Bridge-Limited Convoy: Load, Fuel and Time
A cadet wing must move 24 cadets and 5,400 kg of equipment across a 9 km stretch to a field camp. Two 3-ton trucks are available. Each truck has a kerb weight of 4,200 kg and a gross vehicle weight limit of 7,500 kg. A narrow bridge on the route is posted at 7,000 kg. Cadets weigh 65 kg with kit. Trucks consume 1 litre per 6 km and have 40-litre tanks, currently full. The convoy commander proposes loading both trucks to their normal 3-ton rating, putting 12 cadets in each cab, and crossing in one go. A driver objects that the bridge posting, not the truck rating, governs. The camp needs the equipment within 2 hours; cadets can walk the 9 km at 5 km/h while trucks move at 30 km/h.
1. Using the bridge posting, calculate the maximum payload each truck may carry across. Is the commander's plan legal? Show the arithmetic and identify every limit breached.
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The bridge posting is a gross-mass limit, so it governs the load on the structure.
- Maximum payload per truck on the bridge = 7,000 kg − 4,200 kg = 2,800 kg.
- Commander's load per truck:
- Equipment: 5,400 ÷ 2 = 2,700 kg
- Cadets: 12 × 65 = 780 kg
- Total payload: 2,700 + 780 = 3,480 kg
3,480 kg exceeds the bridge allowance of 2,800 kg by 680 kg. It also exceeds the truck's normal 3-ton payload rating of 3,000 kg by 480 kg. So the plan breaches both limits. The equipment alone, at 2,700 kg per truck, is within the bridge allowance and the truck rating. The cadets are the overload.
2. Propose a crossing plan that moves all cadets and equipment within 2 hours. Support it with timing and fuel calculations, and state any operational condition.
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Plan: load 2,700 kg of equipment on each truck and let the cadets walk; no cadet rides across the bridge.
- Truck crossing time: 9 km ÷ 30 km/h = 0.3 h = 18 min.
- Cadet walking time: 9 km ÷ 5 km/h = 1.8 h = 108 min, which is inside the 2-hour limit with 12 minutes to spare.
- Fuel outbound: 9 ÷ 6 = 1.5 L per truck, so 3 L total. Even a return trip would use about 6 L, far below the 40 L tanks.
The critical condition is loading time. If loading takes more than about 12 minutes, the equipment will miss the 2-hour deadline unless crates are pre-staged. The trucks should cross one at a time, not together.
3. State one hidden assumption in your plan that could invalidate it, and explain how you would check it.
Read the worked answer
The plan assumes the bridge limit is a static gross limit and that only one truck is on the bridge at a time. If both trucks enter the bridge together, the combined mass could exceed 7,000 kg even though each truck is individually under the limit. It also assumes the 2,700 kg is distributed within the truck's axle limits, not concentrated at the rear.
Check by confirming with the bridge authority or engineer that the posting is a single-vehicle gross limit, enforcing a one-truck-at-a-time gap, and checking axle-load distribution before departure. A second assumption is that cadets can sustain 5 km/h in heat with kit; a test walk or a shaded rest plan would verify that.