Springs, neaps and interpolation
1The lesson in plain words
Tables give rates for mean springs and mean neaps. On any other day, work out the rate from that day's tidal range.
Range drives rate
The range of the tide is the height difference between a high water and the next or previous low water. A bigger range moves more water, so streams run faster. Atlases and diamond tables give rates for their standard port’s mean spring range and mean neap range; mean means average. The atlas or tide tables give those two ranges.
Interpolating
Find the day’s range at the standard port. Work out where it lies between the mean neap and mean spring ranges, as a fraction. Apply the same fraction between the neap and spring rates. On the computation of rates diagram, mark the neap and spring rates on their labelled scales. Join the marks and read the rate at today’s range.
Worked example
Mean ranges: springs 4.6 m, neaps 1.8 m. Today HW is 5.0 m and LW 1.3 m: range 3.7 m. The diamond gives springs 2.4 kn, neaps 1.2 kn. Fraction = (3.7 − 1.8) ÷ (4.6 − 1.8) = 1.9 ÷ 2.8 = 0.68. Rate = 1.2 + 0.68 × (2.4 − 1.2) = 1.2 + 0.8 = 2.0 kn.
Outside the mean ranges
On a big spring tide the day's range can exceed the mean spring range, and the stream runs faster than the spring figure. Extending the same straight line gives an estimate; treat it as approximate and keep a margin. Below mean neaps the stream is weaker than the neap figure.
Quick check
A rough rule says neap rates are about half the spring rates. Use it to spot a misread table, not instead of the table. Round to 0.1 kn: the tabulated figures are averages, and wind and air pressure change real streams.
2Key data
- Range
- HW height − LW height at the standard port
- Fraction
- (Day's range − neap range) ÷ (spring range − neap range)
- Rate
- Neap rate + fraction × (spring rate − neap rate)
- Worked example
- Range 3.7 m between 1.8 and 4.6 m → 2.0 kn
- Above mean springs
- Faster than the spring figure; extrapolate with a margin
3Key points
- 1
Rate depends on the day's range at the standard port, not on the date alone.
- 2
Interpolate: the range's place between neaps and springs gives the rate's place.
- 3
Use the computation of rates diagram, or the formula, and round to 0.1 kn.
- 4
Above mean springs the stream is stronger than the spring figure.
4Frequent mistakes
Wrong: It is full moon, so use the spring rate.
Right: Springs come a day or two after new and full moon, and they vary in size. Work from the day's range.
Wrong: Use the range at your own harbour.
Right: Use the range at the standard port named on the table or atlas; that is what the rates refer to.
Wrong: The spring rate is the most a stream can run.
Right: On ranges bigger than the mean spring range the stream runs faster still.
5Practice case & exam keys
Mean ranges are springs 5.0 m and neaps 2.0 m. Today’s range is 5.6 m. Your hourly rates are springs 3.0 kn and neaps 1.4 kn. A crew member says to cap the estimate at 3.0 kn. Do you agree?
Show the answer
No. The range exceeds mean springs. Fraction = (5.6 − 2.0) ÷ (5.0 − 2.0) = 1.2. Estimated rate = 1.4 + 1.2 × (3.0 − 1.4) = 3.32 kn, about 3.3 kn. Treat extrapolation as approximate and retain a margin; 3.0 kn is not a maximum.
Exam keys
- Range = HW − LW at the standard port.
- Rate = neap rate + fraction × (spring rate − neap rate).
- Fraction = (range − mean neap range) ÷ (mean spring range − mean neap range).
- Above mean springs the rate exceeds the spring figure.
Finish this unit
When you've read it, match the terms, then answer three questions. Get them all right to finish the unit; opening the page alone doesn't count.
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