2013 09:10:54 -0700, Gramp's shop wrote:

Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

Bend a piece of thin cutoff around the points?

+1

On 4/15/2013 11:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18 foot radius :-) I have a couple of ideas and will post pix of the process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to trial and error, oui?



Larry


!8' string with a pencil died around one end. Nail in the ground on the
other end.

Or use sketchup to print out a template.

On 4/15/2013 12:20 PM, Leon wrote:
On 4/15/2013 11:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to
trial and error, oui?



Larry


!8' string with a pencil died around one end. Nail in the ground on the
other end.

Or use sketchup to print out a template.



An 18 foot radius template?

On 4/15/2013 12:47 AM, Richard wrote:
On 4/15/2013 12:20 PM, Leon wrote:
On 4/15/2013 11:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to
trial and error, oui?



Larry


!8' string with a pencil died around one end. Nail in the ground on the
other end.

Or use sketchup to print out a template.



An 18 foot radius template?


Did he say wanted the full circle or the 5' arc?

Leon wrote:
On 4/15/2013 12:47 AM, Richard wrote:
On 4/15/2013 12:20 PM, Leon wrote:
On 4/15/2013 11:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to
trial and error, oui?



Larry


!8' string with a pencil died around one end. Nail in the ground on the
other end.

Or use sketchup to print out a template.



An 18 foot radius template?


Did he say wanted the full circle or the 5' arc?

He said he wanted the 5' Chord!

On 4/15/2013 8:26 PM, Leon wrote:
On 4/15/2013 12:47 AM, Richard wrote:
On 4/15/2013 12:20 PM, Leon wrote:
On 4/15/2013 11:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18
foot radius :-) I have a couple of ideas and will post pix of the
process.

On Monday, April 15, 2013 10:14:29 AM UTC-5, Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?



There ought to be an equation for this that would be far superior to
trial and error, oui?



Larry


!8' string with a pencil died around one end. Nail in the ground on the
other end.

Or use sketchup to print out a template.



An 18 foot radius template?


Did he say wanted the full circle or the 5' arc?

He really needs to make about 20 of them. To save time, he will array
the stock in a regular twenty-sided polygon, presumably on the
basketball court of the local high school. This will allow him to mark
all of the pieces in one step with a string and pencil, or if the
ceiling height is sufficient, a compass.

Subject

You math wizards are making a mountain out of a mole hill.

Give me 10 minutes and some 1/4" hard board and I'll give
you a finished template.

I left my calculus in the class room the day I graduated
more years ago than I want to admit.

This is a case where a graphical solution wins hands down.


Lew

On 4/15/2013 10:10 AM, Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an 18 foot radius :-) I have a couple of ideas and will post pix of the process.


Two lengths of PVC pipe. Drill a hole in one end, attach a pencil to
the other at 18'. Draw the arc on the ground, spiking the pivot end in
the ground and putting the wood at the pencil end.

Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an
18 foot radius :-) I have a couple of ideas and will post pix of
the process.
==========================================
"Just Wondering" wrote:

Two lengths of PVC pipe. Drill a hole in one end, attach a pencil
to the other at 18'. Draw the arc on the ground, spiking the pivot
end in the ground and putting the wood at the pencil end.
=========================================
You've obviously never done this.

Lew

Lew Hodgett wrote:
Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an
18 foot radius :-) I have a couple of ideas and will post pix of
the process.
==========================================
"Just Wondering" wrote:

Two lengths of PVC pipe. Drill a hole in one end, attach a pencil
to the other at 18'. Draw the arc on the ground, spiking the pivot
end in the ground and putting the wood at the pencil end.
=========================================
You've obviously never done this.

Lew

I couple of "trammel points" on a piece of steel pipe, along with two
humans, may work. What is your solution?

Bill (who just happens to have 40 feet of Schedule 40 black pipe)

On 4/16/2013 5:19 PM, Bill wrote:
Lew Hodgett wrote:
Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with an
18 foot radius :-) I have a couple of ideas and will post pix of
the process.
==========================================
"Just Wondering" wrote:

Two lengths of PVC pipe. Drill a hole in one end, attach a pencil
to the other at 18'. Draw the arc on the ground, spiking the pivot
end in the ground and putting the wood at the pencil end.
=========================================
You've obviously never done this.

Lew

I couple of "trammel points" on a piece of steel pipe, along with two
humans, may work. What is your solution?

Bill (who just happens to have 40 feet of Schedule 40 black pipe)




I gotta ask Bill why pipe instead of string? and for that matter I have
drilled a hole in a 25' tape measure and anchored a screw through that
hole and held a pencil at the distance desired.

Gramp's shop wrote:
Hah! Now all I need to do is figure out how to draw an arc with
an
18 foot radius :-) I have a couple of ideas and will post pix of
the process.
==========================================
"Just Wondering" wrote:

Two lengths of PVC pipe. Drill a hole in one end, attach a pencil
to the other at 18'. Draw the arc on the ground, spiking the
pivot
end in the ground and putting the wood at the pencil end.
=========================================
You've obviously never done this.

Lew
-----------------------------------------------------------------
I couple of "trammel points" on a piece of steel pipe, along with
two humans, may work. What is your solution?

Bill (who just happens to have 40 feet of Schedule 40 black pipe)

-----------------------------------------------------------------
Lew Hodgett wrote:

From a previous post.

--------------------------------------------------------------
Find a copy of Fred Bingham's book, "Practical Yacht Joinery"
at the library.

A very easy graphical solution is shown.

I laid out all the deck cambers for my boat using it.

Lew

"Gramp's shop" wrote:


I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?
--------------------------------------------------------------
Find a copy of Fred Bingham's book, "Practical Yacht Joinery"
at the library.

A very easy graphical solution is shown.

I laid out all the deck cambers for my boat using it.

Lew

"Gramp's shop" wrote in news:384921f5-292d-40cc-9e3e-
:

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the
depth of the arc at the center point is 2 inches. What is the radius of the circle?

224 inches

There ought to be an equation for this that would be far superior to trial and error, oui?

There is.

radius squared = (radius minus height) squared + (half the distance between endpoints)
squared

In this case:

r^2 = (r - 2)^2 + 30^2
r^2 = r^2 -4r +4 + 900
4r = 904
r = 226

On 04/15/2013 01:47 PM, Doug Miller wrote:
"Gramp's shop" wrote in news:384921f5-292d-40cc-9e3e-
:

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the
depth of the arc at the center point is 2 inches. What is the radius of the circle?

224 inches

There ought to be an equation for this that would be far superior to trial and error, oui?

There is.

radius squared = (radius minus height) squared + (half the distance between endpoints)
squared

In this case:

r^2 = (r - 2)^2 + 30^2
r^2 = r^2 -4r +4 + 900
4r = 904
r = 226



Now we know how long a piece of string is!

On 4/15/2013 2:47 PM, Doug Miller wrote:
"Gramp's shop" wrote in news:384921f5-292d-40cc-9e3e-
:

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the
depth of the arc at the center point is 2 inches. What is the radius of the circle?

224 inches

There ought to be an equation for this that would be far superior to trial and error, oui?

There is.

radius squared = (radius minus height) squared + (half the distance between endpoints)
squared

In this case:

r^2 = (r - 2)^2 + 30^2
r^2 = r^2 -4r +4 + 900
4r = 904
r = 226

I just drew that out. Clever. It's much more elegant solution than the
one I posted. Good work.

Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

Pythagorean Theorem: 30^2 + (r-2)^2 = r^2.
Solution is 226" exactly, which is 18' 10", as hasalready been
disclosed,I believe.
Didn't even need trig. (which surprised me).

Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Trial and error isn't needed, neither is knowing the radius of the arc's
circle.

Put two nails 5' apart in a piece of ply. Put another nail 2" above the
line formed by the first two. Take a batten, bend it between the nails and
draw the arc.



--

dadiOH
____________________________

Winters getting colder? Tired of the rat race?
Taxes out of hand? Maybe just ready for a change?
Check it out... http://www.floridaloghouse.net

On 4/15/13 4:32 PM, dadiOH wrote:
Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to
trial and error, oui?

Trial and error isn't needed, neither is knowing the radius of the arc's
circle.

Put two nails 5' apart in a piece of ply. Put another nail 2" above the
line formed by the first two. Take a batten, bend it between the nails and
draw the arc.


The potential flaws I see in that method are...
....you might get a peak/angle in the curve at the center nail
....you can't always count on getting equal bending at every point along
the length of a piece of wood.

I know it's a standard method to use a long, flexible piece and
something to mark out a curve so I'm certain it works. I would just want
to double check and practice a few times to make sure the bendable thing
was bending equally.


--

-MIKE-

"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com

---remove "DOT" ^^^^ to reply

"-MIKE-" wrote in message
...
On 4/15/13 4:32 PM, dadiOH wrote:
Gramp's shop wrote:
I need to draw an arc for a piece of trim.
The end points of the arc
are 5 feet apart and the depth of the arc at
the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that
would be far superior to
trial and error, oui?

Trial and error isn't needed, neither is
knowing the radius of the arc's
circle.

Put two nails 5' apart in a piece of ply. Put
another nail 2" above the
line formed by the first two. Take a batten,
bend it between the nails and
draw the arc.


The potential flaws I see in that method are...
...you might get a peak/angle in the curve at
the center nail
...you can't always count on getting equal
bending at every point along the length of a
piece of wood.

I know it's a standard method to use a long,
flexible piece and
something to mark out a curve so I'm certain it
works. I would just want
to double check and practice a few times to make
sure the bendable thing
was bending equally.
-MIKE-


Perhaps the curve could be checked by flipping the
layout
stick end for end?

On 4/15/13 7:01 PM, Phil Kangas wrote:
Put two nails 5' apart in a piece of ply. Put
another nail 2" above the
line formed by the first two. Take a batten,
bend it between the nails and
draw the arc.


The potential flaws I see in that method are...
...you might get a peak/angle in the curve at
the center nail
...you can't always count on getting equal
bending at every point along the length of a
piece of wood.

I know it's a standard method to use a long,
flexible piece and
something to mark out a curve so I'm certain it
works. I would just want
to double check and practice a few times to make
sure the bendable thing
was bending equally.
-MIKE-


Perhaps the curve could be checked by flipping the
layout
stick end for end?


Good advice.


--

-MIKE-

"Playing is not something I do at night, it's my function in life"
--Elvin Jones (1927-2004)
--
http://mikedrums.com

---remove "DOT" ^^^^ to reply

Gramp's shop wrote:
I need to draw an arc for a piece of trim. The end points of the
arc
are 5 feet apart and the depth of the arc at the center point is 2
inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior
to
trial and error, oui?
------------------------------------------------

"dadiOH" wrote:

Trial and error isn't needed, neither is knowing the radius of the
arc's circle.

Put two nails 5' apart in a piece of ply. Put another nail 2" above
the line formed by the first two. Take a batten, bend it between
the nails and draw the arc.
---------------------------------------------------------------
Nice try but no cigar.

The end result needed is a cambered beam shape which requires
more than the three points you suggest.

Bingham outlines the method that works in his book.

Have used the method to define the deck cambers which varied from
10' to 16' in length for the boat I built.

BTW, a batten is needed, I used a 3/4" x 3/4" x 1/16" x 96" aluminum
angle which provides a knife edge for fairing out the profile with a
fairing
board.

Lew

"Gramp's shop" wrote:

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

No trig or anything real advanced needed here. Merely that the square
of the hypotenuse of a right triangle = the sum of the squares of the
other two sides

Picture your arc, and a line between the ends of the arc. Now draw
another line from the center of your circle to the midpoint of the
arc, and a third line from the circle center to one of the endpoints.
Now if you have a circle of radius R, you have just drawn a right
triangle with hypotenuse R, one side of R-2, and the other side of 30
(converting the 5-ft width to inches and dividing by 2.

30^2 + (R-2)^2 = R^2

900 + R^2 -4R + 4 = R^2

904 = 4R

R=226"
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.