W2.1 Energy Use in Transportation

Key points

Moving at constant speed = continuously giving energy away: push the medium aside (Drag), push air down (Lift), deform tyres (Rolling resistance), throw away $\frac12 Mv^2$ at every stop (Braking power)
$P_{tot} = P_{drag} + P_{lift} + P_{roll} + P_{brake}$ ; only the terms that apply to the medium (water / air / land)
Energy per distance $= P/v$ = total resistive force → $[\text{J/m}] = [\text{N}]$
Ships: weight carried by Buoyancy. Archimedes’ principle → draught $X$ → submerged area $XW$ → water drag (air drag ≈ 1%)
Compare modes per cargo or person and distance: kWh/(tonne·100 km), kWh/(person·100 km)
Real vehicles: engine efficiency ~25%, start-up losses, climate control, accessories → car 40–120 kWh/100 km (lecture, source K. Blok)

Ship: Buoyancy. Archimedes’ principle → $X$ → $A = XW$ → Drag → $P$ → $E/d = P/v$ → per tonne or person → fuel mass ( $\eta$ , energy density)
Plane: Lift ( $\propto 1/v$ ) + Drag ( $\propto v^3$ ) → optimal speed
Car / bus / train: Drag + Rolling resistance + Braking power

$P_{used}$ = load factor × $P_{engine}$ (HW: 80%, car 60%)
$E/d = P_{used}/v$ → kWh/km ( $\frac{\text{kW}}{\text{km/h}}$ ) → ×100
÷ cargo mass (tonnes) or ÷ persons (full capacity)
Fuel: $m_{fuel} = \frac{E_{mech}}{\eta\, e_{fuel}}$ (HW: gasoline 12.4 kWh/kg, $\eta$ = 25%)

Typical traps

Divide by the cargo (load), not the vehicle’s own mass; per person: full capacity unless told otherwise
Engine power given = maximum → load factor first
knots → km/h (1 knot = 1.85 km/h); bhp → kW (1 bhp ≈ 0.746 kW, not given in HW)
km/h → m/s (÷ 3.6) before cubing $v$
“weight $M$ = 2000 kg” in exam text = mass [kg]; weight as a force = $Mg$ [N]. In ship tasks $W$ = width → write $F_G$ , $F_B$
Model gives mechanical power; fuel needs ÷ $\eta$
Nov 2023 2b answer key: 91.4 → recalculated 93.3 kWh/(person·100 km) (slip in key)

“Derive …” checklist

Write the target ( $E_{lift}/d$ , $E_{float}/d$ , …)
Read the sentence right before it: the hint is there (“power = force × velocity”, “first derive D”)
Use only the formulas and symbols given in the question (not the formula-sheet version of a similar thing)
Check what the next sub-question needs (a number → the expression must contain given values)
Transport: $E/d$ = a force

Exam

Nov 2023 Task 2 (17 pt): hydrofoil water-taxi
a–b floating: Buoyancy. Archimedes’ principle → draught → Drag → $E/d \propto M/L$ ; 93.3 kWh/(person·100 km)
c–e flying: given $F_{lift} = \frac12 C_{lift} A_{wing}\rho_w v^2$ (coefficient model, not the formula-sheet plane formula); $v_{min}$ when $F_B = 0$ → $F_{lift} = Mg$ ; exam sets $E_{lift}/d = F_{lift} = Mg$ ; 68 kWh/(person·100 km) → 27% saved (lift ≈ 99% of it, wing drag ≈ 1%)
Oct 2025 MCQ 5.11: ship at 80% of $v$ over A→B → $E \propto v^2$ → 36% saved
Oct 2025 MCQ 5.12: chain efficiency e-car vs combustion car → Energy Efficiency (W1.6)
Old SET3013: Nov 2016 T1 (container ship + kite), Jan 2018 T1 (A380 lift & drag), Nov 2018 T4 (cargo by boat), Nov 2019 T2 (tanker vs pipeline)