How to Calculate Road Load: Step-by-Step
This guide explains how to calculate road load — the total resistive force a vehicle must overcome to move at a constant speed on a level road. You’ll need vehicle parameters (mass, drag coefficient, frontal area) and test data (coast-down times or speed vs. time). By the end, you’ll have a road load equation in the standard form F = A + B·v + C·v², which is used for fuel economy testing, chassis dynamometer settings, and range estimates for EVs.
What You’ll Need
- Vehicle mass (kg or lb) — from the owner’s manual or a weighbridge
- Aerodynamic drag coefficient (Cd) — from manufacturer data or published tests
- Frontal area (m² or ft²) — from manufacturer specs or approximate from width × height × 0.8
- Tire rolling resistance coefficient (Crr) — typically 0.008–0.015 for passenger car tires on asphalt
- Coast-down data: time and speed readings as the vehicle decelerates in neutral on a flat road (or a dynamometer)
- Air density (�) — about 1.225 kg/m³ at sea level, 15°C; adjust for altitude/temperature
- Spreadsheet or calculator for regression
Step-by-Step
- Gather vehicle data. Record mass (m), drag coefficient (Cd), frontal area (A_f), and rolling resistance coefficient (Crr). If you don’t have Cd or A_f, you can estimate from similar vehicles, but the result will be less accurate.
- Measure coast-down data. On a flat, dry road with no wind, accelerate to a safe speed (e.g., 100 km/h), shift to neutral, and record speed vs. time using a GPS logger or a stopwatch and speedometer. Repeat 3–5 times in both directions to cancel wind and slope effects.
- Convert speeds to m/s. If you recorded in km/h, divide by 3.6. If in mph, multiply by 0.44704. Time should be in seconds.
- Calculate deceleration. For each pair of consecutive speed readings, compute the average speed and the deceleration:
a = (v2 – v1) / (t2 – t1) — note this will be negative. - Compute force. The road load force at each average speed is F = m × |a| (mass times the magnitude of deceleration). Add any known grade force if the road isn’t perfectly flat (F_grade = m·g·sinθ).
- Fit the road load equation. Plot F (y-axis) vs. speed v (x-axis). Fit a quadratic polynomial: F = A + B·v + C·v². Use spreadsheet regression (e.g., LINEST in Excel) or a calculator. The coefficients A, B, C are your road load parameters.
- Alternative: use known coefficients. If you can’t do a coast-down test, calculate the components directly:
Rolling resistance F_rr = m·g·Crr (constant with speed)
Aerodynamic drag F_aero = 0.5·�·Cd·A_f·v²
Then A = F_rr (plus any drivetrain losses), B = 0 (if no speed-dependent term), C = 0.5·�·Cd·A_f. - Validate. Compare your calculated force at a few speeds with the measured coast-down data. If they differ by more than 10%, recheck your mass, Cd, or test conditions.
Common Mistakes
- Unit mix-ups: Using km/h in the formula that expects m/s. Always convert speed to m/s before squaring.
- Ignoring wind: A headwind or tailwind changes the effective speed. Test in calm conditions or average runs in both directions.
- Not accounting for road slope: Even a slight grade adds a large force. Use a flat road or measure the slope and subtract it.
- Using wrong air density: At high altitude or high temperature, � is lower. Use � = 1.225 × (273/(273+T)) × (P/101325) for corrections.
- Forgetting drivetrain losses: The coast-down method includes them, but the component method does not. Add a 5–15% factor if needed.
Tips
- Use a GPS-based accelerometer for smoother speed data than a speedometer.
- Perform coast-down tests at steady speeds, not during gear changes.
- If you’re setting a dynamometer, use the coefficients directly: A, B, C are the load settings.
- For electric vehicles, the same method works; just ensure the drivetrain is in neutral or the motor is disconnected.
- When fitting the quadratic, force the intercept A to be positive (it represents rolling resistance).
Troubleshooting
- If your fitted B coefficient is negative: This can happen with noisy data. It’s physically unlikely; try averaging multiple runs or using a linear fit for low speeds only.
- If the force at low speeds is too high: Check for brake drag or tire pressure. Also make sure the vehicle is in neutral, not in gear.
- If the coast-down data is scattered: Wind is the usual culprit. Re-test on a calmer day, or use a wind sock to confirm.
- If your calculated C is far from expected: Verify the frontal area. A common error is using width × height without the 0.8 correction for rounded corners.
- If you don’t have Cd or A_f: You can still get A, B, C from coast-down data alone — that’s the beauty of the method. Just ensure you have enough data points (at least 10 speeds).
Frequently Asked Questions
What is road load in simple terms?
It’s the sum of all forces that resist a vehicle’s motion: rolling resistance (constant), drivetrain friction (roughly constant), and aerodynamic drag (increases with the square of speed).
Why is road load expressed as a quadratic equation?
Because the forces are either constant (rolling) or proportional to v² (aerodynamic). The linear term B·v is often small and represents speed-dependent bearing losses, but it’s included for accuracy.
Can I calculate road load without a coast-down test?
Yes, if you know mass, Crr, Cd, and frontal area. Use the component method: A = m·g·Crr, C = 0.5·�·Cd·A_f, and B = 0. The result is an estimate; coast-down gives the actual values.
What is the typical range for road load coefficients?
For a mid-size car: A ≈ 100–300 N, B ≈ 0–1 N/(m/s), C ≈ 0.3–0.6 N/(m/s)². For a large SUV, C can be 0.8 or higher.
How do I convert road load to power?
Power (W) = Force (N) × Speed (m/s). So P = A·v + B·v² + C·v³. This is useful for estimating engine or motor power required at a given speed.
Does road load change with tire pressure?
Yes. Lower tire pressure increases rolling resistance (higher A). Always test at the recommended pressure for consistent results.
Related
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.