Zerdly

Haul Road Grade Resistance Calculator

Grade resistance is the component of the truck's weight acting down the slope.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the gross vehicle weight (GVW) in tonnes — the loaded truck mass (empty vehicle weight plus payload), not just the payload.
  2. Enter the ramp grade in percent (a 1-in-12.5 ramp is 8%). Use a negative value for a downgrade.
  3. Enter the rolling resistance in percent — typically 2–4% on a well-maintained haul road, higher on soft or rutted surfaces.
  4. Optionally enter usable engine power at the wheels (kW) to get a rough power-limited steady ramp speed, then verify it against the OEM rimpull/retarder chart.

How it works

Grade resistance is the component of the truck's weight acting down the slope. Using the small-angle approximation (sin ~ tan, valid for typical ramps under ~10%), grade resistance force = GVW (t) x 1000 x 9.81 x (grade% / 100), in newtons. Rolling resistance — the loss from tyre flex and surface deformation — is found the same way with the rolling resistance percentage: force = GVW x 1000 x 9.81 x (RR% / 100). A handy rule of thumb is about 10 N of grade resistance per tonne of GVW for each 1% of grade.

Total resistance is simply grade% + rolling% as an effective grade, and the total rimpull the truck must produce to hold a steady speed equals GVW x 1000 x 9.81 x (total% / 100). If you supply usable wheel power, the tool estimates a steady speed from P = F x v, so speed (m/s) = power (W) / total force (N), then x 3.6 for km/h. This is a power-limited estimate only — it ignores gearing, traction, acceleration and drivetrain losses, so always cross-check the achievable gear and speed on the manufacturer's rimpull chart.

Worked example

240 t truck on an 8% ramp with 3% rolling resistance. A 240 t (GVW) rear-dump climbs a 1-in-12.5 ramp (8% grade) on a maintained road with 3% rolling resistance. Weight force = 240 x 1000 x 9.81 = 2,354,400 N. Grade resistance = 2,354,400 x 8% = 188.35 kN; rolling resistance = 2,354,400 x 3% = 70.63 kN; total = 258.98 kN at an 11% effective grade. With 1,500 kW usable at the wheels, the power-limited steady speed is 1,500,000 / 258,984 = 5.79 m/s = 20.9 km/h — a first-pass number to check against the OEM rimpull chart.

Common mistakes

  • Entering payload instead of GVW. Grade and rolling resistance act on the whole loaded truck, so use gross vehicle weight (empty mass plus payload), not the payload alone.
  • Confusing grade percent with degrees or a 1-in-N ratio. An 8% grade is 1-in-12.5, not 8 degrees. Convert ratios to percent before entering (1-in-10 = 10%).
  • Treating the estimated speed as a guaranteed speed. It is a power-limited steady-state figure ignoring gears and traction — the real achievable gear/speed comes from the OEM rimpull chart, and downhill speed is set by braking/retarder limits, not power.

Frequently asked questions

What rolling resistance should I use for a haul road?

A well-built, well-maintained haul road is typically about 2–3%, and a good sealed or compacted surface can be near 2%. Soft, wet, rutted or poorly maintained roads climb to 4–8% or more. Rolling resistance also rises with tyre penetration into the surface, so it is very sensitive to road maintenance.

Why does grade resistance use sin but the calculator multiplies by grade percent?

Grade resistance is weight x sin(angle), but grade percent is the tangent of the slope angle (rise over run x 100). For the shallow grades on haul roads (under about 10%), sin and tan are almost identical, so multiplying weight by grade% / 100 is accurate to a fraction of a percent. On very steep ramps the small-angle approximation slightly overstates the force.

Can I use this for a downgrade?

Yes — enter a negative grade. The grade resistance then becomes negative (gravity assists the truck), and the total resistance is grade% + rolling%. When the total is zero or negative the tool does not estimate a driving speed, because downhill speed is governed by braking and retarder capacity rather than engine power.

Is the estimated ramp speed reliable for fleet planning?

Treat it as a first-pass sanity check only. It assumes all usable power converts to steady-speed rimpull (P = F x v) and ignores gear steps, traction/coefficient-of-adhesion limits, acceleration and drivetrain losses. Use the OEM rimpull–speed–grade chart for the actual gear and speed, and this tool to understand the resistance the truck is fighting.

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