Surf's+Up+Dude!

Surf's Up Dude!

Alex Buck


Task: Tide Model: Create a tide model using the sine or cosine function for a beach of your choice. Fully explain the components of your model, compare the predictions from your model to actual tide values for the data set used and include a use of your tide model. Your model should include the graph and the function that models your data. How to? 1. You must choose a location and get the tides times for the day. We chose an island called Eleuthera that is located in the Bahamas. It's also important to have background knowledge about tides. The key point is that the time of high tide and low tide change everyday. This means that in order to be accurate, it must only be about one day. Therefore, this problem is based on the tides of January 11, 2012. We used the following link to get our information about tides. [|Tides] This is what we found about tides for January 11, 2012:

2. Next, it's necessary to make a chart with the information of the tides. We included the first two tides from January 12, 2012 in order to see a slight repeat in the shape.


 * Please take note to the times. It is necessary not to have repeating x amounts. Therefore, the times are off of the hour. After the 24 hours there would be a repeat at 6:00 am and 11:54 am so instead it is 30.00 and 35.54. Also, notice that the minutes are in decimals.

3. After we have all of the data, we used a [|scientific calculator] to plug in all of the information. The steps to plug in the information are: List (2nd STAT) Time of Day vaules for list one Height of Tide values for list two

4. Once all the information is in the calculator, you want to use the data to find a sinusoidal regression. To do this: STAT - CALC - C - L1, L2, YVARS - Function - Y1

5. A sin graph has 4 components: y=a*sin(bx+c) +d Using the calculator we got all the four components. This gave us our new equation of: y=1485.5*sin(-5.569x+1.19) +-1402.58

6. Now that we have our equation, we can use the calculator to see the plotted points. STATPLOT (2nd Y=) - Turn on Plot 1 - Zoom 9

7. The last step is to connect the lines and then you have a sin graph of the tides for a 24, or considering the two extra a 36, hour time slot.

8. The completed graph for the 24 hours of January 11, 2012 look like this:

Extra Information: - A tide chart like this is very helpful for fishers. As shown in the picture above, you are able to tell when you will have the best chance of catching fish because the amount of fish has a lot to do with the tide. - The graph the we made would be very accurate for January 11th. The problem is that with changing moon phases, there is a change in height and time of tides consistently. Therefore, you would have to make new graphs with new data in order to be very accurate for other days.