Lunar Cycles and Tide Correlations

by Maximilian Mantius

Submitted : Fall 2012

It is well understood that during new moon and full moon, the tide's range is at its maximum; this is commonly known as a Spring Tide (Cooley). Looking at Table 1 (a representation of tide heights for December 2012), it is evident that the shoreline of Cape Town experiences semi-diurnal tides (two high tides and two low tides each day). My interest sprouted from deciphering at which moon, full or new, resulted in the greatest tidal range. In order to figure such a problem, I specifically took three days before and three days after the new moon (13^th) and the full moon (28^th), including the date of the respective moon phase. I then graphed the comparison—the day of the month on the x-axis and tide height on the y-axis. Next, two polynomial equations were constructed for each graph, one representing the high tide and following low tide at new moon and full moon (f(x)) and one representing the following high and low tide (g(x)); with two equations, I was then able to find the area between the two polynomial equations. After solving a few integrals and initiating substitution, I concluded that the greatest tidal range existed during the new moon phase.

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