Fuel, Weather and the Turning Tide
You are planning a small-boat passage of 36 nautical miles to a rendezvous. The boat makes 6 knots in calm water. Forecast wind on the nose is expected to reduce speed by roughly one knot for the whole passage. You must arrive no later than 14:00. You can depart at 06:00 or wait for a weather window at 09:00, when the wind is forecast to ease and speed loss drops to 0.5 knots, but the tide turns against you at 12:00 and costs a further 1 knot until arrival. Fuel is sufficient for 8 hours at 6 knots; consumption rises roughly with the cube of speed, so running faster is disproportionately expensive. The rendezvous can slip by up to one hour without penalty.
1. Compare the two departure options and recommend one, showing the arithmetic.
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06:00 departure: effective speed 6 - 1 = 5 knots, so 36 / 5 = 7.2 hours, arriving about 13:12. That meets 14:00 with 48 minutes to spare. 09:00 departure: from 09:00 to 12:00 speed is 6 - 0.5 = 5.5 knots, covering 16.5 miles; remaining 19.5 miles at 6 - 0.5 - 1 = 4.5 knots takes 4.33 hours, arriving about 16:20. That misses even the one-hour slippage (latest 15:00) by a wide margin. The 09:00 option is therefore not viable on time at displacement speed. The 06:00 departure is the recommendation, with the 48-minute buffer noted as thin and worth monitoring.
2. Could you simply increase speed on the 09:00 option to arrive on time? Explain the trade-off.
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Required average over 36 miles by 15:00 is 36 / 6 = 6 knots, but the tide penalty of 1 knot means you would need about 7 knots through the water in the final leg, roughly 17 percent above calm-water speed. Fuel use scales with roughly the cube of speed, so that is about 1.17^3, close to 1.6 times the consumption rate, and the tank holds only 8 hours at 6 knots. The margin is too thin to rely on, and the plan assumes the forecast holds. The honest answer is that speeding up is not a reliable fix and should not be presented as one.
3. What single piece of information would most change your recommendation?
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The actual time of the tide turn relative to your position along the route, or a reliable update on the wind at departure. If the adverse tide begins later or the wind eases earlier than forecast, the 09:00 option improves sharply; if the wind strengthens, the 06:00 buffer disappears. The answer should identify the sensitivity and say how you would monitor it (position fixes, updated forecast before departure, a decision point) rather than pretending the forecast is certain.