Clockmakers have made "equation of time" clocks for centuries, but because of their complexity, they are quite rare. Most of them use a kidney shaped cam to move a lever to display the time difference from clock time and local solar time. (note - The Longnow clock uses a three dimensional EOT cam to cover the change over the 10,000 year life of the clock) The main use was to set your house clock to the correct time based on the time your garden sundial displayed. A slightly more clever way to display the difference was to move the minute scale on the clock about its center.
An extremely small number of clocks 'calculated' the difference without the use of a cam. One example is the David Rittenhouse clock at Drexel University. I wrote up a description of the clock for the Horological Science Newsletter some time ago. I also created a simulation of the mechanism using Working Model 2D. A link to the simulation running on a youtube video is below with the text from the HSN article - since it is very difficult to read the text on the simulation on youtube. Rittenhouse's method suggests a mechanical addition to a inexpensive clock that is kept running continuously and just adjusted to the correct time occasionally. Also the formula or a more accurate one for a specific location could be done in code. Bob Holmström Editor Horological Science Newsletter www.hsn161.com http://www.youtube.com/watch?v=7_iovbjamIQ Rittenhouse Equation of Time Mechanism by Bob Holmström The equation of time dial on a clock indicates the difference between 12 noon on a clock dial (mean solar time), and noon as indicated by a sundial (apparent solar time). Early clocks could be set to time using a sundial and a printed table of mean solar time vs. apparent solar time for the location of the clock. Most clocks that go a step further and display equation of time on a dial use an “equation cam” to display the information. The David Rittenhouse Astronomical Musical Clock at Drexel University has an unusual equation of time dial mechanism that uses gearing and linkages to approximate the “equation of time”. Ronald Hoppes book on the Rittenhouse clock reviewed in this issue has a detailed description of the mechanism. Hoppes explains that the earth’s orbit is not circular, not centered on the sun, and the earth’s axis is tilted with respect to its orbit. He goes on to explain that a computer analysis of the three error terms results in a formula for the equation of time: E = 7.665 Sin(A) – 9.665 Sin(2B) – 0.31 Cos(2C) Where: A = [(360/365.25)N] B = [(360/365.25)(N-81)] C = [(360/365.25)(N-173)] N = the day of the year Hoppes explains how Rittenhouse’s combination of gears and linkages displays the equation of time based on the formula above. In order to understand the mechanism, I created a model using Working Model 2D to simulate the mechanism. A movie of the mechanism in motion is available online at: http://www.youtube.com/watch?v=7_iovbjamIQ or search for Rittenhouse and Equation of time at youtube.com – the text below only makes sense if you view the video. View the model full screen if possible and watch the dot on the graph move as the model runs. The horizontal motion of the dot on the end of the orange arm is the vertical axis on the graph. The text below the graph is difficult to read in the video – the important text is as follows: The grey gear rotates once per year and carries the green gear. The rotational axis of the green gear is displaced from the axis of the grey gear to give the constant 7.665. The orange arm attached to the green gear generates the term 9.665 Sin(2B). It rotates twice per year. The length of the arm contributes +/- 0.665 seconds per year on the dial. The blue gear generates the term 0.31 Cos(2C). There is a pin on the blue gear that engages a slot in the light grey lever that produces a rocking motion of the red gear. The red gear and the grey gear share a common axis but are not connected. In the Rittenhouse clock the point at the end of the orange lever is a pin that engages a horizontal rack that also rotates a gear with a pointer to show the equation of time. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
