Simple Goniometer

Part of Surveying

How to build and use a basic angle-measuring instrument from salvaged or hand-made materials.

Why This Matters

When you need to measure angles between distant points — laying out a building foundation, plotting a field boundary, or establishing a road alignment — you need a reliable way to capture and record those angles. A goniometer (from Greek: “angle measurer”) is the most direct tool for this job. Unlike a compass, which only gives magnetic bearings, a goniometer measures the angular difference between any two sightlines regardless of magnetic variation.

In a post-collapse setting you will rarely have a precision theodolite. But you can build a serviceable goniometer from a wooden disc, a straight-edge sighting arm, and a homemade degree scale. Accuracy to within one or two degrees is achievable with careful construction and discipline — sufficient for field boundaries, road alignments, and rough topographic surveys.

Understanding how to build and calibrate a goniometer also teaches you the underlying geometry of angle measurement, which transfers directly to more sophisticated instruments like the transit or plane table.

Materials and Construction

The Base Disc

The core of any goniometer is a flat circular disc marked with a degree scale.

Material options (best to worst):

Material	Advantage	Disadvantage
Dry hardwood (oak, beech)	Easy to work, dimensionally stable when sealed	Warps if wetted
Fired clay disc	Permanent, stable	Fragile, heavy
Sheet copper or bronze	Very stable, long-lasting	Requires metalworking
Thick bark (birch)	Emergency option	Distorts with humidity

Target diameter: 20–30 cm. Larger discs are easier to mark accurately but harder to handle in the field.

Steps:

1. Cut or turn a disc to as close to a true circle as possible. Check by measuring diameter in at least four directions — they should all agree within 2 mm.
2. Find the exact center by drawing two chords and bisecting each (the bisectors will cross at center). Mark the center with a small hole or punch.
3. Seal wood with linseed oil or beeswax before marking the scale.

Dividing the Circle

Dividing a circle into 360 degrees by hand requires patience.

Simple method using a compass:

1. Draw the circle. With the same compass radius, step around the circle — this gives 6 equal 60° arcs automatically (a property of the circle: chord = radius = 60° arc).
2. Bisect each 60° arc to get 30° marks (12 divisions).
3. Bisect again for 15° (24 divisions).
4. Bisect again for 7.5° (48 divisions) — which is close enough to use as a proxy for 10° spacing if you note the small difference.

Better method — 360 via geometry:

1. Construct a regular hexagon (6 × 60°). Subdivide each 60° segment by trisecting (20° each). Then bisect to 10°. Final bisection gives 5° intervals — 72 marks total.
2. Trisecting an angle precisely by hand is impossible with compass alone, but you can use trial and error with a divider set to approximately 1/3 and adjust until the three steps close perfectly.

Numbering: Mark 0° at the top (or at the direction of the fixed reference sightline). Number clockwise 0–360 for surveying convention.

The Sighting Arm (Alidade)

The rotating arm must pivot precisely at the center of the disc.

Construction:

1. Cut a straight wooden arm 5–10 cm longer than the disc radius.
2. Drill a pivot hole at one end sized to fit snugly over a central pin or bolt.
3. Attach a vertical notch or pin at each end of the arm as sighting vanes — one near the pivot (the eye end), one at the far end (the target end).
4. The arm should rotate freely but without wobble. A brass nail through the center works; wrap it with thin leather if the fit is loose.

Sighting Vanes

Two notched vertical pieces of wood or metal create a “peep and bead” sight. The eye notch should be narrow (1 mm); the far vane can be wider. When the target appears centered in both notches, your sightline is true.

Setting Up and Reading Angles

Leveling

A goniometer gives meaningful angles only when the disc is horizontal.

1. Set the instrument on a tripod or flat rock.
2. Use a plumb bob or water level to verify the disc is level in both axes.
3. If the disc tilts even 5°, measured horizontal angles will be incorrect.

Zero Setting

Before measuring any angle, establish a zero reference:

1. Point the sighting arm at your first target (usually the farthest known point, or North).
2. Clamp the disc in place (use a wedge or friction clamp).
3. Rotate the arm to “0” on the scale and lock it — OR note the reading and subtract it from all subsequent readings.

Measuring a Second Angle

1. Unclamp the arm (not the disc).
2. Rotate the arm until the second target is centered in both sighting vanes.
3. Read the angle from the scale where the arm’s index line crosses the disc.
4. The difference between the two readings is the angle between the targets.

Recording convention: Always write down the full reading, not just the difference. If you move the disc accidentally, you can recalculate.

Calibration and Error Checks

Check for Eccentricity

If the pivot hole is not exactly at the center of the disc, every reading will have a systematic error called eccentricity.

Test: Sight a distant target and read the angle (say, 47°). Rotate the disc 180° without moving the arm. Read again. The two readings should differ by exactly 180°. If they don’t, the offset is half the discrepancy — this is your eccentricity error. Note it and apply a correction to all readings.

Check for Graduation Errors

Sight a target at 0°. Rotate the disc exactly 180° (using the scale). Sight back along the same target. If the target is still centered, your 0° and 180° points are truly opposite — this confirms basic graduation accuracy.

Typical Achievable Accuracy

Construction quality	Expected accuracy
Careful hardwood, scribed scale	±1°
Rough wood, estimated scale	±2–3°
Fired clay, geometric division	±0.5°

For most field layout work, ±1° is adequate. A 1° error across 100 m produces a lateral offset of about 1.75 m — acceptable for field boundaries but not for building foundations over long spans.

Practical Applications

Laying Out a Right Angle

Set the goniometer, sight along one side of the desired right angle (record 0°), rotate the arm to 90°, and place a stake on that new sightline. This is faster and more accurate than the 3-4-5 rope method over long distances.

Running a Traverse

A traverse is a series of connected survey lines:

1. Set up at Point A, sight Point B, record bearing.
2. Move to Point B, sight both A and C, record the angle between them.
3. Continue to each new station.
4. The accumulated angles, combined with measured distances, allow you to calculate the position of every point.

Measuring a Field

Walk the perimeter, recording the angle at each corner and the length of each side. Plot on paper using a protractor and scale rule. Calculate area from the plotted shape.

Care and Storage

• Store the disc flat, not on edge (prevents warping).
• Re-oil wooden discs seasonally.
• Check the pivot pin for wear — a loose pivot destroys accuracy.
• Keep sighting vanes clean; a smear of mud across a vane shifts your sightline.

A well-maintained wooden goniometer can last decades. Mark your name and a serial number on it — instruments have a way of wandering away from job sites.