Disclaimer
This is a precursor to the question "Is the solunar theory real?" - which I'm hoping to answer. So I fully understand if you don't believe that the question lives up to the forum's standards. But I have access to data that could prove or disprove the theory given the secret formula. I am also aware that there are many studies that examine the relationship between moon phases and fishing, but this question is about the specific theory that the gravity of the sun and moon would have a combined influence on fishing.
Challenge
Find a general formula that: Given latitude,longitude and date finds (at most) two major "solunar periods" for that day.
Given
A table of daily solunar periods for a given month at a given location and some clues on the formula.
Background
There is a popular theory among sport fishermen called the Solunar Theory. It was invented in the 1930:s by John Alden Knight and it postulates that the movement of the sun and moon affect fishing and hunting. It claims that there are periods during the day, solunar periods, that yield considerably better fishing and hunting results. This seems farfetched but is likely an extrapolation from the fact that salt water fishing is affected by ocean tides. Several web sites publish these tables as a guide for fishermen, but no one has been able to prove or disprove the theory for 80 years.
I want to calculate these solunar periods and I examined several implementations of the solunar theory including http://solunar.com, http://kevinboone.net/README_solunar.html and http://sourceforge.net/projects/solunar/
All of these implementations gave widely different results when tested on the same day and location.
Instead, I have bought a table of solunar periods from the original publisher of the solunar theory. It claims to follow the theory of mr Knight but does not explain how these times are calculated. The interesting problem is finding the general formula for calculating these periods.
Clues
Reading the book "Moon up - Moon down" by J.A. Knight gives the following clues:
- There are usually two major and two minor periods each day.
- Sometimes, there is one period missing which is explained by the fact that the lunar day is slightly longer than 24 hours.
- The minor periods are exactly in between the major ones, i.e. we only need to calculate the major periods.
- In the book, Knight implies that the major periods are based on the hypothetical times of low and high tide if the earth was completely covered with water.
On p.20, he says:
I tried making up a Solunar schedule by determining the resultant of the two forces-the pull of the moon and the pull of the sun-and using as the Solunar period the time that this force was applied directly to our particular longitude-either overhead or underfoot.[...] This schedule proved to be more satisfactory than the one concocted from the use of tidal times, although it still was far from being exact"
On p.54, he says:
At the times of full moon and dark of the moon, the moon and sun are functioning in unison, they, at those times being approximately "in line". That being the case, the resultant of the directions of pull of the heavenly bodies comes pretty close to being the true Solunar period. As the month progresses, the directions of pull of the moon and of the sun move farther apart each day so that, at the times of first quarter, they are approximately at right angles to each other. At these times, the moon can be considered to be the complete control. These are the times where the "moon-up moon-down" system seems to be the correct method of timing. In setting up the schedule, these four times of the month are used as key points. Just at what time of the month the sun ceases to act in conjunction with the moon and just at what point the moon becomes the full control, I cannot say with any authority. This much I do know. By averaging the times of the Solunar periods between these four key points, so that the progression from day to day is smooth, the resultant schedule comes about as close to the true schedule as it is possible to come without knowing the absolute cause.
Data
To find the formula I have a table of Solunar periods for 2015 at the location: Beverly Hills, latitude 34.09663, longitude -118.4124
https://drive.google.com/file/d/0Bwvk-8toPklLZkQ3VXBoNU5yY0E/view?pli=1
The major periods for March 2015 are below
day p1 p2
01 7:35 19:55
02 8:15 20:40
03 9:00 21:20
04 9:40 22:00
05 10:15 22:40 Full moon
06 11:05 23:30
07 11:50 --:--
08 12:15 13:35
09 2:00 14:25
10 2:50 15:15
11 3:40 16:05
12 4:35 17:00
13 5:30 17:55 Last Quarter
14 6:20 18:45
15 7:10 19:40
16 8:05 20:30
17 8:55 21:25
18 9:50 22:15
19 10:40 23:10
20 11:30 --:-- Dark moon
21 0:00 12:30
22 1:05 13:30
23 2:05 14:35
24 3:10 15:30
25 4:00 16:25
26 5:05 17:30
27 5:55 18:20 First Quarter
28 6:40 19:05
29 7:25 19:50
30 8:05 20:30
31 8:50 21:10
Can anyone suggest a formula that explains these numbers given a location and a date? Preferably one that is computationally feasible.
