This method can be also used for machine CAMS.

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:

From y, we can estimate the equation of time (in minutes):

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

Y = 5*229.18*(0.000075 +0.001868*COS(J1) -0.032077*SIN(J1) -0.014615*COS(2*J1) -0.040849*SIN(2*J1))

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

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:

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

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