Fuel Endurance on a Coastal Patrol Leg
A patrol boat must run a straight leg of 168 nautical miles from Namibe to a rendezvous point. Its tanks hold 420 litres, of which 15% is unusable reserve that regulations forbid consuming. At the planned cruising speed the engine burns 12 litres per hour and the boat makes 14 knots. The navigator proposes instead to run at a higher speed of 18 knots, which raises consumption to 18 litres per hour. Wind and current are negligible, and the crew wants the largest possible safety margin on arrival. The commanding officer asks for a judgement, not just a calculation, and reminds the crew that the reserve is a hard limit.
1. Compute the usable fuel and the time and fuel needed for each of the two speeds. Which speed leaves the larger margin?
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Usable fuel = 420 × 0.85 = 357 L (63 L is untouchable reserve).
At 14 kn: time = 168 / 14 = 12 h; fuel = 12 × 12 = 144 L; margin = 357 − 144 = 213 L.
At 18 kn: time = 168 / 18 ≈ 9.33 h; fuel = 18 × 9.33 ≈ 168 L; margin = 357 − 168 = 189 L.
The slower speed leaves the larger margin (213 L vs 189 L). Note that the faster run burns more fuel per mile (18/18 = 1.0 L/nm vs 12/14 ≈ 0.86 L/nm), so speed costs range even though it saves time.
2. Suppose the rendezvous is moved to 260 nautical miles. Does the answer about which speed is safer change? Justify with numbers.
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At 14 kn: time = 260/14 ≈ 18.57 h; fuel ≈ 12 × 18.57 ≈ 223 L; margin ≈ 357 − 223 = 134 L.
At 18 kn: time = 260/18 ≈ 14.44 h; fuel ≈ 18 × 14.44 ≈ 260 L; margin ≈ 357 − 260 = 97 L.
The slower speed still leaves the larger margin, and the gap has widened (134 vs 97 L). The conclusion is stable: the higher speed never becomes the safer choice on this leg because its fuel-per-mile is higher. The real judgement is operational: if time pressure exists, the crew must decide whether a 97 L margin is acceptable, since it is still above the hard reserve.