Hale cycle

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The Hale cycle (George Ellery Hale)is a 22-year cycle in the activity of the magnetic field of the Sun. The Sun's magnetic field reverses polarity roughly every 11 years, and the magnetic poles return to the same state after the next reversal. The cycle can be approximated by a formula( author M.A. Vukcevic):

Y = 100 [ Cos(2π/3 + 2π(t-1941)/(2х11.862)) + Cos 2π(t-1941)/19.859 ]

If the waveform is ‘rectified’ and shown simultaneously with the sunspot records then:

Y = 100 abs [ Cos(2π/3 + 2π(t-1941)/(2х11.862)) + Cos 2π(t-1941)/19.859 ]

( prior to 1810 apply π/2 degrees phase shift i.e. use Sin() function )

Alternatively taking into the account magnetic polarity of sunspots

(with a phase reversal, π degrees phase shift, in the early 1920s) :

Parameters used are:

100 – arbitrary constant used to normalise values in the diagram

11.862 years – Jupiter sidereal orbit period

19.859 years – Jupiter-Saturn synodic period

2π/3 (120º) – angular shift of Jupiter-Saturn synodic period

1941 – Synodic coincidence of Jupiter-Saturn-Uranus ( 3 the most massive and magnetically strongest planets)

A phase shift takes place approximately every 110 or so years, most likely due to the inequality in Jupiter – Saturn orbital properties.. (see ref h-cycle.gif & subcycle.gif)