Electric Heavy Truck Lab: Payload, Range, Hills and Regeneration

Loading Blender-built truck...

speed - power - charge - range at this load - payload -

Stories (presets)

The science

A generic electric long-haul truck, a teaching model. No real vehicle is represented. The topic is inspired by publicly reported battery-electric tractor-trailers (roughly 36–40 t combination weight, battery packs of a few hundred kWh to about a megawatt-hour, megawatt-class charging). All parameters here are textbook-order or illustrative values, not data for any product.

Road load at the wheels: F = ½ ρ C_dA (v+w)|v+w| + C_rr m g cosθ + m g sinθ + 1.03 m a, wheel power P = F v. Defaults: C_d 0.55, A 10 m², C_rr 0.006, ρ 1.2 kg/m³. On the flat at 80 km/h rolling resistance (about 2.1 kN at 36 t) is larger than drag (about 1.6 kN): a heavy truck is a rolling-resistance machine until it goes faster.
The mass budget: m = m_tare + E_batt/e_s + m_payload ≤ GVW, with pack-level specific energy e_s of about 150–200 Wh/kg. Every extra kWh costs 5–7 kg of cargo capacity, and the heavier truck needs more energy per km, so more battery buys less range than it seems. That is the payload–range trade-off curve on the right of the stage.
Energy per km at the battery: E/d = (F/η_d + P_aux/v)(1 + k P/E_batt) with η_d = 0.90 (motor, inverter, gear), a small auxiliary load, and a pack-resistance term (3 % loss at 1C, illustrative). Closed-form range on the flat: R = E_use v / P_term, where E_use is the energy between the start charge and the reserve.
Regeneration: where the wheel force is negative the motor can return power, limited by the smallest of motor/inverter power, the pack's charge acceptance (1C here, falling above 85 % charge: a full battery cannot take regen) and what the brakes must do instead (friction, heat). Round trip drive → regen ≈ 0.90 × 0.75 ≈ 0.68, so a descent never repays a climb in full, and drag and rolling resistance take their share of the potential energy m g Δh on the way down.
Charging: site power (default 1 MW) and the pack limit C_max E_batt (2C below 50 % charge), then a linear taper above 50 % to about 0.12 of that at 100 %. The charging session is why trips stop at 15 % and leave at 80 %: the last 20 % is slow. A smaller pack charges fewer kW in absolute terms, so size matters twice.
Driver rest (public regulation): in the EU a driver must take a break of at least 45 minutes after 4.5 hours of driving (Regulation (EC) No 561/2006), which may be split into 15 + 30 minutes. If charging fits inside that break it is effectively free time; only charging beyond it delays the delivery. The model applies this rule in a simplified form (first part ≥ 15 min, second part ≥ 30 min, a charging stop close to the next break becomes the break). National rules, tolls, working-time and daily driving limits are not modelled.
Diesel comparison (order of magnitude): the same road load, 15 t tare, engine efficiency 0.40 over the cycle, no regeneration, 9.9 kWh per litre, 2.64 kg CO₂ per litre burned. CO₂ at the point of use is zero for the electric truck, but electricity generation is not zero-carbon everywhere; the upstream line uses a stated grid intensity.
Routes: an elevation profile with 21 nodes (every 20 km) interpolated by a C1 cubic spline. Drag the nodes on the route chart to edit it. Speed is held at the set speed unless the truck is power-limited on a climb. Cornering, pitch dynamics, wind that changes along the way and temperature effects are ignored.
Experiments: A compares the time-stepped range against the closed form for increasing payload; B takes a constant-speed descent and checks energy conservation m g Δh = ∫(F_aero+F_roll)v dt + E_regen,wheel + E_friction and the predicted recovery η_R(m g Δh − W_drag+roll) against the simulation.
Illustrations: airflow streaks are a hand-made deflection, not CFD; force arrows are in a compressed (square-root) length scale.

Typical references: Wong, Theory of Ground Vehicles; Gillespie, Fundamentals of Vehicle Dynamics; Ehsani et al., Modern Electric, Hybrid Electric and Fuel Cell Vehicles; MacKay, Sustainable Energy — without the hot air; Regulation (EC) No 561/2006 on driving times and rest periods.

Independent educational model, not affiliated with or endorsed by any company named here; trademarks belong to their owners. Numbers are textbook-level/publicly reported approximations.