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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
