Sample cases for quick verification
| Mass (kg) | Grade (%) | Crr | Speed (km/h) | Total resistance (kN) | Power (kW) |
|---|---|---|---|---|---|
| 15,000 | 8.0 | 0.020 | 10 | ≈ 12.07 | ≈ 33.5 |
| 30,000 | 5.0 | 0.015 | 15 | ≈ 15.09 | ≈ 62.9 |
| 8,500 | 12.0 | 0.030 | 6 | ≈ 10.90 | ≈ 18.2 |
How gradient resistance is calculated
Gradient resistance is the component of weight acting along the slope. For a grade ratio g = rise/run, the slope angle is θ = atan(g).
- Weight (N) = mass × 9.80665 (when using mass)
- Grade (%) = 100 × rise/run
- Gradient resistance = Weight × sin(θ)
- Rolling resistance = (Weight × cos(θ)) × Crr
- Total resistance = gradient + rolling
- Power (W) = total resistance × speed (m/s)
The calculator uses the trigonometric form for accuracy, especially on steeper grades.
Steps to run a reliable check
- Select whether you are entering mass or force.
- Choose slope input: grade, rise/run, or angle.
- Set rolling resistance to match the travel surface.
- Optionally add speed to estimate power demand.
- Apply a safety factor for conservative planning.
- Press Calculate, then export CSV or PDF if needed.
Use the Notes field to capture route assumptions for reporting.
Why gradient resistance matters on site routes
When a loaded vehicle climbs a ramp or haul road, part of its weight acts along the slope and becomes a resisting force. This resistance increases fuel use, reduces speed, and can exceed available tractive effort. For planning, resistance is best expressed in kilonewtons so different loads and grades can be compared.
Interpreting grade, rise/run, and angle inputs
Grade percentage is a measure: grade(%) = 100 × rise/run. A 10% grade means 1 m rise over 10 m run. The calculator converts any slope entry into a grade ratio and a slope angle, so the trigonometric relationships remain accurate on steeper sections and short ramps. For long routes, evaluate each segment separately to identify the controlling steep section.
Rolling resistance and surface condition effects
Rolling resistance depends on surface type, tire condition, and compaction. Typical coefficients range from about 0.01 for smooth paved travel to 0.02–0.06 for unsealed or soft surfaces. Because normal force drops slightly as slopes steepen, rolling resistance is computed from Weight × cos(θ), not from weight alone. Small changes in Crr can meaningfully change the total, especially on low grades where rolling dominates.
Power demand at speed and productivity checks
If speed is provided, the calculator estimates power using P = total resistance × speed. For example, a 15,000 kg load on an 8% grade with Crr = 0.02 produces about 12.07 kN total resistance. At 10 km/h (2.78 m/s), that is roughly 33.5 kW at the wheels, before drivetrain losses.
Using safety factors and exporting reports
Safety factors help cover moisture, rutting, rolling stock variability, and operator behavior. A factor of 1.10 to 1.30 is often used for conservative planning, while commissioning checks may use 1.00 with measured inputs. After calculation, export CSV for estimating worksheets or PDF for submittals, daily reports, and inspection records. If a route includes downhill travel, report the uphill segments separately, since braking performance and traction limits are managed differently.
FAQs
1) What is gradient resistance?
It is the component of weight acting parallel to the slope, resisting uphill motion. It increases with grade and load, and it is calculated using the slope angle derived from the grade ratio.
2) Should I enter mass or weight?
Use mass when you know kilograms from load tickets or equipment specs. Use weight/force when the load is provided as kN, N, or lbf from a manufacturer chart or a measured pull test.
3) What rolling resistance coefficient should I use?
Start with 0.01 for smooth paved access roads, 0.02 for well-compacted gravel, and 0.03–0.06 for soft, rutted, or muddy routes. Adjust using site observations and equipment performance.
4) Why does the calculator use trigonometry?
Trigonometric terms model the slope accurately by splitting weight into parallel and normal components. This improves accuracy on steeper grades compared with small-angle approximations.
5) What does “design total” mean?
Design total is total resistance multiplied by the safety factor. It is a conservative force you can use for equipment sizing, haul road planning, and verifying that available traction is adequate.
6) Is the power result the engine power?
No. The power shown is the mechanical power required at the wheels based on resistance and speed. Engine power must be higher to cover drivetrain losses, accessory loads, and transient conditions.