Fuel Endurance on a Coastal Patrol
A Naval patrol boat carries 1,200 litres of diesel in its main tanks. The engine burns fuel at a rate that depends on speed: at 12 knots it uses 40 litres per hour, and at 18 knots it uses 75 litres per hour. The boat must leave harbour, travel 90 nautical miles out to a checkpoint, spend 1.5 hours on station (fuel burn at 12 knots equivalent, i.e. 40 L/h), and return to the same harbour. A safety regulation requires the boat to dock with at least 15% of its original fuel remaining. The commanding officer wants to know whether running the whole trip at 18 knots is permitted, or whether the boat must slow to 12 knots for the transit legs.
1. Calculate the fuel used for the full trip at 18 knots and decide whether the 15% reserve is respected.
Read the worked answer
Distance each way = 90 nm. At 18 knots, time per leg = 90 / 18 = 5 hours. Two legs = 10 hours of transit. Transit fuel = 10 × 75 = 750 L. On-station burn = 1.5 × 40 = 60 L. Total used = 750 + 60 = 810 L. Reserve required = 15% of 1,200 = 180 L. Fuel left = 1,200 − 810 = 390 L. 390 L ≥ 180 L, so the 18-knot plan is permitted with 390 L remaining.
2. Now test the 12-knot transit option and compare which plan leaves the larger safety margin.
Read the worked answer
At 12 knots, time per leg = 90 / 12 = 7.5 hours. Two legs = 15 hours. Transit fuel = 15 × 40 = 600 L. On-station = 60 L. Total = 660 L. Fuel left = 1,200 − 660 = 540 L, which is above the 180 L reserve. Comparison: 18 knots leaves 390 L; 12 knots leaves 540 L. The slower plan gives a larger absolute margin (540 L vs 390 L) but takes 15 h of transit versus 10 h - a 5-hour time penalty. The faster plan still clears the legal reserve, so speed is a command trade-off of time against margin, not a safety violation.
3. A forecast adds a 2-hour delay on station during which the engine idles at 40 L/h. Does the 18-knot plan still satisfy the reserve?
Read the worked answer
Extra idle time = 2 h × 40 L/h = 80 L. New total used = 810 + 80 = 890 L. Fuel left = 1,200 − 890 = 310 L. Reserve needed = 180 L. 310 L ≥ 180 L, so yes, it still complies, with 130 L of margin above the legal minimum.