Convoy Fuel Reserve With Sand Stretch
A convoy of three vehicles must travel 240 km. Vehicle A has a 120 L tank and consumes 20 L/100 km. Vehicle B has a 90 L tank and consumes 15 L/100 km. Vehicle C has an 80 L tank and consumes 25 L/100 km. All start full. A refuel point at 130 km holds 200 L, but only one vehicle can refuel at a time and each refuel takes 20 minutes. Standing orders require each vehicle to arrive with at least 25% of its tank capacity remaining. The route has a 20 km stretch of soft sand between km 80 and km 100 that increases consumption by 50% for all vehicles. You must determine which vehicle is limiting, whether the plan meets the reserve without refuelling, and how much fuel must be drawn at the refuel point. The commander also asks whether a fuel transfer from another vehicle could replace the refuel point if the pump fails.
1. Calculate each vehicle's fuel remaining on arrival without refuelling, and identify which vehicle is limiting against the 25% reserve.
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The sand stretch adds 50% consumption over 20 km. For a vehicle with rate R L/100 km, the sand segment costs R x 0.20 x 1.5 = 0.30R L instead of 0.20R L, so the extra is 0.10R L. The whole 240 km trip therefore costs 2.40R + 0.10R = 2.50R L.
Vehicle A: 2.50 x 20 = 50 L used; 120 - 50 = 70 L remaining. Reserve is 25% of 120 = 30 L. A is 40 L above reserve. Vehicle B: 2.50 x 15 = 37.5 L used; 90 - 37.5 = 52.5 L remaining. Reserve is 22.5 L. B is 30 L above reserve. Vehicle C: 2.50 x 25 = 62.5 L used; 80 - 62.5 = 17.5 L remaining. Reserve is 20 L. C is 2.5 L below reserve.
The limiting vehicle is C. Without refuelling, C would arrive 2.5 L short of the required reserve, while A and B would meet it.
2. Determine the minimum fuel C must draw at the 130 km refuel point to meet the reserve, and whether the 200 L available is sufficient. Show C's fuel state at 130 km.
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Up to 130 km, C uses 25 x 1.30 = 32.5 L for the normal distance, plus the sand penalty. The sand segment is within the first 130 km, so add 0.10 x 25 = 2.5 L. Total used to 130 km = 35 L. C starts with 80 L, so it arrives at the refuel point with 45 L.
From 130 km to 240 km is 110 km with no sand. Fuel needed = 25 x 1.10 = 27.5 L. If C draws nothing, arrival fuel = 45 - 27.5 = 17.5 L, which is 2.5 L below the 20 L reserve. Therefore the minimum draw is 2.5 L. After drawing 2.5 L, C leaves with 47.5 L and arrives with exactly 20 L.
The refuel point holds 200 L, so 2.5 L is easily sufficient. In practice I would draw a small margin above the minimum, for example 5 L, because the reserve is a minimum and the consumption estimate may vary. Even 5 L is well within the 200 L available, and only C needs to refuel under these figures, so the 20-minute pump time does not create a convoy delay beyond one stop.
3. If the refuel pump fails, can the convoy still meet the reserve by transferring fuel from another vehicle? Use the fuel states at 130 km.
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At 130 km, compute each vehicle's remaining fuel. A has used 20 x 1.30 = 26 L plus 2 L sand penalty = 28 L, so A has 120 - 28 = 92 L. B has used 15 x 1.30 = 19.5 L plus 1.5 L = 21 L, so B has 90 - 21 = 69 L. C has 45 L as calculated.
From 130 km to the finish, A needs 20 x 1.10 = 22 L, so A would arrive with 70 L and needs only 30 L reserve. A can spare 40 L above reserve. B needs 15 x 1.10 = 16.5 L, so B would arrive with 52.5 L and needs 22.5 L reserve. B can spare 30 L. C needs 2.5 L to reach its 20 L reserve.
A transfer of 2.5 L from A to C is safe: A would still arrive with 67.5 L, far above its 30 L reserve. A 5 L transfer is also safe. Therefore the convoy can meet the reserve without the pump if transfer equipment is available and the transfer is recorded. The limiting factor is not fuel quantity but the ability to transfer safely and account for it.