Catenary Arch Directions
| Materials Needed: | Approximate Costs: |
| 1 - 30” x 36” board for backdrop | (ours was donated) |
| 2 - 1 ½” x 3 ½” board (5 ft. long) | $ 4.00 (actually 2” x 4”) |
| 1 - 3 ft. piano hinge | $10.00 |
| 4 - doorstops | $ 9.00 |
| 2 - handles | $ 4.00 |
| 1 - turnbuckle | $ 1.00 |
|
1 - enlarged drawing as arch guide |
(dad’s employment - 1 large candy bar for owner) |
|
Optional: Silver and black acrylic paint |
Construction:
Note: These plans are slightly modified from the plans in the San
Francisco Exploratorium Cookbook Recipe #102.
1. We began by assembling the layout backboard. We used a small art table that was 30” x 36” and attached a 3 ft. piano hinge to the bottom. This allows the backboard to drop away from the base after the arch is constructed. The base was cut from one of the 5 foot boards and measured about 29” long. This would allow us to have a 27” span from the outside walls of the blocks along the base.
We used the Exploratorium Cookbook plans and determined that by using the catenary equation of y(x) = a(cosh (x/a)-1) and the value of a as 5.6 with x and y in inches, the arch would stand 21.4 inches high and measure 24 inches across the base at the inside edge of the blocks.
2. We added doorstops to the back of the backboard to ensure a horizontal surface when placing the blocks in place.
3. We enlarged the Exploratorium Exhibit Graphic on page 102-5 four hundred percent on a CAD computer to reduce distortion. This enlargement was then laminated for additional protection. The graphic layout was then attached to the backboard making sure the base and arch layout were level.
4. The blocks were made from 2” x 4” pine boards. We wanted the blocks to be a little thicker than other models we viewed. Our finished blocks were 1 ½” thick and 3 ½” wide. The length of each block varied with the position in the arch. Since each block needed to be cut to a precise angle, we used the angle table chart as attached and a cutting machine at my dad’s place of employment to cut each piece. We needed to cut two blocks each for numbers 1-10. This would give us ten blocks on each side of the arch. This helped as the angle tolerance was approximately .05°
Block No. Top Angle Bottom Angle
1 89.32° 89.32°
2 89.11° 89.11°
3 88.33° 89.33°
4 88.63° 88.33°
5 87.65° 88.22°
6 86.83° 87.48°
7 85.92° 86.67°
8 83.72° 84.91°
9 83.69° 83.83°
10 78.29° 84.31°
11 79.88° 79.88°
We sanded down the outside surfaces of the blocks, but did not sand the surfaces of the blocks that touch. We did not want to alter any tolerances or friction that would help keep the proper force between the blocks.
5. We used the extra wood blocks that were remaining when the first number 1 blocks were cut to attach to the base. This allowed for the proper angle when the arch was assembled.
6. We then painted the blocks and numbered the blocks starting with number 1 as the base blocks.
7. To finish, we attached a turnbuckle to allow for an easier method of releasing the backboard after the arch was assembled. We also attached a handle to the top of the backboard for easier moving.
Information on Catenary Curves
Related Exhibit:
Catenary Road
(Square Wheels)