Krushke calculator for 3V 3/8

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Domerama

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Feb 1, 2012, 9:15:46 PM2/1/12
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Trial by fire:

I put up a 3V caculator after getting a lot of help from Gerry. He
pointed me to:
http://www.geo-dome.co.uk/forum/article.asp?uname=313

and I used the information to put together a calculator page with
assembly diagram. Right now it's just for a 4/9 (3/8) but I'll make
another for 5/9 (5/8) in the next few days.

Gerry: I will also make a page specifically to explain the Krushke
method and if it's OK, borrow the text and images you posted on geo-
dome. That was a beautiful explanation with great graphics.

Here is the page for the calculator. If there are any errors let me
know:
http://www.domerama.com/calculators/3v-geodesic-dome-calculator/3v-38-flat-base-krushke-calculator/

If anyone would like other calculators to be put up, just let me know.
Same goes if you see something wrong on the site.

Gerry, if you have the Krushke data for a 5V I'd be happy to make a
calculator for it also.

Blair Wolfram

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Feb 1, 2012, 10:09:04 PM2/1/12
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Larry,
3/8 and 5/8 refer to Fullers 3 strut method. 4/9 and 5/9 refer to Kruschke's 4 strut method. They aren't interchangeable.
Blair

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Gerry in Quebec

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Feb 2, 2012, 8:43:38 AM2/2/12
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Hi Larry,
That's quite a comprehensive calculator! Very useful stuff in it. Some
comments and corrections....

- Thes following intro statement on your calculator page is confusing.
"Most calculators on the web for odd frequencies such as 3V and 5V
domes do not give a flat base at the hemisphere (1/2 of a sphere)."
Class I domes, like those described on the Desert Domes and GeoDome
websites, do not split into hemispheres when the frequency is odd. So
the question of a flat base at the equator doesn't arise. The flat
base problem pertains to the non-hemispheric truncations -- just above
and below the equator. For the conventional 3v (class I, method 1),
the dome doesn't sit flat at either of the two useful truncations, 4/9
and 5/9. For the conventional 4v, the hemispheric version (6/12) sits
flat, but the 5/12 and 7/12 versions do not. As with the conventional
3v, the conventional 5v does not split into hemispheres because the
frequency is odd. And it does not sit flat at the 7/15 and 8/15
truncations just above and below the equator.

- There are problems with your calculation categories: Area, Radius,
Diameter and Circumference. With non-hemispheric domes, you need to
distinguish between spherical radius and floor radius. The way your
calculator works now, those four parameters relate to the equatorial
plane, not the floor plane. In the section titled "Geodesic Dome
floor", the output number you list in the green box as the floor area
is in fact the area of the dome's equator, a great circle.

- You calculate floor area as if it were the area of a circle. Floor
area, of course, will be less than the area of a circle circumscribing
the floor. Also, instead of having circumference as a parameter, it
would be more useful to have the perimeter of the dome footprint,
i.e., the cumulative length of the 15 edges of the footprint.

- With the 3v Fuller-Kruschke dome, the floor radius is 0.982247 times
the spherical radius. This number, together with the chord factors of
the B and C struts that form the floor perimeter (footprint), results
in the following equation for floor area: 2.9426 x R squared, where R
is the spherical radius. (So the coefficient of floor area is "a
little shy of pi".)

- The surface area of the dome shell (not included in your calculator)
would be helpful in calculating the materials required for sheathing
and roofing the dome. For the 4/9ths, low-profile version of the dome,
the area is 4.9199 R squared. For the 5/9ths, high-profile, it's
7.2222 x R squared.

- You've set up the calculator so that any units of measure can be
used. That's good, but then in the "Geodesic Dome floor" section, you
say the area is in square feet. It would be useful to make it clear
that for those particular calculations -- square feet, cubic feet of
concrete, and 4 x 8 sheets -- the input radius or diameter should be
in feet.

- The section on connectors appears to give information for a 4v icosa
hemisphere rather than a 3v icosa, 4/9 dome. There should be 46
connectors of various types, not 91.

- In the section "Seating Capacity", you may want to round your
numbers to the nearest integer so that you don't have "fractions of
people".

Also, spelling and a typo...
- Change "Krushke" to "Kruschke". Two occurrences.
- Change "also a a reverse" to "also a reverse"

I didn't look at the other calculations such as weight and cost.
Cheers,
- Gerry


On Feb 1, 9:15 pm, Domerama <youngro...@gmail.com> wrote:
> Trial by fire:
>
> I put up a 3V caculator after getting a lot of help from Gerry. He
> pointed me to:http://www.geo-dome.co.uk/forum/article.asp?uname=313
>
> and I used the information to put together a calculator page with
> assembly diagram. Right now it's just for a 4/9 (3/8) but I'll make
> another for 5/9 (5/8) in the next few days.
>
> Gerry: I will also make a page specifically to explain the Krushke
> method and if it's OK, borrow the text and images you posted on geo-
> dome. That was a beautiful explanation with great graphics.
>
> Here is the page for the calculator. If there are any errors let me
> know:http://www.domerama.com/calculators/3v-geodesic-dome-calculator/3v-38...

Gerry in Quebec

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Feb 2, 2012, 9:57:25 AM2/2/12
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Ah, the old bone of contention... 3/8 vs 4/9, 5/8 vs 5/9.

When Kruschke first spelled out Fuller's truncation math in 1972, he
used the terminology of the day: 3/8 and 5/8, putting them in
quotation marks. He didn't talk about 4/9 and 5/9. When I was
struggling with the level-base problem many years ago, I thought it
would be more transparent and useful to have the numerator denote the
number of rows of triangles in the dome and the denominator denote the
number of rows of triangles in the parent polyhedron (tetra, octa,
icosa). After all, what did Fuller & associates mean by "3/8" and
"5/8"? Was it the volume of the dome compared with the volume of the
geodesic sphere? The volume of the spherical cap encasing the dome
versus the volume of the dome circumsphere? The height of the dome
divided by the diameter of the parent polyhedron? It was unclear,
imprecise. So I started using the ratio of dome triangle rows to
polyhedron triangle rows to describe truncations in my correspondence
and pamphlets.... only to find out that Blair Wolfram at Dome Inc. was
also using that same system! So I thought, 'Okay, if a well known dome
manufacturer finds it useful, it's probably a good way to talk about
domes with others interested in the subject.'

I hope 3/8 and 5/8 are eventually relegated to the status of
historical footnotes.

- Gerry in Quebec

On Feb 1, 10:09 pm, Blair Wolfram <thedome...@gmail.com> wrote:
> Larry,
> 3/8 and 5/8 refer to Fullers 3 strut method. 4/9 and 5/9 refer to Kruschke's 4 strut method. They aren't interchangeable.
> Blair
>
> Sent from my iPhone
>
> On Feb 1, 2012, at 8:15 PM, Domerama <youngro...@gmail.com> wrote:
>
>
>
> > Trial by fire:
>
> > I put up a 3V caculator after getting a lot of help from Gerry. He
> > pointed me to:
> >http://www.geo-dome.co.uk/forum/article.asp?uname=313
>
> > and I used the information to put together a calculator page with
> > assembly diagram. Right now it's just for a 4/9 (3/8) but I'll make
> > another for 5/9 (5/8) in the next few days.
>
> > Gerry: I will also make a page specifically to explain the Krushke
> > method and if it's OK, borrow the text and images you posted on geo-
> > dome. That was a beautiful explanation with great graphics.
>
> > Here is the page for the calculator. If there are any errors let me
> > know:
> >http://www.domerama.com/calculators/3v-geodesic-dome-calculator/3v-38...
>
> > If anyone would like other calculators to be put up, just let me know.
> > Same goes if you see something wrong on the site.
>
> > Gerry, if you have the Krushke data for a 5V I'd be happy to make a
> > calculator for it also.
>
> > --
> > You received this message because you are subscribed to the "Geodesic Help" Google Group
> > --
> > To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
> > --
> > To post to this group, send email to geodes...@googlegroups.com
> > --
> > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en- Hide quoted text -
>
> - Show quoted text -

Blair Wolfram

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Feb 2, 2012, 10:12:18 AM2/2/12
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Also, the 4v class1 method 1 uses 5 struts and only has a natural flat truncation at the hemisphere 6/12. The 4v class 1 method 2 uses 6 struts and sits flat at 5/12, 6/12, and 7/12.
Blair

Sent from my iPhone

Blair Wolfram

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Feb 2, 2012, 10:22:06 AM2/2/12
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Gerry,
I'm traveling through Sunday so I can't offer actual counts, but I think if you total the triangles in the 3v 3 strut dome not including the missing triangles in the natural openings as the numerator; and use the total number of triangles in the complete sphere, the fraction reduces close to 3/8 and 5/8. Likewise if you include all the triangles in method 2, the fraction reduces close to 4/9. Your description of rows of triangles in a dome to rows of triangles in a sphere is 100 percent.
Blair

Sent from my iPhone

Gerry in Quebec

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Feb 2, 2012, 2:17:11 PM2/2/12
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Larry,
Here are the bend angles for the 4 struts. The ones you give in the
calculator are for another version of the dome.

A: 9.49 degrees
B: 11.02
C: 12.17
D: 12.74

If you want to include the bend angles as calculated values, here's
the equation:

bend angle = arcsin (chord factor / 2)

- Gerry in Quebec


On Feb 1, 9:15 pm, Domerama <youngro...@gmail.com> wrote:
> Trial by fire:
>
> I put up a 3V caculator after getting a lot of help from Gerry. He
> pointed me to:http://www.geo-dome.co.uk/forum/article.asp?uname=313
>
> and I used the information to put together a calculator page with
> assembly diagram. Right now it's just for a 4/9 (3/8) but I'll make
> another for 5/9 (5/8) in the next few days.
>
> Gerry: I will also make a page specifically to explain the Krushke
> method and if it's OK, borrow the text and images you posted on geo-
> dome. That was a beautiful explanation with great graphics.
>
> Here is the page for the calculator. If there are any errors let me
> know:http://www.domerama.com/calculators/3v-geodesic-dome-calculator/3v-38...

Paul Kranz

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Feb 2, 2012, 2:30:56 PM2/2/12
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Gerry:

By "bend" are we talking dihedral?

Paul sends...

Gerry in Quebec

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Feb 2, 2012, 2:54:05 PM2/2/12
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Hi Paul,
No, by bend angle I mean the angle at which the squashed end of a pipe
strut must be bent. It's 90 degrees minus the axial angle. The term
dihedral is generally reserved for the angle between the triangular
faces of the dome, or between the floor and an up-pointing triangle in
the bottom row of triangles.

Larry,
It would help if your calculator included an illustration of the axial
angle / bend angle of a strut (what you refer to simply as "angle").

- Gerry



On Feb 2, 2:30 pm, Paul Kranz <p...@revivetheflame.com> wrote:
> Gerry:
>
> By "bend" are we talking dihedral?
>
> Paul sends...
>

Paul Kranz

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Feb 2, 2012, 2:55:57 PM2/2/12
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Gerry:

Do you have an illustration of that?

Paul sends...

Gerry Toomey

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Feb 2, 2012, 3:26:07 PM2/2/12
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Illustration attached.
 
AA-&-bend-angle.JPG

Paul Kranz

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Feb 2, 2012, 3:31:10 PM2/2/12
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Gerry:

B-E-A-U-T-ful! Thank you.

Paul sends...

On Thu, Feb 2, 2012 at 3:26 PM, Gerry Toomey <toomey...@gmail.com> wrote:
Illustration attached.

Gerry in Quebec

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Feb 2, 2012, 5:04:23 PM2/2/12
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Hi Blair,
Here are the numbers associated with your hypothesis about the origin
of truncation fractions. (I've assumed that by method 2 your really
meant the Fuller-Kruschke truncatable-dome layouts).

[Total triangles in 3v icosa, "3/8" dome] - [triangles comprising 5
natural trapezoidal openings] = 75 - 15 = 60 = numerator

Total triangles in 3v icosa geodesic sphere = 20 icosa faces x v
squared = 20 x 9 = 180 = denominator
Numerator over denominator = 60/180 = 2.67 / 8, which is not too far
from 3/8.

[Total triangles in 3v icosa, "5/8" dome] - [triangles comprising 5
natural trapezoidal openings] = 105 - 15 = 90 = numerator

Total triangles in 3v icosa geodesic sphere = 20 icosa faces x v
squared = 180 = denominator
Numerator over denominator = 90/180 = 4/8, which is not really all
that far from 5/8.

[Total triangles in the Fuller-Kruschke "4/9" dome] / [total triangles
in 3v icosa geodesic sphere] = 75/180 = 3.75 / 9, which is pretty darn
close to 4/9.

[Total triangles in the Fuller-Kruschke "5/9" dome] / [total triangles
in 3v icosa geodesic sphere] = 105/180 = 5.25 / 9 which is also pretty
close to 5/9.

Blair, have you ever thought of taking up numerology as a hobby? Bon
voyage.
- Gerry

cammy

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Aug 18, 2015, 12:47:54 PM8/18/15
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Hi,

Sorry don't know if this is the right place to post this, but currently finishing a dome I started ages ago, then got distracted by life, and now finally have the time to complete. Anyways went on your website ( www.domerama.com ) to check my lengths with your brilliant calculators. It says the page speed service has been suspended. I was wondering if you have the calculators anywhere else?

Many Thanks
Cammy

William Fisher

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Aug 19, 2015, 6:13:57 AM8/19/15
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Cameron Gray

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Aug 19, 2015, 10:51:46 AM8/19/15
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Thanks that's great, does it have Kruschke calculator do you know? I cant seem to find one.




On Wed, Aug 19, 2015 at 11:13 AM, William Fisher <fisher...@gmail.com> wrote:
Try this site. http://www.ziptiedomes.com/geodesic-dome-calculators/3v-38-geodesic-dome-calculator.htm

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Dick Fischbeck

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Aug 19, 2015, 3:21:07 PM8/19/15
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Repost - Might help.


posted by    Gerry07/02/2010 18:36:49
Dear Scrdcow,
Lots of questions! Since the conventional 3v icosa dome does not sit flat at the 5/8ths mark (also sometimes called 5/9ths), consider using another geometry.

The Fuller-Kruschke version of the 3v icosa has 4 strut lengths instead of 3, and 3 kinds of isosceles triangles instead of 2. But it has the major advantage of sitting flat, without the need to adjust the bottom row of triangles.

Here are the chord factors, namely the edge lengths when the dome's spherical radius i 1 unit:

A = 0.329706
B = 0.382290
C = 0.421489
D = 0.441056

I will now attempt to insert a jpg line drawing to show which strut goes where. The floor radius of this dome is 0.982247 times the spherical radius. The height of the 5/8ths version (what I call 5/9ths) is 1.187592 times the spherical radius.

This dome is used by many dome-home manufacturers to avoid the problem you mention, the need to level the dome if you use the conventional geometry (alternate division, also called class I, method 1).

Gerry 

Gerry in Quebec

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Aug 19, 2015, 4:26:06 PM8/19/15
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Cammy,

Do you use SketchUp? If so, you may want to download one of Taff's Kruschke dome models in the Trimble 3D Warehouse and then use SketchUp's measurement tools to find various dimensions.

 

https://3dwarehouse.sketchup.com/model.html?id=11523bfa33e6123d2137e32e8ebf2b1

https://3dwarehouse.sketchup.com/model.html?id=fe572326700e392a2137e32e8ebf2b1

 

Alternatively, if you post more details of your dome project, you should be able to get specific answers from me and other members of the group.

 

* * *

 

About the calculators at the Zip-Tie Domes website..... I raised this topic on Yahoo's Dome Times discussion group several months back. Here's the conversation about the math problems lurking in those on-line tools:

 

https://groups.yahoo.com/neo/groups/DomeTimes/conversations/messages/14200

 

- Gerry in Quebec

Simon Kitt

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Aug 22, 2015, 7:14:45 AM8/22/15
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Hey there firstly thanks for the brilliant work with domerama.com it's helped me create some stunning coppiced structures!

Secondly I have become over 3 years hopelessly reliant on it 2 weeks ago half way through my latest build this page speed thing popped up and my heart has sunk.

Can you please please please admin the site and get it up and running again?

Do you need funds to keep it going?

I for one would chip in a bit to keep it running surely there must be others as well?

I really need access to domerama it's such an invaluable resource to me.

Hope you can find the time.

Thanks so so much

Simon Kitt

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Aug 25, 2015, 7:05:08 AM8/25/15
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Gentle bump...

Ralph Edge

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Sep 30, 2015, 5:56:20 PM9/30/15
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Someone in another thread thinks it is possible the creator of Domerama died...

Anyway, it turns out archive.org has a copy of the website...browsing it is very slow and a lot of stuff doesn't work.  I made a script to download the whole website to my computer, and am working out some kinks to get a static copy of the website up and going.  I've got the calculators working now, but some links, images, and other assets are still not working correctly.  If you would like me to let you know when I get a copy of the website back up and going, shoot me an email and I'll do that.

On Tuesday, August 25, 2015 at 7:05:08 AM UTC-4, Simon Kitt wrote:
Gentle bump...

biagiodicarlo

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Oct 1, 2015, 2:27:55 AM10/1/15
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I am interested in getting a copy of Domerama
Thank you very much,
Biagio






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Calvin Glover

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Oct 1, 2015, 6:27:48 PM10/1/15
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Me too.  Thanks.

 
Calvin
 

“A man sees in the world what he carries in his heart.” -Goethe

Cameron Gray

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Oct 1, 2015, 6:42:45 PM10/1/15
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Yeah me too please

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KDome

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Oct 3, 2015, 5:10:22 AM10/3/15
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On Wednesday, September 30, 2015 at 2:56:20 PM UTC-7, Ralph Edge wrote:
Someone in another thread thinks it is possible the creator of Domerama died... If you would like me to let you know when I get a copy of the website back up and going, shoot me an email and I'll do that.


On Tuesday, August 25, 2015 at 7:05:08 AM UTC-4, Simon Kitt wrote:
Gentle bump...

Bump again. Yes please! I will donate to the cause too as I am in a panic without domerama!

Ralph Edge

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Oct 3, 2015, 10:47:58 AM10/3/15
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Donations for Web hosting would be appreciated. My PayPal is ralp...@yahoo.com

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Danijel Dankic

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Jan 26, 2016, 9:32:18 PM1/26/16
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What heppened to the link with the working Krushke calculator?

Ralph Edge

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Jan 26, 2016, 10:36:21 PM1/26/16
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