Spring Tides and Two Trips: Choosing the Right Day
A Year 11 class must plan two trips in the week beginning Monday the 3rd: a rocky-shore ecology survey that needs a low tide below 0.5 m and must run between 09:00 and 15:00 on a school day, and an evening stargazing session at the same beach that needs genuinely dark skies. The bus is available on Monday, Tuesday or Wednesday only. The tide table (heights above chart datum) gives: Mon 3rd, new Moon, low 09:40 (0.3 m), high 15:55 (3.4 m); Tue 4th, low 10:25 (0.4 m), high 16:40 (3.3 m); Fri 7th, first quarter, low 12:35 (1.0 m), high 18:50 (2.6 m); Wed 12th, full Moon, low 10:15 (0.2 m), high 16:30 (3.5 m). The teacher says Monday is best because it has the lowest low tide in the table. A student argues for Wednesday the 12th instead, because 0.2 m is lower still.
1. Calculate the tidal range on each of the four listed days and use the Moon phases to explain why the ranges differ.
Read the worked answer
Ranges (high minus low):
- Mon 3rd: 3.4 - 0.3 = 3.1 m
- Tue 4th: 3.3 - 0.4 = 2.9 m
- Fri 7th: 2.6 - 1.0 = 1.6 m
- Wed 12th: 3.5 - 0.2 = 3.3 m
Explanation. Tides are driven mainly by the Moon's gravitational pull, with a smaller contribution from the Sun. At new Moon (3rd) and full Moon (12th) the Sun, Earth and Moon are in line, so the two pulls act along the same axis and their tidal bulges add together. The water is pulled higher at high tide and falls further at low tide, giving a large range: a spring tide. Around first quarter (7th) the Sun and Moon pull at roughly right angles, so the solar bulge partly fills in the lunar low tide and flattens the lunar high tide. The range shrinks: a neap tide. The 4th is one day after new Moon, so it is still close to spring conditions and 2.9 m is expected. The 12th has the largest range in the table, which is consistent with a full Moon.
Note the term 'spring tide' refers to the tide springing up, not to the season.
2. Decide which day the class should book, using all the constraints given. Address both the teacher's reasoning and the student's argument.
Read the worked answer
List the constraints: low tide below 0.5 m, between 09:00 and 15:00, on a school day, bus available Monday to Wednesday, and dark skies needed for the stargazing.
- Mon 3rd: 09:40, 0.3 m. Fits both tide constraints.
- Tue 4th: 10:25, 0.4 m. Fits, with less margin.
- Fri 7th: 12:35, 1.0 m. Fails the 0.5 m rule; only 1.6 m of tidal range and the rock platform would still be largely covered.
- Wed 12th: 10:15, 0.2 m. The tide fits, but the 12th is the following week, outside the planning week, and the bus is not available then. The student's tide evidence is correct (0.2 m is lower than 0.3 m) but it does not survive the scheduling constraint.
The teacher's reasoning is also wrong: Monday does not have the lowest low tide in the table, because the 12th is lower. The right conclusion is reached for a different reason.
Book Monday the 3rd. It has the lowest low tide of the three available days, mid-morning so the platform is well exposed, and the new Moon means no moonlight that evening, so the stargazing can follow the same day. Tuesday is a reasonable backup, only 0.1 m higher.
3. The class plans to be on the rock platform from 09:00 to 12:30 on Monday. Estimate the tide height at 12:30 and explain why Tuesday's low tide is 45 minutes later than Monday's. Comment on the safety of the plan.
Read the worked answer
Tide height at 12:30. The tide rises from low 0.3 m at 09:40 to high 3.4 m at 15:55, a rise of 3.1 m over 6 h 15 min (375 min). 12:30 is 170 min after low:
fraction of rise = 170 / 375 = 0.45
height = 0.3 + 0.45 x 3.1 = 0.3 + 1.40 = about 1.7 m
Daily lag. The Moon takes about 24 h 50 min to return to the same position relative to a point on Earth (a lunar day), because the Moon is also orbiting Earth. So successive low tides are about 12 h 25 min apart and about 50 min later each day. Tuesday's low at 10:25 is 45 min after Monday's 09:40, which matches this pattern within the rounding of a published table.
Safety. At 12:30 the water is roughly 1.7 m above chart datum, well over the 0.3 m low, so the lower platform is already flooding and the class could be cut off. The plan should end at about 11:30, with a rule that nobody works below the mid-platform after 11:00. The 1.7 m figure is only an estimate: real tides do not rise linearly, and the water actually rises fastest around mid-tide, so the true height at 12:30 is likely to be a little higher than this, which makes the plan less safe, not more.