How to draw a sundial correction curve - equation of time - in AutoCAD/ GStarCAD/ ZwCAD

Draw the EoT or any other Fourrier series in your CAD

This method can be also used for machine CAMS.

    CAM: a projection on a rotating part in machinery, designed to make sliding contact with another part while rotating and to impart reciprocal or variable motion to it.

Check the following video:

The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of reconcile a difference. The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion. Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.

According to the National Oceanic & Atmospheric Administration (NOAA), the General Solar Position Calculations are:
First, the fractional year y is calculated, in radians:

    y = (2*Pi/365)*(day_of year ‐ 1 + (hour‐12)/24)

    From y, we can estimate the equation of time (in minutes):
    eqtime = 229.18* (0.000075 +0.001868*cos(y) ‐0.032077*sin(y) ‐0.014615*cos(2*y) ‐0.040849*sin(2*y))

Translated into LitioLAB format, this can be rewritten as follows:

    J1 = r2d(2.0*PI/365.0*(x-1.0))
    Y = 5*229.18*(0.000075 +0.001868*COS(J1) -0.032077*SIN(J1) -0.014615*COS(2*J1) -0.040849*SIN(2*J1))

The 5 factor at the begining is for better time-scale visualization.

    ZwCAD users need to check LitioLAB user manual to review the math functions available and how to adapt the formulas to ZwCAD.

    The R2D (radians-to-degrees) conversion function is not available in ZwCAD. Use 180/PI as a multiplying factor instead.

Thus, we get the curve of the equation of time, which can be seen on sundials.

We can copy and paste these equations and with some few changes we can get a curved graph, as can be found in some other sundials.

The equations of the examples of this video are as follows:

Linear graph

    J1 = r2d(2.0*PI/365.0*(x-1.0))
    Y = 5*229.18 *(0.000075 +0.001868*COS(J1) -0.032077*SIN(J1) -0.014615*COS(2*J1) -0.040849*SIN(2*J1))

Curved (circular) graph:

    J1 = r2d(2.0*PI/365.0*(u-1.0))
    J2 = 5*229.18*(0.000075 +0.001868*COS(J1) -0.032077*SIN(J1) -0.014615*COS(2*J1) -0.040849*SIN(2*J1))
    R = 150+j2*0.5
    A = 5*pi/4+u/360*pi*0.5

The 5 factor at the begining is for better time-scale visualization.

And since these graphs are polylines, they can be further processed in AutoCAD/GStarCAD/ZwCAD and eventually, they can be used for CNC machining, laser cutting or 3D printing.

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