An architectural compass is the dome builder's friend, so let's get acquainted with the new toys we will need to design an earthbag dome on paper. We will need:
• An architectural-student-quality drawing compass (preferably with an expandable arm)
• A three-sided architect's (or engineer's) scale ruler (in inch or centimeter increments)
• A good mechanical pencil and eraser
• A combo circle template (optional)
• A flat surface with a square edge like a pane of glass or Plexiglas or a sheet of Masonite
(or drafting board) to use as a square edge for the T-square to follow
Some light-stick tape for tacking down our drawing paper without tearing it (Fig. 11.10).
We also like to have a sheet of graph paper taped to the surface of our plate glass drafting board to use as a quick reference for aligning drawing paper.
As a rule of thumb, all measurements for domes (and circular structures) are defined by their interior diameter. This measurement remains constant, whereas the exterior measurements may vary according to what thickness the walls become. There are many bags and tubes with different size widths available, and many different ways to finish the exterior of an earthbag dome. For practice, let's design a small 14-foot (4.2 m) interior diameter dome using a half-inch (1.25 cm) scale.
Align your drawing paper with the center of the drawing board and tape the corners. Using the T-square as a guide, set the ruled architect's (engineer's) scale against it horizontally on the page and mark the centerline on the paper where you want the ground level of your structure to begin. Leave a few inches of free space at the bottom of the paper. For now, we are going to design a dome with a floor level that begins at grade level. Using the scale of one-half-inch (1.25 cm) equal to one-foot (30 cm) ratio, draw a line equal to 14 feet (4.2 m), with seven feet (2.1 m) on either side of your center mark. This is the interior diameter of the dome (Fig. 11.11).
Turn the T-square vertically on the board and place the half-inch (1.25 cm) scale ruler along the center mark. From the center of the diameter, measure 14 feet (4.2 m) up and draw a line. This line denotes both the interior (vertical) height of the dome (14 feet [4.2 m]) and the (horizontal) radius (7 feet [2.1 m]) (Fig. 11.12).
We are going to mark the spot where our compass pivot point will be positioned. The compass formula is one-half of the radii from the interior diameter width of the dome. Divide the radius in half (7 feet [2.1 m] divided by 2 = 3.5 feet [1.05 m]). Make a mark three and one-half feet (1.05 m) beyond the end of your interior diameter line. Repeat this process on the opposite side of the horizontal line (Fig. 11.13).
Use the architectural compass to create the outline of the dome. Adjust the spread of the compass so it will reach from the fixed pivot point (3.5 feet [1.05 m] beyond the end of your horizontal line) to the other end of the 14-foot (4.2 m) diameter horizontal line. This is where our springline will begin. With steady pressure, swing the compass arm up to meet the 14-foot (4.2 m) height mark (Fig. 11.14a).
Reverse the process to complete the other side (Fig. 11.14b).
11.14b | |||
Adjust the compass to accommodate the thickness of the bag walls you will be building. As an example, for a 50-lb. bag with a 15-inch (38 cm) working width, use the scale ruler to extend the 14-foot (4.2 m) diameter base line 15 inches (38 cm) more on either side. From the original fixed compass point, lengthen the arm to reach to the exterior wall mark on the opposite side of the dome and swing the free end of the compass arm up to the top of the dome
Repeat for the other side of the dome (Fig. 11.16a).
We now have the basic shape of the dome with its interior, exterior, width, and height measurements (Fig. 11.16b).
We'll do a drawing of the same structure highlighting many different features, always beginning with the same basic shape we just drew. We'll do an elevation drawing that shows what the building looks like from grade perspective, and another that highlights a sunken floor or underground room. Another drawing will show window and door placements, or roof details, etc. But first, let's establish the measurements we'll need to transfer onto the construction-size building compass to create the same profile we drew on paper. (See Chapter 3, page 48).
Ideally, this drawing is easiest to read when done on a large piece of paper or cardstock using a large scale, like one inch (2.5 cm) equals one foot (30 cm). Or work in metric, if this is easier for you. If you don't have a drawing compass large enough to draw this expanded profile, then you can scribe the profile with a pencil tied to a string (Fig. 11.17).
The centerline from top to bottom of the dome represents the construction-size building compass. Starting at the bottom, use the T-square and mark along its length every one-half-inch (which is the equivalent of six inches on our scale) of height or, if using centimeters, every 1.25 centimeters (which would be the equivalent of 10 cm).
Align the T-square horizontally along the first height mark. Draw a line from this height mark to the interior edge of the dome wall (Fig. 11.18).
These measurements are what you will refer to when adjusting the length (radius) of the building compass arm during construction. This process aids us in duplicating the profile from paper to reality.
Remember the Catenary arch? To test the dynamic forces of our compass formula we hang a chain on a cut-away view of our drawing. Check to see that the chain hangs well within the middle third of the wall. If the chain strays from the center (either inside or out) we can do two things: increase the thickness of the walls and/or free hand a new profile that more closely follows the shape of the hanging chain (Fig. 11.20).
Measure this horizontal distance between centerline and interior edge of wall and write this measurement along the wall of the dome.
Round off the number to the nearest one-half-inch or centimeter. Repeat this process, going up the vertical compass line until each height mark has a corresponding radius measurement (Fig.11.19).
11.19
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a^k \ | |
/ / " |
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/ / 10 |
\ | |
/ v |
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/ 8' |
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/ 7' |
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5' | ||
H' |
(o'T\ | |
3' | ||
S! | ||
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I |
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11.20: The suspended chain should hang within the center third of the roof and walls, and, where the chain exits the compass profile, is where buttressing is added.
You may be wondering why we don't calculate the compass measurements based on the height of each row of bags. At first, that is what we did (on paper). We measured the height of our working bags at five inches (12.5 cm), and proceeded to calculate all of our radius adjustments at five-inch (12.5 cm) increments. This worked fine at first while the lower bags were only stepped in one to two inches (2.5-5 cm). When we started overhanging them three to four inches (7.5-10 cm), the portion of the bag that remained on the underlying row started flattening down to four inches (10 cm) and eventually three and one-half inches (8.75 cm) in thickness (Fig. 11.21).
This is one of those phenomena that one only discovers by doing it. We couldn't count on the row of bags conforming to our role model on paper. Making pre-calculations provides reference points to help keep us on track along the way. We know, for example, that at the five-foot (1.5 m) height we want to be at a radius of six feet, three inches (187.5 cm) exactly, for this 14-foot (4.2 m) diameter dome. If a row finishes out at a height in between the marks on the compass, we just split the difference. Pre-measuring on paper gives us a reference guide that helps to speed the process during construction.
As long as we are within one-half-inch (1.25 cm) of our radius, we still feel fairly accurate. We are dealing with a mushy medium, after all, that will squish out here and there. It's partly the nature of the material. For the sake of creative license, and given unforeseeable circumstances, feel free to make alterations, as long as they maintain the structural integrity of the dome.
If all of this sounds terribly confusing and complex, it is simply because it has yet to become familiar to you. Liken it to trying to explain how to drive using a stick shift to someone who has never even sat in a car. After a while it will become automatic. Relax;you'll get it.
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