8v geodesic dome calculations

[HSL]

I have built six residential dome homes over the past 15 years, all 45 feet or more in diameter and around 32-37 feet tall.  I am now in the planning stage of building an 8v hubless dome consisting of 640 triangles.  My question is one concerning dihedral angles and their calculation.  As you go up a dome from base to vertex, there are fewer and fewer triangles, starting at the base with 40 bottom bases triangles. The next group up and the three above also have 40 base triangles. Upon hitting the 6th level, the number of triangles per level decreases by five until you have the final vertex with five triangles making up the top pentagon. Of course, the angle between triangles is 72 degrees, whereas the angle between triangles on the bottom base layers is 9 degrees.   So, how do we compensate for this change in dihedral angle as we go up the dome?   

[lemondealc]

That's awesome! Can you share some pictures of the homes you've built? 

As for your question, can you clarify what you mean by "compensate". What is the problem you are trying to solve?

On Mon, Sep 25, 2023 at 8:20 AM HSL <livel...@gmail.com> wrote:

I have built six residential dome homes over the past 15 years, all 45 feet or more in diameter and around 32-37 feet tall.  I am now in the planning stage of building an 8v hubless dome consisting of 640 triangles.  My question is one concerning dihedral angles and their calculation.  As you go up a dome from base to vertex, there are fewer and fewer triangles, starting at the base with 40 bottom bases triangles. The next group up and the three above also have 40 base triangles. Upon hitting the 6th level, the number of triangles per level decreases by five until you have the final vertex with five triangles making up the top pentagon. Of course, the angle between triangles is 72 degrees, whereas the angle between triangles on the bottom base layers is 9 degrees.   So, how do we compensate for this change in dihedral angle as we go up the dome?   

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[Bryan L]

Hello HSL,

the dihedral angles don't change as you go up. They are the same between any particular pair of faces that are repeated around the dome.

On Mon, 25 Sept 2023 at 23:20, HSL <livel...@gmail.com> wrote:

I have built six residential dome homes over the past 15 years, all 45 feet or more in diameter and around 32-37 feet tall.  I am now in the planning stage of building an 8v hubless dome consisting of 640 triangles.  My question is one concerning dihedral angles and their calculation.  As you go up a dome from base to vertex, there are fewer and fewer triangles, starting at the base with 40 bottom bases triangles. The next group up and the three above also have 40 base triangles. Upon hitting the 6th level, the number of triangles per level decreases by five until you have the final vertex with five triangles making up the top pentagon. Of course, the angle between triangles is 72 degrees, whereas the angle between triangles on the bottom base layers is 9 degrees.   So, how do we compensate for this change in dihedral angle as we go up the dome?   

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[Paul Kranz]

HSL: The dihedral angle is a function of the shape of two triangles touching a common edge as their corners touch a common sphere. It has nothing to do with where they are on the sphere. The dihedral angle is a matter of trigonometry-- nothing else. Gerry's calculator is attached.

Paul sends...

On Mon, Sep 25, 2023 at 9:20 AM HSL <livel...@gmail.com> wrote:

I have built six residential dome homes over the past 15 years, all 45 feet or more in diameter and around 32-37 feet tall.  I am now in the planning stage of building an 8v hubless dome consisting of 640 triangles.  My question is one concerning dihedral angles and their calculation.  As you go up a dome from base to vertex, there are fewer and fewer triangles, starting at the base with 40 bottom bases triangles. The next group up and the three above also have 40 base triangles. Upon hitting the 6th level, the number of triangles per level decreases by five until you have the final vertex with five triangles making up the top pentagon. Of course, the angle between triangles is 72 degrees, whereas the angle between triangles on the bottom base layers is 9 degrees.   So, how do we compensate for this change in dihedral angle as we go up the dome?   

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Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

[Ashok Mathur]

Dear HSL

The number of triangles changes at each level even in the case of 2v domes, 3v domes etc etc.

So how are dihedral angles taken care in the case of simple domes hubless domes?

If you know the answer to that, you can figure it out for complex hubless domes also.

Regards

Ashok

On Mon, Sep 25, 2023 at 6:50 PM HSL <livel...@gmail.com> wrote:

I have built six residential dome homes over the past 15 years, all 45 feet or more in diameter and around 32-37 feet tall.  I am now in the planning stage of building an 8v hubless dome consisting of 640 triangles.  My question is one concerning dihedral angles and their calculation.  As you go up a dome from base to vertex, there are fewer and fewer triangles, starting at the base with 40 bottom bases triangles. The next group up and the three above also have 40 base triangles. Upon hitting the 6th level, the number of triangles per level decreases by five until you have the final vertex with five triangles making up the top pentagon. Of course, the angle between triangles is 72 degrees, whereas the angle between triangles on the bottom base layers is 9 degrees.   So, how do we compensate for this change in dihedral angle as we go up the dome?   

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[Sharky]

Hi All,

Paul, how does one use the Gerry's calculator you posted. Is there any tutorial on how to use it?

Many thanks !

[Paul Kranz]

Hey, Sharky, you put in the chord factors for the two triangles you want to get the dihedral angle. The angle is a function of the chord factors irrespective of the radius of the circumscribing sphere. In fact, the radius is 1 as indicated.

Paul sends...

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/0c8f0976-7dd5-414d-b466-fca17572386en%40googlegroups.com.

[Gerry in Quebec]

Hi HSL,

Apart from the question of dihedral angles,  you may wish to consider alternative subdivision methods for your 8v dome. Depending on the construction method for the "hubless" dome (panel dome?) you  plan to build, and on your building height and floor area requirements, one method of geodesic subdivision may be better than another. For example, maybe you would like to build a dome that is not as tall as a hemisphere but has a flat base nevertheless. There are solutions to that design problem. 

Here's a Geodesic Help conversation from 2017, regarding 8 frequency domes that may be of interest to you: 

https://groups.google.com/g/geodesichelp/c/960EgZfW7hw/m/E_YJmOcPVkQJ

- Gerry in Québec