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1. Astronomy
The equation of time is an astronomical concept that quantifies the difference between true solar noon (when the sun passes the zenith) and mean solar noon throughout the year. This difference results from the irregularity of the Earth’s path around the Sun, combined with the tilt of its axis. This concept is essential to understanding why the moment of noon (when the sun reaches its highest point in the sky, the zenith) does not exactly correspond to the time shown on our watches and clocks.
Influenced by these two factors, the length of an astronomical day (true solar day) is not constant and fluctuates throughout the year depending on the Earth’s position around the Sun. Our calendars and our time measurement scale, on the other hand, consider days of a constant average length (24 h) throughout the year (mean solar day). The equation of time expresses the difference between these two values.
2. Factors
- The Earth’s elliptical orbit: it follows an elliptical path around the Sun. It is known that the Earth moves faster when it is closer to the Sun (perihelion, around January 3) and more slowly when it is farther from the Sun (aphelion, around July 4) (Kepler’s Law). As a result, the interval between two instances of the Sun at the zenith of a point lengthens as the Earth moves away from the Sun and shortens as the Earth approaches the Sun.
- The tilt of the Earth’s Axis : The Earth’s Axis is tilted relative to its orbital plane by about 23.5°, which causes seasonal variations in the angle of illumination from the Sun, thereby affecting its apparent position.
The Equation of time results from the combination of these two effects, and it manifests as a function that varies throughout the year. It can be expressed by a mathematical relationship giving the difference (in minutes) between mean solar time and true solar time.
3. Value of the Equation of time
Figure 1
Value of the equation of time
Click on the animation to enlarge it
The amplitude of the equation of time reaches about 16 minutes of difference. This difference varies throughout the year, reaching maximum values in spring and autumn, and a minimum around the winter (December 21) and summer (June 21) solstices. For example, in February, the equation of time can be +14 minutes (the sun appears “ahead” of mean solar time), while in November, it can reach about -16 minutes (the sun appears “behind”).
4. Practical applications
The equation of time is important for several applications, including:
- Astronomical navigation : When their GPS is down, sailors use true solar time to determine their geographic position, and the equation of time makes it possible to correct the time shown by a watch.
- Sundials must take the equation of time into account in order to provide an accurate rendering of true solar time.
- Astronomy and solar observation : The equation of time allows astronomers to correct the time shown by a watch or a standard chronometer in order to obtain an accurate solar time during observations.
In summary, the equation of time is an astronomical phenomenon resulting from the combination of the Earth’s elliptical orbit and the tilt of its axis, causing variations in true solar time compared to mean solar time. Although the term “equation of time” may suggest a complex mathematical problem, it is in fact a periodic function that proves useful in fields such as navigation, astronomy, and timekeeping in general.
5. Construction
In practice, an Equation of time mechanism is relatively simple and does not require many components. However, its drive mode deserves attention, and its components must be designed and manufactured with great precision to guarantee the accuracy of the information.
The astronomical tab of this chapter showed us that the annual curve of the value of the Equation of time is as follows:
Figure 2
Equation of time value
Click on the animation to enlarge it
5.1 Design of the Equation of time Cam
To mechanically translate this information, it is necessary to transcribe this curve into a circular expression in order to draw a Cam which will drive the equation of time indicator. The circular projection of this curve corresponds to the following model:
Cette courbe peut ainsi être directement utilisée pour tracer la forme et le contour exacts de la came d’équation du temps. La came ainsi dessinée servira de programmation mécanique pour l’affichage de la fonction.
6. Operating principle
The equation of time cam is fixed to the equation of time wheel, generally driven by an intermediate wheel.
The Equation of time wheel must complete one Lathe in one astronomical year, that is 365.25 Days. It is therefore incorrect to drive an Equation of time mechanism by a perpetual Date / Calendar based on the Gregorian calendar, which breaks down the leap-year cycle into three years of 365 Days and one year of 366 Days. By driving an Equation of time mechanism with a perpetual Date / Calendar, an error of 0.25 Day per year is generated, that is 0.75 Day of error after three years. This difference can lead to a relatively significant reading error. It is therefore preferable to use an annual Date / Calendar or, better still, to specifically calculate a Gear to ensure the correct rotation speed of the Equation of time wheel (1 Lathe/365.25 Days).
A feeler is held in contact with the periphery of the Cam by a spring. The feeler is located at the end of a large pivoting lever.
As it rotates, the Cam will move the feeler, which will pivot in one direction or the other following the contour of the Cam.
The other end of the feeler, located opposite its pivot point, ends in a toothed sector (rack). This meshes with the equation of time pinion, which carries the equation of time hand. The angular value of the display is determined from the gear ratio between the feeler’s sector and the equation of time pinion.
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