Como Funciona O Relógio Do Sol

How a sundial actually tells time

A sundial is a flat or angled surface with a stick or blade called a gnomon. The gnomon casts a shadow on markings etched or painted on the dial face, and the position of that shadow indicates the hour. That's the simple version, but it's not the full picture because the geometry gets complicated quickly.

como funciona o relógio do sol

It depends on your latitude. The gnomon must be angled to match the latitude of where it's installed. If you live in São Paulo at roughly 23.5°S, the gnomon tilts 23.5 degrees from horizontal, pointing toward the celestial south pole. A gnomon that's parallel to Earth's axis makes the shadow move at a constant angular speed throughout the day, which is what you want for even hour spacing. That's why many correct sundials have a gnomon shaped like a triangle plate rather than just a round rod — the edge creates a clean shadow line that's easier to read. The hour lines themselves aren't evenly spaced like on a clock face. They get progressively farther apart as you move away from noon. Near sunrise and sunset the lines are bunched together; around solar noon they spread out. The exact spacing follows a formula involving tangent functions based on the hour angle and your latitude, but in practice most people either use pre-calculated tables or software like Sundial Master to generate the layout. I've wasted hours trying to derive the angles by hand before just letting a calculator spit out the numbers.

The time a sundial shows is solar time, which means it's based on where the sun actually is in the sky right now. Solar time differs from the clock time you use every day for a few reasons. The Earth's orbit is elliptical, not circular, so the planet moves faster near perihelion in January and slower near aphelion in July. The tilt of the axis also affects things. These two effects combine into something called the equation of time, which can make solar time run up to about 16 minutes ahead or behind mean solar time over the course of a year. Then there's longitude correction. Brazil uses Brasília time, which is based on the 45°W meridian. If your sundial is in a city east or west of that line, you need to adjust. A place like Recife, farther east, will read solar time roughly 15 minutes ahead of Brasília time at the same moment. A city in the far west of the country runs behind. Without accounting for this, your sundial will be off by a noticeable margin during routine use.

I installed a horizontal dial in a backyard in Belo Horizonte once and got confused by a consistent 20-minute gap between the sundial reading and my phone. The equation of time was contributing maybe 8 minutes depending on the date, but the bulk of the offset came from longitude. Belo Horizonte sits around 44°W, roughly one degree east of the 45°W standard meridian for Brasília time, and each degree of longitude is about four minutes of time. Combined with the timezone offset and the equation of time on that particular date, the total discrepancy was larger than I expected. Once I mapped both factors, the sundial was actually tracking correctly the whole time. There are other subtleties people miss. A vertical sundial on a south-facing wall reads differently than a horizontal one, and the formulas change. An equatorial sundial — the kind with the dial plate parallel to the equator and the gnomon perpendicular to it — has evenly spaced hour lines, but it only works well for roughly half the year because the shadow disappears when the sun is on the opposite side of the celestial equator. Vertical declining dials, mounted on walls that aren't perfectly facing true south, require even more complex calculations. Most decorative sundials you see in parks aren't built to any of these standards, so they look nice but tell time inaccurately unless they were designed by someone who actually did the math.

Reading accuracy is another practical concern. A thin gnomon produces a fuzzy shadow edge due to the finite angular size of the sun. The sun isn't a point source; it spans about half a degree in the sky. That means the shadow has a penumbra, a region where the light is partially blocked. The thicker your gnomon, the fuzzier the shadow boundary becomes, and the harder it is to read the hour precisely. I found that a plate gnomon about 3 to 5 millimeters thick gives the sharpest practical shadow edge for a typical garden sundial. A solid triangular blade works better than a round rod for this reason. Seasonal changes matter too. On a horizontal dial, the shadow length varies dramatically from summer to winter. In winter the sun sits lower in the sky, so shadows stretch much farther across the dial face. If your hour markings don't extend far enough outward, the dial becomes unusable for several months. I once looked at a poorly designed dial in a public square and realized the outermost hour lines were completely unreachable in June, making the device useless for half the year. A properly sized dial for a mid-latitude location needs markings that extend to at least 1.5 to 2 times the length of the noon shadow.

If you want to build one yourself, the process starts with picking a location and noting the exact latitude. You then decide on the dial type — horizontal is the most straightforward for beginners. Calculate or generate the hour line angles using a tool or spreadsheet based on the standard formula: the angle from the noon line for each hour is arctan of sin of latitude times tan of the hour angle. Hour angles are 15 degrees per hour from solar noon. Mark the lines on a flat surface, install the gnomon at the local latitude pointing true south, and calibrate by comparing the reading against a known accurate time source on a day when the equation of time is close to zero, ideally around early April or late August when the correction is minimal. The main limitation of a sundial is that it only works during daylight and fails completely on overcast days. It also stops working in polar regions during their respective winters when the sun doesn't rise above the horizon for weeks. There's no workaround for those conditions other than accepting them. If you need a reliable time reference regardless of weather, a quartz watch or phone is the practical choice. A sundial is better thought of as an instrument of interest and observation rather than a serious timekeeping device for daily use.