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IB Math Portfolio Type 2

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Introduction

Period 4

30 October 2008

Tide Modeling Around the World

Every place in the world has a tide that is unique to it. The following project discusses tidal behavior and the changes in tides. Practical applications are used to show how tides can have an important affect on people’s lives.

Part 1

The following data is a 24 hour period of tide levels for Atka Alaska. The recorded tide levels start on October 28th, 2008 at 0:00:00 and ends on October 29th, 2008 at 0:00:00.

Date/Time                              Obs.  

(Local Time)                             (ft.)    

10/28/2008 00:00:00  YDT   0.25  

10/28/2008 01:00:00  YDT  -0.00  

10/28/2008 02:00:00  YDT   0.14  

10/28/2008 03:00:00  YDT   0.54  

10/28/2008 04:00:00  YDT   0.79  

10/28/2008 05:00:00  YDT   1.39  

10/28/2008 06:00:00  YDT   1.91  

10/28/2008 07:00:00  YDT   2.28  

10/28/2008 08:00:00  YDT   2.47  

10/28/2008 09:00:00  YDT   2.77  

10/28/2008 10:00:00  YDT   2.73  

10/28/2008 11:00:00  YDT   2.78  

10/28/2008 12:00:00  YDT   2.92  

10/28/2008 13:00:00  YDT   2.82  

10/28/2008 14:00:00  YDT   2.87  

10/28/2008 15:00:00  YDT   2.88  

10/28/2008 16:00:00  YDT   2.82  

10/28/2008 17:00:00  YDT   2.81  

10/28/2008 18:00:00  YDT   2.76  

10/28/2008 19:00:00  YDT   2.52  

10/28/2008 20:00:00  YDT   2.04  

10/28/2008 21:00:00  YDT   1.61  

10/28/2008 22:00:00  YDT   1.05  

10/28/2008 23:00:00  YDT   0.49  

10/29/2008 00:00:00  YDT   0.01  

Part 2

Tide Height Versus Time of Dayimage00.png

 Time of Day (hrs)

I graphed the equationy=1.5+1.8sin(.205387x-1). My graphs showed that for October 28th, 2008 for Atka, Alaska the tide’s maximum was (12,3.3) and the tide’s two minimums were at    (-2,-.3)

...read more.

Middle

In this case, t will represent the time of day as the x value for each specific one hour interval. The variable h will represent the height of the specific tide level as our y value.

In the equation y=d+asin(bx-c), a represents the amplitude. Amplitude is the absolute value of a added and subtracted to the midline of the graph. To find the amplitude of the graph, one must take the maximum value minus the minimum value and divide by 2. Therefore, the equation for the amplitude of this graph will be: 3-0/2 which means that the amplitude is 1.5.

In the equation y=d+asin(bx-c), b represents the period, or how often the graph repeats. To get the period, one must use the equation 2π/b. The variable b represents the point at which the graph starts repeating. Therefore, in this graph, b equals 30. So the equation for the period of this graph will be b=2π/30. The period of the graph is b= π/15, or .2094395.

In the equation y=d+asin(bx-c), c represents a horizontal shift.

...read more.

Conclusion

Part 10

Because the tides of this particular area of Atka, Alaska do not repeat in a 24 hour period, runners would have to go running every other day if they wanted to go at the lowest tide.

Part 11

My original model fits the tides relatively accurately. The maximum point for my original function was (12, 3.3) and the minimum was (-2, -.3). The maximum point for the regression function was (13, 3.1) and the minimum was (-2.40,-.28). The horizontal shift and period were all consistent between the two graphs. The amplitude and vertical shift both had to be slightly altered to fit the local tide trends better.

Surfline Model

These are the tides predicted for Salt Creek Beach, California. My model does not fit even remotely close to this data. This data has two maximums and two minimums, which automatically means my function would not work for this one, considering in a 24 hour period my tides only have one maximum point.

2008-10-30  3:34 AM PDT   1.83 feet  Low Tide

2008-10-30  9:46 AM PDT   5.92 feet  High Tide

2008-10-30  4:59 PM PDT  -0.27 feet  Low Tide

2008-10-30 11:16 PM PDT   3.56 feet  High Tide

Works Cited

http://www.surfline.com/surf-report/salt-creek_4233/

http://www.graphmatica.com/

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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