Tidal Height Calculation for a Bar Crossing
You plan to cross the Breede River mouth (South Africa) at 10:00 SAST on 15 March. The charted depth at the bar is 2.5 m below Chart Datum (CD). Your vessel draws 1.8 m. You require a minimum under-keel clearance of 0.5 m. The tide tables for the nearest standard port (Cape Town) give the following: HW at 06:00, height 1.8 m; LW at 12:00, height 0.4 m. The time difference between Cape Town and the Breede River mouth is +1 hour (Breede is 1 hour later). The height difference between Cape Town and Breede is -0.2 m (Breede heights are 0.2 m lower). Use the rule of twelfths to estimate tidal heights.
1. Calculate the predicted height of tide at the Breede River mouth at 10:00 SAST on 15 March.
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First, adjust the tide times and heights to the local port. Cape Town HW at 06:00 becomes 07:00 at Breede. LW at 12:00 becomes 13:00 at Breede. The tidal range at Cape Town is 1.8 - 0.4 = 1.4 m. At Breede, the heights are 0.2 m lower, so HW = 1.8 - 0.2 = 1.6 m, LW = 0.4 - 0.2 = 0.2 m. Range at Breede = 1.4 m (same). The time from HW (07:00) to 10:00 is 3 hours. The duration of fall from HW to LW is 13:00 - 07:00 = 6 hours. Using the rule of twelfths, in the first 3 hours (half the fall), the tide falls by 6/12 of the range (since 1st hour:1/12, 2nd:2/12, 3rd:3/12, total 6/12). So fall = 0.5 * 1.4 = 0.7 m. Height at 10:00 = HW height - fall = 1.6 - 0.7 = 0.9 m above CD. Alternatively, using the rule of twelfths directly: after 3 hours, the tide has fallen 6/12 of the range, so height = 1.6 - 0.7 = 0.9 m.
2. Determine whether your vessel can safely cross the bar at 10:00, and state the under-keel clearance.
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Charted depth at the bar = 2.5 m (below CD). Predicted tide height at 10:00 = 0.9 m. Actual depth = charted depth + tide height = 2.5 + 0.9 = 3.4 m. Your vessel's draught = 1.8 m. Under-keel clearance (UKC) = actual depth - draught = 3.4 - 1.8 = 1.6 m. Required minimum UKC = 0.5 m. Since 1.6 m > 0.5 m, you can safely cross. However, consider factors such as swell, squat, and chart accuracy. The margin is 1.1 m above the minimum, which is adequate for a small vessel in slight sea conditions. But always allow for dynamic effects: reduce speed to minimize squat and keep a sharp lookout for breaking waves on the bar.