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Mirror Heliograph

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Visual Signal Methods
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Mirror Heliograph

A mirror heliograph throws a beam only about 9.3 m wide for every kilometre of distance, so the signaller must hold the aim to a fraction of a degree, and because the sun moves 15 degrees an hour the beam drifts off a target 5 km away in roughly a minute unless the mirror is re-aimed. Its range is set by the curve of the Earth, not the mirror: two stations with eyes about 49 m above the plain between them are the most that reach 50 km.

Part of Signal Systems and Communication

A heliograph signals by flashing reflected sunlight, and the arithmetic of its narrow beam decides how it is aimed, how long the aim lasts and how far it can reach.

Three Numbers Decide Whether A Flash Is Seen

The method itself, the sighting hand and the simple flash code, is in the parent article; the narrow-beam principle is derived in Mirror and Light Signals. This page works out what that narrowness demands. The sun spans about 0.53 degrees, 0.0093 radians (a recalled value that the other article also uses), and a flat mirror cannot make a tighter beam than that.

Worked Example: Beam, Tolerance And Sun Drift

  • Beam width. At distance d the beam is d x 0.0093 wide. At 5 km: 5,000 x 0.0093 = 46.5 m. At 50 km: 50,000 x 0.0093 = 465 m.
  • Aim tolerance. The half-width in angle is 0.0093 / 2 = 0.00465 radians, 4.65 milliradians, at any distance. A watcher sees the flash only while inside it.
  • Mirror tilt. A reflection turns the beam by twice the mirror’s tilt, so moving the beam by 4.65 milliradians needs a mirror tilt of 4.65 / 2 = 2.3 milliradians, which is 2.3 x 0.0573 = 0.13 degrees. On a 10 cm mirror that moves one edge by only 0.1 to 0.2 mm.
  • Sun drift. The sun’s apparent motion is 360 degrees in 24 hours, 15 degrees an hour, 0.25 degrees (4.4 milliradians) a minute. For a fixed mirror the reflected beam turns by the same angle as the sun does. A beam centred on the target is therefore half-width, 4.65 milliradians, off after 4.65 / 4.4 = about 1.1 minutes.

Two practical results follow. First, a short message of a minute or so can be sent with a fixed mirror; a long one needs the mirror re-aimed, which in practice means a second person watching for the reply flash. Second, tilting the mirror to flash is a poor way to flash: a tilt of 0.13 degrees is below hand tremor, so the flash comes out ragged. Cover and uncover the mirror with a shutter or hand, and keep the mirror steady.

Range: The Curve Of The Earth Sets It

The parent article says a mirror is visible at 50 km or more. The geometry shows what that takes. Each station’s horizon is about 3.57 x the square root of its eye height in metres, in kilometres, and the two add.

  • For two equal heights and a 50 km separation, each station needs a 25 km horizon: the square root of h = 25 / 3.57 = 7.0, so h = 49 m.
  • At 15 km (the longest relay spacing in the parent article) each needs 7.5 km: the square root of h = 2.1, so h = 4.4 m.
  • Standing on level ground with eyes at 1.7 m, a watcher’s own horizon is 4.65 km, so two people on flat ground reach about 9.3 km.

The 50 km figure therefore needs hilltops or very tall towers at both ends, and a clear line between them. A mirror on level ground does not reach it. Standard refraction extends these figures by a few percent (the observation-posts article puts it at roughly 7%), and haze and terrain subtract far more than that.

Step 1: Fix the stations and the schedule. Because the sun’s direction changes, agree times of day when the sun lies neither nearly behind the signaller nor nearly behind the receiver. When the sun is almost directly behind the receiver, the mirror must face the sun nearly head-on and the signaller aims while looking toward the sun, which is a dazzle risk; choose another hour.

Step 2: Aim with a sighting aid. Follow the parent article’s finger method, then check by reply. The signaller cannot see where the beam falls, so the first flash is confirmed only when the receiver answers.

Step 3: Send attention, then wait. Three flashes, a pause for the reply flash or flag, then the message in short groups.

Step 4: Re-aim every minute or two. Move the beam by a few milliradians; the receiver’s reply tells you when it has drifted.

Step 5: Stop on cloud. A cloud over the sun ends the message without warning; agree a fallback, a horn or a runner.

  • No reply, bright sun, clear line. The beam is off the target by more than 23 m at 5 km. Re-aim a little at a time and wait for the reply.
  • Reply is weak or flickering. The mirror is dirty or crazed, the air is hazy, or the beam is only brushing the receiver’s edge.
  • Reply stops mid-message. Cloud, or the sun has drifted the beam off. Check the sky before the aim.

Common Mistakes

  • Treating the mirror size as range. A bigger mirror adds a little to the beam width and brightness, not to the horizon.
  • Flashing by tilting. A 0.13 degree movement is below hand steadiness.
  • Aiming once and walking away. In about a minute the beam has drifted.

Safety

A mirror flash can damage eyes and ignite tinder

Never aim the beam at a face and never look into the mirror’s reflection of the sun. A curved or lens-shaped reflector concentrates heat and can ignite dry tinder or the signaller’s clothing. A signaller on a rock outcrop or tower needs a fixed way down and must not lean out to aim.

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