Sphere radius

[Blair Wolfram]

Can anyone help me with this sphere? 

What is the sphere radius for a low profile dome with a 100' diameter that measures 20' height at its center?

I can't visualize how to set up the problem, other than starting by calculating the hypotenuse for a right triangle with a 20' leg and a 50' leg.

Thank you,

Blair

--

Blair F. Wolfram
Founder, Dome Inc.

thedo...@domeincorporated.com

http://www.hurricanedomes.com

888-DOME-INC or 612-333-3663

[Adrian Rossiter]

Hi Blair

On Fri, 27 May 2022, Blair Wolfram wrote:
> Can anyone help me with this sphere?
> What is the sphere radius for a low profile dome with a 100' diameter that
> measures 20' height at its center?
> I can't visualize how to set up the problem, other than starting by
> calculating the hypotenuse for a right triangle with a 20' leg and a 50'
> leg.

Call the height of the base above the sphere centre l, then

R = l + 20

Rearranging

l = R - 20

Using Pythagorus on your triangle

R^2 = l^2 + 50^2

Substiute for l

R^2 = (R - 20)^2 + 50^2
R^2 = R^2 - 40*R + 400 + 2500
40*R = 2900
R = 72.5

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[Paul Kranz]

Blair: Is the dome based upon a Platonic polyhedron? Paul sends...

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[vine...@gmail.com]

Good morning Blair,

 

Let us call the C the cord of your arc. This cord has a length of 100.

Let us call A the arrow of your arc. This arrow has a length of 20.

 

Then the formula to calculate the radius is: C^2/8A + A/2

 

Or 10 000 / 160 + 10 = 72,5 is your radius.

 

This formula is derived from the construction of right-angled triangles such as this example where the arrow is “f” and not “A”.

 

 

Best regards,

 

Pierre

 

De : geodes...@googlegroups.com <geodes...@googlegroups.com> De la part de Blair Wolfram
Envoyé : 27 mai 2022 03:18
À : geodesichelp <geodes...@googlegroups.com>
Objet : Sphere radius

 

Can anyone help me with this sphere? 

What is the sphere radius for a low profile dome with a 100' diameter that measures 20' height at its center?

I can't visualize how to set up the problem, other than starting by calculating the hypotenuse for a right triangle with a 20' leg and a 50' leg.

 

Thank you,

 

Blair

 

--

Blair F. Wolfram
Founder, Dome Inc.

thedo...@domeincorporated.com

http://www.hurricanedomes.com

888-DOME-INC or 612-333-3663

--

[glenn pete]

This is an elliptical  I posted the equation for elliptical on an earlier post and was looking for someone who may have a program for one with different frequencies so I could determine the approximate strut length that I could use comfortably by myself to build and the only response was ( what is this ?) Good luck  otherwise Google the equation for ellipsis

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[Adrian Rossiter]

Hi Glenn

On Fri, 27 May 2022, glenn pete wrote:
> This is an elliptical I posted the equation for elliptical on an earlier
> post and was looking for someone who may have a program for one with
> different frequencies so I could determine the approximate strut length
> that I could use comfortably by myself to build and the only response was (
> what is this ?) Good luck otherwise Google the equation for ellipsis

The Antiprism poly_form program will map a geodesic sphere onto an
ellipsoid, and optionally try to equalize the edge lengths on the
ellipsoid

https://www.antiprism.com/programs/poly_form.html

poly_form geo_o_8 -n 0 -a e -E 0.5,0.5,0.14| antiview -R -70,0,0
poly_form geo_o_8 -n 1000 -a e -E 0.5,0.5,0.14| antiview -R -70,0,0

You can display edge numbers with 'antiview -n e', and look up
edge lengths with off_query.

[Ashok Mathur]

Dear Glen

 In a spherical dome based on an icosahedron, it is possible to generate a small set of connected triangles, that when rotated and displaced cover the entire sphere.

Similar thing is not possible in case of an elliptical dome. At best there is a four fold symmetry so that only one fourth of vertices need to be calculated.

Hugh Kenner in Geodesic Maths Chapter 13 page 84 on wards describes how to do this. The book is readily available online for free reading.

A new Zealand architect, whose name I vageuly remember as Ritche has doe tons of practical work on such domes.

You can look at the following links also

1.       Elliptical domes (geo-dome.co.uk)

2.       Monolith dome calculator for a thin shell dome Ellipsoid Dome Calculator (monolithicdome.com)

3.       CAD solution here elliptical dome | MCAD Central

4.       Parametric design and calculation of circular and elliptical tens...: Ingenta Connect

5.       Behind a paywall Structural behavior and design methods of Tensegrity domes - ScienceDirect

6.       How To Create Domes, Spheres & Other Curved Shapes in Sketchup - YouTube

 Regards

Ashok

Regards

Ashok

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[Blair Wolfram]

Hello Adrian and Pierre;

I sincerely thank you both for responding to my request for spherical mathematical help. I've been asked to help with repairs to this acrylic covered dome damaged by hail last month. This is a ribbed dome with 234 trapezoid panels divided into 7 rows, and I need this calculation to determine arc measures for the edges of the panels.

Adrian, I work often with Gerry and he expresses nothing but respect for your work. Thank you for stepping up.

Blair

--

Sphere

Blair F. Wolfram
Founder, Dome Inc.

[Ashok Mathur]

Dear Glenn 

Consider the overwhelming advantage of a geodesic dome over a geodesic ellipsoidial structure.

All aspects of a spherical geodesic structure get described by three parameters : its radius, frequency and class of subdivision.

You needs several more magnitude of parameters to define an ellipsoidal structure.

But those who want such structures for the advantages they offer, make their own calculations that are not difficult to do.

Think spreadsheets rather than conventional programmes.

Regards

Ashok

Sent from e-cards my iPhone

On 01-Jun-2022, at 6:22 AM, glenn pete <007gle...@gmail.com> wrote:



And this is 2022 and no program for this what have programmers been doing? solid works has been around a long time I am really disappointed in the so called professionals just saying I mean like are you people being paid to stay in boxes?

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Blair F. Wolfram
Founder, Dome Inc.

thedo...@domeincorporated.com

http://www.hurricanedomes.com

888-DOME-INC or 612-333-3663

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[glenn pete]

Due to the thinking not leaving  the box that's your opinion thanks I will have to discard it though and have a great one

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[John Hurt]

I would like to start a thread on the pros and cons of SolidWorks, AntiPrism, Google Sketchup, and other software packages for geodesic domes and other space frame construction.

I need to decide which package to use for my work.

Your input would be very helpful.

John Hurt

[Ashok Mathur]

Dear John

Please consider two things.

Does the software you wish to choose allow easy import of data from other software. If so choose that software you already have knowledge.

What is software that most others in the group use? Does your software allow you to import data from it.

In this group the software mentioned most often are SketchUp and Antiprism. Both are powerful with plenty of work already done readily available.

Regards

Ashok

Sent from my iPhone

On 02-Jun-2022, at 6:43 PM, John Hurt <you...@johnhurt.com> wrote:

I would like to start a thread on the pros and cons of SolidWorks, AntiPrism, Google Sketchup, and other software packages for geodesic domes and other space frame construction.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/0caeea1a-056d-418f-8381-e4f78ba72dfan%40googlegroups.com.

[Ashok Mathur]

For space frame construction of serous quality consider formin as it allows you to generate unique structures.

I can send a link later on.

Ashok

Sent from my iPhone

On 02-Jun-2022, at 6:43 PM, John Hurt <you...@johnhurt.com> wrote:

I would like to start a thread on the pros and cons of SolidWorks, AntiPrism, Google Sketchup, and other software packages for geodesic domes and other space frame construction.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/0caeea1a-056d-418f-8381-e4f78ba72dfan%40googlegroups.com.

[Ashok Mathur]

Dear John

There was a spelling error in the program name that may have prevented you from locating it.

The correct name is FORMAIN.

First link that describes the software is here

SPACE STRUCTURES SHAPING AND VISUALIZATION... (tripod.com)

One link that may be useful is

https://www.semanticscholar.org/paper/EXAMPLES-OF-APPLICATION-OF-PROGRAMMING-LANGUAG

Another useful link is

Configuration of Various Space Structures using Formex Algebra (ijert.org)

Basics can be understood here

[PDF] Basics of Formian-K | Semantic Scholar

Regards

Ashok

Regards

Ashok

[Ken Brown]

The semanticscholar link did not work for me. Is this the one?

[PDF] EXAMPLES OF APPLICATION OF PROGRAMMING LANGUAGE FORMIAN IN ENGINEERING AND ARCHITECTONIC EDUCATION AND IN PROFESSIONAL DESIGN | Semantic Scholar
<https://www.semanticscholar.org/paper/EXAMPLES-OF-APPLICATION-OF-PROGRAMMING-LANGUAGE-IN-Rȩbielak-Ishikawa/2166f880a6a6b0c53b9cd1e7c74e2be4c1758898>

Ken G. Brown

On Jun 3, 2022, at 01:22, Ashok Mathur <ashokch...@gmail.com> wrote:



To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAD-a3OjtwKpMOWKHS_08_zxsjKo_55%2BPsvj7GEPUoa78Qhd63Q%40mail.gmail.com.

[Ashok Mathur]

Dear Ken

Yes that link works and the pdf file can be downloaded from another link on the landing page.

I am honoured that at least one person has followed the links I had sent.

Besides the links from Poland, the more recent links come from a University in UK.

Regards

Ashok

Sent from my iPhone

On 03-Jun-2022, at 4:25 PM, 'Ken Brown' via Geodesic Help Group <geodes...@googlegroups.com> wrote:

The semanticscholar link did not work for me. Is this the one?

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/026FB7B7-9382-42A8-83AF-D44DC20FB18B%40mac.com.

[Ashok Mathur]

Dear Ken

The recent starting points can be followed from here

Prof Hoshyar Nooshin | University of Surrey

Regards

Ashok