SME
Grade 12 Science · Problem type
Spring and neap tides
Use this for “Is the tide a spring or a neap tide at the first-quarter Moon, and how big is the range?”
Diagram
Neap tide: the Sun’s pull is about 0.46 of the Moon’s, so the tidal range is 0.54 times the Moon’s alone.
Range: 1.08 m.
This is an example. Type your own values to start a new problem.
θ
Moon’s angle from the Sun
example · °
m
Range from the Moon alone
example
R
Tidal range
worked out (not typed)
Formulas
R
=
m
×
√(1
+
0.46
2
+
2
×
0.46
×
cos(2
×
θ
))
1.08
=
2
×
√(1
+
0.46
2
+
2
×
0.46
×
cos(2
×
90°))
Assumptions
•
The Sun’s tidal pull is 0.46 of the Moon’s.
•
In line (new or full Moon): spring tides; at right angles (quarter Moon): neap tides.
•
Coastlines make real ranges differ.
Step-by-step
WE KNOW
θ = 90°, m = 2 m
FIND
tidal range (R)
Step 1 · Find tidal range (R)
Use R = m × √(1 + 0.46² + 2 × 0.46 × cos(2 × θ))
Each body raises two bulges, 180° apart, so they add at twice the angle: in line they add, at right angles they partly cancel.
R
=
2
×
√(1
+
0.46
2
+
2
×
0.46
×
cos(2
×
90°))
R
=
2
×
√(1
+
0.46
2
+
2
×
0.46
×
cos(180°))
R
=
2
×
√(1
+
0.2116
+
2
×
0.46
×
(−1))
R
=
2
×
√(1
+
0.2116
+
0.92
×
(−1))
R
=
2
×
√
1 + 0.2116 − 0.92
R
=
2
×
√
0.2916
R
=
2
×
0.54
R
=
1.08
m
(Sun
and
Moon
at
right
angles:
a
neap
tide)
Check
Put the numbers back in. Both sides should match.
1.08
=
2
×
√(1
+
0.46
2
+
2
×
0.46
×
cos(2
×
90°))
✓
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