Input Parameters
Results
Rolling resistance force (Frr): - N
Rolling resistance torque (Trr): - N·m
Power loss due to rolling friction (P): - W
Deceleration if only rolling resistance acts (a): - m/s²
Energy lost over distance (W): - J
| # | Mass (kg) | Crr | Radius (m) | Speed (m/s) | Slope (°) | Normal force (N) | Frr (N) | Trr (N·m) | P (W) | a (m/s²) | Work (J) |
|---|
Example Data Table
The following scenarios illustrate how rolling resistance changes with mass, wheel radius, speed, and the coefficient of rolling resistance.
| Scenario | Mass (kg) | Crr | Radius (m) | Speed (m/s) | Slope (°) |
|---|---|---|---|---|---|
| Warehouse trolley on smooth concrete | 150 | 0.01 | 0.10 | 1.5 | 0 |
| Bicycle on paved road | 85 | 0.004 | 0.35 | 7.0 | 2 |
| Cart on soft soil | 300 | 0.04 | 0.25 | 0.8 | 0 |
| Steel wheel on rail | 1000 | 0.001 | 0.40 | 5.0 | 0 |
Formula Used
Rolling friction (or rolling resistance) is modeled as a force opposing motion due to deformation at the contact between wheel and surface.
- Normal force: N = m · g · cos(θ) (unless overridden).
- Rolling resistance force: Frr = Crr · N.
- Rolling resistance torque: Trr = Frr · r.
- Power loss: P = Frr · v.
- Deceleration (simplified): a = Frr / m.
- Work/energy lost: W = Frr · d.
Here m is mass, g is gravitational acceleration, r is wheel radius, v is linear speed, and d is travel distance.
How to Use This Calculator
- Enter the total mass of the system and choose its unit.
- Specify the rolling resistance coefficient Crr based on wheel and surface.
- Provide the effective wheel radius together with the appropriate length unit.
- Set the linear speed and corresponding unit to evaluate power losses.
- Optionally enter the slope angle, gravity, and travel distance for advanced analysis.
- If you already know the normal force, enter it to override the automatic calculation.
- Click Calculate to compute rolling resistance force, torque, power, deceleration, and energy loss.
- Review the numerical summary and the detailed results table below the calculator.
- Use the CSV or PDF buttons to export your results for documentation or further processing.
This tool is suitable for engineering design studies, educational work, and quick checks of rolling performance in practical applications.
Engineering Insights on Rolling Friction
1. Role of Rolling Resistance in Motion
Rolling resistance determines how much effort is required to keep wheels moving. Even small increases in resistance significantly raise energy demand for vehicles, trolleys, and conveyors, especially when operating continuously under industrial conditions.
2. Influence of Wheel and Surface Materials
The coefficient of rolling resistance heavily depends on material pairing. Hard wheels on smooth, rigid tracks typically show low coefficients, while soft tires on rough or deformable ground generate higher losses and noticeable heat buildup.
3. Effect of Load and Contact Geometry
Increasing load compresses the contact patch between wheel and surface. This changes deformation patterns and can either increase or decrease resistance, depending on material stiffness and wheel diameter chosen during system design.
4. Speed Dependence of Rolling Losses
At low speeds, rolling resistance is dominated by deformation hysteresis. As speed rises, internal damping and temperature effects can increase energy loss, sometimes making rolling resistance comparable to aerodynamic drag in importance.
5. Slope Angle and Required Tractive Effort
When a system moves uphill, rolling resistance adds to the gravitational component of the load. Designers must ensure motors or human operators can overcome both effects without excessive strain or unacceptable speed reduction.
6. Using Calculated Results for System Sizing
Calculated rolling resistance force, torque, and power help size motors, gearboxes, and drive components. Engineers can quickly compare design options, investigate load scenarios, and select appropriate safety factors for long-term reliability.
7. Practical Validation and Safety Margins
Although analytical models are useful, real systems may behave differently due to contamination, wear, misalignment, and temperature variation. Always combine calculator output with tests, standards, and inspection procedures before finalizing designs.
Frequently Asked Questions
1. What does this rolling friction calculator estimate?
It estimates rolling resistance force, torque, power loss, deceleration, and energy dissipated over distance for a wheel-and-load system on a level or inclined surface using typical engineering assumptions.
2. Which value should I use for the rolling resistance coefficient?
Use values from manufacturer data, engineering handbooks, or standards. Different combinations of tire, wheel, track, and temperature conditions produce different coefficients, so choose numbers matching your real application.
3. Why can I override the normal force directly?
Some applications already provide measured or computed normal force from separate structural calculations. Overriding normal force lets you skip mass and slope estimation while still evaluating rolling resistance quickly.
4. Does this tool include aerodynamic drag or bearing friction?
No. The calculator isolates rolling resistance only. Other losses, such as aerodynamic drag, bearing friction, or drive-train inefficiencies, must be estimated separately and combined during overall performance analysis.
5. Can I use it for multiple wheels supporting one load?
Yes. Model the system by distributing the total load across wheels, then summing rolling resistance from each. For identical wheels sharing load equally, divide the mass or normal force by the number of wheels.
6. How accurate are the calculated power and energy losses?
Accuracy depends mainly on input data quality and assumptions. When coefficients, loads, and distances are realistic, results provide useful engineering estimates, but critical designs should always be confirmed through testing and standards.