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					TEACHERS' NOTES - EXPLORING TIDAL CYCLES

Learning objectives:        Students should understand that tides are caused by the grav
                                     attraction between the ocean and the Sun and the M
                            Students should understand that the effects of the Sun and th
                                     can be represented by formulae to generate a simple
                            Students should be able to interpret these models as represen
                            Students should be able to answer simple questions relating t

This spreadsheet presents a very simplified simulation of the tidal cycle. To help students
are spring and neap tides, a simple cycle due to the Sun alone is generated first. This is s
of four days only, to show a smooth curve. Later, we will need to look at a longer period, s
for a longer period but with longer time intervals - this generates a ragged curve but one th
cyclically.

Adding the Moon to the model means that we have to incorporate the effects of the Moon'
Including the Moon has three effects. First, the tidal range is increased. Second, tides no
at local midday and midnight. Third, and most noticeable, the tidal range changes from da
and neap- tides.

Students can be provided with their own copy of the spreadsheet(*). There is a series of q
which will test their understanding of the basic ideas covered here. The spreadsheet can
to the class using a digital projector or interactive whiteboard

NOTE THAT THIS SIMULATION IS NOT A TIDAL PREDICTOR - MAKE PUPILS AWARE

(*) BEFORE PROVIDING THIS SPREADSHEET FOR CLASS USE, DELETE ALL WORK
s are caused by the gravitational
n and the Sun and the Moon
effects of the Sun and the Moon
ulae to generate a simple model
hese models as represented in graphs
mple questions relating to the graphs

l cycle. To help students to understand why there
 generated first. This is shown for a period
 look at a longer period, so the graph is repeated
a ragged curve but one that still obviously repeats


e the effects of the Moon's orbit around the Earth.
 eased. Second, tides no longer occur
al range changes from day to day, giving spring-


(*). There is a series of questions at the end
e. The spreadsheet can be demonstrated


- MAKE PUPILS AWARE OF THE SAFETY WARNING

SE, DELETE ALL WORKSHEETS WHOSE TITLES ARE IN CAPITALS
EXPLORING THE TIDAL CYCLE

Tides occur because the ocean is being pulled towards the Moon and the Sun by gravity.
The Earth orbits around the Sun, and the Moon orbits around the Earth. The Earth also
spins (rotates) around its axis. Because of these different movements, the tidal cycle is qu
It is easier to understand if you look first at the Earth and Sun, and forget about the Moon.
If the Moon were missing, and the Earth continued to orbit around the Sun and rotated on
once per day, each place on the Earth would experience two tides per day. Imagine that t
gravity pulled the oceans into a bulge. This bulge would always face towards the Sun, wit
on the opposite side. As the Earth rotated, any place on the surface would pass under on
these bulges every twelve hours, with a 'high' tide at local (solar) noon and a second high
The tidal cycle with just the effects of the Sun's gravity is represented in the charts 'Sun 4d
The data that generated these charts can be found in the preceding worksheets. The first
days only, to demonstrate the regular cycle, with high tides at local midday and local midn
plot shows data for a full month. The same cycle is present throughout the period, althoug
is more 'ragged' because the tidal height is calculated only every two hours, rather than ev
We can now add the Moon into the picture. Although the Moon is very much smaller than
is closer to the Earth its gravitational attraction is about twice as large. But the Moon also
Earth, completing an orbit in just under 28 days. At two points in this orbit, the Moon and
combining their gravity to give the highest - or 'spring' tides. This occurs at full Moon, whe
the opposite side of the Earth to the Sun, and fourteen days later at the new Moon, when
the same side as the Sun. In between these times, the gravity of the Sun and Moon pull in
meaning that the difference between high and low tide is smaller - these are 'neap' tides.
The orbit of the Moon also means that tides don't occur at exactly the same time each day
about 12 hours 25 minutes between successive high tides. Look at the chart 'Spring and
n and the Sun by gravity.
  Earth. The Earth also
ments, the tidal cycle is quite complicated.
nd forget about the Moon.
d the Sun and rotated on its axis
s per day. Imagine that the Sun's
ace towards the Sun, with a second bulge
ace would pass under one of
 noon and a second high tide at midnight.
 nted in the charts 'Sun 4d' and 'Sun 28d'.
ing worksheets. The first plot is for four
 al midday and local midnight. The second
ughout the period, although the plot
 two hours, rather than every 20 minutes.
s very much smaller than the Sun, because it
arge. But the Moon also orbits around the
 this orbit, the Moon and Sun are lined up,
 occurs at full Moon, when the Moon is on
 at the new Moon, when the Moon is on
  the Sun and Moon pull in different directions,
- these are 'neap' tides.
y the same time each day. Instead, there is
 at the chart 'Spring and neap' tides.
SAFETY WARNING

THIS TIDAL SIMULATOR IS A VERY SIMPLIFIED R
THE TIDAL CYCLE

IT SHOULD NOT BE USED FOR NAVIGATION OR
WHERE AN ACCURATE KNOWLEDGE OF LOCAL

THE CALCULATIONS USED IN THIS SPREADSHE
TO ILLUSTRATE THE PRINCIPLE OF TIDAL CYCL
PROVIDE AN ACCURATE PREDICTION OF LOCAL

PLEASE CONSULT LOCAL TIDE TABLES OR ACC
TIDAL MODELS IF YOU ARE WORKING ON THE S
COASTAL WATERS
 SIMPLIFIED REPRESENTATION OF


VIGATION OR ANY ACTIVITY
GE OF LOCAL TIDES IS NEEDED

S SPREADSHEET ARE SIMPLY USED
 F TIDAL CYCLES, AND WILL NOT
 ION OF LOCAL TIDES

BLES OR ACCURATE COMPUTER
ING ON THE SHORE OR IN
            Calculation time interval =        0.3 hours           Values are calculated every 20 minutes
            Interval between high tides =       12 hours           High tides occur at exactly the same time each day
            Maximum depth range =              3.0 metres

Elapsed time Elapsed time Elasped time Phase       Height above
(days)       (hours)      (radians)                low water (m)
       0.00          0.00           0.00      0.50           3.0
       0.01          0.33           0.17      0.49           3.0
       0.03          0.67           0.35      0.47           2.9
       0.04          1.00           0.52      0.43           2.8
       0.06          1.33           0.70      0.38           2.6
       0.07          1.67           0.87      0.32           2.5
       0.08          2.00           1.05      0.25           2.3
       0.10          2.33           1.22      0.17           2.0
       0.11          2.67           1.40      0.09           1.8
       0.13          3.00           1.57      0.00           1.5
       0.14          3.33           1.75     -0.09           1.2
       0.15          3.67           1.92     -0.17           1.0
       0.17          4.00           2.09     -0.25           0.8
       0.18          4.33           2.27     -0.32           0.5
       0.19          4.67           2.44     -0.38           0.4
       0.21          5.00           2.62     -0.43           0.2
       0.22          5.33           2.79     -0.47           0.1
       0.24          5.67           2.97     -0.49           0.0
       0.25          6.00           3.14     -0.50           0.0
       0.26          6.33           3.32     -0.49           0.0
       0.28          6.67           3.49     -0.47           0.1
       0.29          7.00           3.67     -0.43           0.2
       0.31          7.33           3.84     -0.38           0.4
       0.32          7.67           4.01     -0.32           0.5
       0.33          8.00           4.19     -0.25           0.7
       0.35          8.33           4.36     -0.17           1.0
       0.36          8.67           4.54     -0.09           1.2
       0.38          9.00           4.71      0.00           1.5
       0.39          9.33           4.89      0.09           1.8
       0.40          9.67           5.06      0.17           2.0
       0.42         10.00           5.24      0.25           2.3
       0.43         10.33           5.41      0.32           2.5
       0.44         10.67           5.59      0.38           2.6
       0.46         11.00           5.76      0.43           2.8
       0.47         11.33           5.93      0.47           2.9
       0.49         11.67           6.11      0.49           3.0
       0.50         12.00           6.28      0.50           3.0
       0.51         12.33           6.46      0.49           3.0
       0.53         12.67           6.63      0.47           2.9
       0.54         13.00           6.81      0.43           2.8
       0.56         13.33           6.98      0.38           2.6
       0.57         13.67           7.16      0.32           2.5
       0.58         14.00           7.33      0.25           2.3
       0.60         14.33           7.50      0.17           2.0
       0.61         14.67           7.68      0.09           1.8
       0.63         15.00           7.85      0.00           1.5
       0.64         15.33           8.03     -0.09           1.2
       0.65         15.67           8.20     -0.17           1.0
       0.67         16.00           8.38     -0.25           0.7
       0.68         16.33           8.55     -0.32           0.5
       0.69         16.67           8.73     -0.38           0.4
0.71   17.00    8.90   -0.43   0.2
0.72   17.33    9.08   -0.47   0.1
0.74   17.67    9.25   -0.49   0.0
0.75   18.00    9.42   -0.50   0.0
0.76   18.33    9.60   -0.49   0.0
0.78   18.67    9.77   -0.47   0.1
0.79   19.00    9.95   -0.43   0.2
0.81   19.33   10.12   -0.38   0.4
0.82   19.67   10.30   -0.32   0.5
0.83   20.00   10.47   -0.25   0.7
0.85   20.33   10.65   -0.17   1.0
0.86   20.67   10.82   -0.09   1.2
0.88   21.00   11.00    0.00   1.5
0.89   21.33   11.17    0.09   1.8
0.90   21.67   11.34    0.17   2.0
0.92   22.00   11.52    0.25   2.2
0.93   22.33   11.69    0.32   2.5
0.94   22.67   11.87    0.38   2.6
0.96   23.00   12.04    0.43   2.8
0.97   23.33   12.22    0.47   2.9
0.99   23.67   12.39    0.49   3.0
1.00   24.00   12.57    0.50   3.0
1.01   24.33   12.74    0.49   3.0
1.03   24.67   12.92    0.47   2.9
1.04   25.00   13.09    0.43   2.8
1.06   25.33   13.26    0.38   2.6
1.07   25.67   13.44    0.32   2.5
1.08   26.00   13.61    0.25   2.3
1.10   26.33   13.79    0.17   2.0
1.11   26.67   13.96    0.09   1.8
1.13   27.00   14.14    0.00   1.5
1.14   27.33   14.31   -0.09   1.2
1.15   27.67   14.49   -0.17   1.0
1.17   28.00   14.66   -0.25   0.8
1.18   28.33   14.84   -0.32   0.5
1.19   28.67   15.01   -0.38   0.4
1.21   29.00   15.18   -0.43   0.2
1.22   29.33   15.36   -0.47   0.1
1.24   29.67   15.53   -0.49   0.0
1.25   30.00   15.71   -0.50   0.0
1.26   30.33   15.88   -0.49   0.0
1.28   30.67   16.06   -0.47   0.1
1.29   31.00   16.23   -0.43   0.2
1.31   31.33   16.41   -0.38   0.4
1.32   31.67   16.58   -0.32   0.5
1.33   32.00   16.76   -0.25   0.7
1.35   32.33   16.93   -0.17   1.0
1.36   32.67   17.10   -0.09   1.2
1.38   33.00   17.28    0.00   1.5
1.39   33.33   17.45    0.09   1.8
1.40   33.67   17.63    0.17   2.0
1.42   34.00   17.80    0.25   2.2
1.43   34.33   17.98    0.32   2.5
1.44   34.67   18.15    0.38   2.6
1.46   35.00   18.33    0.43   2.8
1.47   35.33   18.50    0.47   2.9
1.49   35.67   18.68    0.49   3.0
1.50   36.00   18.85    0.50   3.0
1.51   36.33   19.02    0.49   3.0
1.53   36.67   19.20    0.47   2.9
1.54   37.00   19.37    0.43   2.8
1.56   37.33   19.55    0.38   2.6
1.57   37.67   19.72    0.32   2.5
1.58   38.00   19.90    0.25   2.3
1.60   38.33   20.07    0.17   2.0
1.61   38.67   20.25    0.09   1.8
1.63   39.00   20.42    0.00   1.5
1.64   39.33   20.59   -0.09   1.2
1.65   39.67   20.77   -0.17   1.0
1.67   40.00   20.94   -0.25   0.7
1.68   40.33   21.12   -0.32   0.5
1.69   40.67   21.29   -0.38   0.4
1.71   41.00   21.47   -0.43   0.2
1.72   41.33   21.64   -0.47   0.1
1.74   41.67   21.82   -0.49   0.0
1.75   42.00   21.99   -0.50   0.0
1.76   42.33   22.17   -0.49   0.0
1.78   42.67   22.34   -0.47   0.1
1.79   43.00   22.51   -0.43   0.2
1.81   43.33   22.69   -0.38   0.4
1.82   43.67   22.86   -0.32   0.5
1.83   44.00   23.04   -0.25   0.8
1.85   44.33   23.21   -0.17   1.0
1.86   44.67   23.39   -0.09   1.2
1.88   45.00   23.56    0.00   1.5
1.89   45.33   23.74    0.09   1.8
1.90   45.67   23.91    0.17   2.0
1.92   46.00   24.09    0.25   2.3
1.93   46.33   24.26    0.32   2.5
1.94   46.67   24.43    0.38   2.6
1.96   47.00   24.61    0.43   2.8
1.97   47.33   24.78    0.47   2.9
1.99   47.67   24.96    0.49   3.0
2.00   48.00   25.13    0.50   3.0
2.01   48.33   25.31    0.49   3.0
2.03   48.67   25.48    0.47   2.9
2.04   49.00   25.66    0.43   2.8
2.06   49.33   25.83    0.38   2.6
2.07   49.67   26.01    0.32   2.5
2.08   50.00   26.18    0.25   2.2
2.10   50.33   26.35    0.17   2.0
2.11   50.67   26.53    0.09   1.8
2.13   51.00   26.70    0.00   1.5
2.14   51.33   26.88   -0.09   1.2
2.15   51.67   27.05   -0.17   1.0
2.17   52.00   27.23   -0.25   0.7
2.18   52.33   27.40   -0.32   0.5
2.19   52.67   27.58   -0.38   0.4
2.21   53.00   27.75   -0.43   0.2
2.22   53.33   27.93   -0.47   0.1
2.24   53.67   28.10   -0.49   0.0
2.25   54.00   28.27   -0.50   0.0
2.26   54.33   28.45   -0.49   0.0
2.28   54.67   28.62   -0.47   0.1
2.29   55.00   28.80   -0.43   0.2
2.31   55.33   28.97   -0.38   0.4
2.32   55.67   29.15   -0.32   0.5
2.33   56.00   29.32   -0.25   0.8
2.35   56.33   29.50   -0.17   1.0
2.36   56.67   29.67   -0.09   1.2
2.38   57.00   29.85    0.00   1.5
2.39   57.33   30.02    0.09   1.8
2.40   57.67   30.19    0.17   2.0
2.42   58.00   30.37    0.25   2.3
2.43   58.33   30.54    0.32   2.5
2.44   58.67   30.72    0.38   2.6
2.46   59.00   30.89    0.43   2.8
2.47   59.33   31.07    0.47   2.9
2.49   59.67   31.24    0.49   3.0
2.50   60.00   31.42    0.50   3.0
2.51   60.33   31.59    0.49   3.0
2.53   60.67   31.76    0.47   2.9
2.54   61.00   31.94    0.43   2.8
2.56   61.33   32.11    0.38   2.6
2.57   61.67   32.29    0.32   2.5
2.58   62.00   32.46    0.25   2.2
2.60   62.33   32.64    0.17   2.0
2.61   62.67   32.81    0.09   1.8
2.63   63.00   32.99    0.00   1.5
2.64   63.33   33.16   -0.09   1.2
2.65   63.67   33.34   -0.17   1.0
2.67   64.00   33.51   -0.25   0.7
2.68   64.33   33.68   -0.32   0.5
2.69   64.67   33.86   -0.38   0.4
2.71   65.00   34.03   -0.43   0.2
2.72   65.33   34.21   -0.47   0.1
2.74   65.67   34.38   -0.49   0.0
2.75   66.00   34.56   -0.50   0.0
2.76   66.33   34.73   -0.49   0.0
2.78   66.67   34.91   -0.47   0.1
2.79   67.00   35.08   -0.43   0.2
2.81   67.33   35.26   -0.38   0.4
2.82   67.67   35.43   -0.32   0.5
2.83   68.00   35.60   -0.25   0.8
2.85   68.33   35.78   -0.17   1.0
2.86   68.67   35.95   -0.09   1.2
2.88   69.00   36.13    0.00   1.5
2.89   69.33   36.30    0.09   1.8
2.90   69.67   36.48    0.17   2.0
2.92   70.00   36.65    0.25   2.3
2.93   70.33   36.83    0.32   2.5
2.94   70.67   37.00    0.38   2.6
2.96   71.00   37.18    0.43   2.8
2.97   71.33   37.35    0.47   2.9
2.99   71.67   37.52    0.49   3.0
3.00   72.00   37.70    0.50   3.0
3.01   72.33   37.87    0.49   3.0
3.03   72.67   38.05    0.47   2.9
3.04   73.00   38.22    0.43   2.8
3.06   73.33   38.40    0.38   2.6
3.07   73.67   38.57    0.32   2.5
3.08   74.00   38.75    0.25   2.2
3.10   74.33   38.92    0.17   2.0
3.11   74.67   39.10    0.09   1.8
3.13   75.00   39.27    0.00   1.5
3.14   75.33   39.44   -0.09   1.2
3.15   75.67   39.62   -0.17   1.0
3.17   76.00   39.79   -0.25   0.8
3.18   76.33   39.97   -0.32   0.5
3.19   76.67   40.14   -0.38   0.4
3.21   77.00   40.32   -0.43   0.2
3.22   77.33   40.49   -0.47   0.1
3.24   77.67   40.67   -0.49   0.0
3.25   78.00   40.84   -0.50   0.0
3.26   78.33   41.02   -0.49   0.0
3.28   78.67   41.19   -0.47   0.1
3.29   79.00   41.36   -0.43   0.2
3.31   79.33   41.54   -0.38   0.4
3.32   79.67   41.71   -0.32   0.5
3.33   80.00   41.89   -0.25   0.7
3.35   80.33   42.06   -0.17   1.0
3.36   80.67   42.24   -0.09   1.2
3.38   81.00   42.41    0.00   1.5
3.39   81.33   42.59    0.09   1.8
3.40   81.67   42.76    0.17   2.0
3.42   82.00   42.94    0.25   2.2
3.43   82.33   43.11    0.32   2.5
3.44   82.67   43.28    0.38   2.6
3.46   83.00   43.46    0.43   2.8
3.47   83.33   43.63    0.47   2.9
3.49   83.67   43.81    0.49   3.0
3.50   84.00   43.98    0.50   3.0
3.51   84.33   44.16    0.49   3.0
3.53   84.67   44.33    0.47   2.9
3.54   85.00   44.51    0.43   2.8
3.56   85.33   44.68    0.38   2.6
3.57   85.67   44.85    0.32   2.5
3.58   86.00   45.03    0.25   2.3
3.60   86.33   45.20    0.17   2.0
3.61   86.67   45.38    0.09   1.8
3.62   87.00   45.55    0.00   1.5
3.64   87.33   45.73   -0.09   1.2
3.65   87.67   45.90   -0.17   1.0
3.67   88.00   46.08   -0.25   0.8
3.68   88.33   46.25   -0.32   0.5
3.69   88.67   46.43   -0.38   0.4
3.71   89.00   46.60   -0.43   0.2
3.72   89.33   46.77   -0.47   0.1
3.74   89.67   46.95   -0.49   0.0
3.75   90.00   47.12   -0.50   0.0
3.76   90.33   47.30   -0.49   0.0
3.78   90.67   47.47   -0.47   0.1
3.79   91.00   47.65   -0.43   0.2
3.81   91.33   47.82   -0.38   0.4
3.82   91.67   48.00   -0.32   0.5
3.83   92.00   48.17   -0.25   0.7
3.85   92.33   48.35   -0.17   1.0
3.86   92.67   48.52   -0.09   1.2
3.87   93.00   48.69   0.00   1.5
3.89   93.33   48.87   0.09   1.8
3.90   93.67   49.04   0.17   2.0
3.92   94.00   49.22   0.25   2.2
3.93   94.33   49.39   0.32   2.5
3.94   94.67   49.57   0.38   2.6
3.96   95.00   49.74   0.43   2.8
3.97   95.33   49.92   0.47   2.9
3.99   95.67   50.09   0.49   3.0
4.00   96.00   50.27   0.50   3.0
e same time each day
                                                               Model tidal range with Sun's gravity only - 4 days


                                             10.0



                                              9.0



                                              8.0
Tidal height above low water mark (metres)




                                              7.0



                                              6.0



                                              5.0



                                              4.0



                                              3.0



                                              2.0



                                              1.0



                                              0.0
                                                 0.00   1.00                            2.00                        3.00   4.00
                                                                                     Time (days)
            Calculation time interval =          2.0 hours             Values are calculated every 2 hours - only a sixth of the frequency use
            Interval between high tides =      12.00 hours             High tides occur at exactly the same time each day
            Maximum depth range =                3.0 metres

Elapsed time Elapsed time Elasped time Phase           Height above
(days)       (hours)       (radians)                   low water (m)
       0.00              0         0.00         0.50            3.0
       0.08              2         1.05         0.25            2.3
       0.17              4         2.09        -0.25            0.8
       0.25              6         3.14        -0.50            0.0
       0.33              8         4.19        -0.25            0.7
       0.42             10         5.24         0.25            2.3
       0.50             12         6.28         0.50            3.0
       0.58             14         7.33         0.25            2.3
       0.67             16         8.38        -0.25            0.8
       0.75             18         9.42        -0.50            0.0
       0.83             20        10.47        -0.25            0.8
       0.92             22        11.52         0.25            2.3
       1.00             24        12.57         0.50            3.0
       1.08             26        13.61         0.25            2.3
       1.17             28        14.66        -0.25            0.8
       1.25             30        15.71        -0.50            0.0
       1.33             32        16.76        -0.25            0.7
       1.42             34        17.80         0.25            2.3
       1.50             36        18.85         0.50            3.0
       1.58             38        19.90         0.25            2.3
       1.67             40        20.94        -0.25            0.8
       1.75             42        21.99        -0.50            0.0
       1.83             44        23.04        -0.25            0.7
       1.92             46        24.09         0.25            2.2
       2.00             48        25.13         0.50            3.0
       2.08             50        26.18         0.25            2.3
       2.17             52        27.23        -0.25            0.8
       2.25             54        28.27        -0.50            0.0
       2.33             56        29.32        -0.25            0.7
       2.42             58        30.37         0.25            2.3
       2.50             60        31.42         0.50            3.0
       2.58             62        32.46         0.25            2.3
       2.67             64        33.51        -0.25            0.8
       2.75             66        34.56        -0.50            0.0
       2.83             68        35.60        -0.25            0.8
       2.92             70        36.65         0.25            2.3
       3.00             72        37.70         0.50            3.0
       3.08             74        38.75         0.25            2.3
       3.17             76        39.79        -0.25            0.8
       3.25             78        40.84        -0.50            0.0
       3.33             80        41.89        -0.25            0.8
       3.42             82        42.94         0.25            2.2
       3.50             84        43.98         0.50            3.0
       3.58             86        45.03         0.25            2.3
       3.67             88        46.08        -0.25            0.8
       3.75             90        47.12        -0.50            0.0
       3.83             92        48.17        -0.25            0.7
       3.92             94        49.22         0.25            2.3
       4.00             96        50.27         0.50            3.0
       4.08             98        51.31         0.25            2.3
       4.17            100        52.36        -0.25            0.7
4.25   102    53.41   -0.50   0.0
4.33   104    54.45   -0.25   0.8
4.42   106    55.50    0.25   2.3
4.50   108    56.55    0.50   3.0
4.58   110    57.60    0.25   2.2
4.67   112    58.64   -0.25   0.8
4.75   114    59.69   -0.50   0.0
4.83   116    60.74   -0.25   0.8
4.92   118    61.78    0.25   2.3
5.00   120    62.83    0.50   3.0
5.08   122    63.88    0.25   2.3
5.17   124    64.93   -0.25   0.8
5.25   126    65.97   -0.50   0.0
5.33   128    67.02   -0.25   0.7
5.42   130    68.07    0.25   2.2
5.50   132    69.12    0.50   3.0
5.58   134    70.16    0.25   2.3
5.67   136    71.21   -0.25   0.8
5.75   138    72.26   -0.50   0.0
5.83   140    73.30   -0.25   0.7
5.92   142    74.35    0.25   2.3
6.00   144    75.40    0.50   3.0
6.08   146    76.45    0.25   2.3
6.17   148    77.49   -0.25   0.8
6.25   150    78.54   -0.50   0.0
6.33   152    79.59   -0.25   0.7
6.42   154    80.63    0.25   2.2
6.50   156    81.68    0.50   3.0
6.58   158    82.73    0.25   2.3
6.67   160    83.78   -0.25   0.8
6.75   162    84.82   -0.50   0.0
6.83   164    85.87   -0.25   0.7
6.92   166    86.92    0.25   2.3
7.00   168    87.96    0.50   3.0
7.08   170    89.01    0.25   2.3
7.17   172    90.06   -0.25   0.8
7.25   174    91.11   -0.50   0.0
7.33   176    92.15   -0.25   0.7
7.42   178    93.20    0.25   2.2
7.50   180    94.25    0.50   3.0
7.58   182    95.29    0.25   2.3
7.67   184    96.34   -0.25   0.8
7.75   186    97.39   -0.50   0.0
7.83   188    98.44   -0.25   0.7
7.92   190    99.48    0.25   2.3
8.00   192   100.53    0.50   3.0
8.08   194   101.58    0.25   2.3
8.17   196   102.63   -0.25   0.8
8.25   198   103.67   -0.50   0.0
8.33   200   104.72   -0.25   0.8
8.42   202   105.77    0.25   2.2
8.50   204   106.81    0.50   3.0
8.58   206   107.86    0.25   2.3
8.67   208   108.91   -0.25   0.8
8.75   210   109.96   -0.50   0.0
8.83   212   111.00   -0.25   0.7
8.92   214   112.05    0.25   2.2
 9.00   216   113.10    0.50   3.0
 9.08   218   114.14    0.25   2.3
 9.17   220   115.19   -0.25   0.7
 9.25   222   116.24   -0.50   0.0
 9.33   224   117.29   -0.25   0.7
 9.42   226   118.33    0.25   2.2
 9.50   228   119.38    0.50   3.0
 9.58   230   120.43    0.25   2.3
 9.67   232   121.47   -0.25   0.8
 9.75   234   122.52   -0.50   0.0
 9.83   236   123.57   -0.25   0.7
 9.92   238   124.62    0.25   2.2
10.00   240   125.66    0.50   3.0
10.08   242   126.71    0.25   2.3
10.17   244   127.76   -0.25   0.7
10.25   246   128.81   -0.50   0.0
10.33   248   129.85   -0.25   0.7
10.42   250   130.90    0.25   2.2
10.50   252   131.95    0.50   3.0
10.58   254   132.99    0.25   2.3
10.67   256   134.04   -0.25   0.8
10.75   258   135.09   -0.50   0.0
10.83   260   136.14   -0.25   0.7
10.92   262   137.18    0.25   2.3
11.00   264   138.23    0.50   3.0
11.08   266   139.28    0.25   2.3
11.17   268   140.32   -0.25   0.8
11.25   270   141.37   -0.50   0.0
11.33   272   142.42   -0.25   0.7
11.42   274   143.47    0.25   2.3
11.50   276   144.51    0.50   3.0
11.58   278   145.56    0.25   2.3
11.67   280   146.61   -0.25   0.8
11.75   282   147.65   -0.50   0.0
11.83   284   148.70   -0.25   0.8
11.92   286   149.75    0.25   2.2
12.00   288   150.80    0.50   3.0
12.08   290   151.84    0.25   2.3
12.17   292   152.89   -0.25   0.8
12.25   294   153.94   -0.50   0.0
12.33   296   154.99   -0.25   0.7
12.42   298   156.03    0.25   2.2
12.50   300   157.08    0.50   3.0
12.58   302   158.13    0.25   2.3
12.67   304   159.17   -0.25   0.8
12.75   306   160.22   -0.50   0.0
12.83   308   161.27   -0.25   0.7
12.92   310   162.32    0.25   2.3
13.00   312   163.36    0.50   3.0
13.08   314   164.41    0.25   2.3
13.17   316   165.46   -0.25   0.8
13.25   318   166.50   -0.50   0.0
13.33   320   167.55   -0.25   0.7
13.42   322   168.60    0.25   2.2
13.50   324   169.65    0.50   3.0
13.58   326   170.69    0.25   2.3
13.67   328   171.74   -0.25   0.8
13.75   330   172.79   -0.50   0.0
13.83   332   173.83   -0.25   0.8
13.92   334   174.88    0.25   2.3
14.00   336   175.93    0.50   3.0
14.08   338   176.98    0.25   2.3
14.17   340   178.02   -0.25   0.8
14.25   342   179.07   -0.50   0.0
14.33   344   180.12   -0.25   0.7
14.42   346   181.17    0.25   2.2
14.50   348   182.21    0.50   3.0
14.58   350   183.26    0.25   2.3
14.67   352   184.31   -0.25   0.8
14.75   354   185.35   -0.50   0.0
14.83   356   186.40   -0.25   0.7
14.92   358   187.45    0.25   2.2
15.00   360   188.50    0.50   3.0
15.08   362   189.54    0.25   2.3
15.17   364   190.59   -0.25   0.8
15.25   366   191.64   -0.50   0.0
15.33   368   192.68   -0.25   0.7
15.42   370   193.73    0.25   2.2
15.50   372   194.78    0.50   3.0
15.58   374   195.83    0.25   2.2
15.67   376   196.87   -0.25   0.8
15.75   378   197.92   -0.50   0.0
15.83   380   198.97   -0.25   0.8
15.92   382   200.01    0.25   2.2
16.00   384   201.06    0.50   3.0
16.08   386   202.11    0.25   2.3
16.17   388   203.16   -0.25   0.8
16.25   390   204.20   -0.50   0.0
16.33   392   205.25   -0.25   0.7
16.42   394   206.30    0.25   2.2
16.50   396   207.35    0.50   3.0
16.58   398   208.39    0.25   2.3
16.67   400   209.44   -0.25   0.7
16.75   402   210.49   -0.50   0.0
16.83   404   211.53   -0.25   0.7
16.92   406   212.58    0.25   2.2
17.00   408   213.63    0.50   3.0
17.08   410   214.68    0.25   2.3
17.17   412   215.72   -0.25   0.8
17.25   414   216.77   -0.50   0.0
17.33   416   217.82   -0.25   0.7
17.42   418   218.86    0.25   2.3
17.50   420   219.91    0.50   3.0
17.58   422   220.96    0.25   2.3
17.67   424   222.01   -0.25   0.8
17.75   426   223.05   -0.50   0.0
17.83   428   224.10   -0.25   0.7
17.92   430   225.15    0.25   2.2
18.00   432   226.19    0.50   3.0
18.08   434   227.24    0.25   2.3
18.17   436   228.29   -0.25   0.8
18.25   438   229.34   -0.50   0.0
18.33   440   230.38   -0.25   0.8
18.42   442   231.43    0.25   2.2
18.50   444   232.48    0.50   3.0
18.58   446   233.53    0.25   2.3
18.67   448   234.57   -0.25   0.8
18.75   450   235.62   -0.50   0.0
18.83   452   236.67   -0.25   0.7
18.92   454   237.71    0.25   2.2
19.00   456   238.76    0.50   3.0
19.08   458   239.81    0.25   2.3
19.17   460   240.86   -0.25   0.7
19.25   462   241.90   -0.50   0.0
19.33   464   242.95   -0.25   0.7
19.42   466   244.00    0.25   2.3
19.50   468   245.04    0.50   3.0
19.58   470   246.09    0.25   2.3
19.67   472   247.14   -0.25   0.8
19.75   474   248.19   -0.50   0.0
19.83   476   249.23   -0.25   0.7
19.92   478   250.28    0.25   2.2
20.00   480   251.33    0.50   3.0
20.08   482   252.37    0.25   2.3
20.17   484   253.42   -0.25   0.8
20.25   486   254.47   -0.50   0.0
20.33   488   255.52   -0.25   0.8
20.42   490   256.56    0.25   2.2
20.50   492   257.61    0.50   3.0
20.58   494   258.66    0.25   2.3
20.67   496   259.70   -0.25   0.8
20.75   498   260.75   -0.50   0.0
20.83   500   261.80   -0.25   0.7
20.92   502   262.85    0.25   2.3
21.00   504   263.89    0.50   3.0
21.08   506   264.94    0.25   2.3
21.17   508   265.99   -0.25   0.7
21.25   510   267.04   -0.50   0.0
21.33   512   268.08   -0.25   0.7
21.42   514   269.13    0.25   2.3
21.50   516   270.18    0.50   3.0
21.58   518   271.22    0.25   2.3
21.67   520   272.27   -0.25   0.8
21.75   522   273.32   -0.50   0.0
21.83   524   274.37   -0.25   0.8
21.92   526   275.41    0.25   2.2
22.00   528   276.46    0.50   3.0
22.08   530   277.51    0.25   2.3
22.17   532   278.55   -0.25   0.8
22.25   534   279.60   -0.50   0.0
22.33   536   280.65   -0.25   0.7
22.42   538   281.70    0.25   2.2
22.50   540   282.74    0.50   3.0
22.58   542   283.79    0.25   2.3
22.67   544   284.84   -0.25   0.7
22.75   546   285.88   -0.50   0.0
22.83   548   286.93   -0.25   0.8
22.92   550   287.98    0.25   2.2
23.00   552   289.03    0.50   3.0
23.08   554   290.07    0.25   2.3
23.17   556   291.12   -0.25   0.8
23.25   558   292.17   -0.50   0.0
23.33   560   293.22   -0.25   0.7
23.42   562   294.26    0.25   2.2
23.50   564   295.31    0.50   3.0
23.58   566   296.36    0.25   2.3
23.67   568   297.40   -0.25   0.7
23.75   570   298.45   -0.50   0.0
23.83   572   299.50   -0.25   0.7
23.92   574   300.55    0.25   2.3
24.00   576   301.59    0.50   3.0
24.08   578   302.64    0.25   2.3
24.17   580   303.69   -0.25   0.8
24.25   582   304.73   -0.50   0.0
24.33   584   305.78   -0.25   0.7
24.42   586   306.83    0.25   2.2
24.50   588   307.88    0.50   3.0
24.58   590   308.92    0.25   2.3
24.67   592   309.97   -0.25   0.8
24.75   594   311.02   -0.50   0.0
24.83   596   312.06   -0.25   0.7
24.92   598   313.11    0.25   2.2
25.00   600   314.16    0.50   3.0
25.08   602   315.21    0.25   2.3
25.17   604   316.25   -0.25   0.8
25.25   606   317.30   -0.50   0.0
25.33   608   318.35   -0.25   0.7
25.42   610   319.40    0.25   2.3
25.50   612   320.44    0.50   3.0
25.58   614   321.49    0.25   2.2
25.67   616   322.54   -0.25   0.8
25.75   618   323.58   -0.50   0.0
25.83   620   324.63   -0.25   0.7
25.92   622   325.68    0.25   2.2
26.00   624   326.73    0.50   3.0
26.08   626   327.77    0.25   2.3
26.17   628   328.82   -0.25   0.8
26.25   630   329.87   -0.50   0.0
26.33   632   330.91   -0.25   0.7
26.42   634   331.96    0.25   2.3
26.50   636   333.01    0.50   3.0
26.58   638   334.06    0.25   2.3
26.67   640   335.10   -0.25   0.7
26.75   642   336.15   -0.50   0.0
26.83   644   337.20   -0.25   0.7
26.92   646   338.24    0.25   2.2
27.00   648   339.29    0.50   3.0
27.08   650   340.34    0.25   2.3
27.17   652   341.39   -0.25   0.8
27.25   654   342.43   -0.50   0.0
27.33   656   343.48   -0.25   0.7
27.42   658   344.53    0.25   2.2
27.50   660   345.58    0.50   3.0
27.58   662   346.62    0.25   2.3
27.67   664   347.67   -0.25   0.7
27.75   666   348.72   -0.50   0.0
27.83   668   349.76   -0.25   0.8
27.92   670   350.81    0.25   2.2
28.00   672   351.86   0.50   3.0
2 hours - only a sixth of the frequency used in the earlier graph
e same time each day
                                                               Model tidal cycle with Sun's gravity only - 28 days


                                             10.0



                                              9.0



                                              8.0
Tidal height above low water mark (metres)




                                              7.0



                                              6.0



                                              5.0



                                              4.0



                                              3.0



                                              2.0



                                              1.0



                                              0.0
                                                 0.00   7.00                            14.00                        21.00   28.00
                                                                                     Time (days)
             Calculation time interval =         2.0 hours        This is the time step used for the calculations
             Interval between high tides =     12.43 hours        This is the time difference between successive high or low tides - no
             Maximum depth range =              10.0 metres       This is maximum height difference between high- and low-water - n
             Ratio springs to neaps =           2.00              This how much larger the tidal range is at spring tides than at neap

Elapsed time Elapsed time Elasped time Phase rotationPhase orbit Tidal range Height above
(days)       (hours)       (radians)                              (metres)     low water (m)
        0.00             0           0.00     -0.50          0.75         7.50           1.3
        0.08             2           1.01     -0.27          0.74         7.41           3.0
        0.17             4           2.02      0.22          0.73         7.31           6.6
        0.25             6           3.03      0.50          0.72         7.22           8.6
        0.33             8           4.04      0.31          0.71         7.12           7.2
        0.42            10           5.06     -0.17          0.70         7.03           3.8
        0.50            12           6.07     -0.49          0.69         6.94           1.6
        0.58            14           7.08     -0.35          0.68         6.85           2.6
        0.67            16           8.09      0.12          0.68         6.76           5.8
        0.75            18           9.10      0.47          0.67         6.67           8.2
        0.83            20         10.11       0.39          0.66         6.58           7.5
        0.92            22         11.12      -0.06          0.65         6.49           4.6
        1.00            24         12.13      -0.45          0.64         6.40           2.1
        1.08            26         13.14      -0.42          0.63         6.32           2.4
        1.17            28         14.16       0.01          0.62         6.24           5.1
        1.25            30         15.17       0.43          0.62         6.16           7.6
        1.33            32         16.18       0.45          0.61         6.08           7.7
        1.42            34         17.19       0.05          0.60         6.00           5.3
        1.50            36         18.20      -0.40          0.59         5.93           2.6
        1.58            38         19.21      -0.47          0.59         5.86           2.3
        1.67            40         20.22      -0.10          0.58         5.79           4.4
        1.75            42         21.23       0.36          0.57         5.72           7.1
        1.83            44         22.24       0.48          0.57         5.65           7.7
        1.92            46         23.26       0.15          0.56         5.59           5.8
        2.00            48         24.27      -0.32          0.55         5.53           3.2
        2.08            50         25.28      -0.49          0.55         5.47           2.3
        2.17            52         26.29      -0.20          0.54         5.42           3.9
        2.25            54         27.30       0.28          0.54         5.37           6.5
        2.33            56         28.31       0.50          0.53         5.32           7.7
        2.42            58         29.32       0.25          0.53         5.28           6.3
        2.50            60         30.33      -0.23          0.52         5.24           3.8
        2.58            62         31.34      -0.50          0.52         5.20           2.4
        2.67            64         32.35      -0.30          0.52         5.16           3.5
        2.75            66         33.37       0.19          0.51         5.13           5.9
        2.83            68         34.38       0.49          0.51         5.10           7.5
        2.92            70         35.39       0.34          0.51         5.08           6.7
        3.00            72         36.40      -0.13          0.51         5.06           4.3
        3.08            74         37.41      -0.48          0.50         5.04           2.6
        3.17            76         38.42      -0.38          0.50         5.02           3.1
        3.25            78         39.43       0.08          0.50         5.01           5.4
        3.33            80         40.44       0.46          0.50         5.00           7.3
        3.42            82         41.45       0.41          0.50         5.00           7.0
        3.50            84         42.47      -0.03          0.50         5.00           4.9
        3.58            86         43.48      -0.44          0.50         5.00           2.8
        3.67            88         44.49      -0.44          0.50         5.01           2.8
        3.75            90         45.50      -0.03          0.50         5.02           4.9
        3.83            92         46.51       0.41          0.50         5.03           7.1
        3.92            94         47.52       0.46          0.51         5.05           7.3
        4.00            96         48.53       0.08          0.51         5.07           5.4
        4.08            98         49.54      -0.38          0.51         5.10           3.1
4.17   100    50.55   -0.48   0.51   5.13   2.5
4.25   102    51.57   -0.13   0.52   5.16   4.3
4.33   104    52.58    0.34   0.52   5.19   6.8
4.42   106    53.59    0.49   0.52   5.23   7.6
4.50   108    54.60    0.19   0.53   5.27   6.0
4.58   110    55.61   -0.30   0.53   5.31   3.4
4.67   112    56.62   -0.50   0.54   5.36   2.3
4.75   114    57.63   -0.23   0.54   5.41   3.7
4.83   116    58.64    0.25   0.55   5.47   6.4
4.92   118    59.65    0.50   0.55   5.52   7.8
5.00   120    60.67    0.28   0.56   5.58   6.6
5.08   122    61.68   -0.20   0.56   5.64   3.9
5.17   124    62.69   -0.49   0.57   5.71   2.2
5.25   126    63.70   -0.32   0.58   5.78   3.1
5.33   128    64.71    0.15   0.58   5.84   5.9
5.42   130    65.72    0.48   0.59   5.92   7.9
5.50   132    66.73    0.36   0.60   5.99   7.2
5.58   134    67.74   -0.10   0.61   6.07   4.4
5.67   136    68.75   -0.47   0.61   6.15   2.1
5.75   138    69.77   -0.40   0.62   6.23   2.5
5.83   140    70.78    0.05   0.63   6.31   5.3
5.92   142    71.79    0.45   0.64   6.39   7.9
6.00   144    72.80    0.43   0.65   6.48   7.8
6.08   146    73.81    0.01   0.66   6.56   5.1
6.17   148    74.82   -0.42   0.67   6.65   2.2
6.25   150    75.83   -0.45   0.67   6.74   1.9
6.33   152    76.84   -0.06   0.68   6.83   4.6
6.42   154    77.85    0.39   0.69   6.92   7.7
6.50   156    78.86    0.47   0.70   7.02   8.3
6.58   158    79.88    0.12   0.71   7.11   5.8
6.67   160    80.89   -0.35   0.72   7.20   2.5
6.75   162    81.90   -0.49   0.73   7.30   1.4
6.83   164    82.91   -0.17   0.74   7.39   3.8
6.92   166    83.92    0.31   0.75   7.49   7.3
7.00   168    84.93    0.50   0.76   7.58   8.8
7.08   170    85.94    0.22   0.77   7.67   6.7
7.17   172    86.95   -0.27   0.78   7.77   2.9
7.25   174    87.96   -0.50   0.79   7.86   1.1
7.33   176    88.98   -0.27   0.80   7.96   2.9
7.42   178    89.99    0.22   0.80   8.05   6.8
7.50   180    91.00    0.50   0.81   8.14   9.0
7.58   182    92.01    0.31   0.82   8.23   7.5
7.67   184    93.02   -0.17   0.83   8.32   3.6
7.75   186    94.03   -0.49   0.84   8.41   0.9
7.83   188    95.04   -0.35   0.85   8.50   2.0
7.92   190    96.05    0.12   0.86   8.58   6.0
8.00   192    97.06    0.47   0.87   8.67   9.1
8.08   194    98.08    0.39   0.87   8.75   8.4
8.17   196    99.09   -0.06   0.88   8.83   4.4
8.25   198   100.10   -0.45   0.89   8.91   1.0
8.33   200   101.11   -0.42   0.90   8.99   1.2
8.42   202   102.12    0.01   0.91   9.06   5.1
8.50   204   103.13    0.43   0.91   9.13   8.9
8.58   206   104.14    0.45   0.92   9.20   9.1
8.67   208   105.15    0.05   0.93   9.27   5.4
8.75   210   106.16   -0.40   0.93   9.34   1.3
8.83   212   107.18   -0.47   0.94   9.40   0.6
 8.92   214   108.19   -0.10   0.95    9.46   4.1
 9.00   216   109.20    0.36   0.95    9.52   8.5
 9.08   218   110.21    0.48   0.96    9.57   9.6
 9.17   220   111.22    0.15   0.96    9.62   6.5
 9.25   222   112.23   -0.32   0.97    9.67   1.9
 9.33   224   113.24   -0.49   0.97    9.72   0.2
 9.42   226   114.25   -0.20   0.98    9.76   3.0
 9.50   228   115.26    0.28   0.98    9.80   7.7
 9.58   230   116.28    0.50   0.98    9.83   9.9
 9.67   232   117.29    0.25   0.99    9.87   7.5
 9.75   234   118.30   -0.23   0.99    9.89   2.7
 9.83   236   119.31   -0.50   0.99    9.92   0.1
 9.92   238   120.32   -0.30   0.99    9.94   2.1
10.00   240   121.33    0.19   1.00    9.96   6.8
10.08   242   122.34    0.49   1.00    9.98   9.9
10.17   244   123.35    0.34   1.00    9.99   8.4
10.25   246   124.36   -0.13   1.00    9.99   3.7
10.33   248   125.37   -0.48   1.00   10.00   0.2
10.42   250   126.39   -0.38   1.00   10.00   1.2
10.50   252   127.40    0.08   1.00   10.00   5.8
10.58   254   128.41    0.46   1.00    9.99   9.6
10.67   256   129.42    0.41   1.00    9.98   9.1
10.75   258   130.43   -0.03   1.00    9.97   4.7
10.83   260   131.44   -0.44   1.00    9.95   0.6
10.92   262   132.45   -0.44   0.99    9.93   0.7
11.00   264   133.46   -0.03   0.99    9.91   4.7
11.08   266   134.47    0.41   0.99    9.88   9.0
11.17   268   135.49    0.46   0.98    9.85   9.5
11.25   270   136.50    0.08   0.98    9.81   5.8
11.33   272   137.51   -0.38   0.98    9.78   1.3
11.42   274   138.52   -0.48   0.97    9.74   0.3
11.50   276   139.53   -0.13   0.97    9.69   3.7
11.58   278   140.54    0.34   0.96    9.65   8.3
11.67   280   141.55    0.49   0.96    9.60   9.7
11.75   282   142.56    0.19   0.95    9.54   6.8
11.83   284   143.57   -0.30   0.95    9.49   2.2
11.92   286   144.59   -0.50   0.94    9.43   0.3
12.00   288   145.60   -0.23   0.94    9.37   2.8
12.08   290   146.61    0.25   0.93    9.30   7.3
12.17   292   147.62    0.50   0.92    9.23   9.6
12.25   294   148.63    0.28   0.92    9.17   7.6
12.33   296   149.64   -0.20   0.91    9.09   3.2
12.42   298   150.65   -0.49   0.90    9.02   0.5
12.50   300   151.66   -0.32   0.89    8.94   2.1
12.58   302   152.67    0.15   0.89    8.87   6.3
12.67   304   153.69    0.48   0.88    8.79   9.3
12.75   306   154.70    0.36   0.87    8.70   8.2
12.83   308   155.71   -0.10   0.86    8.62   4.1
12.92   310   156.72   -0.47   0.85    8.54   1.0
13.00   312   157.73   -0.40   0.84    8.45   1.6
13.08   314   158.74    0.05   0.84    8.36   5.4
13.17   316   159.75    0.45   0.83    8.27   8.7
13.25   318   160.76    0.43   0.82    8.18   8.5
13.33   320   161.77    0.01   0.81    8.09   5.1
13.42   322   162.79   -0.42   0.80    8.00   1.7
13.50   324   163.80   -0.45   0.79    7.90   1.4
13.58   326   164.81   -0.06   0.78    7.81   4.5
13.67   328   165.82    0.39   0.77   7.72   8.0
13.75   330   166.83    0.47   0.76   7.62   8.6
13.83   332   167.84    0.12   0.75   7.53   5.9
13.92   334   168.85   -0.35   0.74   7.43   2.4
14.00   336   169.86   -0.49   0.73   7.34   1.4
14.08   338   170.87   -0.17   0.72   7.25   3.8
14.17   340   171.88    0.31   0.72   7.15   7.2
14.25   342   172.90    0.50   0.71   7.06   8.5
14.33   344   173.91    0.22   0.70   6.97   6.5
14.42   346   174.92   -0.27   0.69   6.87   3.2
14.50   348   175.93   -0.50   0.68   6.78   1.6
14.58   350   176.94   -0.27   0.67   6.69   3.2
14.67   352   177.95    0.22   0.66   6.60   6.4
14.75   354   178.96    0.50   0.65   6.52   8.2
14.83   356   179.97    0.31   0.64   6.43   7.0
14.92   358   180.98   -0.17   0.63   6.35   3.9
15.00   360   182.00   -0.49   0.63   6.26   1.9
15.08   362   183.01   -0.35   0.62   6.18   2.8
15.17   364   184.02    0.12   0.61   6.10   5.7
15.25   366   185.03    0.47   0.60   6.03   7.9
15.33   368   186.04    0.39   0.59   5.95   7.3
15.42   370   187.05   -0.06   0.59   5.88   4.6
15.50   372   188.06   -0.45   0.58   5.81   2.4
15.58   374   189.07   -0.42   0.57   5.74   2.6
15.67   376   190.08    0.01   0.57   5.67   5.1
15.75   378   191.10    0.43   0.56   5.61   7.4
15.83   380   192.11    0.45   0.55   5.55   7.5
15.92   382   193.12    0.05   0.55   5.49   5.2
16.00   384   194.13   -0.40   0.54   5.44   2.8
16.08   386   195.14   -0.47   0.54   5.38   2.5
16.17   388   196.15   -0.10   0.53   5.34   4.5
16.25   390   197.16    0.36   0.53   5.29   6.9
16.33   392   198.17    0.48   0.52   5.25   7.5
16.42   394   199.18    0.15   0.52   5.21   5.8
16.50   396   200.20   -0.32   0.52   5.17   3.3
16.58   398   201.21   -0.49   0.51   5.14   2.5
16.67   400   202.22   -0.20   0.51   5.11   4.0
16.75   402   203.23    0.28   0.51   5.08   6.4
16.83   404   204.24    0.50   0.51   5.06   7.5
16.92   406   205.25    0.25   0.50   5.04   6.3
17.00   408   206.26   -0.23   0.50   5.03   3.8
17.08   410   207.27   -0.50   0.50   5.01   2.5
17.17   412   208.28   -0.30   0.50   5.01   3.5
17.25   414   209.30    0.19   0.50   5.00   5.9
17.33   416   210.31    0.49   0.50   5.00   7.5
17.42   418   211.32    0.34   0.50   5.00   6.7
17.50   420   212.33   -0.13   0.50   5.01   4.3
17.58   422   213.34   -0.48   0.50   5.02   2.6
17.67   424   214.35   -0.38   0.50   5.03   3.1
17.75   426   215.36    0.08   0.50   5.05   5.4
17.83   428   216.37    0.46   0.51   5.07   7.3
17.92   430   217.38    0.41   0.51   5.09   7.1
18.00   432   218.39   -0.03   0.51   5.12   4.9
18.08   434   219.41   -0.44   0.51   5.15   2.7
18.17   436   220.42   -0.44   0.52   5.18   2.7
18.25   438   221.43   -0.03   0.52   5.22   4.9
18.33   440   222.44    0.41   0.53   5.26   7.1
18.42   442   223.45    0.46   0.53   5.30   7.4
18.50   444   224.46    0.08   0.53   5.35   5.4
18.58   446   225.47   -0.38   0.54   5.40   3.0
18.67   448   226.48   -0.48   0.54   5.45   2.4
18.75   450   227.49   -0.13   0.55   5.51   4.3
18.83   452   228.51    0.34   0.56   5.56   6.9
18.92   454   229.52    0.49   0.56   5.62   7.8
19.00   456   230.53    0.19   0.57   5.69   6.1
19.08   458   231.54   -0.30   0.58   5.75   3.3
19.17   460   232.55   -0.50   0.58   5.82   2.1
19.25   462   233.56   -0.23   0.59   5.90   3.6
19.33   464   234.57    0.25   0.60   5.97   6.5
19.42   466   235.58    0.50   0.60   6.04   8.0
19.50   468   236.59    0.28   0.61   6.12   6.7
19.58   470   237.61   -0.20   0.62   6.20   3.7
19.67   472   238.62   -0.49   0.63   6.28   1.9
19.75   474   239.63   -0.32   0.64   6.37   2.9
19.83   476   240.64    0.15   0.65   6.45   6.0
19.92   478   241.65    0.48   0.65   6.54   8.2
20.00   480   242.66    0.36   0.66   6.63   7.4
20.08   482   243.67   -0.10   0.67   6.72   4.3
20.17   484   244.68   -0.47   0.68   6.81   1.8
20.25   486   245.69   -0.40   0.69   6.90   2.3
20.33   488   246.71    0.05   0.70   6.99   5.3
20.42   490   247.72    0.45   0.71   7.08   8.2
20.50   492   248.73    0.43   0.72   7.18   8.1
20.58   494   249.74    0.01   0.73   7.27   5.1
20.67   496   250.75   -0.42   0.74   7.36   1.9
20.75   498   251.76   -0.45   0.75   7.46   1.6
20.83   500   252.77   -0.06   0.76   7.55   4.5
20.92   502   253.78    0.39   0.76   7.65   8.0
21.00   504   254.79    0.47   0.77   7.74   8.7
21.08   506   255.81    0.12   0.78   7.83   5.9
21.17   508   256.82   -0.35   0.79   7.93   2.2
21.25   510   257.83   -0.49   0.80   8.02   1.1
21.33   512   258.84   -0.17   0.81   8.11   3.6
21.42   514   259.85    0.31   0.82   8.20   7.5
21.50   516   260.86    0.50   0.83   8.29   9.1
21.58   518   261.87    0.22   0.84   8.38   6.8
21.67   520   262.88   -0.27   0.85   8.47   2.8
21.75   522   263.89   -0.50   0.86   8.56   0.7
21.83   524   264.90   -0.27   0.86   8.64   2.7
21.92   526   265.92    0.22   0.87   8.72   6.9
22.00   528   266.93    0.50   0.88   8.81   9.4
22.08   530   267.94    0.31   0.89   8.89   7.8
22.17   532   268.95   -0.17   0.90   8.96   3.5
22.25   534   269.96   -0.49   0.90   9.04   0.6
22.33   536   270.97   -0.35   0.91   9.11   1.8
22.42   538   271.98    0.12   0.92   9.18   6.1
22.50   540   272.99    0.47   0.93   9.25   9.4
22.58   542   274.00    0.39   0.93   9.32   8.6
22.67   544   275.02   -0.06   0.94   9.38   4.4
22.75   546   276.03   -0.45   0.94   9.44   0.7
22.83   548   277.04   -0.42   0.95   9.50   1.0
22.92   550   278.05    0.01   0.96   9.56   5.1
23.00   552   279.06    0.43   0.96   9.61   9.1
23.08   554   280.07    0.45   0.97   9.66   9.3
23.17   556   281.08    0.05   0.97    9.70    5.4
23.25   558   282.09   -0.40   0.97    9.75    1.1
23.33   560   283.10   -0.47   0.98    9.79    0.4
23.42   562   284.12   -0.10   0.98    9.82    4.0
23.50   564   285.13    0.36   0.99    9.86    8.6
23.58   566   286.14    0.48   0.99    9.89    9.8
23.67   568   287.15    0.15   0.99    9.91    6.5
23.75   570   288.16   -0.32   0.99    9.94    1.8
23.83   572   289.17   -0.49   1.00    9.96    0.1
23.92   574   290.18   -0.20   1.00    9.97    3.0
24.00   576   291.19    0.28   1.00    9.98    7.8
24.08   578   292.20    0.50   1.00    9.99   10.0
24.17   580   293.22    0.25   1.00   10.00    7.5
24.25   582   294.23   -0.23   1.00   10.00    2.7
24.33   584   295.24   -0.50   1.00   10.00    0.0
24.42   586   296.25   -0.30   1.00    9.99    2.0
24.50   588   297.26    0.19   1.00    9.98    6.8
24.58   590   298.27    0.49   1.00    9.97    9.9
24.67   592   299.28    0.34   1.00    9.96    8.4
24.75   594   300.29   -0.13   0.99    9.94    3.7
24.83   596   301.30   -0.48   0.99    9.91    0.2
24.92   598   302.32   -0.38   0.99    9.89    1.3
25.00   600   303.33    0.08   0.99    9.86    5.8
25.08   602   304.34    0.46   0.98    9.82    9.5
25.17   604   305.35    0.41   0.98    9.79    9.0
25.25   606   306.36   -0.03   0.97    9.75    4.7
25.33   608   307.37   -0.44   0.97    9.71    0.8
25.42   610   308.38   -0.44   0.97    9.66    0.8
25.50   612   309.39   -0.03   0.96    9.61    4.7
25.58   614   310.40    0.41   0.96    9.56    8.9
25.67   616   311.41    0.46   0.95    9.50    9.4
25.75   618   312.43    0.08   0.94    9.45    5.8
25.83   620   313.44   -0.38   0.94    9.38    1.5
25.92   622   314.45   -0.48   0.93    9.32    0.5
26.00   624   315.46   -0.13   0.93    9.26    3.8
26.08   626   316.47    0.34   0.92    9.19    8.1
26.17   628   317.48    0.49   0.91    9.12    9.5
26.25   630   318.49    0.19   0.90    9.04    6.7
26.33   632   319.50   -0.30   0.90    8.97    2.4
26.42   634   320.51   -0.50   0.89    8.89    0.6
26.50   636   321.53   -0.23   0.88    8.81    2.9
26.58   638   322.54    0.25   0.87    8.73    7.2
26.67   640   323.55    0.50   0.86    8.65    9.3
26.75   642   324.56    0.28   0.86    8.56    7.4
26.83   644   325.57   -0.20   0.85    8.47    3.3
26.92   646   326.58   -0.49   0.84    8.39    0.9
27.00   648   327.59   -0.32   0.83    8.30    2.3
27.08   650   328.60    0.15   0.82    8.21    6.2
27.17   652   329.61    0.48   0.81    8.12    8.9
27.25   654   330.63    0.36   0.80    8.03    7.9
27.33   656   331.64   -0.10   0.79    7.93    4.2
27.42   658   332.65   -0.47   0.78    7.84    1.3
27.50   660   333.66   -0.40   0.77    7.75    1.9
27.58   662   334.67    0.05   0.77    7.65    5.3
27.67   664   335.68    0.45   0.76    7.56    8.4
27.75   666   336.69    0.43   0.75    7.46    8.2
27.83   668   337.70    0.01   0.74    7.37    5.1
27.92   670   338.71   -0.42   0.73   7.27   2.0
28.00   672   339.73   -0.45   0.72   7.18   1.7
 r the calculations
etween successive high or low tides - notice that tides are about 50 minutes later each day
erence between high- and low-water - notice the larger range when the Moon's gravity is included
 al range is at spring tides than at neap tides
                                                      Model tidal cycle with Moon and Sun, giving spring and neap tides


                                           10.0



                                            9.0



                                            8.0
Tidal height above lowest water (metres)




                                            7.0



                                            6.0



                                            5.0



                                            4.0



                                            3.0



                                            2.0



                                            1.0



                                            0.0
                                               0.00       7.00                        14.00                       21.00   28.00
                                                                                    Time (days)
illustrations by STEP
Please answer the following questions relating to the three graphs. Type your answers int
spaces after the questions. The information that you need to answer the questions is in th
and in the introduction.
PLEASE TYPE YOUR NAME HERE:
Chart 'Sun 4d'

Question 1 (5 marks)
At what times of day does high tide occur on this graph?


Question 2 (5 marks)
What is the tidal range (vertical distance between high- and low-water)?


Chart 'Sun 28d'

Question 3 (15 marks)
Whilst the chart 'Sun 4d' is plotted for four days only, and 'Sun 28d' is plotted for a period
of 28 d, they both represent the same data. Why does the 28 day chart look 'jagged', whe
the 4 day chart is smooth?




Chart 'Sun and Moon'

Question 4 (20 marks)
Why do high tides no longer occur at the same time of day when the Moon is included in t


Question 5 (15 marks)
Why is the tidal range greater in this graph than in the earlier charts?


Question 6 (10 marks)
How many times does the tidal range reach its maximum value during the 28 day period p
Question 7 (10 marks)
What name is given to the tides when the tidal range is at a minimum in a given place?


Question 8 (20 marks)
Why does the tidal range change over the 28 day period plotted on the graph?
 s. Type your answers into the
swer the questions is in the charts




8d' is plotted for a period
 y chart look 'jagged', whereas




 the Moon is included in the model?




uring the 28 day period plotted in the graph?
mum in a given place?



on the graph?
Please answer the following questions relating to the three graphs. Type your answers int
spaces after the questions. The information that you need to answer the questions is in th
and in the introduction.

Chart 'Sun 4d'

Question 1 (5 marks)
At what times of day does high tide occur on this graph?
High tide occurs at midday (noon) and midnight. Bonus marks for adding 'local' midday an

Question 2 (5 marks)
What is the tidal range (vertical distance between high- and low-water)?
The tidal range is 3 metres. Ensure that units are given.

Chart 'Sun 28d'

Question 3 (15 marks)
Whilst the chart 'Sun 4d' is plotted for four days only, and 'Sun 28d' is plotted for a period
of 28 d, they both represent the same data. Why does the 28 day chart look 'jagged', whe
the 4 day chart is smooth?
The results for the four-day chart are calculated for twenty-minute time-steps, whereas the
for the twenty-eight day chart are only calculated for two hour time steps. This means tha
will be less smooth, even though the data are the same. Give marks for 'interval', 'frequen

Chart 'Sun and Moon'

Question 4 (20 marks)
Why do high tides no longer occur at the same time of day when the Moon is included in t
The Moon's orbit means that the tidal 'bulge' arrives slightly later each day

Question 5 (15 marks)
Why is the tidal range greater in this graph than in the earlier charts?
The Moon has about twice the gravitational attraction of the Sun, so increases the tidal ran

Question 6 (10 marks)
How many times does the tidal range reach its maximum value during the 28 day period p
The tidal range reaches its maximum value twice during the period
Question 7 (10 marks)
What name is given to the tides when the tidal range is at a minimum in a given place?
These are neap tides

Question 8 (20 marks)
Why does the tidal range change over the 28 day period plotted on the graph?
At spring tides, when the tidal range is at its maximum, the gravity of the Sun and Moon w
same direction. At neap tides, when the tidal range is lower, the Moon's gravity operates a
angles to the Sun's gravity. Maximum marks for including Sun, Moon, spring, neap, gravit
 s. Type your answers into the
swer the questions is in the charts




or adding 'local' midday and midnight.




8d' is plotted for a period
 y chart look 'jagged', whereas

e time-steps, whereas the results
e steps. This means that the curve
arks for 'interval', 'frequency'




 the Moon is included in the model?
 each day



 so increases the tidal range


uring the 28 day period plotted in the graph?
mum in a given place?



on the graph?
 y of the Sun and Moon work in the
 Moon's gravity operates at right
Moon, spring, neap, gravity

				
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