5.2 Using Admiralty Tidal Curves for Height at Any Time

5.2 Using Admiralty Tidal Curves for Height at Any Time

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Limitations of the Rule of Twelfths

The Rule of Twelfths (1/12 in hour 1, 2/12 in hour 2, 3/12 in hour 3, 3/12 in hour 4, 2/12 in hour 5, 1/12 in hour 6) assumes a pure sinusoidal wave with equal 6-hour durations between HW and LW. In coastal navigation, this assumption frequently fails:

1. Estuarine Friction: Narrow approaches delay flood waves, creating rapid floods (e.g., 4 hours) and sluggish ebbs (e.g., 8 hours).
2. Shallow-Water Harmonics: In shallow waters (e.g., the English Channel and the Solent), interaction between primary frequencies generates overtides ($M_4, M_6$), resulting in double high waters (Southampton) or extended stands (Weymouth, Saint-Malo).
3. Empirical Profiles: Official Admiralty curves represent tidal observations at the port, representing its characteristic local profile.

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Anatomy of the Admiralty Tidal Curve

Read the layout and instructions on the actual port curve. The following describes a common HW-centred format:

1. High Water Height Scale (Top Axis): Graduated in metres across the port's High Water range.
2. Low Water Height Scale (Bottom Axis): Graduated in metres across the port's Low Water range.
3. The Diagonal Transfer Line: A straight pencil line drawn by the navigator directly connecting the plotted Low Water on the bottom scale to High Water on the top scale.
4. The Central Curve Box: Contains the empirical profile curves:
   • Mean Springs Curve: Heavy solid line (red or black).
   • Mean Neaps Curve: Dashed line (blue or black).
   • On intermediate tides, the navigator interpolates between the curves based on tidal range.
5. The Time Axis & Entry Boxes (Base Axis): Use the printed reference event and hour labels. HW-centred curves use HW as zero; a curve such as Cowes uses LW. Fill the boxes from that event, without assuming identical limits on both sides.

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Problem 1: Height of Tide at a Specific Clock Time

HW-centred exercise: A skipper needs the height of tide at1530BST to check depth before anchoring.

Step-by-Step Graphical Protocol

1. Extract Predictions: Obtain HW time (1300 BST, 5.2m) and LW time (1915 BST, 1.2m). For this hypothetical exercise, mean spring range is 4.0m and mean neap range 2.0m: the 4.0m range uses the spring curve. The supplied curve factor at HW +2h30m is 0.55.
2. Plot Heights: Mark LW (1.2m) on the bottom scale and HW (5.2m) on the top scale. Join them with a straight pencil line (the diagonal line).
3. Populate Time Boxes: Write HW time (1300) beneath the central 'HW' (0h) marker. Fill in adjacent hourly boxes:
   • Before HW: 1200 (-1h), 1100 (-2h), 1000 (-3h).
   • After HW: 1400 (+1h), 1500 (+2h), 1600 (+3h), 1700 (+4h).
4. Locate Target Time: Find 1530 on the base axis (+2.5h after HW, midway between 1500 and 1600).
5. Project to Curve: Project vertically straight UP from 1530 to intersect the Spring curve.
6. Transfer to Diagonal: From the curve intersection, travel horizontally across to intersect the diagonal line.
7. Read Height: Project vertically to the available height scale, following the printed layout. The supplied factor gives Height of Tide = 1.2 + (0.55 × 4.0) = 3.4 metres. A real calculation requires the actual port curve.

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Problem 2: Safe Tidal Window for a Required Height

HW-centred exercise: Find the earliest and latest times when water level meets the stated drying-bar requirement.

Formulating Required Height of Tide

$\text{Required Depth} = \text{Vessel Static Draught} + \text{Under-Keel Clearance Margin (UKC)}$ $\text{Required Height of Tide} = \text{Required Depth} - \text{Charted Depth}$

Worked Crossing Scenario

• Vessel draught: 1.8 metres.
• Prudent UKC margin: 0.8 metres.
• Harbour entrance bar: Charted drying height of 1.4 metres (sounded as $\underline{1.4}\text{m}$).
• Required Height: $1.8\text{m} + 0.8\text{m} + 1.4\text{m} = \mathbf{4.0\text{ metres}}$.
• Port predictions: HW 1400 BST (5.0m); LW 2015 BST (1.0m). For this hypothetical exercise, mean spring range is 4.5m and mean neap range 2.5m, giving (4.0−2.5)/(4.5−2.5) = 0.75. The supplied interpolated curve crosses factor 0.75 at HW −1h50m and HW +1h50m.

Reverse Plotting Protocol

1. Plot Diagonal: Join LW (1.0m) on the bottom scale to HW (5.0m) on the top scale.
2. Enter Required Height: Locate $4.0\text{m}$ on the horizontal height scale.
3. Project to Diagonal: Project vertically from $4.0\text{m}$ to intersect the diagonal line.
4. Transfer Horizontally to Curves: Required factor = (4.0−1.0)/(5.0−1.0) = 0.75. Draw the corresponding horizontal line across the curve box. For the supplied exercise readings:
   • Flood intersection (before HW): occurs at -1h 50m before HW.
   • Ebb intersection (after HW): occurs at +1h 50m after HW.
5. Drop to Time Axis: Drop vertically down from both curve intersections to the time boxes:
   • HW time is 1400 BST.
   • Earliest Safe Arrival Time = $1400 - 0150 = \mathbf{1210\text{ BST}}$.
   • Latest Safe Departure Time = $1400 + 0150 = \mathbf{1550\text{ BST}}$.
6. Conclusion: Safe crossing window spans 3 hours 40 minutes (from 1210 to 1550 BST).

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Asymmetric Curves & Tidal Stands

In regions such as the Solent, Portland, and the Channel Islands, skippers encounter specialized curve features:

1. Duration Corrections: When the time interval between LW and HW departs from 6 hours, some Admiralty curves provide auxiliary duration tables to scale the time axis.
2. Dual High Waters & Stands: In Southampton Water and Portsmouth, overtides produce a secondary rise or prolonged stand. A horizontal line across the curve may intersect at multiple points, providing extended deep-water transit windows.