๐ Lesson 3
D3
Rolling Resistance, Grade Resistance & Tractive Effort
Rolling resistance is the force that slows down a vehicle moving on a surface because of how the tires and ground deform; grade resistance is the extra force needed to pull a vehicle uphill (or saved when going downhill); tractive effort is the total pulling force the engine can deliver to move the vehicle.
๐ฏ Learning Objectives
- โ Calculate rolling resistance and grade resistance for haul trucks operating on mine haul roads
- โ Analyze tractive effort curves to determine maximum sustainable grade for a given truckโload combination
- โ Apply adhesion limits and powerโspeed relationships to diagnose hauling bottlenecks
- โ Design haul road gradients that balance energy efficiency and equipment utilization
๐ Why This Matters
In open-pit mines, 30โ40% of total operating costs stem from haulage โ and over 70% of haul truck fuel consumption is spent overcoming rolling and grade resistance. Misestimating these forces leads to underutilized trucks, excessive tire wear, premature engine failure, or unsafe operation on steep grades. Mastering these fundamentals enables engineers to optimize fleet selection, road design, and dispatch strategies โ directly impacting safety, cost, and sustainability.
๐ Core Principles
Rolling resistance arises from hysteresis losses in tires, road surface deformation (especially on gravel), and bearing friction โ modeled as a coefficient (a) multiplied by gross vehicle weight. Grade resistance depends solely on vehicle mass and road inclination: it increases linearly with grade % (approximated as sinฮธ โ tanฮธ for small angles). Tractive effort bridges mechanical power and adhesion: it must exceed total resistance (rolling + grade + acceleration) to move the vehicle, but cannot exceed the product of axle weight and coefficient of adhesion (typically 0.6โ0.8 on dry gravel). Power-limited tractive effort declines with speed (TE = Power / Speed), while adhesion-limited TE caps the maximum usable force at low speeds.
๐ Key Calculation
The total resistance (R_total) a haul truck must overcome is the sum of rolling resistance (R_r), grade resistance (R_g), and acceleration resistance (often neglected in steady-state analysis). Tractive effort (TE) must satisfy TE โฅ R_total while respecting adhesion limits. The most critical design check compares available TE at crawl speed against R_total on the steepest segment.
๐ก Worked Example
Problem: A 220-tonne payload CAT 797F operates on a 10% grade (5.71ยฐ) haul road with rolling resistance coefficient a = 0.03. Gross vehicle weight = 360 tonnes. Adhesion coefficient ฮผ = 0.7. Engine-rated drawbar pull at 0 km/h = 950 kN. Calculate total resistance and verify if tractive effort is sufficient.
1.
Step 1: Convert gross weight to force: W = 360,000 kg ร 9.81 m/sยฒ = 3,531,600 N โ 3532 kN
2.
Step 2: Rolling resistance R_r = a ร W = 0.03 ร 3532 kN = 105.96 kN
3.
Step 3: Grade resistance R_g = W ร sin(5.71ยฐ) โ 3532 kN ร 0.10 = 353.2 kN (since grade % โ sinฮธ for small ฮธ)
4.
Step 4: R_total = R_r + R_g = 105.96 + 353.2 = 459.2 kN
5.
Step 5: Compare to available TE = 950 kN > 459.2 kN โ sufficient. Also check adhesion limit: ฮผ ร axle weight (assume 80% on drive axles) = 0.7 ร 0.8 ร 3532 kN = 1978 kN > 950 kN โ not adhesion-limited.
Answer:
The total resistance is 459 kN; available tractive effort (950 kN) exceeds this by >100%, confirming safe operation on this grade.
๐๏ธ Real-World Application
At BHPโs Escondida copper mine (Chile), haul road redesign reduced average grade from 8.5% to 6.2% and improved surfacing to lower rolling resistance coefficient from 0.042 to 0.028. This cut average fuel consumption per tonne-km by 14%, extended tire life by 22%, and enabled a 12% increase in effective payload utilization โ all validated using rolling/grade resistance models aligned with SAE J2264 and SME Guidelines for Haul Road Design.
๐ Case Connection
๐ Canadian Gold Mine: Steep Ramp Optimization in Narrow Vein Underground
Excessive truck cycle times and premature tire/brake wear due to suboptimal ramp gradient (15%) combined with tight hori...