Fuel Consumption Modeling for Diesel & Electric Haul Trucks
Fuel consumption modeling predicts how much diesel or electricity a haul truck uses to move material over a specific route and load — like a car’s MPG, but for massive mining trucks.
⚠️ Why It Matters
📘 Definition
Fuel consumption modeling for diesel and electric haul trucks is a physics- and data-driven engineering methodology that quantifies energy demand per ton-kilometer under dynamic operational conditions, accounting for vehicle mass, grade, rolling resistance, aerodynamic drag, drive-train efficiency, battery state-of-charge (for electric), and duty cycle. It integrates empirical powertrain calibration, terrain digital elevation models (DEMs), and real-time telematics to support fleet optimization, infrastructure planning, and emissions forecasting in surface and underground mine transport systems.
🎨 Concept Diagram
AI-generated illustration for visual understanding
💡 Engineering Insight
Never trust a fuel model built solely on manufacturer ‘rated’ power curves — real-world diesel engines operate 15–25% below peak efficiency 70% of the time due to transient loading, ambient temperature, and aftertreatment backpressure. For battery-electric trucks, the single largest source of model error is inaccurate SOC-to-energy mapping under high C-rate discharge (>1.5C) and sub-zero temperatures; always validate using calorimetrically referenced cell-level test data, not just pack voltage.
📖 Detailed Explanation
Going deeper, modern models incorporate time-varying dynamics: gear-shift timing affects engine operating point and thus BSFC (brake-specific fuel consumption); tire slip ratio modifies effective rolling resistance; and battery internal resistance rises with temperature and SOC, causing voltage sag and reduced usable capacity. These nonlinearities require either high-fidelity co-simulation (e.g., AVL CRUISE™ + MATLAB/Simulink) or physics-informed machine learning (PIML) trained on multi-year telematics archives.
At the advanced level, models must address fleet-scale interactions: traffic density alters acceleration/deceleration patterns; battery degradation changes regen capability and charging time windows; and ore variability (e.g., wet vs dry, density shifts) modifies payload mass and thus GVW distribution. The most robust implementations embed uncertainty quantification (e.g., Monte Carlo on RRC and grade inputs) and link directly to mine planning software (e.g., Deswik, MineSuite) to evaluate trade-offs between haul road maintenance cost, energy cost, and production schedule adherence.
🔄 Engineering Workflow
📋 Decision Guide
| Rock/Field Condition | Recommended Design Action |
|---|---|
| High-Grade Haul Route (>8% ascending, >6% descending) with frequent stops | Deploy battery-electric trucks with high-torque low-RPM motors and ≥40% regen recovery; optimize haul cycle sequencing to maximize downhill regeneration |
| Low-Grade, Long-Haul (>3 km round trip), Dry Gravel Surface (RRC ≈ 0.015) | Use high-efficiency diesel-electric drives (e.g., AC traction) with predictive cruise control; avoid oversizing battery capacity if electrifying |
| Underground Ramp System (8–10% grade, confined ventilation, limited charging infrastructure) | Select trolley-assisted or opportunity-charged battery-electric trucks with thermal management; model battery SOH degradation using real-world charge/discharge profiles |
| Mixed Fleet Operation (Diesel + Battery-Electric) on Shared Haul Roads | Implement dynamic traffic management (DTM) to separate high-braking-demand descents for electric units; calibrate fuel/energy models using shared GNSS-telematics datasets |
📊 Key Properties & Parameters
Gross Vehicle Weight (GVW)
210–400 tonnes (off-highway rigid frame haul trucks)Total mass of the fully loaded truck including chassis, engine/battery, fuel/electrolyte, operator, and payload.
Dominates tractive effort requirement and regenerative braking potential; directly scales rolling resistance and grade-related power demand.
Road Grade Profile
−8% to +12% (common in open-pit mines; ±0.14 rad)Vertical slope (as % or radians) along the haul cycle, derived from high-resolution DEMs or survey-grade GNSS.
Grades >5% increase diesel fuel use by 20–40% per km; governs optimal gear selection and electric motor thermal derating.
Rolling Resistance Coefficient (RRC)
0.012–0.035 (gravel, well-maintained haul roads)Dimensionless factor representing energy loss due to tire deformation and road surface interaction, normalized per unit weight.
A 0.005 increase in RRC raises fuel consumption by ~7–9% at constant speed; highly sensitive to road moisture, aggregate size, and compaction.
Drive-Train Efficiency (η)
0.32–0.38 (diesel-mechanical), 0.82–0.89 (battery-electric drivetrain, including inverter & motor losses)Ratio of mechanical power delivered to wheels versus chemical (diesel) or electrical (battery) input power.
Lower η forces higher fuel/energy throughput to achieve same work — critical for TCO analysis and battery sizing.
Regenerative Braking Recovery Rate
25–45% (modern battery-electric haul trucks; <5% for diesel-hydraulic retarders)Fraction of kinetic + potential energy recovered during descent and braking, stored back in battery or dissipated.
Each 10% improvement reduces net energy consumption by 3–6% on mixed-grade cycles — decisive for ROI on electrification.
📐 Key Formulas
Tractive Power Requirement
P_trac = (m·g·sinθ + m·a + C_r·m·g·cosθ + 0.5·ρ·C_d·A·v²) · vInstantaneous mechanical power needed at wheels to overcome grade, acceleration, rolling resistance, and aerodynamic drag.
| Symbol | Name | Unit | Description |
|---|---|---|---|
| P_trac | Tractive Power | W | Instantaneous mechanical power needed at the wheels |
| m | Vehicle Mass | kg | Total mass of the vehicle |
| g | Gravitational Acceleration | m/s² | Standard acceleration due to gravity |
| θ | Road Grade Angle | rad | Angle of incline (positive uphill) |
| a | Vehicle Acceleration | m/s² | Longitudinal acceleration of the vehicle |
| C_r | Rolling Resistance Coefficient | dimensionless | Coefficient representing resistance due to tire deformation and road interaction |
| ρ | Air Density | kg/m³ | Mass density of ambient air |
| C_d | Drag Coefficient | dimensionless | Dimensionless quantity quantifying aerodynamic drag |
| A | Frontal Area | m² | Projected cross-sectional area of the vehicle perpendicular to motion |
| v | Vehicle Speed | m/s | Instantaneous forward speed of the vehicle |
Diesel Fuel Consumption (Volumetric)
Ḟ_fuel = (P_e · BSFC) / (ρ_fuel · η_trans)Volumetric fuel flow rate based on engine brake power, brake-specific fuel consumption, fuel density, and transmission efficiency.
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Ḟ_fuel | Volumetric fuel flow rate | m³/s | Volume of diesel fuel consumed per unit time |
| P_e | Engine brake power | W | Effective mechanical power output of the engine |
| BSFC | Brake-specific fuel consumption | kg/(kW·h) or kg/J | Mass of fuel consumed per unit energy output of the engine |
| ρ_fuel | Fuel density | kg/m³ | Mass per unit volume of diesel fuel |
| η_trans | Transmission efficiency | dimensionless | Ratio of output power to input power of the transmission system |
Battery Energy Consumption (Net)
E_net = ∫(P_batt(t) dt) = ∫((P_trac(t)/η_mot·inv) + P_aux(t)) dt − E_regenNet battery energy used per haul cycle, accounting for drivetrain losses, auxiliaries, and regenerative recovery.
| Symbol | Name | Unit | Description |
|---|---|---|---|
| E_net | Net Battery Energy Consumption | Joules (J) or kWh | Net energy drawn from the battery per haul cycle, accounting for traction power losses, auxiliary loads, and subtracting regenerated energy |
| P_batt(t) | Battery Power | Watts (W) | Instantaneous power delivered by the battery at time t |
| P_trac(t) | Traction Power | Watts (W) | Instantaneous mechanical power delivered to the wheels at time t |
| η_mot·inv | Motor-Inverter Efficiency | dimensionless | Combined efficiency of motor and inverter converting battery electrical power to mechanical traction power |
| P_aux(t) | Auxiliary Power | Watts (W) | Instantaneous power consumed by auxiliary systems (e.g., cooling, lighting, HVAC) at time t |
| E_regen | Regenerated Energy | Joules (J) or kWh | Total energy recovered and returned to the battery during braking/regeneration per haul cycle |
🏭 Engineering Example
Chuquicamata Open Pit, Codelco, Chile
Porphyry copper ore (in situ density 2.65 g/cm³; blasted muck density 1.82 g/cm³)🏗️ Applications
- Mine fleet decarbonization roadmap development
- Haul road design optimization (grade smoothing, camber, surfacing)
- Battery procurement & charging infrastructure sizing
- Real-time dispatch optimization (energy-aware routing)
📋 Real Project Case
Chilean Copper Mine: Autonomous Haul Fleet Deployment
A Tier-1 copper mine in the Atacama Desert, northern Chile, deployed an autonomous haul fleet across its open-pit operation. The site processes ~450 ktpd of ore and waste, with a 2.8-km average haul distance and 320-m vertical lift. The project involved retrofitting and integrating 42 autonomous 290-tonne CAT 794 AC electric drive haul trucks into existing dispatch and traffic management systems.