computation of flat sundials. fer j. de vries

end notes

Not only shadow points have to be computed but also the height of the (pole) style and the angle for the substyle.
This also can be done with the same mainprocedure.

To calculate these constants of the dial use these 5 routines with input decl = 90° and t = 0°, but don't use the 2 decision points.
Then v = arcsin(z3). (no test of quadrant is necessary)

If v = 0 then the style is parallel to the dial's face and there isn't an intersectionpoint of the style with the dial
else: the coordinates of the intersectionpoint are x,y.
The substyle can be drawn from the footpoint of the gnomon ( point 0, 0 ) to this intersectionpoint.

The value of v equals with the latitude where the sundial's plane becomes a horizontal plane.
Also remember that if v > 0 the endpoint of the style points to the north pole and the hourlines run clockwise but if v < 0 the endpoint of the style points to the south pole and the hourlines run anticlockwise.

However not necessary to construct your sundial I also give a formula to compute the hourangle of the substyle ts.
tan ts = sin i * sin d / (cos phi * cos i + sin phi * sin i * cos d)
Controle ts for the right quadrant.

Fomulae to compute the equation of time and the sun's declination out of a daynumber:

L              = DAGNR*360/365.2422 - 80.412001           DEGREES

EQUATION       =   - 109.2587*SIN( L) - 428.0240*COS( L) 
                   + 595.9691*SIN(2L) -   2.1295*COS(2L)
                   +   4.5072*SIN(3L) +  19.2449*COS(3L)  SECONDS (of time)

LAMBDA         = L +   0.4365*SIN( L) +   1.8636*COS( L)
                   -   0.0179*SIN(2L) +   0.0089*COS(2L)  DEGREES 

EPSILON        = 23.43746                                 DEGREES 

DECLINATION    = ARCSIN(SIN LAMBDA * SIN EPSILON)         DEGREES 

Strictly these formulae are for 2014 (a year between two leap years) and for 12.00 UT, but for sundials you can use them during a long time.
See also 'Cousins', page 236, for such a fomula for the year 1931.

If you want to calculate these formulae for a certain year in the period 1901 - 2099 download my program
equadecl.zip. 26 kB

Or download a table with average values for the period 2000-2099.
12kB

graph for the equation of time and the sun's declination