Introduction: The Foamboard Octant

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Sextants and Octants are similar instruments. Both measure angles and are used in celestial navigation. The sextant has this name because its scale is one sixth of the full circle ( 60 degrees ). The Octant scale is thinner: 1/8 of the circle or 45 degrees. The instrument optics are the same with a scale of two arc degrees per degree ( so the octant, with its 45 degree scale, can measure up to 90 degree angles)

Modern celestial navigation instruments are smaller than old ones. This shrinking was possible by precision optics and mechanics. In the old times, when instruments were made of wood, precision was obtained by increased sizes. For those large instruments, the octant design was more convenient than the sextant, because it is slender.

This DIY project is like those old octants. It is large in size, making it possible to read angles with precision within a couple minutes.

Well...We'll see about that !

Step 1: Materials

  • 2 Foamboards large enough to mount an A3 sized page
  • 2 pages of A3 premium presentation paper (density around 150 g/m2)
  • 2 glass mirrors rectangular 50 mm x 20 mm x 3mm thick. Found in glass shops, cut from scrap.
  • 1 welder helmet glass filter ( 5.5x11 cm - ask for shade #14 ). Found on construction shops.
  • Lego plastic shaft and two plastic nuts (see photos)
  • 2 shallow Lego bricks with axis holes (to the axis assembly)
  • more Lego bricks for mounting mirrors and filter (see below)
  • Epoxy glue two components (30 minute cure)
  • Cyanoacrylate glue ( Super Bonder )
  • Spray Mount adhesive ( to bond the printouts with minimum distortion )
  • White glue for paper ( for bonding the Vernier scale )
  • Paper cutter ( Olfa type )
  • Steel wool sponge (window cleaner)
  • Scissors, square ruler, ruler, paper clips, adhesive tape, sand paper #200...

The instrument frame and arm are made of foamboard. Foamboard is basically a sandwich of paper with foam in between. It is commonly used for the mounting of prints and photographs and as backing in picture frames. Found in stationary stores. It's about 5 mm thick and that gives it a relatively solid structure and flatness.

Note that this material will not stand either rough handling or moisture. There are other kinds of plastic and wood boards that could be used to build a more resistant instrument. You are encouraged to do that. I went with foamboard because I had it around and it is so easy to cut. Very light too. But fragile.

Step 2: The Octant Parts: Frame, Arm and Vernier

The two full resolution images containing the Octant parts are to be printed on wide A3 paper, using 600 dpi resolution. A3 paper dimensions are 297x420 mm. It can also be printed on A4 paper, if you don't have access to a wide printer. Note that you loose precision when you go smaller :(

To print smaller image, resize both pages by the same amount (%)

Note: Don't use instructable image to print. They are low resolution. Download the images from the links below.

Full resolution images:

and

I actually used A3+ format paper, the widest page my printer can take. This is a little larger than A3. A3+ is 329 x 483 mm and resulted in an octant of 37.5 cm of radius, which is large enough.

The instrument frame and arm images were printed on premium presentation paper ( density 145 g/m2 ) which is heavier and deforms less than regular office paper. The design uses a minimum of printing ink, to reduce paper deformation while printing.

Also to minimize deformation while bonding the paper to the board, a spray mount adhesive was used. The scale must be bond flat without bubbles or wrinkles. Any visible deformation will ruin the instrument precision.

Printer precision check
The scale image in this design was generated using formulas and is geometrically correct. What your printer will actually print is a different matter. But I found modern printers can do a good job.

Once you have the printed pages, perform a couple checks see how precise it is. Measure the radius R of the octant at different points ( 0, 45° and 90°). They must match to a fraction of a mm. Measure the distance D between 0 tick and the center line of the instrument. This must be:

D = R * Sin(22.5°) = R * 0.3827

For instance: If R=34.10 cm, D must be 13.05 cm

The distance from 90° to the center line must be the same.

If you have a navigation divider, measure a fixed arc at different points of the scale. This will give you and idea of the precision that can be obtained with your octant.

Pasting the scale pages to the foamboard

Use minimum amount of adhesive spray (don't let the page get wet). Do the job outside and spray the paper in regular movements, until the whole page is covered. Allow the adhesive to dry for 15 seconds and paste the page to the foam board in one forward movement. A clean paste operation will produce a perfect flat scale. No removing and re-pasting allowed. If you mess it, print another scale .

Press the page with a heavy book on a flat surface and allow it to dry for some time.

Cut the pieces

With a sharp Paper Cutter, cut the frame and arm pieces . Cut along the main scale arc carefully. Cut the piece around the small scale (the Vernier). Smooth the arc edges with sand paper. Note that the main scale and the vernier must touch each other and the arm rotation must be smooth across the whole arc (see photo).

Cut off the arm window. The Vernier scale piece will be bond to the back of the arm, but don't do that yet !

This will be the last thing after the axis is mounted and the mirrors are in position. So wait.

Step 3: The Octant Axis

The arm axis setup must be sturdy and allow arm rotation, without slack. The foamboard itself is not capable of that (too soft), so I used Lego blocks and a plastic shaft to build the axis assembly. The blocks were bonded to the frame and arm foamboard pieces.

Note: Lego pieces used in this project, I'm not sponsored by Lego.

There are many kinds of Lego pieces that can be used to build a simple rotation axis. I choose two shallow bricks with axis holes, a small-headed short shaft and two nuts. The small head is important, to avoid interference with the arm mirror tower.

The shallow bricks used are conveniently about the same thickness of the foamboard ( about 4 mm). They were bonded to the foamboard with epoxy glue ( two component 30 minutes cure time).

The arm brick is bonded to the back of the foamboard. The frame brick is bond to the front of the frame.

In preparation to the bonding operation, position the Lego brick over the frame so that the hole center coincides with the printed center. Trace the brick outline with a pencil. Cut out the top layer of paper of the foamboard (the rectangle to fit the Lego piece). Scratch the foam out, leaving only the bottom paper layer untouched. Now you have a little pool on the foamboard

In the Lego bricks, protect the axis hole to avoid epoxy contamination. I used adhesive tape rolls for that, fitted to the hole diameter ( 5 mm ) (see photo)

Mix a small quantity of the epoxy glue (equal parts of the two components) and drop it on the rectangle on the foamboard. Spread the glue evenly. Insert the brick, so that brick and foamboard surfaces are about even. Clean up any epoxy that overflows.

Allow some 15 minutes for the epoxy to half-cure. Now hold the brick and gently remove the axis hole protection rolls, before they get too tightly attached to the epoxy. Make sure not to contaminate the axis hole with epoxy, or displace the brick while removing the roll.

Press the brick on a flat surface and allow the glue to cure for a couple hours.

Embed the other axis brick similarly to the front of the frame.

Step 4: Mirrors

This octant uses two equal sized rectangular mirrors. Those can be obtained and cut in glass shops. They have a lot of mirror scrap, so it should not cost much, if anything. Two rectangles of size 20x50mm - 3mm thick glass mirror.

Mirror is glass coated with a thin layer of reflective silver on one of the surfaces. Since the silver rusts in contact with air and humidity, it is covered with a protective epoxy layer (the back of the mirror)

One of the mirrors in the octant must be half-silvered. This is the one fixed to the instrument frame. It combines the light ray coming from the other mirror to the horizon image.

Check this Youtube video about making the half-silvered mirror:


The half silvered mirror is obtained by splitting it in two and removing the epoxy and silver layers on one side. Half of the mirror becomes regular glass. The other half remains a reflective.

The protective epoxy in the back of the mirror is hard. I used the paper cutter blade for the removal job. With the blade point, make a longitudinal cut along the middle of the mirror. Then, with the blade inclined, gently scratch the epoxy out. It will come out as a fine powder. The glass itself is very hard and will not be easily spoiled. But avoid using the blade point on it, except for the center line. Use the blade edge inclined instead. After a couple minutes of scratching, you begin to see the silver under the vanishing epoxy.

Once the epoxy is gone, use a wet steel wool sponge (window cleaner) to remove the silver. You will notice that the glass is very hard to scratch, but work with care. After a while you have your new half silvered mirror.

To mount the mirrors to the frame and arm, they were bonded to regular sized Lego bricks (10mm thick). I used 2x2 bricks. For the semi-transparent mirror I had to cut out the 4 brick bumps ( because I could see their tips through the transparent part, which is also 10 mm )

The mirror was bonded to the Lego brick with cyanoacrylate glue ( Super Bonder ). It is important to bond the mirror at 90° angle to the horizontal surface of the brick. Use the square ruler face-to-face to the mirror on the bond operation, working on a flat surface.

The mirror towers are made with some shallow Lego bricks. Use one extra brick on the frame mirror tower, so that both mirrors are at the same height in relation to frame plane. The arm mirror tower is 5mm lower then the frame tower, to allow for the arm thickness.

The arm mirror must be positioned so that its mirrored surface (i.e. the back of the mirror ) is over the center of the axis, and it pivots on that axis. In order to avoid interference between the instrument axis and the arm mirror, I chose a shaft with a small head (see photo)

Bond the mirror tower base to the arm with Super Bonder.

Position the Vernier scale on the arm window, underneath the arm main piece. Do not bond it yet. This will be done last, after the mirrors are mounted, on the initial calibration. Fix it temporarily with paper clips.

Mount the arm and the frame using the Lego plastic shaft. Lock it in place with the two nuts. Make sure the arm can swing smoothly over the 90 degree range. Use fine sand paper to remove any bumps in the main scale.

Step 5: Initial Calibration

Now you have 3 pieces: the frame, the arm and the Vernier.

Set the arm position to zero ( align the A tick in the Vernier with 0 tick in the main scale )
Now take a sight of a point located far away, at least a few hundred meters.

In this zero position, the two mirrors should be parallel. But there is probably a small error in this parallelism. Holding the instrument vertically and with the horizontal axis aiming to the chosen point, look through the frame mirror. You will see the selected point directly and its reflected image on the arm mirror. Swing the arm gently so that the reflected and the direct images are both at the same vertical altitude. Press the arm and frame together to freeze the arm in that position. Now bond the Vernier scale, so that the point A and scale 0 ticks match perfectly. I used white paper glue for that. Super Bonder is too fast for a precise positioning.

Step 6: Vernier Scale

While reading the angle on the sextant scale, you get degrees and minutes up to the smallest tick of the scale. In the case of this Octant, the smallest scale division (tick) is 20 minutes. Each degree is 3 ticks wide. The Vernier (the secondary scale attached to the arm) is used to evaluate the fraction of tick, to get the complete reading up to a minute of arc. No point in trying to get the fraction of minute with this kind of scale.

The tick marked A in the Vernier points the measured angle in the main scale (see photo).

Reading vernier scale
When Vernier tick A is between two main scale ticks, the fraction of the 20 minutes must be estimated. Find which of the 20 ticks in the Vernier aligns with one on the main scale. This is a number between 0 and 19, and must be added to the main scale reading.

Check the photos with scale readings:

In reading 1, the main scale reads 65 degrees and tick A is between the second and third inside that degree. So that's 40 minutes more. The ticks on the Vernier and main scale align on the 7th tick. That adds to 65 degrees and 47 minutes.

In reading 2, the main scale reads 44 degrees plus zero minutes. The Vernier 6th tick aligns with the main scale, so we have 44 deg and 06 minutes.

Step 7: Sun Filter: Protect Your Eye !

During the day, the only celestial objects that you can see are the Sun and - sometimes - the Moon. So it is nice to be able to use the octant observe the Sun. There is the problem of the intense light of the Sun, that can cause harm to the eye, if observed directly, without suitable filter, even for a short period.

To remedy that, sextants have a bunch of dark filters that you can add to the line of sight

In this design, a welder mask glass filter was used (ask on construction shops for shade number #14) . This is a very dark filter, safe for Sun observation. It costs about a dollar. The filter must be located between the two mirrors and cover the arm mirror completely. It must be positioned perpendicular to the light ray. See the frame plan.

The welder glass filter I found comes in a rectangular shape of 11cm x 5.5 cm . I had mine cut in half by guy from the glass shop, a bit larger than the mirrors, with 55 mm x 35 mm.

Note that the filter placement must not interfere with the movement of the arm between 0 and 90 degrees. The arm has to have room to move underneath the filter. The filter cannot be too far from the arm either, or the Sun light reflected will pass between the arm and filter and hit your eye.

Since the filter is mounted with Lego bricks, it is removable for observing other stuff than the Sun. Only the base brick is bonded.

Note: This Nasa site suggests that, for eye safety, one should use at least welder shade number 12 (#14 is even better). The text focuses on eclipse observations, which are particularly dangerous because people stare at the Sun for a long period on those events

https://eclipse2017.nasa.gov/safety

This page reviews Sun filter safety, including welder glass #14:

https://www.rasc.ca/tov/safety

Other Sun safety tips:

  • Install the Sun shade before the observation starts
  • Previously set the expected instrument altitude before the observation, so you don't waste so much time looking for the Sun.
  • Perform the observation as fast as you can. With preparation, it should take only a few seconds to adjust the octant arm
  • If it takes too long or if you feel uncomfortable, stop the observation immediately

In short: take care with Sun light !

Step 8: Finishing Touches

As a finishing touch, I added a spring cut out of a plastic card. It presses the arm to the frame, so that the main scale and Vernier are leveled.

This is it. Let me know if you build one.

Links to related work