NavList:

That's a great way to analyze this problem! Yes, tide clocks can be set to display tide times with rather good accuracy whenever the tides have "normal" twice daily behavior. It's great to see some numbers on the relative merits of setting at "full and change" (as they used to say) versus setting at any old day of the month. Your analysis can be applied to a tide clock "in your head," too. If you advance the time of high tide by a fixed number every day, how far out would you be after five or ten days? Obviously, by your analysis, you'll do better if you start at the Spring tides. By the way, do you get any improvement if you set on the actual date of the Spring tide instead of the date of the Moon phase? The lag or so-called "age of the tide" is location-dependent, but usually one to three days after the Sun-Moon alignment. And can you calculate the proper settings directly from the phases of the standard harmonics? 

Frank Reed