Dihedral Angles of 3V Kruschke 5/9 dome

[Kevin Creedy]

Hello,

I'm working on a greenhouse project of building a 16 foot in diameter 5/9 geodesic dome and would like to build the frames first and then assemble them. I've been using the calculator on domerama.com for the Kruschke flat bottom 4/9 and 5/9 domes.

I looked at previous posts and did find the information I'm seeking, but the files seem to be missing. I am mostly interested in knowing what the dihedral angles are of the dome so I can divide them in half and make my triangle angles accordingly.

I'm really enjoying thinking about geodesic domes and planning a build. Super excited at times. I would really appreciate any help you may offer.

Kind regards,

Kevin

[Kevin Creedy]

The dome calculator on domerama.com gives degrees of 9.49, 11.02, 12.16 and 12.74. Is this the dihedral angles?

Thank you,

Kevin

[Dx G]

Those look like axial angles.  Think of it like an arm pit, its the angle where a radial line from the dome center would meet the surface.

Although I'm not trying to talk you out of a Kruschke dome, just wanted to make sure you were aware of other domes that can have a flat truncation

1) Almost any octahedral

2) Edge up 3f icosa class 1 alternate

3) Edge up 2f icosa class 2 method 3 triacon.  You can also use a Pentakis Dodeca for this one.  Although they make use of some half triangles at the base, nice feature for these is that all the triangles and all the dihedral angles are all the same, which simplifies a lot of things. 

4) Also note that Hugh Kenner's book has some specific strut length corrections to flatten a routine 3f icos class 1 alternate of either a 3/8 or 5/8 type

  There are likely more, but those come to mind.

DxG

[Kevin Creedy]

Thank you for the information, I really appreciate it. I will take some time to research those.

I'm drawn to the triangle layout on the Kruschke 5/9 dome, they create patterns that I've been designing my greenhouse around.

On the math calculations that Gerry Toomey (May 2015) shared, are the 5 cord factors the same for a 5/9 Kruschke dome? I'm going to do the calculations with my family and see if we can come up with the dihedral angles. :)

Thank you for the help!

Kind regards,

Kevin

[Dx G]

Some of the other domes only use 2 or 3 chord factors, so that makes things a bit easier.  Domes like that are fine for smaller structures.  As the diameter increases, the triangles get big enough that one needs to go to a higher frequency to keep the struts from getting too long and weakening the frame.   

  Another I didn't mention earlier is a 2f Class 1 ico alternate.  That one is quite common and unlike the edge up designs, does not require cutting triangles.

Enjoy the project

DxG

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[Kevin Creedy]

Thank you again,

I feel pretty set on doing the developing work for the 3V Kruschke design if anyone know the cord factors I would really appreciate them in order to do the calculations of the dihedral angles.

Kind regards,

Kevin

[Dx G]

Kevin,

  If you don't already have these, they will likely help you a great deal.

First, previous discussion related to your questions.

https://groups.google.com/g/geodesichelp/c/zVmMJrlKPss

   In particular, on 2/4/22, Blair posted a copy of Kruschke's book.  Some of the highlighted lines are not readable, but I see page 31 has a discussion of the dihedral angles, and a very nice collection of data from there on that should be helpful.

Later, there are links to more discussions on the flat truncation issues. 

Hopefully that will reduce the effort needed to move the project ahead. No sense reinventing....save your talents for the new stuff. As they say, the reach should exceed the grasp.

DxG

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[Cindi Hanshew]

Hi, 

Paul Robinson has some really easy plans on YouTube,

https://youtu.be/Y13QaCWF39M

https://youtu.be/MTvCKO0uByg

https://youtu.be/3T22C4VLqCs

Cindi Hanshew
260-210-5288
Crit...@gmail.com

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[Kevin Creedy]

Thank you for all the information, I think I know why you were directing me to a different dome design, I appreciate that and will probably do so. The 3V Kruschke model seems to have 6 different angles you have to cut in order to create the dome. I may be wrong, but that's as I understand it now after seeing the dihedral angles.

Kind regards,

Kevin

[Paul Kranz]

Make Your Own Kruschke Model. Print on cardstock, cut out and tape together. Paul sends...

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/b84b1a8b-f5e1-442b-8d29-642b5f541a09n%40googlegroups.com.

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Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

[Dx G]

Kevin,

  In terms of saving time and effort, I think you make a good decision looking at some of the other domes.  One of the best for uniform parts is the Pent Dod.  Made of one panel size, and all have the same dihedral angle.  The edge up configuration gives you a flat base, although several base panels are triangles cut in half, unless you put a door there, which further reduces those too.

https://mathworld.wolfram.com/PentakisDodecahedron.html

DxG

From: Dx G <yipp...@gmail.com>
Date: Fri, Nov 18, 2022 at 9:08 AM
Subject: Re: Dihedral Angles of 3V Kruschke 5/9 dome
To: <geodes...@googlegroups.com>

Kevin,

  If you don't already have these, they will likely help you a great deal.

First, previous discussion related to your questions.

https://groups.google.com/g/geodesichelp/c/zVmMJrlKPss

   In particular, on 2/4/22, Blair posted a copy of Kruschke's book.  Some of the highlighted lines are not readable, but I see page 31 has a discussion of the dihedral angles, and a very nice collection of data from there on that should be helpful.

Later, there are links to more discussions on the flat truncation issues. 

Hopefully that will reduce the effort needed to move the project ahead. No sense reinventing....save your talents for the new stuff. As they say, the reach should exceed the grasp.

DxG

On Fri, Nov 18, 2022 at 8:53 AM Kevin Creedy <kevinx...@gmail.com> wrote:

Thank you again,

I feel pretty set on doing the developing work for the 3V Kruschke design if anyone know the cord factors I would really appreciate them in order to do the calculations of the dihedral angles.

Kind regards,

Kevin

On Friday, November 18, 2022 at 9:46:46 AM UTC-5 yipp...@gmail.com wrote:

Some of the other domes only use 2 or 3 chord factors, so that makes things a bit easier.  Domes like that are fine for smaller structures.  As the diameter increases, the triangles get big enough that one needs to go to a higher frequency to keep the struts from getting too long and weakening the frame.   

  Another I didn't mention earlier is a 2f Class 1 ico alternate.  That one is quite common and unlike the edge up designs, does not require cutting triangles.

Enjoy the project

DxG

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[Gerry in Quebec]

Hi Kevin,

Do you still need help with your dome design, 3v Kruschke or other type? Dihedral angles can be calculated for any geodesic dome directly from the chord factors. There are various ways to build panel domes, and the compound angles required to cut the struts making up each triangular frame depend on the particular construction method selected.

- Gerry in Québec 

[Paul Kranz]

Gerry: Is there a formula for converting a chord factor to a dihedral angle? Paul sends...

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[Gerry in Quebec]

Hi Paul,

It seems like it was only yesterday that you first posed that question. In fact, it was nearly 11 years ago, in February 2012 to be more precise. How time flies! And how well Google Groups, with Taff's help I'm sure, seems to squirrel away posts and uploaded files.

Here's the portion of our conversation containing an Excel dihedral angle calculator, which also spells out the underlying equation. You need all three chord factors of a dome triangle to calculate any of the dihedral angles along the edges.

https://groups.google.com/g/geodesichelp/c/a5upLyCT8f4/m/yxncHDeerCcJ

The output is the dihedral angle between a triangle on the surface of a geodesic dome or sphere and the triangle formed by a chord (one of the three triangle edges) and the two radii terminating at the ends of that chord. This is what Joe Clinton, one of the godfathers of geodesic math, refers to as a "partial dihedral angle". To get the full dihedral angle between two surface triangles, do the  calculation twice, once for each triangle, and then add the two numbers together.

Cheers,

- Gerry in frigid Québec (minus 15 degrees early this morning)

 

[Paul Kranz]

Gerry: Good stuff, thanks. 74° in Tampa, FL!! Paul sends...

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[Dx G]

They had 4-6 feet of snow west of us, but turned to rain on the warm side of the storm. If it had been colder, it would have been snow here too and we'd be buried.  We get the cold side later this week as the storm spirals off to the east, and when *we* hit   -15, that's F here rather than C Gerry :-)

As usual, Gerry does beautiful work.  Had a question though.  Kenner uses a simple multistep trig method, which he reduces into an equation.  I want to compare his approach/method to Gerry's equations(s) when I get a chance.  I'm curious to see whether or not they are actually both the same approach, perhaps with different algebraic arrangements, or whether they are actually different in some way.    Any insights appreciated, as my comparison may be unnecessary or perhaps already been done. 

DxG

[Gerry Toomey]

Hi Dan (aka DxG),

Despite all the good work Hugh Kenner did trying to explain the geometry of domes in his1976 book Geodesic Math and How to Use It, that publication is riddled with both descriptive and math errors. These include his explanation of dihedral angles in chapter 17, About Angles. His formula works for only a narrow range of triangle pairs. It's too bad the publisher, the University of California Press Berkeley, didn't get its act together to correct Kenner's errors before reprinting the book in 2003. (Not long after that, I offered to help them edit and correct any future edition but never got a response.... maybe because I'm a science journalist not a mathematician!) 

Many years ago, a guy named Bob Burkhardt set up a website to record and correct the errors in Kenner's book. I made a number of contributions to that "errata" list, including comments on the dihedral angle calcs. Burkhardt's list can be found here:

https://bobwb.tripod.com/synergetics/hugh/index.html

Cheers,

- Gerry in Québec (yes, where we use Celsius rather than Fahrenheit degrees)

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[Dx G]

Hi Gerry -

  Yes, I would agree.  In fact, I think you were the one that sent me the errata link some time ago.  Back then,  I printed it out, went through my copy of the book and made notations.  I also found a few boo-boos myself that were not on his list.

  However, I see that my copy of the list predated the one in the link you just attached, by several years.  So I'll see if I have anything to add to the newer list that is not already there.  I did make a note in my copy of the book with the dihedral angle formula you provided for triangles with unequal sides.  So that partly answers my original question, since that formula is yours. 

    While I was working on my creased diamond panel calculator, I used that formula (yours) and successfully validated it against about a dozen known dome dihedral angles.  These were important when one makes a flange to connect the panels. However, when I looked at the formulas in the spreadsheet you generously provided, it did not look like a cookie-cutter version.  However, I wasn't sure if they were, or not, related, or perhaps one set an algebraically reduced/rearranged version of the other.  That's what I intended to look at later on, and was asking about.   Could be once I look through the cell addresses, it will be obvious.

thx