Post by Ron Walker on Apr 21, 2023 11:01:21 GMT -7
FORMULA FOR DOME PATTERN
1-Take desired circumference of the dome, divide that by the number of desired gores to find the width of each gore at the base of the dome.
2-To find your constant: 90 divided by 1/4 of the circumference equals your constant.
3-To find the width of the gore at intervals from the base towards the zenith:
a-Multiply the constant by the distance up from the base.
b-Find the cosine of that number.
c-Multiply the cosine by the width of the gore's base. The answer is your width at the distance up from the base.
An example: Since I wanted as large a dome as possible from the material I had, I went about this a bit backwards. Just follow along.
The material I found came in a roll 52 inches wide. I found that I needed two inches on either side of the gore to make the support collar for the gore. Thus each gore could be 48 inches at the base. I decided to use a total of 14 gores as this made as large a dome as I could build in the space I had available. Thus I am starting the above calculation with a circumference of 672 inches.
As in the above calculation:
1-Desired circumference 672 inches. Total number of gores 14. Thus 672 divided by 14 equals a 48 inch base for each gore.
2-90 divided by 672/4 equals 0.5357 which is my constant for the above dome.
3-a-0.5357(40)=21.428
3-b-cos21.428=0.93088
3-c-0.93088(48inches)=44.6822 or 44 11/16 inches.
If you followed that at all you would understand the each gore has a base that is 48 inches wide and that at a distance of 40 inches up along the gore toward the zenith of the dome, each gore would have a width of 44 11/16 inches. Now it is best to make a template and then cut the material for the gores from the template. Be sure to allow the extra material on both edges to make the support collar. We made calculations for every two inches along the gore's 1/4 circumference of the dome.
The is an example from the calculations for my large dome. Before this was tackled we made a small baby dome to make sure we were doing everything right. Calculations and pictures will follow both on the experimental dome and the full size one as construction begins.
1-Take desired circumference of the dome, divide that by the number of desired gores to find the width of each gore at the base of the dome.
2-To find your constant: 90 divided by 1/4 of the circumference equals your constant.
3-To find the width of the gore at intervals from the base towards the zenith:
a-Multiply the constant by the distance up from the base.
b-Find the cosine of that number.
c-Multiply the cosine by the width of the gore's base. The answer is your width at the distance up from the base.
An example: Since I wanted as large a dome as possible from the material I had, I went about this a bit backwards. Just follow along.
The material I found came in a roll 52 inches wide. I found that I needed two inches on either side of the gore to make the support collar for the gore. Thus each gore could be 48 inches at the base. I decided to use a total of 14 gores as this made as large a dome as I could build in the space I had available. Thus I am starting the above calculation with a circumference of 672 inches.
As in the above calculation:
1-Desired circumference 672 inches. Total number of gores 14. Thus 672 divided by 14 equals a 48 inch base for each gore.
2-90 divided by 672/4 equals 0.5357 which is my constant for the above dome.
3-a-0.5357(40)=21.428
3-b-cos21.428=0.93088
3-c-0.93088(48inches)=44.6822 or 44 11/16 inches.
If you followed that at all you would understand the each gore has a base that is 48 inches wide and that at a distance of 40 inches up along the gore toward the zenith of the dome, each gore would have a width of 44 11/16 inches. Now it is best to make a template and then cut the material for the gores from the template. Be sure to allow the extra material on both edges to make the support collar. We made calculations for every two inches along the gore's 1/4 circumference of the dome.
The is an example from the calculations for my large dome. Before this was tackled we made a small baby dome to make sure we were doing everything right. Calculations and pictures will follow both on the experimental dome and the full size one as construction begins.
