Convoy Fuel, Reserve and Detour
A convoy must travel 140 km from barracks to a training area, complete a 35 km tactical loop at the destination, and return by the same 140 km route. The lead vehicle has an 80-litre tank and consumes 12 litres per 100 km when loaded. Standing orders require at least 15 litres remaining in the tank at all times. The route officer proposes a detour of 60 km each way to avoid a bridge weight restriction. The vehicle can carry two 20-litre jerry cans, but these must not be used to breach the reserve. Diesel costs £1.42 per litre. The budget holder has authorised £150 for this vehicle's fuel. You must decide whether the detour is feasible without jerry cans, whether the budget covers the fuel, and what maximum one-way detour is possible with the jerry cans while keeping the reserve.
1. Calculate the fuel required for the base route and for the proposed 60 km-each-way detour. Decide whether the detour is feasible without using the jerry cans.
Read the worked answer
Base distance = 140 + 35 + 140 = 315 km. The detour adds 60 km out and 60 km back = 120 km, so total distance = 435 km. Fuel = distance ÷ 100 × 12. Base: 3.15 × 12 = 37.8 L. With detour: 4.35 × 12 = 52.2 L. Usable fuel without breaching reserve = 80 − 15 = 65 L. After the detour, remaining = 80 − 52.2 = 27.8 L, which is above the 15 L reserve. Therefore the detour is feasible without jerry cans, with 12.8 L of margin above the reserve.
2. Calculate the fuel cost of the detour route and state whether it fits the £150 authorisation. Include the cost of filling the tank if that is how the budget is drawn.
Read the worked answer
Fuel used on the detour route = 52.2 L. Cost = 52.2 × £1.42 = £74.12 (52.2 × 1.42 = 74.124). This is well within £150. If the budget is drawn as a full tank, 80 × £1.42 = £113.60, also within £150. The remaining authorisation is £150 − £74.12 = £75.88 on a consumption basis, or £36.40 on a fill basis. A judgement should be recorded: the consumption basis is the true cost of the trip, while the fill basis ties up cash in unused fuel.
3. Because of additional kit, consumption rises to 14 L/100 km. With the two jerry cans available, calculate the maximum one-way detour that still preserves the 15 L reserve. State any assumption about when the cans are used.
Read the worked answer
Total usable fuel = (80 − 15) + (2 × 20) = 65 + 40 = 105 L. At 14 L/100 km, maximum distance = 105 ÷ 14 × 100 = 750 km. Base route is 315 km, so extra distance available = 750 − 315 = 435 km. A one-way detour x adds 2x km, so 2x ≤ 435, x ≤ 217.5 km. The maximum one-way detour is 217.5 km, about 218 km in whole-kilometre planning. Assumption: the jerry cans are carried full and their contents are treated as usable before the reserve is touched. If the cans are reserved for emergencies only, the figure falls back to 65 ÷ 14 × 100 = 464.3 km total, giving x ≤ (464.3 − 315) ÷ 2 = 74.6 km.