Question 1

At sunset your vessel is in position DR 20°N, and you observe the Sun bearing 284° by compass as it sets. The Sun's declination from the Almanac is 15°N. How do you calculate and apply the compass error?

Accepted Answer

Compass error by amplitude: (1) AMPLITUDE formula: Sin(Amplitude) = Sin(Declination) / Cos(Latitude). Sin(Amp) = Sin(15°) / Cos(20°) = 0.2588 / 0.9397 = 0.2754. Amplitude = arcsin(0.2754) = 15.98° ≈ W16°N (at sunset, the Sun bears West; declination N = amplitude toward North = W16°N); (2) TRUE BEARING of Sun at setting = 270° + 16° = 286°T (bearing is W of S at sunset when declination is N — actually 286°T; W16°N = 360−(90−16)... correct method: at sunset, body bears West + amplitude toward declination; W16°N = 360° − (90°−16°) = 286°T); (3) COMPASS BEARING observed = 284°C; (4) ERROR: True bearing − Compass bearing = 286° − 284° = +2°. Variation from chart for the area. If the variation is 5°W, then deviation = error − variation = +2° − (−5°) = +7°E. If True bearing > Compass: compass is reading LOW = compass is pointing too far west = westward error... Error: True − Compass = +2° — compass reads LESS than true = compass error is 2° East (compass is low by 2° = it needs to read higher = add 2° = East). Compass error by amplitude is a standard OOW practical astronomy exercise. The amplitude observation: when a celestial body (Sun, Moon, or bright planet) rises or sets, its TRUE bearing can be calculated from its declination and the observer's latitude. The difference between the true bearing and the compass bearing = compass error (= variation + deviation combined). Amplitude bearing reference: at SUNSET the Sun bears WEST; declination NORTH = amplitude toward NORTH (i.e., bearing is west of true west = less than 270°, but True bearing > 270° — some sources state amplitude as angular distance from E or W toward N or S). For N declination at sunset: True bearing = 270° + amplitude angle. For S declination at sunset: True bearing = 270° − amplitude angle. Error = True − Compass. If result is positive = East error. If negative = West error. Practical application: compare with chart variation. Residual = deviation for that heading. This checks the compass deviation card. At OOW level, the candidate must correctly state: (a) the formula; (b) whether to add or subtract based on hemisphere/sunset/sunrise; (c) the formula for error from True and Compass bearings; (d) how to separate error into variation and deviation.

Question 2

The charted clearance under a bridge at MHWS is 8.2m. Your vessel has an air draught of 7.4m. HW at the standard port today is 4.8m at 1400. LW before it was 0.6m. The bridge is at a secondary port; seasonal correction +0.1m. You need to pass at 1030. Is it safe?

Accepted Answer

Step-by-step tidal calculation using the Rule of Twelfths (or use Admiralty Tide Tables co-tidal and range factor): (1) Range at standard port = HW 4.8m − LW 0.6m = 4.2m; (2) Duration of rise: LW to HW — need LW time. Assume LW was 0730 (HW 1400 = roughly 6h 30m duration — typical semi-diurnal). Duration ≈ 6h 30m; (3) Time from LW to 1030 = 3 hours; (4) Using Rule of Twelfths — first hour rises 1/12, second 2/12, third 3/12: in 3h the tide has risen (1+2+3)/12 × 4.2m = 6/12 × 4.2m = 2.1m; (5) Height at 1030 = LW + rise = 0.6 + 2.1 = 2.7m; (6) Charted MHWS = 8.2m = height of bridge above Chart Datum (CD). Bridge clearance at 1030 = 8.2 − 2.7 = 5.5m (height of bridge above 1030 water level); (7) Apply seasonal correction: +0.1m raises water level slightly: clearance = 5.5 − 0.1 = 5.4m; (8) Air draught 7.4m vs clearance 5.4m — NOT SAFE by 2.0m. The vessel cannot safely pass at 1030. Tidal clearance calculations appear in virtually every OOW oral. The examiner specifically tests whether the candidate understands that MHWS is the MINIMUM clearance marked on the chart (because that is when the water level is highest, reducing the gap to the bridge). At non-MHWS times, the water is lower than MHWS and the clearance is GREATER. However, this question reverses the trap — the water at 1030 is NOT at MHWS but still high enough to reduce clearance below the air draught. Rule of Twelfths: the tidal rise/fall in a semi-diurnal tide follows the pattern 1:2:3:3:2:1 twelfths per hour. This is an approximation valid for most semi-diurnal ports. For critical calculations (air draught, UKC), always use the Admiralty Tide Tables (NP201 series) and the tidal prediction curves for the standard port, applying secondary port differences (time and height corrections). Seasonal corrections: applied to the tabulated heights to account for seasonal variation in mean sea level (meteorological effects, barometric pressure). In UK waters the seasonal correction to MHWS is typically ±0.1-0.2m and must not be ignored for critical clearances.

Question 3

Your vessel has a maximum draught of 7.8m. The charted depth of the entrance channel is 8.5m below Chart Datum. HW was at 0600 with a height of 4.2m. You enter at 0800. The port requires 0.6m minimum UKC. Is there sufficient water?

Accepted Answer

Depth of water calculation: (1) Time from HW to 0800 = 2 hours — the tide is FALLING; (2) Range: HW 4.2m, assume LW (next) approximately 0.8m (typical UK 3.4m range). Falling tide — using Rule of Twelfths from HW: first hour falls 1/12, second hour falls 2/12; in 2 hours tide has fallen (1+2)/12 × 3.4m = 3/12 × 3.4 = 0.85m; (3) Height at 0800 = HW − fall = 4.2 − 0.85 = 3.35m above CD; (4) Actual depth of water = charted depth + tidal height = 8.5 + 3.35 = 11.85m; (5) UKC = depth of water − draught = 11.85 − 7.8 = 4.05m; (6) Required UKC = 0.6m; available UKC = 4.05m — SAFE with considerable margin. Note: in a real tidal approach, the pilot would calculate on the minimum tidal window and dynamic UKC accounting for squat at approach speed. UKC calculation integrating tidal heights and charted depths is a core OOW competency. The fundamental formula: Actual depth = Charted depth (below CD) + Tidal height above CD. UKC = Actual depth − Vessel draught. The confusion in option B is a classic trap — the charted depth alone does not define whether the vessel can navigate safely; the charted depth at chart datum combined with the tidal height at the time gives the actual available water depth. Entering on a falling tide: option C is incorrect — entering on a falling tide is standard practice; the critical factor is whether there is sufficient UKC throughout the entry. What IS prohibited is entering at a state of tide where the minimum UKC cannot be maintained throughout the transit. Squat: in real port approaches, squat (the dynamic sinkage of a vessel underway, typically 0.1-0.4m depending on speed and canal effect) must be subtracted from the available UKC. A 15-knot vessel in a shallow channel may squat 0.3-0.5m — this must be accounted for in the tidal calculation. The minimum UKC (0.6m in this question) is a port-specific requirement often specified in port authority sailing directions or the pilot card.