5.1 Secondary Port Calculations: Time & Height Differences

5.1 Secondary Port Calculations: Time & Height Differences

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Standard Ports vs. Secondary Ports

The UK Hydrographic Office cannot publish 365-day tables for every coastal inlet. The appropriate regional ATT volume organizes tidal coverage into two tiers:

1. Standard Ports: Ports with published daily predictions (e.g., Dover, Portsmouth, Plymouth, Brest). ATT Part I tabulates daily times and heights of High Water (HW) and Low Water (LW) in the stated time zone, with the applicable prediction guidance.
2. Secondary Ports: Coastal locations whose tides mirror a designated Standard Port with predictable time lags and range variations. ATT Part II lists secondary ports by geographical index number, tabulating differences relative to their parent Standard Port.

Because secondary ports lie within the same co-tidal system as their parent Standard Port, astronomical variations reproduce at the secondary port with consistent mathematical offsets.

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Architecture of Admiralty Tide Tables (ATT) Part II

ATT Part II displays differences in a standardized tabular format containing three core datasets:

1. Position & Reference Port: Port index number, geographical coordinates (lat/long), and the assigned Standard Port.
2. Time Differences (HW and LW): Tabulated against specified Standard Port clock times; these vary by location, so use the actual column headings.
3. Height Differences: Tabulated against four primary tidal levels of the Standard Port:
   • MHWS (Mean High Water Springs): Height difference at mean spring high water.
   • MHWN (Mean High Water Neaps): Height difference at mean neap high water.
   • MLWN (Mean Low Water Neaps): Neap low water difference.
   • MLWS (Mean Low Water Springs): Spring low water difference.

Sample ATT Part II Extract: Secondary Port 'Sandy Cove'

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Time Standards & British Summer Time (BST)

Read the time zone printed for the port and differences table. The fictional table in this section uses Universal Time (UT / GMT).

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Linear Interpolation Protocol

Standard Port daily tides rarely match exact reference hours or datum levels, requiring linear interpolation:

1. Time Interpolation

For Standard Port time $T$ between reference times $T_1$ and $T_2$ with differences $D_1$ and $D_2$: $\text{Interpolated Diff} = D_1 + \left( \frac{T - T_1}{T_2 - T_1} \right) \times (D_2 - D_1)$ $\text{Secondary Time} = T + \text{Interpolated Diff}$

2. Height Interpolation

For Standard Port height $H$ between datum levels $H_1$ and $H_2$ with differences $\Delta H_1$ and $\Delta H_2$: $\text{Interpolated Height Diff} = \Delta H_1 + \left( \frac{H - H_1}{H_2 - H_1} \right) \times (\Delta H_2 - \Delta H_1)$ $\text{Secondary Height} = H + \text{Interpolated Height Diff}$

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Comprehensive Worked Numerical Scenario

A yacht plans to enter Sandy Cove on 15 June (draught 1.8m, BST active).

Standard Port (Port Victoria) Daily Predictions

From ATT Part I: HW at 0430 UT (5.4m); LW at 1045 UT (1.1m). Datums: MHWS = 6.0m, MHWN = 4.8m, MLWN = 1.8m, MLWS = 0.6m.

Calculation Steps

1. High Water Time (Sandy Cove):

   • 0430 UT is between 0000 (+0040) and 0600 (+0020).
   • Elapsed: 270/360 min = 0.75. Change: (+20) - (+40) = -20 min.
   • Diff at 0430: $+40 + (0.75 \times -20) = \mathbf{+0025}$.
   • Secondary HW: $0430 + 0025 = \mathbf{0455\text{ UT}}$ ($\mathbf{0555\text{ BST}}$).

2. High Water Height (Sandy Cove):

   • 5.4m is midway between MHWN (4.8m) and MHWS (6.0m) (range 1.2m, offset 0.6m, ratio 0.5).
   • Diff change: $(+0.6) - (+0.2) = +0.4\text{m}$.
   • Diff at 5.4m: $+0.2 + (0.5 \times 0.4) = \mathbf{+0.4\text{m}}$.
   • Secondary HW Height: $5.4\text{m} + 0.4\text{m} = \mathbf{5.8\text{m}}$.

3. Low Water Time (Sandy Cove):

   • 1045 UT is between 0600 (+0030) and 1200 (+0050).
   • Elapsed: 285/360 min = 0.792. Change: (+50) - (+30) = +20 min.
   • Diff at 1045: $+30 + (0.792 \times 20) = +30 + 16 = \mathbf{+0046}$.
   • Secondary LW: $1045 + 0046 = \mathbf{1131\text{ UT}}$ ($\mathbf{1231\text{ BST}}$).

4. Low Water Height (Sandy Cove):

   • 1.1m is between MLWS (0.6m) and MLWN (1.8m) (range 1.2m, offset 0.5m, ratio $0.5/1.2 = 0.417$).
   • Diff change: $(-0.1) - (-0.3) = +0.2\text{m}$.
   • Diff at 1.1m: $-0.3 + (0.417 \times 0.2) = -0.3 + 0.083 = \mathbf{-0.2\text{m}}$.
   • Secondary LW Height: $1.1\text{m} + (-0.2\text{m}) = \mathbf{0.9\text{m}}$.

Admiralty Pro-Forma Summary

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Practical Examination Pitfalls

1. Sign Confusion: Height differences often carry negative signs (e.g., -0.2m). Adding a negative decreases height ($1.1\text{m} + (-0.2\text{m}) = 0.9\text{m}$). Reversing signs risks groundings.
2. Column Misalignment: Always interpolate HW predictions against HW difference columns, and LW predictions against LW difference columns.
3. Double Summer Time Addition: Keep all arithmetic in UT until the final step, then add 1 hour for BST once.