Is there a function that could express tidal height changes at any day? It's really importnant...?

Question

Using general sine formula, I derived a function that fit the curve of the tidal heights changes over a period of 24h. As you might know, Moon comes out every day 50min later than day before, and therefore, there is a small shift (C) in the next day. On the 3rd day, shift is going to be 2XC, on 4th 3XC and so on. Therefore, the first function, that fit the 1st day, due to all those new and increasing shifts, won't fit exactly any of the curves in the future.

Is there a function (something similar to the sequence principal?) that could follow the the tidal curve over longer period of time, and I mean, a general one, since I don't want to deduce 10th day by obtaining 9 days before :)

Any kind of help would be extremely useful, since I'm not that level of math yet:) and you should know something about that how Moon affects Earth also...I guess. You can also include any useful links you think I should look at. Thanks:)

Answer 1

I do not have a correction factor for you.
You have considered that the lunar cycle is about 28 days and of course you know there are two tidal cycles per day. Part of the Starry Night program on the Internet may help you, but you may have to purchase the good version.
Using lunar effects alone you cannot really predict real tides at any particular location because of the varying effects of winds, seasonal oceanic currents, precession, drag, bottom topography , etc. That is why we have almanacs which are principally based on historical data. Also there are already printed tidal charts for many locations, but I do not know if those are empirically based or calculated.
Using some of those tide charts and an almanac and then comparing them to your formula, perhaps a correction factor can be fitted.

Answer 2

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