Introduction: Inexpensive Cardboard 2V Planetarium Dome

About: I am a recently graduated student from the University of Kentucky with an interest in aviation, astronomy, and sustainability. I love DIY projects!

I am a huge astronomy nerd, but I live in the middle of a Bortle level 8-9 city, so convenient stargazing opportunities are down the drain for me. So I was inspired to create my own mini planetarium in my room so I could watch the stars whenever I pleased.

If you like it, please vote for it in the Space contest! :)

The manual presented here is creating a simple, two frequency dome that can be used for projecting spherical images onto its surface. It can be used to watch movies, stargaze from the comfort of your home, create your very own laser shows or simply as a cool hideaway. I will be using Stellarium software to project the sky onto the finished dome.

This manual is broken into three parts: space calculations, dome construction and Mirror Dome projection. Materials can be swapped for increased stability, however cardboard will be used in this construction. It is a relatively cheap material. Overall, the entire dome can cost around $50-90 depending on the size of the planetarium. The only true expenses for this project is the projector and the computer needed to run the software. However, you can find these items pretty cheap if you buy them used.

It took me around a month to complete this dome while balancing my full time school schedule at the same time, so with dedication I feel like it could potentially be completed in 20 - 30 days. I hope you enjoy! If you run across any errors, please let me know.

Please note: ALL measurements are in INCHES

Supplies

Paper

Pencil

Calculator

Piece of string or yarn

Straightedge/ruler

Tape measure/meter stick

Marking tape

Large cardboard sheets (preferably white on one side) : Amazon ~ $25

200-300 Large Binder Clips : Amazon ~ $30

Exacto Knife/Box cutter/precise cutting tool : Amazon ~ $5

18 inch half dome mirror : Amazon ~ $25

Stellarium software (FREE)

OPTIONAL: White Duct Tape

Step 1: Measuring the Ground

Inspect the ground where the dome is to be placed, and imagine a maximized square on that ground.

Place a piece of tape on the top left vertice of that square horizontally. Using a long straight edge, place another piece of tape at the top right vertice in line with the first one. Go back to the first vertice and using a straight edge, place a vertical piece of tape on top of the horizontal piece perpendicularly. It should make a + shape. Do the same for the right vertice. Using a measuring tool, measure the length between these two crosses starting from the inside.

Mark this dimension l on a piece of paper (drawing a diagram helps).

Step 2: Make a Square

We want to make a square from this length. Measure vertically downward the same length and repeat step 1 and from above to get a figure that looks like the one below.

Step 3: Find the Center

Find the center of the square (and the radius R of the largest circle that can fit within the square) by dividing l by 2.

R = l/2

We now need to take into account measurement error, so subtract one inch from the radius. We would rather have a dome that is too small rather than too big and will not fit in the allocated space.

r = R - 1

Mark this new radius on the diagram.

Step 4: Triangles, Triangles, Triangles!

We will be using two different triangles for the dome construction, an equilateral and an isosceles triangle. Using the radius that was determined from the last step, we can now calculate the side lengths of these triangles.

S1=0.618r

S2=0.546r

* Coefficients were determined from scaling a unit (1m) radius dome

* Units are all in inches

On the diagram, draw the two triangles as seen in the picture and fill in the side lengths that were calculated above. Label the equilateral triangle as A and the isosceles as B.

Step 5: One Last Calculation...

Calculate the connecting flap width using the below formula. Record this value as w.

w=0.0762r


Height is independent of length, thus height can be determined at the end of dome construction.

This completes the space calculations section!

Step 6: Let's Start Building!

Cut two relatively long pieces of string off and tie the end of each to a pencil.

Lay them both flat and measure S1 and S2 from the length of each string. Cut the string at both of the correct measurements. Set the string and pencils aside for now, however take into account which one is S1 and S2. Take a piece of cardboard and lay it flat, white side facing down. Take a ruler and measure a line of length S1. Draw this line on the cardboard. The goal is to draw triangle A onto the cardboard, starting with the bottom edge. Label the endpoints E and F.

Step 7: Some Geometry and Some Arcs

Grab the pencil with the S1 string length. Holding the loose end of the string at point E, draw an arc with the pencil.

Do the same at point F, until you get something that resembles the image above.

Step 8: Draw Two Triangles and Cut Them Out

Mark the intersection of those two arcs as G.

Take a straight edge and draw lines EG and FG to create triangle A. Label this triangle as “A” by writing A in the center of it lightly. Repeat the last few steps, however this time use the S2 string to create triangle B. Label this triangle as “B” by writing B in the center of it lightly. Cut them both out using the knife, box cutter or precise cutting tool.

Step 9: Make 10 a Triangles and 30 B Triangles

Now onto the longest step of them all...

We need to make several more of these triangles. We need 10x of A and 30x of B. to do this quicker, we can use the templates that we created above and trace them onto the cardboard.

Go ahead and make 10 of triangle A and 30 of triangle B. Make sure to separate the piles of triangle A and triangle B.

I'll wait patiently.

Step 10: Measure the Flap Width

Whew! Now that you have two stacks of triangles, we now need to cut the flaps that will connect them together. Take one of the triangles and flip it over so that the white side is facing up.

Using a ruler along each side of the triangle, lightly mark at the calculated connecting flap width w from both points on the line.

Do this for each side of the triangle, it should look like the diagram below.

Step 11: Connect the Dots

Connect the corresponding points to make a smaller, inner triangle.

Step 12: Score the Cardboard

Using a straight edge along the inner triangle lines, score (do not cut through) the line so that the lines can be folded easily. A good method to do this is to use a knife along the line but with less pressure so that the cut is not made all the way through. Practice on scrap cardboard until you are able to perfect a method for scoring.

After scoring, remove the three small diamond edge shapes from the triangle by cutting them all the way off.

Try folding the edges of the triangle backwards so that the white part of the cardboard can be viewed without seeing the flaps.

Step 13: Measure and Score the Rest of the Triangles

Another long step. Repeat steps 10-12 for all 40 triangles, both A and B.

Make sure that triangles A and B remain separate from each other!

Step 14: Now We Can Start Assembling the Dome

Assemble a pentagon using five triangle B’s. The longer side (S1) should be on the edges of the pentagon. The white side should face towards the ground and the flaps should connect on the sides.

Use 2-3 binder clips on each edge to temporarily secure the flaps to one another. The final shape should make a small “bowl” with the center of the pentagon rising off the floor a very small distance.

Step 15: Create Five More of These

Create 5 more of these pentagon shapes using the rest of the triangle B’s in the same fashion. Set one of these pentagons to the side for now. You should have 6 in total.

Step 16: Arrange Them Into a Dome

Arrange the five pentagons into a circular pattern on the floor.

Stand two of the pentagons up on their side on one edge and put an A triangle between the gap. Secure the flaps with binder clips again. Do this for each missing triangle around the dome.

Add five A triangles into the gaps at the top of the pentagons, securing with binder clips again.

Finally, add the last pentagon that you sat aside to the top of the dome. Attach it with binder clips.

Step 17: OPTIONAL: Hot Glue

For a more permanent attachment, you may want to use hot glue to attach the flaps to one another. Nuts and bolts also work for a permanent option.

Step 18: Determine Planetarium Height

Because the dome is complete, you can now determine how tall it should be. On your diagram, mark your desired height as i. This value is how far off the floor the dome will be lifted. We will be using cardboard rectangles to achieve this goal. The value i can be any height depending on the audience, however keep in mind the taller the dome the larger the angle you will need to project upward.

Now, we must add the width of w to i due to the needed flap to connect it to the dome.

Rectangle Height h=i+w

Step 19: Measure and Cut, Again

Using a ruler, measure the dimensions of the rectangle and cut it from the cardboard.

Step 20: Measure and Score, Again

Just like with the triangle flaps, measure w along one of the horizontal edges and both of the vertical edges. Score the line and cut off the remaining squares in the corners.

Step 21: Make 10 of These...

Repeat the past few steps to create 10 of these rectangles.

Step 22: Assemble the Final Dome!

Now, assemble 9 of the rectangles into a circle so that it forms a hollow “cylinder.” Secure the flaps together with binder clips. The part of the rectangle that does not contain flaps should be on the ground.

Gently lift the dome on top of the base, securing the flaps of the bottom of the triangles to the top of the rectangle flaps with clips. This is easier with 4 or more people. One person should go around the dome aligning the panels and securing them while the others hold the dome up.

The last rectangle can either be omitted as a doorway, or it can be added and hinged. Inside the dome, there will most likely be gaps between the triangles where things did not align perfectly.

OPTIONAL: Once the dome is secured and aligned in a desirable way, use the white duct tape to cover the joints where the triangles meet. This will help curb the light leaks and give the inside of the dome an overall smoother appearance.

* I was going to paper mache the inside for a smoother appearance but have not had time yet.

Step 23: Get Creative

Here's your chance to be creative. The physical planetarium at this point is completed, so feel free to paint the outside of the dome (make sure to prime the cardboard so it does not warp), touch up the rough edges for a more aesthetic look, or add any decorations that seem cool to you. I hot glued the final dome together so I could get rid of the bulky binder clips. However I left the bottom part unglued for an easy disassembly if ever needed.

This completes the dome construction section.

Step 24: Add Some Stars!

Place the half dome mirror at the edge of one of the rectangles on the ground.

Place the projector a few feet in front of the mirror. The sky image will have the best quality on the opposite side from the mirror, and will have the worst quality on the dome next to the mirror.

Step 25: Get Stellarium

Get the Free App Here (https://stellarium.org)

Stellarium is an open-source free-software planetarium, licensed under the terms of the GNU General Public License version 2, available for Linux, Windows, and macOS.

Start Stellarium. Zoom all the way out until the screen looks like the image above.

Step 26: Configure the App for Projection

Turn on the “spheric mirror distortion”, by opening the “Configuration” window, clicking on the “Tools” tab, and checking the “spheric mirror distortion” box. The image should now look like a semicircle with the horizon lying along the bottom.

Step 27: Fine Tune the Position

Try projecting the view onto the mirror. You may need to fine tune the height, distance and orientation of the projector to get the best image quality. Use an angled surface to play with the angle. You will need to play around with this section to get the best view.

In Stellarium, you can use the arrow keys to move around the world. You can also set the time and date of the world, good for viewing past astronomical events. Using the toolbar at the bottom of the screen, you can speed up time and animate the sky.

* Projecting videos works as well, as long as they are full screen and high enough resolution. The only issue with this is that the video is backwards when projected from the mirror.

This completes the mirror dome projection section.

Step 28: Tweak and Enjoy

I have uploaded some videos of the quality that you can expect from this manual.

However, the true quality will all depend on your projector quality. Obviously, the higher the resolution the projector is, the clearer the image will be when projected. There will always be some distortion in the image due to the nature of the spherical mirror.

Feel free to improve upon this! It is simply a starter version. There is room to grow such as the best way to remove the gaps in the inner dome, the best projector setup and the optimal height vs radius ratio.

Once again, if you like this idea, please vote for it in the Space contest! :)

Thank you!

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