A Horizontal Dial for London
- The Dial Reads
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- The Clock Reads
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- Add to the Dial
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- Equation of Time
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- Solar Noon
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Style height -- Zone --
Set the Dial
Print the Dial
Exact millimetres, a gnomon to cut, a ruler check.
The SVG holds the plate at the width set above, every hour, half and quarter line, the date lines, the analemma, the gnomon template at true size with its style height, a 50 mm square and a 100 mm scale bar. The text is cut as outlines, so an engraver or a laser needs no fonts.
Download Poster
The dial at 4096 pixels, ready to frame.
The same plate with the shadow at the moment set above, the place and the date: a square PNG, 4096 pixels a side.
How It Is Drawn
One vector method, checked against the published tables.
The plate and the style
A flat dial is a plane with an outward normal N. A wall turned d west of south and leaning back r from vertical faces azimuth 180° + d. The style points at the celestial pole P, so its height above the plate is SH = asin |N · P|. For a horizontal plate that is the latitude; for a south wall, 90° minus it.
The hour lines
At hour angle H and declination δ the Sun lies along S = cos δ (Q cos H − E sin H) + sin δ P, with E east and Q the top of the celestial equator. The style's shadow runs from the root along D = P − (P · N / S · N) S and the nodus shadow lands at −(S · u, S · v) / S · N nodus heights from the foot. Horizontal, vertical, declining, reclining, polar and equatorial dials are this one construction on different planes; the closed forms in the British Sundial Society glossary are the receipts.
The date lines and the analemma
Each date line is the nodus shadow through one day at a fixed declination: the solstices at ±23.44°, the equinox at 0°, and the Sun's entry into each sign at ±20.15° and ±11.47°. The figure of eight is the nodus shadow at 12:00 on the zone's standard clock, every day of the year.
The analemmatic dial
Hour points sit on an ellipse, x = M sin H, y = M sin φ cos H, and the vertical gnomon stands on the date scale at Z = M cos φ tan δ, after Rohr. Its shadow then passes through the hour point on every day of the year.
The clock
The dial reads local apparent time. The clock reads the zone: clock = dial − E − 4 min × (λ − λzone) + DST, where E is the equation of time from Meeus chapter 28, E = L0 − 0.0057183° − α + Δψ cos ε, λzone is 15° for every hour of standard offset, and daylight saving comes from the zone's own rules.
Receipts
| Checked | Against | Worst error | Tolerance |
|---|---|---|---|
| 65 hour lines, SH, SD; φ 50°, wall 25° W | Sabanski, Sundial Primer worksheet | 0.0000005° | 0.01° |
| Style height and substyle; φ 44.23°, wall 42.2° W | Sabanski, figure 2 | 0.0035° | 0.005° |
| Horizontal dial at 52°, 1 to 5 pm | Ta'bois, Clocks, April 1986 | 0.038° | 0.05° |
| Every dial type at 20°, 40°, 51.5°, 60° | BSS closed forms | under 0.01° | 0.01° |
| SVG hour lines | The engine | under 0.01° | 0.01° |
| Equation of time, 1992 Oct 13 | Meeus, example 28.a | 0.66 s | 1 s |
| Its four extremes and four zeros | Epoch-2000 table | 3.9 s, 0.46 day | 6 s, 1 day |
| Solar noon at Greenwich, three dates | US Naval Observatory | 26 s | 32 s |
| Sunrise and sunset, six events | US Naval Observatory | 0.44 min | 1 min |
| Equation of time, every day of 2026 | BSS four-term fit | 29.9 s, a miss | 20.4 s |
The miss is the fit's, in mid-December, where four harmonics cannot follow the curve; the same engine meets Meeus to 0.66 s. It stays in the suite as an expected failure.
Limits
- The shadow edge is soft. The Sun is half a degree wide, so a shadow 1 m long blurs across about 9 mm, and no flat dial reads closer than a minute or two.
- The style is drawn as a knife edge. A gnomon cut from 6 mm plate throws two edges; split the plate along the substyle by its thickness.
- The Sun comes from the low-accuracy series in Meeus chapter 25, so the equation of time is good to about 2 seconds.
- No refraction in the lines. Near the horizon the air lifts the Sun by up to half a degree.
- The dial is only as true as the wall's measured direction. An error of 1° in the wall tilts the style off the pole, and the page cannot measure your wall.