Re: Preventing Rod Gnomon Bending

[tloc54452]

 All of the "scary equations" were hidden in the spreadsheet I sent out.  
Hidden so as not to scare anyone.  Did the spreadsheet arrive unreadable?  
Unfathomable?

John B


 



 

-Original Message-
From: Roger Bailey <[EMAIL PROTECTED]>
To: John Carmichael <[EMAIL PROTECTED]>; 'Sundial List' <[EMAIL PROTECTED]>
Sent: Wed, 1 Oct 2008 8:29 pm
Subject: Re: Preventing Rod Gnomon Bending
















Hi John,


 


In general, a tube is stiffer than a rod if you are 
looking at bending from the weight.  This is why structures are made from I 
beams not solid chunks of steel. Engineers use the moment of inertia (second 
moment of area) to calculate the effect of weight distributed at a distance 
from 
the center. An I beam is best, a tube is next best, a rod with all that weight 
in the middle not contributing to the strength is the worst. A round rod is not 
as stiff as a square or rectangular bar for the same reasons. As noted, 
anything 
in the tube only contributes by keeping the sides apart and adds weight. Ditto 
internal structures. They only add weight close to the center. Thickness of the 
tube is very important. For scary equations see 
http://en.wikipedia.org/wiki/Second_moment_of_area 


 


Regards, Roger Bailey  PEng*


 


*Unfortunately my PEng only applies for chemical 
engineering nor sundial or other structural design.







From: John Carmichael 


Sent: Wednesday, October 0
1, 2008 11:46 AM


To: 'Sundial List' 


Subject: Preventing Rod Gnomon Bending










Hi Guys:


 


I’m designing a large 15 foot tall southwest declining nearly 
vertical dial that will have a very long polar axis oriented rod gnomon.  
But I’ve come across a potential problem that I’ve never had to deal with 
before 
and am seeking your expert advice or suggestions.


 


Setup:


The gnomon rod will be unusually long because one end will be 
attached near the sundial face and the other end will go down and be firmly 
attached to the ground.  The reason that it will go all the way to the 
ground is because a second horizontal dial will be on the ground that will use 
the same gnomon.  The original specs have the gnomon rod diameter as 2 
inches, but it can be made wider if need be.  The gnomon length will be 
about 25 feet.  We have not decided if the gnomon will be a hollow tube 
(like a metal pipe) or a solid metal rod.  We want to avoid using any 
gnomon support struts and we want to prevent bending. 
  


 


Problem:


Since I’m not a metal structural engineer, I am concerned 
that the 2” diameter, 25 foot long gnomon might sag under its own weight or 
bend 
if kids hang on it.  Keep in mind that it is attached at both ends, which 
should help prevent bending.  Here are my questions:


 


1. 
Do hollow pipes bend
 easier than solid rods? (I’m guessing they do, but 
I’m not sure.)


2. 
Can a hollow pipe be made to bend less if it is filled with concrete? Or 
will the added weight just make bending worse? (This idea occurred to me 
because 
I’ve noticed that the metal pipe collision barriers around gas station pumps 
are 
filled with concrete.  Is this to prevent them from bending if a car hits 
them?)


3. 
Would increasing the diameter of the gnomon give it added strength and prevent 
bending?


 


Any help much appreciated!


 


Thx


 


John


 











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Re: Preventing Rod Gnomon Bending

[tloc54452]

 Most tubes aren't perfectly straight, so it behooves one to rotate the tube 
until the high point is up.

I agree that axial compliance is needed.  However, sockets tend to be a little 
loose, and so you might lose your rigid support status.  (Rigid supports cause 
three bends in a bar while simple supports only cause one so rigid is much 
stiffer and stronger.)  So how about a double elastic hinge?  Everyone know 
what that is?  Maybe I should sketch it when I get a chance.  A double elastic 
hinge would keep the axes of the ends of the tube pointing at each other while 
allowing for expansion ad contraction.  I think I would put the solid 
connection at the lower end of the gnomon and the double elastic hinge at the 
upper end where it would be less attractive to monkey with.  If it doesn't fit 
the aesthetics, it could have a cover over it.

John B


 


 

-Original Message-
From: Larry Bohlayer / Celestial Products <[EMAIL PROTECTED]>
To: 'Sundial List' <[EMAIL PROTECTED]>
Sent: Wed, 1 Oct 2008 7:44 pm
Subject: RE: Preventing Rod Gnomon Bending

































John,



 



In the structural engineering of bridges,
I believe that beams are often produced with a calculated curvature such that
when in place the flexure under its own weight puts it into straight line. Such
might be possible with your gnomon as well, BUT I think you will have to design
one of the=2
0end supports to allow for expansion/contraction movement. This could
simply be a socket welded to vertical face that allows the gnomon rod to slide
inside the socket.



 






Larry Bohlayer



Celestial Products



P.O. Box 801



Middleburg, VA 20118



540-338-4040



[EMAIL PROTECTED]






 
















From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On
Behalf Of John Carmichael

Sent: Wednesday, October 01, 2008
2:47 PM

To: 'Sundial List'

Subject: Preventing Rod Gnomon
Bending






 



Hi
Guys:



 



I’m
designing a large 15 foot tall southwest declining nearly vertical dial that
will have a very long polar axis oriented rod gnomon.  But I’ve come
across a potential problem that I’ve never had to deal with before and am
seeking your expert advice or suggestions.



 



Setup:



The
gnomon rod will be unusually long because one end will be attached near the
sundial face and the other end will go down and be firmly attached to the
ground.  The reason that it will go all the way to the ground is because a
second horizontal dial will be on the ground that will use the same
gnomon.  The original specs have the gnomon rod diameter as 2 inches, but
it can be made wider if need be.  The gnomon length will be about 25
feet.  We have not decided if the gnomon will be a hollow tube (like a
metal pipe) or a solid me
tal rod.  We want to avoid using any gnomon
support struts and we want to prevent bending.   



 



Problem:



Since
I’m not a metal structural engineer, I am concerned that the 2”
diameter, 25 foot long gnomon might sag under its own weight or bend if kids
hang on it.  Keep in mind that it is attached at both ends, which should
help prevent bending.  Here are my questions:



 



1. Do hollow pipes bend easier than solid
rods? (I’m guessing they do, but I’m not sure.)



2. Can a hollow pipe be made to bend less
if it is filled with concrete? Or will the added weight just make
bending worse? (This idea occurred to me because I’ve noticed that the
metal pipe collision barriers around gas station pumps are filled with
concrete.  Is this to prevent them from bending if a car hits them?)



3. Would increasing the diameter of the
gnomon give it added strength and prevent bending?



 



Any
help much appreciated!



 



Thx



 



John



 






 





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Re: Preventing Rod Gnomon Bending

[Roger Bailey]

Hello John B , John C and all,

The spreadsheet is excellent. I agree. "Don't speculate, calculate. The 
spreadsheet simply and elegantly calculates for round hollow pipe very well. I 
have added a few lines for standard pipe 2" & 3" Sch 40 and 80 as these are 
commonly available.

My comments speculated on different shapes without looking closely at the math. 
A square hollow  hollow box is slightly better than a round hollow tube of the 
same OD and ID as the factors multiplying the length to fourth power are 1/12 
for the box and Pi/64 for the pipe.  

John C, I would not put a box section inside the round tube. Unless welded al 
the way along, the benefit is just additive. You gain much more for the same 
weight with a thicker pipe where the benefit is based on the difference in the 
fourth power of the diameters. Thicker pipe is also cheaper and easier.

To show how the shear stress has to be carried through the material, try this 
experiment with a couple of 2x4s. Lay a 2x4 between two supports and stand on 
the middle of the span. Laid flat it really bends. On edge it bends much less. 
One 2x4 on edge bends less that two 2x4s laid flat one on top of the other.

Base on the formula for the second moment of area for a rectangle, 1/12 x b x 
h^4, one on edge is twice as stiff as two laid flat. 

Regards, Roger


   
From: [EMAIL PROTECTED] 
Sent: Thursday, October 02, 2008 7:21 AM
To: [EMAIL PROTECTED] ; [EMAIL PROTECTED] ; [EMAIL PROTECTED] 
Subject: Re: Preventing Rod Gnomon Bending


All of the "scary equations" were hidden in the spreadsheet I sent out.  Hidden 
so as not to scare anyone.  Did the spreadsheet arrive unreadable?  
Unfathomable?

John B






-Original Message-
From: Roger Bailey <[EMAIL PROTECTED]>
To: John Carmichael <[EMAIL PROTECTED]>; 'Sundial List' <[EMAIL PROTECTED]>
Sent: Wed, 1 Oct 2008 8:29 pm
Subject: Re: Preventing Rod Gnomon Bending


Hi John,

In general, a tube is stiffer than a rod if you are looking at bending from the 
weight.  This is why structures are made from I beams not solid chunks of 
steel. Engineers use the moment of inertia (second moment of area) to calculate 
the effect of weight distributed at a distance from the center. An I beam is 
best, a tube is next best, a rod with all that weight in the middle not 
contributing to the strength is the worst. A round rod is not as stiff as a 
square or rectangular bar for the same reasons. As noted, anything in the tube 
only contributes by keeping the sides apart and adds weight. Ditto internal 
structures. They only add weight close to the center. Thickness of the tube is 
very important. For scary equations see 
http://en.wikipedia.org/wiki/Second_moment_of_area 

Regards, Roger Bailey  PEng*

*Unfortunately my PEng only applies for chemical engineering nor sundial or 
other structural design.

From: John Carmichael 
Sent: Wednesday, October 01, 2008 11:46 AM
To: 'Sundial List' 
Subject: Preventing Rod Gnomon Bending


Hi Guys:

I’m designing a large 15 foot tall southwest declining nearly vertical dial 
that will have a very long polar axis oriented rod gnomon.  But I’ve come 
across a potential problem that I’ve never had to deal with before and am 
seeking your expert advice or suggestions.

Setup:
The gnomon rod will be unusually long beca use one end will be attached near 
the sundial face and the other end will go down and be firmly attached to the 
ground.  The reason that it will go all the way to the ground is because a 
second horizontal dial will be on the ground that will use the same gnomon.  
The original specs have the gnomon rod diameter as 2 inches, but it can be made 
wider if need be.  The gnomon length will be about 25 feet.  We have not 
decided if the gnomon will be a hollow tube (like a metal pipe) or a solid 
metal rod.  We want to avoid using any gnomon support struts and we want to 
prevent bending.   

Problem:
Since I’m not a metal structural engineer, I am concerned that the 2” diameter, 
25 foot long gnomon might sag under its own weight or bend if kids hang on it.  
Keep in mind that it is attached at both ends, which should help prevent 
bending.  Here are my questions:

1. Do hollow pipes bend easier than solid rods? (I’m guessing they do, but I’m 
not sure.)
2. Can a hollow pipe be made to bend less if it is filled with concrete? Or 
will the added weight just make bending worse? (This idea occurred to me 
because I’ve noticed that the metal pipe collision barriers around gas station 
pumps are filled with concrete.  Is this to prevent them from bending if a car 
hits them?)
3. Would increasing the diameter of the gnomon give it added strength and 
prevent bending?

Any help much appreciated!

Thx

John




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RE: Preventing Rod Gnomon Bending

[John Carmichael]

Hi all:

 

I can't get over all the letters and even phone calls I've received from you
all.  What a bunch of great smart and kind people!

 

I'm leaning to the idea of inserting a slightly smaller square tube inside
the round tube, then welding it to the outer round tube at both ends.
Several guys suggested this.  It makes sense.

 

They say to weld the inner square tube so that one of the corners of the
square tube is at the top and not a flat side on top.  This also makes
sense.

 

Everybody seems to agree on the following:

 

1. Tubes are less bendable than solid rods

2. Tubes are less expensive than rods

3. Filling the tube with cement won't help and might make things worse.

4. Wider diameter tubes are stronger than thinner tubes

5. Thick tube walls help prevent bending. (one person suggested that the
tube wall thickness be .125 inch minimum)

 

I've learned a lot from this discussion.  Hope it helps some of you with
your future projects too.

 

Thanks everybody!

 

John

 

John L. Carmichael

Sundial Sculptures

925 E. Foothills Dr.

Tucson AZ 85718-4716

USA

Tel: 520-6961709

Email:   [EMAIL PROTECTED] 

 

My Websites:

(business) Sundial Sculptures: http://www.sundialsculptures.com
  

(educational) Chinook Trail Sundial:
http://advanceassociates.com/Sundials/COSprings/

(educational) Earth & Sky Equatorial Sundial:
http://advanceassociates.com/Sundials/Earth-Sky_Dial/  

(educational) My Painted Wall Sundial:
http://www.advanceassociates.com/WallDial 

(educational) Painted Wall Sundials:
http://advanceassociates.com/WallDial/PWS_Home.html 

(educational) Stained Glass Sundials: http://www.stainedglasssundials.com
  

(educational) Sundial Cupolas, Towers & Turrets:
http://StainedGlassSundials.com/CupolaSundial/index.html 

 

From: Lloyd Tackitt [mailto:[EMAIL PROTECTED] 
Sent: Thursday, October 02, 2008 9:53 AM
To: John Carmichael
Subject: Re: Preventing Rod Gnomon Bending

 

One other possibility worth mentioning - there is a type of structural steel
that is a square tube - very rigid.

 

- Original Message 
From: John Carmichael <[EMAIL PROTECTED]>
To: Lloyd Tackitt <[EMAIL PROTECTED]>
Sent: Thursday, October 2, 2008 10:14:25 AM
Subject: RE: Preventing Rod Gnomon Bending

Hi Loyd:

 

You agree with many of the other guys, so you all must be right!

 

I'm so glad I asked you all.

 

Thanks so much for writing.  I REALLY appreciate it.

 

Take care,

 

John

 

From: Lloyd Tackitt [mailto:[EMAIL PROTECTED] 
Sent: Wednesday, October 01, 2008 12:22 PM
To: John Carmichael
Subject: Re: Preventing Rod Gnomon Bending

 

If you can get thick walled pipe you will do better than getting a solid
rod.  The thick wall pipe is more rigid than a solid rod, possibly due to
the increased weight of the rod, plus the somewhat truss like effect of the
pipe wall.

 

Pipe generally comes in 20 foot sections, to get one in 25' may be a special
order, or it could be done with a threaded coupler, if the coupler isn't
considered unsightly in your design.

 

If you can go larger diameter you will gain rigidity, as long as you remain
with thick wall pipe.  4" pipe will be more rigid than 2" pipe for instance.
Drill stem (as used by oil drilling rigs) is a very thick wall pipe that
would be ideal, but it may be hard to find where you are.  

 

Concrete won't help the rigidity issue for you in this case.  Concrete in
bollards (collision barriers) adds weight mostly, and keeps water and debris
from accumulating inside.

 

Have you considered a steel beam?  An "H" (sometimes referred to as "I"
beam) beam is very rigid.  This assumes that the gnomon doesn't have to be
round.  They can be purchased in varying dimensions and lengths.  

 

Hope this helps and not confuses.

 

- Original Message 
From: John Carmichael <[EMAIL PROTECTED]>
To: Sundial List <[EMAIL PROTECTED]>
Sent: Wednesday, October 1, 2008 1:46:56 PM
Subject: Preventing Rod Gnomon Bending

Hi Guys:

 

I'm designing a large 15 foot tall southwest declining nearly vertical dial
that will have a very long polar axis oriented rod gnomon.  But I've come
across a potential problem that I've never had to deal with before and am
seeking your expert advice or suggestions.

 

Setup:

The gnomon rod will be unusually long because one end will be attached near
the sundial face and the other end will go down and be firmly attached to
the ground.  The reason that it will go all the way to the ground is because
a second horizontal dial will be on the ground that will use the same
gnomon.  The original specs have the gnomon rod diameter as 2 inches, but it
can be made wider if need be.  The gnomon length will be about 25 feet.  We
have not decided if the gnomon will be a hollow tube (like a metal pipe) or
a solid metal rod.  We want to avoid using any gnomon support struts and we
want to prevent bending.   

 

Problem:

Since I'm not a

RE: Preventing Rod Gnomon Bending

[John Carmichael]

 

Hi Roger:

 

This comment of yours is most important, and if it’s true, then that would be 
the way to go.  I trust you, so I’ll probably do what you say.

 

You said:

John C, I would not put a box section inside the round tube. Unless welded all 
the way along, the benefit is just additive. You gain much more for the same 
weight with a thicker pipe where the benefit is based on the difference in the 
fourth power of the diameters. Thicker pipe is also cheaper and easier.

 

Thanks Roger!  I hope the other guys agree with you.

 

John C

 

 

 

 

From: Roger Bailey [mailto:[EMAIL PROTECTED] 
Sent: Thursday, October 02, 2008 10:02 AM
To: [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]
Subject: Re: Preventing Rod Gnomon Bending

 

Hello John B , John C and all,

 

The spreadsheet is excellent. I agree. "Don't speculate, calculate. The 
spreadsheet simply and elegantly calculates for round hollow pipe very well. I 
have added a few lines for standard pipe 2" & 3" Sch 40 and 80 as these are 
commonly available.

 

My comments speculated on different shapes without looking closely at the math. 
A square hollow  hollow box is slightly better than a round hollow tube of the 
same OD and ID as the factors multiplying the length to fourth power are 1/12 
for the box and Pi/64 for the pipe.  

 

John C, I would not put a box section inside the round tube. Unless welded al 
the way along, the benefit is just additive. You gain much more for the same 
weight with a thicker pipe where the benefit is based on the difference in the 
fourth power of the diameters. Thicker pipe is also cheaper and easier.

 

To show how the shear stress has to be carried through the material, try this 
experiment with a couple of 2x4s. Lay a 2x4 between two supports and stand on 
the middle of the span. Laid flat it really bends. On edge it bends much less. 
One 2x4 on edge bends less that two 2x4s laid flat one on top of the other.

 

Base on the formula for the second moment of area for a rectangle, 1/12 x b x 
h^4, one on edge is twice as stiff as two laid flat. 

 

Regards, Roger

 

 

   

From: [EMAIL PROTECTED] 

Sent: Thursday, October 02, 2008 7:21 AM

To: [EMAIL PROTECTED] ; [EMAIL PROTECTED] ; [EMAIL PROTECTED] 

Subject: Re: Preventing Rod Gnomon Bending

 

All of the "scary equations" were hidden in the spreadsheet I sent out.  Hidden 
so as not to scare anyone.  Did the spreadsheet arrive unreadable?  
Unfathomable?

John B

 

 

-Original Message-
From: Roger Bailey <[EMAIL PROTECTED]>
To: John Carmichael <[EMAIL PROTECTED]>; 'Sundial List' <[EMAIL PROTECTED]>
Sent: Wed, 1 Oct 2008 8:29 pm
Subject: Re: Preventing Rod Gnomon Bending

Hi John,

 

In general, a tube is stiffer than a rod if you are looking at bending from the 
weight.  This is why structures are made from I beams not solid chunks of 
steel. Engineers use the moment of inertia (second moment of area) to calculate 
the effect of weight distributed at a distance from the center. An I beam is 
best, a tube is next best, a rod with all that weight in the middle not 
contributing to the strength is the worst. A round rod is not as stiff as a 
square or rectangular bar for the same reasons. As noted, anything in the tube 
only contributes by keeping the sides apart and adds weight. Ditto internal 
structures. They only add weight close to the center. Thickness of the tube is 
very important. For scary equations see  
 
http://en.wikipedia.org/wiki/Second_moment_of_area 

 

Regards, Roger Bailey  PEng*

 

*Unfortunately my PEng only applies for chemical engineering nor sundial or 
other structural design.

From:   John Carmichael 

Sent: Wednesday, October 01, 2008 11:46 AM

To:   'Sundial List' 

Subject: Preventing Rod Gnomon Bending

 

Hi Guys:

 

I’m designing a large 15 foot tall southwest declining nearly vertical dial 
that will have a very long polar axis oriented rod gnomon.  But I’ve come 
across a potential problem that I’ve never had to deal with before and am 
seeking your expert advice or suggestions.

 

Setup:

The gnomon rod will be unusually long beca use one end will be attached near 
the sundial face and the other end will go down and be firmly attached to the 
ground.  The reason that it will go all the way to the ground is because a 
second horizontal dial will be on the ground that will use the same gnomon.  
The original specs have the gnomon rod diameter as 2 inches, but it can be made 
wider if need be.  The gnomon length will be about 25 feet.  We have not 
decided if the gnomon will be a hollow tube (like a metal pipe) or a solid 
metal rod.  We want to avoid using any gnomon support struts and we want to 
prevent bending.   

 

Problem:

Since I’m not a metal structural engineer, I am concerned that the 2” diameter, 
25 foot long gnomon might sag under its own weight or bend if kids hang on it. 

RE: Preventing Rod Gnomon Bending

[Yan Seiner]

On Thu, October 2, 2008 10:30 am, John Carmichael wrote:
>
>
> Hi Roger:
>
>
>
> This comment of yours is most important, and if it’s true, then that
> would be the way to go.  I trust you, so I’ll probably do what you say.
>
>
>
> You said:
>
> John C, I would not put a box section inside the round tube. Unless welded
> all the way along, the benefit is just additive. You gain much more for
> the same weight with a thicker pipe where the benefit is based on the
> difference in the fourth power of the diameters. Thicker pipe is also
> cheaper and easier.
>
>
>
> Thanks Roger!  I hope the other guys agree with you.

I think you can get extruded tubes that have internal reinforcing extruded
as part of the tube.  Most likely these would be aluminum and I don't know
if that's appropriate for your design.

-- 
  o__
  ,>/'_  o__
  (_)\(_),>/'_o__
Yan Seiner  (_)\(_)   ,>/'_ o__
   Personal Trainer  (_)\(_),>/'_o__
 Professional Engineer (_)\(_)   ,>/'_
Who says engineers have to be pencil necked geeks?  (_)\(_)

You are an adult when you realize that everyone's an idiot. You are wise
when you include yourself.


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Homogeneous Analemmatic Sundial

[Alex Ware]

-BEGIN PGP SIGNED MESSAGE-
Hash: SHA1

Hi,
I've been reading the postings about the homogeneous analemmatic
sundial and wish
to create one as part of a piece of work for school (admittedly, this is
beyond
what is asked- I'm just fascinated by these sundials and want to try
my hand at a
more obscure design).

http://www.analemma.nl/homogeneous%20analemmatic%20sundials%20v2.1%20pdf.pdf
and http://www.de-zonnewijzerkring.nl/zw-arch/eng-home-zw-08-06.htm

I'm having some trouble figuring out how the two trenches and the pivots p
and q
cause the center ring to be displaced on one dimension only instead of
causing
the whole ring to rotate.

If anyone would be so kind as to point me to any further reading for this
type
of dial- or help explain how this works (and any other advice) it would be
greatly appreciated.

Many Thanks,
Alex Ware


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Version: GnuPG v1.4.9 (GNU/Linux)
Comment: http://getfiregpg.org

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avwAniyaMBFXOTxj41LAy5zLdY+gdylP
=c76/
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Re: Preventing Rod Gnomon Bending

[tloc54452]

 Oh, I concur wholeheartedly.  If it's an end attachment it's one thing, but if 
you want to fill the tube with it so as to make the tube stiffer, there are 
actually better ways.  I also agree with the guy who said don't make your wall 
too thin.  If it's too thin, it's not dent resistant.  A dent is a kink 
starter, so very bad thing.  If you want to fill the tube with something to 
help it keep its form, I'd suggest high density foam.  At a few pounds per 
cubic foot, it weighs nothing compared to the steel, but should help ward off 
collapses somewhat.  Also, someone suggested extruded aluminum tube with built 
-in reinforcement.  Good stuff, but not very straight in long lengths.  If you 
can't find it in the size you want, extrusion dies aren't too many thousands of 
$.  Of course, that's more than foam-filled aluminum or steel would be.  You 
should check into lengths of pipe very soon.  It can be hard to get just what 
you want in a very long length.


 
John B



 

-Original Message-
From: John Carmichael <[EMAIL PROTECTED]>
To: 'Roger Bailey' <[EMAIL PROTECTED]>; [EMAIL PROTECTED]; [EMAIL PROTECTED]
Sent: Thu, 2 Oct 2008 10:30 am
Subject: RE: Preventing Rod Gnomon Bending

























 



Hi Roger:



 



This comment of yours is most important, and if it’s true, then
that would be the way to go.  I trust you, so I’ll probably do wha
t you say.



 



You said:



John C, I would not put a box section
inside the round tube. Unless welded all the way along, the benefit is just
additive. You gain much more for the same weight with a thicker pipe where the
benefit is based on the difference in the fourth power of the
diameters. Thicker pipe is also cheaper and easier.



 



Thanks
Roger!  I hope the other guys agree with you.



 



John
C



 



 



 



 









From: Roger Bailey
[mailto:[EMAIL PROTECTED] 

Sent: Thursday, October 02, 2008 10:02 AM

To: [EMAIL PROTECTED]; [EMAIL PROTECTED];
[EMAIL PROTECTED]

Subject: Re: Preventing Rod Gnomon Bending









 






Hello
John B , John C and all,









 









The
spreadsheet is excellent. I agree. "Don't speculate, calculate. The
spreadsheet simply and elegantly calculates for round hollow pipe very well. I
have added a few lines for standard pipe 2" & 3" Sch 40 and
80 as these are commonly available.









 









My
comments speculated on different shapes without looking closely at the math. A
square hollow  hollow box is slightly better than a round hollow tube
of the same OD and ID as the factors multiplying the length to fourth power are
1/12 for the box and Pi/64 for the pipe.  









 









John
C, I would not=2
0put a box section inside the round tube. Unless welded al the
way along, the benefit is just additive. You gain much more for the same weight
with a thicker pipe where the benefit is based on the difference in the fourth
power of the diameters. Thicker pipe is also cheaper and easier.









 









To
show how the shear stress has to be carried through the material, try this
experiment with a couple of 2x4s. Lay a 2x4 between two supports and stand
on the middle of the span. Laid flat it really bends. On edge it bends
much less. One 2x4 on edge bends less that two 2x4s laid flat one on top of the
other.









 









Base
on the formula for the second moment of area for a rectangle, 1/12 x b x h^4,
one on edge is twice as stiff as two laid flat. 









 









Regards,
Roger









 









 









   















From: [EMAIL PROTECTED]










Sent: Thursday, October
02, 2008 7:21 AM









To: [EMAIL PROTECTED]
; [EMAIL PROTECTED]
; [EMAIL PROTECTED]










Subject: Re: Preventing Rod
Gnomon Bending















 









All of the
"scary equations" were hidden in the spreadsheet I sent out. 
Hidden so as not to scare anyone.  Did the spreadsheet arrive
unreadable?  Unfathomable?



John
 B









 









 






-Original Message-

From: Roger Bailey <[EMAIL PROTECTED]>

To: John Carmichael <[EMAIL PROTECTED]>;
'Sundial List' <[EMAIL PROTECTED]>

Sent: Wed, 1 Oct 2008 8:29 pm

Subject: Re: Preventing Rod Gnomon Bending









Hi
John,









 









In
general, a tube is stiffer than a rod if you are looking at bending from the
weight.  This is why structures are made from I beams not solid chunks of
steel. Engineers use the moment of inertia (second moment of area) to calculate
the effect of weight distributed at a distance from the center. An I beam is
best, a tube is next best, a rod with all that weight in the middle not
contributing to the strength is the worst. A round rod is not as stiff as a
square or rectangular bar for the same reasons. As noted, anything in the tube
only contributes by keeping the sides apart and adds weight. Ditto internal
structures. They only add weight close to the center. Thickness of the tube is
very important. For scary equations see 
http://en.wikipedia.org/wiki/Second_moment_of_a

Re: Homogeneous Analemmatic Sundial

[Chris Lusby Taylor]

Hi Alex,
Congratulations on taking up this challenge. I'm sure you'll enjoy it.

The diagrams on the de-zonnewijzerkring.nl site don't fully explain the 
mechanism.
It is based on the trammel of Archimedes which is used to draw ellipses. 
Normally, the grooves are fixed and the rod moves, with two points on it (p and 
q) constrained to slide in the two grooves. The sundial, on the other hand, 
fixes the end point p, forcing the other groove to move up and down as the rod 
rotates. What is not explained is that the grooved piece (the grey disk) must 
still be constrained somehow to stop it rotating. It must only move up and 
down. This could be done by putting a more fixed plugs in the vertical groove, 
above and below p.

In practice, you should make the grey disk bigger than shown if you are nearer 
the equator than the Netherlands (about 50 degrees North) since the sliding 
distance C needed gets greater as you approach the equator. Note that, in the 
Tropics, the date scale needs to slide so far it actually obstructs the gnomon, 
so you would have to modify the mechanism if you live in the Tropics.
The dial can be adjusted for any longitude or time zone simply by rotating the 
time scale. To adjust for a different latitude, you'd have to make the lengths 
C and D adjustable. That seems quite feasible to me, though perhaps a bit 
fiddly. 

Good luck with realising this fascinating dial

Chris Lusby Taylor
51.4N 1.3W



- Original Message - 
  From: Alex Ware 
  To: sundial@uni-koeln.de 
  Sent: Thursday, October 02, 2008 8:40 PM
  Subject: Homogeneous Analemmatic Sundial


  -BEGIN PGP SIGNED MESSAGE-
  Hash: SHA1

  Hi,
  I've been reading the postings about the homogeneous analemmatic
  sundial and wish
  to create one as part of a piece of work for school (admittedly, this is 
beyond
  what is asked- I'm just fascinated by these sundials and want to try
  my hand at a
  more obscure design).

  http://www.analemma.nl/homogeneous%20analemmatic%20sundials%20v2.1%20pdf.pdf
  and http://www.de-zonnewijzerkring.nl/zw-arch/eng-home-zw-08-06.htm

  I'm having some trouble figuring out how the two trenches and the pivots p 
and q
  cause the center ring to be displaced on one dimension only instead of causing
  the whole ring to rotate.

  If anyone would be so kind as to point me to any further reading for this type
  of dial- or help explain how this works (and any other advice) it would be
  greatly appreciated.

  Many Thanks,
  Alex Ware


  -BEGIN PGP SIGNATURE-
  Version: GnuPG v1.4.9 (GNU/Linux)
  Comment: http://getfiregpg.org

  iEYEARECAAYFAkjlI7UACgkQwTJKNkPO7HTJYgCfW7m5UNMOF2wyDYgXseKkT2JP
  avwAniyaMBFXOTxj41LAy5zLdY+gdylP
  =c76/
  -END PGP SIGNATURE-





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Re: Homogeneous Analemmatic Sundial

[Alex Ware]

Sorry I neglected to mention my latitude; I'm about 50.7N- so the distance C
mentioned will be approximately the same as for the article.
I had a quick search for the trammel of Archimedes and found this:
http://www.ps.missouri.edu/rickspage/vector06/index.html and it
seems that this allows the dial to work as an analemmatic dial in a clever
way.

I presume I can make the dial out of wood or perspex and use some kind of
bearings for the pivots?

Many Thanks,
Alex Ware

On Thu, Oct 2, 2008 at 10:54 PM, Chris Lusby Taylor wrote:

>  Hi Alex,
> Congratulations on taking up this challenge. I'm sure you'll enjoy it.
>
> The diagrams on the de-zonnewijzerkring.nl site don't fully explain the
> mechanism.
> It is based on the trammel of Archimedes which is used to draw ellipses.
> Normally, the grooves are fixed and the rod moves, with two points on it (p
> and q) constrained to slide in the two grooves. The sundial, on the other
> hand, fixes the end point p, forcing the other groove to move up and down as
> the rod rotates. What is not explained is that the grooved piece (the grey
> disk) must still be constrained somehow to stop it rotating. It must only
> move up and down. This could be done by putting a more fixed plugs in the
> vertical groove, above and below p.
>
> In practice, you should make the grey disk bigger than shown if you are
> nearer the equator than the Netherlands (about 50 degrees North) since the
> sliding distance C needed gets greater as you approach the equator. Note
> that, in the Tropics, the date scale needs to slide so far it actually
> obstructs the gnomon, so you would have to modify the mechanism if you live
> in the Tropics.
> The dial can be adjusted for any longitude or time zone simply by rotating
> the time scale. To adjust for a different latitude, you'd have to make the
> lengths C and D adjustable. That seems quite feasible to me, though perhaps
> a bit fiddly.
>
> Good luck with realising this fascinating dial
>
> Chris Lusby Taylor
> 51.4N 1.3W
>
>
>
> - Original Message -
>
>  *From:* Alex Ware <[EMAIL PROTECTED]>
> *To:* sundial@uni-koeln.de
> *Sent:* Thursday, October 02, 2008 8:40 PM
> *Subject:* Homogeneous Analemmatic Sundial
>
> -BEGIN PGP SIGNED MESSAGE-
> Hash: SHA1
>
> Hi,
> I've been reading the postings about the homogeneous analemmatic
> sundial and wish
> to create one as part of a piece of work for school (admittedly, this is
> beyond
> what is asked- I'm just fascinated by these sundials and want to try
> my hand at a
> more obscure design).
>
>
> http://www.analemma.nl/homogeneous%20analemmatic%20sundials%20v2.1%20pdf.pdf
> and http://www.de-zonnewijzerkring.nl/zw-arch/eng-home-zw-08-06.htm
>
> I'm having some trouble figuring out how the two trenches and the pivots p
> and q
> cause the center ring to be displaced on one dimension only instead of
> causing
> the whole ring to rotate.
>
> If anyone would be so kind as to point me to any further reading for this
> type
> of dial- or help explain how this works (and any other advice) it would be
> greatly appreciated.
>
> Many Thanks,
> Alex Ware
>
>
> -BEGIN PGP SIGNATURE-
> Version: GnuPG v1.4.9 (GNU/Linux)
> Comment: http://getfiregpg.org
>
> iEYEARECAAYFAkjlI7UACgkQwTJKNkPO7HTJYgCfW7m5UNMOF2wyDYgXseKkT2JP
> avwAniyaMBFXOTxj41LAy5zLdY+gdylP
> =c76/
> -END PGP SIGNATURE-
>
>
>  --
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
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Re: Preventing Rod Gnomon Bending

[Chris Lusby Taylor]

Hi John,
There used to be someone who made sundials with gnomons that might have been 
very suitable, but he seems more interested in stained glass and painted wall 
sundials these days ;-)

Why not use a tensioned wire or rod? I'm thinking of sailing yacht rigging, 
which may not be perfectly straight but surely gains a great deal from being 
under tension.
For your size of dial, the gnomon needs to be around 1 inch diameter, I think, 
for the shadow to be clear. That's massive by sailing standards, but perhaps 
you could have a relatively thin wire encased in something light to get the 
diameter up.
Depending on how much droop you can tolerate, the tension would have to be 
great, so a material with high tensile strength to weight ratio would be 
needed. Stainless steel, perhaps, or carbon fibre.

Just a thought
Chris

  - Original Message - 
  From: John Carmichael 
  To: 'Sundial List' 
  Sent: Wednesday, October 01, 2008 7:46 PM
  Subject: Preventing Rod Gnomon Bending


  Hi Guys:

   

  I'm designing a large 15 foot tall southwest declining nearly vertical dial 
that will have a very long polar axis oriented rod gnomon.  But I've come 
across a potential problem that I've never had to deal with before and am 
seeking your expert advice or suggestions.

   

  Setup:

  The gnomon rod will be unusually long because one end will be attached near 
the sundial face and the other end will go down and be firmly attached to the 
ground.  The reason that it will go all the way to the ground is because a 
second horizontal dial will be on the ground that will use the same gnomon.  
The original specs have the gnomon rod diameter as 2 inches, but it can be made 
wider if need be.  The gnomon length will be about 25 feet.  We have not 
decided if the gnomon will be a hollow tube (like a metal pipe) or a solid 
metal rod.  We want to avoid using any gnomon support struts and we want to 
prevent bending.   

   

  Problem:

  Since I'm not a metal structural engineer, I am concerned that the 2" 
diameter, 25 foot long gnomon might sag under its own weight or bend if kids 
hang on it.  Keep in mind that it is attached at both ends, which should help 
prevent bending.  Here are my questions:

   

  1. Do hollow pipes bend easier than solid rods? (I'm guessing they do, but 
I'm not sure.)

  2. Can a hollow pipe be made to bend less if it is filled with concrete? Or 
will the added weight just make bending worse? (This idea occurred to me 
because I've noticed that the metal pipe collision barriers around gas station 
pumps are filled with concrete.  Is this to prevent them from bending if a car 
hits them?)

  3. Would increasing the diameter of the gnomon give it added strength and 
prevent bending?

   

  Any help much appreciated!

   

  Thx

   

  John

   



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Test -- Ignore

[Tom Egan]

In case you're wondering why I'm sending so many test messages, I'm 
having a hard time getting my ISP to stop blocking mail from the sundial 
mailing list.

-- 
Outside of a dog, a book is a man's best friend.  Inside of a dog it's too dark 
to read.
   
Groucho Marx  1895 - 1977

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RE: Preventing Rod Gnomon Bending

[John Carmichael]

You made me smile Chris.

 

Believe me, my first thought was to use a thick stranded cable held under
tension by a huge counterweight something like my stone dials (which I still
make by the way!).  That would have easily solved the problem.  It even
occurred to me that I could put the tensioned cable inside of a larger thin
wall tube so that the tube covering would cast a thicker shadow. The cable
would hold up the tube and keep it straight. It's a neat idea, because then
you could use a smaller cable and counterweight.

 

But my job on this project is to work with a famous modern metal artist from
California and turn his weird sculpture idea into a sundial.  His design
does not permit the cable solution. ( His name is Jon Seeman.  See
http://www.jonseeman.com/ ).  I tell you, this is the hardest sundial design
project I've ever had because of all the crazy angles and multiple parts.

 

Not only that, but everything has to be approved by a committee and the City
Council. Ugh!  I hate committees!  Puts too many cooks in the kitchen.  They
are contsantly changing the design perimeters.  And the artist doesn't use
CAD and only works in pencil sketches.  It'll probably take months to
finish. 

 

Good thought though about the cable!

 

John C

 

 

From: Chris Lusby Taylor [mailto:[EMAIL PROTECTED] 
Sent: Thursday, October 02, 2008 3:14 PM
To: John Carmichael; 'Sundial List'
Subject: Re: Preventing Rod Gnomon Bending

 

Hi John,

There used to be someone who made sundials with gnomons that might have been
very suitable, but he seems more interested in stained glass and painted
wall sundials these days ;-)

 

Why not use a tensioned wire or rod? I'm thinking of sailing yacht rigging,
which may not be perfectly straight but surely gains a great deal from being
under tension.

For your size of dial, the gnomon needs to be around 1 inch diameter, I
think, for the shadow to be clear. That's massive by sailing standards, but
perhaps you could have a relatively thin wire encased in something light to
get the diameter up.

Depending on how much droop you can tolerate, the tension would have to be
great, so a material with high tensile strength to weight ratio would be
needed. Stainless steel, perhaps, or carbon fibre.

 

Just a thought

Chris

 

- Original Message - 

From: John Carmichael   

To: 'Sundial   List' 

Sent: Wednesday, October 01, 2008 7:46 PM

Subject: Preventing Rod Gnomon Bending

 

Hi Guys:

 

I'm designing a large 15 foot tall southwest declining nearly vertical dial
that will have a very long polar axis oriented rod gnomon.  But I've come
across a potential problem that I've never had to deal with before and am
seeking your expert advice or suggestions.

 

Setup:

The gnomon rod will be unusually long because one end will be attached near
the sundial face and the other end will go down and be firmly attached to
the ground.  The reason that it will go all the way to the ground is because
a second horizontal dial will be on the ground that will use the same
gnomon.  The original specs have the gnomon rod diameter as 2 inches, but it
can be made wider if need be.  The gnomon length will be about 25 feet.  We
have not decided if the gnomon will be a hollow tube (like a metal pipe) or
a solid metal rod.  We want to avoid using any gnomon support struts and we
want to prevent bending.   

 

Problem:

Since I'm not a metal structural engineer, I am concerned that the 2"
diameter, 25 foot long gnomon might sag under its own weight or bend if kids
hang on it.  Keep in mind that it is attached at both ends, which should
help prevent bending.  Here are my questions:

 

1. Do hollow pipes bend easier than solid rods? (I'm guessing they do, but
I'm not sure.)

2. Can a hollow pipe be made to bend less if it is filled with concrete? Or
will the added weight just make bending worse? (This idea occurred to me
because I've noticed that the metal pipe collision barriers around gas
station pumps are filled with concrete.  Is this to prevent them from
bending if a car hits them?)

3. Would increasing the diameter of the gnomon give it added strength and
prevent bending?

 

Any help much appreciated!

 

Thx

 

John

 


  _  


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Re: Preventing Rod Gnomon Bending

[tloc54452]

 Maybe everyone understands a double elastic hinge, but in case there is one 
person who doesn't, sketch attached.  Thinner plates are welded to a base 
plate.  Not shown, the gnomon tube goes through the holes in the thinner plates 
and is welded to them.  As I was saying, this thing could be covered if it 
doesn't fit with the aesthetics of the rest of the design.

John C, looks like that guy can do anything with metal.  Cool!


 
John B




 

-Original Message-
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thu, 2 Oct 2008 9:49 am
Subject: Re: Preventing Rod Gnomon Bending











 Most tubes aren't perfectly straight, so it behooves one to rotate the tube 
until the high point is up.



I agree that axial compliance is needed.  However, sockets tend to be a little 
loose, and so you might lose your rigid support status.  (Rigid supports cause 
three bends in a bar while simple supports only cause one so rigid is much 
stiffer and stronger.)  So how about a double elastic hinge?  Everyone know 
what that is?  Maybe I should sketch it when I get a chance.  A double elastic 
hinge would keep the axes of the ends of the tube pointing at each other while 
allowing for expansion and contraction.  I think I would put the solid 
connection at the lower end of the gnomon and the double elastic hinge at the 
upper end where it would be less attractive to monkey with.  If it doesn't fit 
the aesthetics, it
 could have a cover over it.



John B





 





 



-Original Message-

From: Larry Bohlayer / Celestial Products <[EMAIL PROTECTED]>

To: 'Sundial List' <[EMAIL PROTECTED]>

Sent: Wed, 1 Oct 2008 7:44 pm

Subject: RE: Preventing Rod Gnomon Bending






































John,





 





In the structural engineering of bridges,
I believe that beams are often produced with a calculated curvature such that
when in place the flexure under its own weight puts it into straight line. Such
might be possible with your gnomon as well, BUT I think you will have to design
one of the end supports to allow for expansion/contraction movement. This could
simply be a socket welded to vertical face that allows the gnomon rod to slide
inside the socket.





 









Larry Bohlayer





Celestial Products





P.O. Box 801





Middleburg, VA 20118





540-338-4040





[EMAIL PROTECTED]









 





















From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On
Behalf Of John Carmichael


Sent: Wednesday, October 01, 2008
2:47 PM


To: 'Sundial List'


Subject: Preventing Rod Gnomon
Bending









 





Hi
Guys:





 





I’m
designing a large 15 foot tall southwest declining nearly vertical dial that
will have a very long20polar axis oriented rod gnomon.  But I’ve come
across a potential problem that I’ve never had to deal with before and am
seeking your expert advice or suggestions.





 





Setup:





The
gnomon rod will be unusually long because one end will be attached near the
sundial face and the other end will go down and be firmly attached to the
ground.  The reason 
that it will go all the way to the ground is because a
second horizontal dial will be on the ground that will use the same
gnomon.  The original specs have the gnomon rod diameter as 2 inches, but
it can be made wider if need be.  The gnomon length will be about 25
feet.  We have not decided if the gnomon will be a hollow tube (like a
metal pipe) or a solid metal rod.  We want to avoid using any gnomon
support struts and we want to prevent bending.   





 





Problem:





Since
I’m not a metal structural engineer, I am concerned that the 2”
diameter, 25 foot long gnomon might sag under its own weight or bend if kids
hang on it.  Keep in mind that it is attached at both ends, which should
help prevent bending.  Here are my questions:





 





1. Do hollow pipes bend easier than solid
rods? (I’m
 guessing they do, but I’m not sure.)





2. Can a hollow pipe be made to bend less
if it is filled with concrete? Or will the added weight just make
bending worse
? (This idea occurred to me because I’ve noticed that the
metal pipe collision barriers around gas station pumps are filled with
concrete.  Is this to prevent them from bending if a car hits them?)





3. Would increasing the diameter of the
gnomon give it added strength and prevent bending?





 





Any
help much appreciated!





 





Thx





&
nbsp;





John





 









 






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Find phone numbers fast with the New AOL Yellow Pages! 



 





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Re: Preventing Rod Gnomon Bending

[wee-meng lee]

> Oh, I concur wholeheartedly.  If it's an end attachment it's one thing, but 
> if you want to fill the tube with it so as to make the tube stiffer, there 
> are actually better ways. 

One idea that I see occuring naturally in flight feathers of birds.  To prevent 
the quill tube wall from collapsing by the stress of flapping wings, it has 
spaced discs in the quill tube.  "Nature" has been known to have the best 
design for high strength, low material, light structures.

To apply it to this question, perhaps 50 of these wheel shaped discs (so that 
the discs will be at right angles to the tube on its own) can be spaced out on 
a thin steel cable and pulled thru the 25 foot tube.  The cable ends are then 
attached securely to the tube.  The disc spacing in the centre might be a 
little closer than the ends as there're more bending stresses there.  In the 
quill tubes, the disc spacing is closer where the feather attaches to the 
bird's wing.

rgds
weemeng
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Re: Preventing Rod Gnomon Bending

[Bill Gottesman]

Dangerous territory for me; I am not an engineer.

That said, see attached pdf.  Could a cable or rod strung internally in 
the hollow pole/gnomon be placed under tension, causing the pole to bow 
upwards against gravity?  The rod or cable could have a turnbuckle to 
make the tension adjustable, until it equally counteracts the droop from 
gravity.


Must do some experimenting first, so that it does not bend pole 
unexpectedly sideways, or helically.


-Bill


Carmichael Pole.pdf
Description: Adobe PDF document
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