The tide height is a function of the earth/sun/moon systems. Earth and Moon aren't at a fixed distance from eachother, and neither is the sun, so every day is a unique tide but you can predict the range.
The analog way to do it is to make a gear for each point of data in the system and synchronize all their gears. Then you use them all to rotate one final gear, which will show you the prediction for the time you've chosen.
