# Domes, Spires and Vaults: Steps for Dome Panel Layout

Formulas:

Full Circle Circumference = 2 x Radius x Pi.
Half Circle Circumference = Radius x Pi.
Pi = 3.141592

Domes come in many heights, radii, diameters, shapes and sizes. For our layout example, we are going to do an entry canopy designed as a true hemispherical half dome. The height is also the radius "R" and is one half of the base diameter. The base of the dome is the dome equator.

## A. Determine Dome Circumference and Panel Width at Base

Calculating the complete dome circumference at the base and dividing that amount by the number of panels will establish the width of each panel at the base.

Dome Radius "R" = 36"
Dome Base Circumference "C" = 2 x Pi x R = 2 x 3.141592 x 36 = 226.194624 inches

If one half of a dome is built, the number of total dome panels should be an even number.

Assuming 16 dome panels for the full dome, each panel base dimension at the equator is therefore
226.194624 / 16 = 14.137" wide.

Figure A. Plan

## B. Establish Dome Height and Panel Layout Concept

In a perfectly hemispherical dome, the dome height will be equal to its radius, 36 inches. Each of the eight panels will run from the base to the top center (vertex) of the dome. The shape of each panel will gradually decrease from its widest point at the base to its narrowest point at the vertex.

The shape of the panel is determined by two items: The panel length from base to vertex and the decreasing panel widths from base to vertex. The panel length can be determined by calculation. This length is equal to one fourth of the dome circumference or 226.194624 / 4 = 56.549". Since it is difficult to fabricate dome panels to a complete point, each panel length will be stopped approximately 2" short of the dome vertex and fabricated at 54 inches in length.

The panel widths can be determined by slicing the dome in parallel horizontal slices or Stations, each slice represents a full circle of decreasing size. The radius of each of the circles will allow calculating the circumference at that Station. Dividing that Station circumference by 16 will give the width of each panel at that Station. This process is similar to the base panel width calculation.

We now have established that our panels are 14.137 inches wide at the base and 54 inches long. Depending on the dome rib design, additional widths will be added to each panel (See Table 4.7.17.1).

Figure B. Elevation

Table 4.7.17.1 Dome Panel Calculations: Calculations for Dome With 36-Inch Radius and Stations at 6 inches

Dome Radius = 36"
Panels quantity = 16
Pi = 3.141592
Circumference = 2 x Pi x Radius
For Double Locked Seam For "T" Style or Dbl. Locked Cap Seam
Station Radius Decimal Circle Circumference รท 16 Measure from Guide Line Add 1.5" from Guide Line Add 2.125" from Guide Line Add 1.75" from Guide Line To Each Side
A. Points B. Points
1 36 36.000 14.137164 7.0685 8.5685 9.1935 8.8185
2 35 7/16 35.4375 13.91627081 6.9581 8.4581 9.0831 8.7081
3 33 31/32 33.96875 13.33949416 6.6697 8.1697 8.7947 8.4197
4 31 17/32 31.53125 12.38229034 6.911 7.6911 8.3161 7.9411
5 28 7/32 28.21875 11.08147491 5.5407 7.0407 7.6657 7.2907
6 24 3/32 24.09375 9.461591531 4.73079 6.23079 6.85579 6.48079
7 19 5/16 19.3125 7.583999438 3.7919 5.2919 5.9169 5.5419
8 13 31/32 13.96875 5.485514156 2.7427 4.2427 4.8677 4.4927
9 8 1/4 8.2500 3.23976675 1.61988 3.1198 3.7448 3.36988
10 5 5/16 5.3125 2.086213438 1.0431 2.5431 3.1681 2.7931

## C. Establish the Number of Dome Panel Stations, Quarter Dome Section

The shape of the panels can be determined by plotting their width at various points up the dome. We will call these points Stations. For a 36-inch radius dome, Stations every 4 to 6 inches apart give accurate results. Larger domes can have stations spaced farther apart and smaller domes, closer together. We will use 6 inches. A partial section of a quarter dome simulates a typical panel section. Make a full scale layout of the dome arc using the 36-inch radius on a sheet of metal. Divide this arc with Stations every 6 inches along the length of the arc. Number the stations from the base up, Number 1 through 10.

Figure C. Partial Elevation - Quarter Dome

## D. Typical Panel Layout

Using a piece of metal at least 18 inches wide by 54 inches long, place a centerline along it length. This will become the guideline of the pattern for the dome panels. Starting at the base using the dividers place station marks at 6-inch intervals on the pattern centerline and number the stations 1 through 10 to correspond to the quarter dome layout in Detail C.

Figure D. Typical Panel Layout - Double Locked Seam Rib Layout (See Table 4.7.17.1 above)

On the Quarter Dome Section draw horizontal lines, parallel to the base, from the station marks to the vertical axis. Measure the length of each of these station lines. This corresponds to the radius of the dome at this point. Using this radius calculate the circumference of the dome at this station and divide it by the number of panels, 16, to determine the width of the panel at this station. Adding the respective dimensions for the vertical legs and flanges at each side completes the width of the panel at each Station (See Table 4.7.17.1 above).

Panel dimensions are all determined from the common guideline. These are points "A" and "B" on the panel. Completing each station up the panel and connecting all the "A" points and all the "B" point leads to the panel pattern. This first pattern can be cut and used to trace and cut the remaining 7 panels.

## E. Dome Assembly

When all 8 panels have been cut, the flanges are formed on each edge using beading machines. The panels are then curved with stretching tools to match the dome radius. The rib seam indicated is a double locked standing seam. The panels are cleated to the deck with cleats spaced at 12" O.C. For bolder seams, double locked batten seamed systems can also be used and their installation is only limited by the dome diameter.

Figure E. Dome Seam/Rib Detail - Double Locked Seam Rib