The question
It's a summer's day, so BST is in force. You want to know the height of tide at Port Bay, a secondary port, at 1320 BST, and whether a yacht drawing 1.9m can cross a patch charted at 1.8m. Port Bay's standard port is Standard Harbour.
Step 1: the standard port's tides for the day
From the tide tables for Standard Harbour, which are in UT:
| Time (UT) | Height | |
|---|---|---|
| High water | 0900 | 4.5m |
| Low water | 1510 | 1.0m |
Step 2: the secondary port differences
The almanac gives Port Bay's differences against Standard Harbour like this:
| High water | Low water | ||
|---|---|---|---|
| 0000 and 1200 | +0010 | 0500 and 1700 | +0010 |
| 0600 and 1800 | +0030 | 1100 and 2300 | +0010 |
| MHWS | MHWN | MLWN | MLWS | |
|---|---|---|---|---|
| Standard Harbour | 5.0m | 4.0m | 1.5m | 0.5m |
| Port Bay difference | −0.4 | −0.2 | −0.1 | +0.1 |
Step 3: interpolate the time differences
Standard Harbour's high water is at 0900. That falls between the 0600 column (+0030) and the 1200 column (+0010), exactly halfway. So the difference is halfway between +30 and +10 minutes: +0020.
Low water at 1510 falls between 1100 and 1700, but both give +0010, so there's nothing to interpolate: +0010.
Step 4: interpolate the height differences
Do the same with heights, using the standard port's heights on the day. High water of 4.5m is halfway between MHWN (4.0m, difference −0.2) and MHWS (5.0m, difference −0.4), so the difference is −0.3m.
Low water of 1.0m is halfway between MLWS (0.5m, difference +0.1) and MLWN (1.5m, difference −0.1), so the difference is 0.0m.
Step 5: Port Bay's tides, then convert to BST
| Standard Harbour (UT) | Difference | Port Bay (UT) | Port Bay (BST) | |
|---|---|---|---|---|
| HW time | 0900 | +0020 | 0920 | 1020 |
| HW height | 4.5m | −0.3 | 4.2m | |
| LW time | 1510 | +0010 | 1520 | 1620 |
| LW height | 1.0m | 0.0 | 1.0m | |
Do every step in UT, and only add the hour for BST at the very end. Converting halfway through is the single most common way to lose marks.
Step 6: height of tide at 1320 BST
1320 BST is three hours after Port Bay's high water at 1020 BST. The range is 4.2 − 1.0 = 3.2m.
In the exam you'd use Standard Harbour's tidal curve: mark the high and low water heights, draw the range line, go in at HW+3 on the time scale, read off the factor, and multiply it by the range. Height of tide = low water height + (factor × range).
As a quick check, the rule of twelfths says that three hours after high water the tide has fallen 1 + 2 + 3 = 6 twelfths of the range, which is half: 3.2 × 6 ÷ 12 = 1.6m. So the height of tide is 4.2 − 1.6 = about 2.6m. Halfway between high and low water at the halfway time makes sense.
Step 7: can we cross?
Depth of water = charted depth + height of tide = 1.8 + 2.6 = 4.4m. Take off the 1.9m draught and there's 2.5m under the keel, a comfortable margin, before you allow for swell or a low barometer.