Describe the engineering of light rail and metro public transport systems, calculate passenger-carrying capacity and energy use per passenger-kilometre, and compare with private vehicles

Light rail energy per passenger-kilometre.

Effective passengers: $450 \times 0.65 = 292.5$.

Energy per passenger-km: $4.5 / 292.5 = 0.0154$ kWh per pass-km = 15.4 Wh per pass-km.

Passenger car comparison.

Petrol energy per 100 km: $8 \times 33 = 264$ MJ = 73.3 kWh.

Energy per passenger-km at 1.2 passengers: $73.3 / (100 \times 1.2) = 0.611$ kWh per pass-km = 611 Wh per pass-km.

Result. The light rail uses about $611 / 15.4 = 40$ times less energy per passenger-kilometre than a single-occupant petrol passenger car in city driving. This is a typical figure and is the central engineering argument for urban rail systems.

The advantage comes from three factors. (1) Steel wheel on steel rail has very low rolling resistance (about 0.1 percent of vehicle weight, versus 1.5 percent for tyres on bitumen). (2) Regenerative braking returns electrical energy to the catenary or substation. (3) High vehicle utilisation means the energy cost of moving the vehicle is divided across many passengers.

Markers reward (1) the load-factor calculation, (2) unit conversion of petrol energy, (3) the energy-per-passenger-kilometre comparison, (4) a comment on rolling resistance or regenerative braking, and (5) units in every answer.

Marking criteria: 1 mark for correctly identifying the load-factor formula, 1 mark for correct substitution, 1 mark for the correct final answer (165 passengers) with no units error (a pure number, not a rate).

This sits within the typical 30 to 40 Wh per passenger-km range for an articulated electric bus.

Marking criteria: 1 mark for dividing vehicle energy by passenger number, 1 mark for correct unit conversion from kWh to Wh, 1 mark for the final answer with a comment comparing it to the typical range.

(a) Efficiency ratio.

Sydney Metro uses about 75 times less energy per passenger-kilometre than the petrol car.

(b) Why Metro beats the electric bus. (1) Rolling resistance: Metro runs on steel wheels on steel rail, with rolling resistance roughly ten times lower than a rubber tyre on bitumen used by the bus, so less energy is lost to friction for the same vehicle mass moved. (2) Vehicle utilisation: A Metro train carries up to 1100 passengers, far more than a single articulated bus (typically under 100), so the substantial fixed energy cost of moving the vehicle itself is divided across many more passengers, lowering the per-passenger figure even though both are electrically driven and can both use regenerative braking.

Marking criteria: 1 mark for the correct ratio (75), 1 mark for stating rolling resistance as one reason with a comparative statement, 1 mark for explaining the mechanism (friction loss scales with resistance, not just naming it), 1 mark for stating vehicle utilisation/capacity as a second reason, 1 mark for explaining that dividing a similar fixed energy cost across more passengers lowers the per-passenger figure.

Number of services per hour: $60 / 7.5 = 8$ services per hour.

Marking criteria: 1 mark for correctly finding the number of services per hour from the headway, 1 mark for correct substitution, 1 mark for the correct final answer, 1 mark for units (passengers per hour, one direction, stated explicitly).

(1) Rolling resistance

A steel wheel running on a steel rail experiences rolling resistance roughly ten times lower than a rubber tyre on bitumen, so less of the input energy is lost to friction for a given vehicle mass and speed.

(2) Regenerative braking with grid return

Electric trains and trams convert kinetic energy back to electricity when decelerating, feeding it back into the catenary or substation for use by other accelerating vehicles nearby, whereas most private cars dissipate braking energy as heat in the brakes.

(3) Vehicle utilisation

The energy required to move the vehicle itself (which does not scale linearly with passenger count) is shared across many more passengers on a train or tram than in a typical private car, which in Sydney averages only 1.2 occupants.

Marking criteria: 1 mark for each of the three distinct, correctly explained reasons (not just named), with a mechanism given for each rather than a bare label.

This is a 7-mark EVALUATE: markers reward a judgement supported by contrasted engineering and economic evidence, not a simple list of pros and cons.

Band 6 plan.

• Thesis: light rail delivers superior long-term capacity, energy efficiency and reliability for a genuinely high-demand corridor, but its far higher upfront capital cost and construction disruption mean an improved bus service is the better engineering choice unless patronage is forecast to be sustained and high.
• Capacity: a light rail vehicle (300 to 450 passengers) with 4 to 8 minute headways vastly exceeds a single bus (around 70 to 100 passengers articulated); matching the same passenger throughput by bus alone requires many more vehicles, more drivers, and eventually road-space competing with general traffic.
• Energy efficiency: light rail's steel-wheel-on-rail rolling resistance and regenerative braking give roughly half the energy per passenger-kilometre of a bus (typically 15 to 20 Wh versus 30 to 40 Wh per passenger-km), assuming comparable load factors, so operating costs and emissions per passenger fall as patronage rises.
• Capital cost and disruption: light rail requires new track, overhead or ground-level power supply, and often utility relocation, at roughly A$100 million per kilometre, plus years of construction disruption to the corridor (as seen on Sydney's CBD and South East Light Rail). A frequency-boosted bus service uses existing road infrastructure and can be implemented within months at a fraction of the cost.
• Reliability and dedicated right-of-way: light rail on a segregated corridor is not delayed by general traffic congestion the way a bus sharing mixed traffic is, giving more predictable journey times as an outer-suburban corridor grows.
• Judgement: for a corridor with confirmed strong and growing demand, light rail's higher capacity and lower long-run energy cost per passenger justify the capital outlay; for a corridor with uncertain or moderate demand, an enhanced bus service is the more prudent engineering decision because it avoids stranding a very large capital investment if patronage does not eventuate.

Marker's note: top-band answers explicitly compare BOTH systems on at least three dimensions (capacity, energy/operating cost, capital cost/disruption), use realistic Australian figures for each, and finish with a conditional judgement tied to patronage certainty rather than declaring one option universally superior.

Step 1: total capital cost.

Option A (light rail): $10\ \text{km} \times 100\ \text{million/km} = 1000\ \text{million} = 1.0\ \text{billion}$ (A$1.0 billion)

Option B (bus): $10\ \text{km} \times 5\ \text{million/km} = 50\ \text{million}$ (A$50 million)

Step 2: total passenger-trips over 20 years.

Option A: $12{,}000 \times 365 \times 20 = 87{,}600{,}000$ passenger-trips.

Option B: $8{,}000 \times 365 \times 20 = 58{,}400{,}000$ passenger-trips.

Step 3: capital cost per passenger-trip.

Option A: $1{,}000{,}000{,}000 / 87{,}600{,}000 = 11.42$ (A$11.42 per trip).

Option B: $50{,}000{,}000 / 58{,}400{,}000 = 0.86$ (A$0.86 per trip).

Comment. On CAPITAL COST alone, the bus option is far more cost-effective per passenger trip (about A$0.86 versus A$11.42), because its infrastructure cost is a small fraction of light rail's despite carrying fewer passengers. This calculation ignores operating cost, energy cost per passenger-kilometre (where light rail is more efficient), reliability, and capacity headroom for further patronage growth beyond 12,000 per day, all of which would favour light rail in a fuller economic comparison; a real feasibility study must include these factors, not capital cost alone.

Marking criteria: 1 mark for correct total capital cost for each option, 1 mark for correct total passenger-trips for each option, 1 mark for correct capital cost per passenger-trip for each option, 1 mark for correctly identifying that the bus is cheaper by this narrow metric, 1 mark for explicitly naming at least one factor the calculation ignores (operating cost, energy efficiency, capacity headroom, reliability), 1 mark for units and currency notation consistent throughout.