I guess I'm easily confooz'd, BB. It took me three re-readings to realize I was looking at two of the same thing.
So sorry, no sarcasm aimed at you. "How To Lie With Statistics" is a book every scientist here should read; if you haven't already read it, I think you'd find it amusing, as well as useful for analyzing propaganda of all types. It emphasizes the importance of handling graphs in standard ways so readers don't get misled unintentionally. There's nothing in it that addresses repeated abscissa scales, pro or con, so it's not specifically relevant to your graph. If the title jarred you by its proximity to a discussion of your methodology, I apologise.
decided to begin from start again, and check over my data-collection. Seems the planetary positions I got from the software Asynx Planteraium don´t match with those I get from the site www.fourmilab.ch/cgi-bin/uncgi/Solar/action?sys=-Sf (up to +/- 10 deg for Saturn, +/-5 deg for Jupiter) Do anybody know a reliable source for planetary positions/angles?
The result is that now my pre-1750 data show very much the same patterns as the data after 1750. A couple cycles don´t fit in perfectly, and indicate that the minimum-dates are not quite correct - which should be expected with these old reconstructed data...
so far I really haven´t presented any theory yet, but rather showed some patterns and correlations. Here are some more findings
-there seem to be a "perihelion-effect" from Jupiter, which Tilmari has examined thoroughly (Jovian cycle 11,86 yr). -the (half) synodic Jupiter-Saturn period 9,93 yr also has great influence on solar cycle strength/length. Also showed in the publication by Wilson, Carter and Waite. -the synodic Earth-Jupiter period of 399 days shows up in SSN-data (Vukcevic), and the Venus-Jupiter period of 237 days may also be a subcycle.
This tells me it is time to look at the tidal cycle of 11,08 years (Wood, and later Hung), which mainly is supposed to be caused by Venus, Earth and Jupiter.
Here is what it looks like:
some interesting aspects:
-there is a period of almost 5 years where there never has been a monthly sunspotnumber of zero. In fact a full year where it never has been below 20... this certainly looks interesting! This probably means a couple solar cycles have experienced being forced to begin or extend... -further there seems to be subcycles of about 10 months or ~300 days. The cycle divided in 13 gives 311 days. -at the declining part of the cycle the subcycles seem to split up in half, or about 4-6 months. Not sure if this is a real effect, or only shows up in the averages...
The tidal cycle of Wood is not fixed, and can differ from the average 11,08 years by up to a couple years. What do the planetary alignments look like during this cycle?
For SC23 I checked three months where the average shows nice peaks - month 33, 52 and 65. SC23 however did not show peaks at these exact months... but maybe I still will get some idea of the mechanism:
-seems that when Venus, Earth and Jupiter are (almost) lined up, it favors high SSN. Earlier when I studied EaJu and VeJu, I saw a rise in SSN up to conjunction, and then a drop down to opposition. -I guess Ve-Ea-Ju are most favorable lined up once every 11,08 years (over a time-interval that is), causing a positive effect on SSN. And the rest of the time the planets are more or less out of sync.
Lastly I checked a cycle of 9,37 years that Tilmari found in his research. This cycle also looked pretty good, but I think it is caused by the same effect as the 11,08 year cycle.
9,37 years is also a multiple of 311 days, and when I looked at Ve-Ea-Ju at SSN-tops in the average cycle, I saw similar planetary alignments as in the 11,08 yr cycle...
311 days are interesting. 0,85 years or 10,22 months... some multiples are: 9,37 years (cycle in strength, Tilmari) 10,22 years - a very common SC-length 11,07 years - the average SC-length 11,93 years - close to the Jovian cycle of 11,86 years 12,78 years - ? 13,63 years - ?
btw also reminds me of a couple publications that showed a 150-160 day cycle in solar flux... half of 311 days.... hmmm
---- so, another important piece in the puzzle here - which one is next?
the 11 yr VeEaJu-cycle could be the missing piece that regulates the struggle between the 11,86 yr Ju-cycle and the 9,96 yr JuSa-cycle:
The Ju-cycle is the stronger of Ju and JuSa, and favors long cycles. For a period of ~10 SC the Ju-cycle dominates while JuSa goes in and out of sync (giving strong or weak cycles).
At the end of this period the minimum of the SC are shifted ahead towards the beginning of the tidal-max interval of VeEaJu. This results in forced starts of SC, and causes the Ju-cycle to loose its grip.
Then the JuSa-cycle can take over the domination, and holds it for ~7 SC. When under the JuSa grip, short and strong cycles are favored. The short cycles mean that the minimum are shifted back towards the end of the tidal-max interval of VeEaJu, which results in prolonged SCs. This causes JuSa to loose its grip, and Ju takes over again...
This supercycle should be around 178 years, and we are now at a point where the SC is being prolonged. That means JuSa is about to loose its grip, and the longer and weaker Ju-cycles will take over.
Makes sense doesn´t it ?
I would like to bring up again this humoristic image, that shows the solar cycle "bullmarkets and bearmarkets". These are periods of JuSa-dominated cycles (short and strong) and Ju-dominated cycles (long and weak).
-color-codes and values before 1750 are not quite correct, but still the diagram shows my point
Jose's 178.8 cycle only works back a few hundred years, I have plotted the last 34 grand minima and the cycle so far is coming out at 172 years, close to the N+U period. I have plotted the grand minima and maxima against the 11000 yr C14 graph and it lines up perfectly, but need to do further work.
I have not yet starting focusing on grand minimum, length and stability of supercycle, and what causes it...
I have to work it out for myself from the start and the mechanism for single solar cycles, and don´t know yet where I will end up.
At the moment I am focused on three cycles: Ju 11,86 - JuSa 9,96 and VeEaJu 11,08
The Jovian cycle is special as no other planets are involved. The two other should be the same kind of effect, and could therefore perhaps be expressed by one cycle, maybe related to barycenter, momentum or something...
The JuSa connection shows that when Ju-Sa are in line (conjunct/opposite) we get low/decreasing sunspot activity. When they are at right angles, we get high/rising activity.
This indicates that when Uranus and Neptun also are conjunct/opposite, we may see some grand minimum effect... but not unless also JuSa fall out of phase. This happens by two mechanisms: -after a period of short and strong cycles, with minimum crossing the Jupiter aphelion (Ju out of phase). When the minimum get close to the end of the VeEaJu "tidal max" interval, the solar cycle is forced to prolong, and then JuSa get out of phase -or in the middle of a long period of strong Ju-phase, where the minimums are locked near the Jupiter perihelion. First we see one or more cycles that seem to get in phase with JuSa. Then a very short cycle that seem to indicate that Ju is getting out of phase, but the time/conditions are not right and Ju strikes back causing a very long solar cycle and JuSa to fall out of phase.
But what about the VeEaJu-syzygys? Aren´t they telling us that conjunctions/oppositions favor high sunspot activity? Maybe JuSa and VeEaJu are not the same kind of effect after all?
--------- One problem is that most of the planetary synodic cycles are not fixed, which may cause the supercycles neither to be fixed but rather to be within an interval some longer cycles that I find interesting are: -Uranus-Neptun ~171 years -Jupiter-Saturn resets every ~59 years, and multiplied by three we get ~178 years which is a number where many planetary cycles resonate -Every ~100 years the JuSa (x5) resonate with the VeEaJu-cycle (x9)
-the sharpest cluster of minima is at ~45deg before the Jupiter perihelion, which would be around November 2009 -a minimum sometime in 2008-2010 will indicate that JuSa is out of phase for SC24, and gives us a weak cycle of SSN <100 -SC23 was prolonged by the fact that the declining phase happened at the same time as the VeEaJu "tidal-max" (the regulator of solar cycle). This is what forces JuSa to fall out of phase, and will end the solar cycle "bull-market" of short and strong cycles. This is similar to what happened at SC4 and SC-11
just had an epiphany... indeed there are three cycles and three mechanisms that rule the solar cycle...
I have been looking for one mechanism that explains it all, but it is a complex of three:
-the Jovian is a 11,86 year cycle that depresses sunspot activity before and around the Jupiter perihelion (also Saturn, but weaker) But by what mechanism? -the angular momentum (specially Jupiter and Saturn) winds up the solar dynamo and generates the "energy" (weak cycles if JuSa out of phase, and grand minima when also Uranus-Neptun are alligned correctly) -the tidal forces by Venus, Earth and Jupiter has a maximum on average every 11,08 years, and provokes extra sunspot creation, flares and CMEs, and drain the energy that has build up
It is all about seeing the complete picture... and surely there could be more pieces in the puzzle...
---- the optimal configuration for a strong cycle would then be: -a minimum a bit after Jupiter perihelion -a minimum at JuSa angle around 70/250 deg, and Uranus/Neptun at near right angle -a minimum 3-5 years before VeEaJu tidal max
Not unexpected does SC19 fit in nicely: -minimum at 70 deg after Ju perihelion, and 122 deg after Sa perihelion -at JuSa 231 deg and UrNe 93 deg -about 5 years before tidal max