Rolling Resistance Calculator

General Physics

This tool calculates the force of rolling resistance and the power required to overcome it. Enter the parameters below to get started.

Practical Examples

Explore these common scenarios to understand how the calculator works.

Standard Passenger Car

Car on Asphalt

A typical car driving on a standard asphalt road.

Crr: 0.012, Mass: 1500 kg

Gravity: 9.807 m/s², Velocity: 100 kmh

Racing Bicycle on Concrete

Bicycle

A professional racing bicycle on a smooth concrete surface.

Crr: 0.005, Mass: 85 kg

Gravity: 9.807 m/s², Velocity: 40 kmh

Heavy Truck on a Highway

Truck

A fully loaded semi-truck traveling at highway speed.

Crr: 0.007, Mass: 40000 lb

Gravity: 9.807 m/s², Velocity: 65 mph

Mars Rover Exploration

Rover on Mars

Calculating the rolling resistance for a rover on the Martian surface.

Crr: 0.15, Mass: 900 kg

Gravity: 3.721 m/s², Velocity: 0.1 ms

Other Titles
Understanding the Rolling Resistance Calculator: A Comprehensive Guide
Delve into the physics of rolling resistance, its calculation, real-world implications, and the science behind this powerful tool.

What is Rolling Resistance?

  • Defining the Force
  • Factors Influencing Rolling Resistance
  • Rolling Resistance vs. Other Frictional Forces
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed.
Key Influencing Factors
Several factors affect the magnitude of rolling resistance: the material of the wheel and surface, the radius of the wheel, the normal force pushing the objects together, and the surface adhesion and deformation.
Distinction from Sliding Friction
Unlike sliding friction, which occurs between surfaces in relative sliding motion, rolling resistance occurs when one object rolls over another. It is generally much lower than sliding friction, which is why wheels are a fundamental invention for transportation.

Step-by-Step Guide to Using the Rolling Resistance Calculator

  • Inputting the Coefficient
  • Entering Mass and Gravity
  • Specifying Velocity for Power Calculation
Our calculator simplifies the process of determining rolling resistance. Follow these steps for an accurate calculation.
1. Enter the Rolling Resistance Coefficient (Crr)
This dimensionless value is crucial. You can find typical values for different material pairings online or in engineering handbooks. For example, car tires on asphalt typically have a Crr between 0.010 and 0.015.
2. Provide Mass and Gravity
Enter the object's mass and select the appropriate unit. The calculator uses this to determine the normal force (N = m * g). You can use Earth's gravity or select another celestial body for different scenarios.
3. Set the Velocity
To calculate the power required to overcome rolling resistance, you must provide the object's velocity. Ensure you select the correct unit (m/s, km/h, or mph).

Calculation Example

  • Force (Frr) = 0.012 * 1500 kg * 9.807 m/s² = 176.53 N
  • Power = 176.53 N * 27.78 m/s (100 km/h) = 4903.7 Watts

Real-World Applications of Rolling Resistance

  • Automotive Industry and Fuel Efficiency
  • Railway Engineering
  • Sports Science and Equipment Design
The concept of rolling resistance is not just academic; it has significant real-world consequences across various fields.
Vehicle Fuel Economy
In the automotive industry, rolling resistance is a major contributor to a vehicle's energy consumption. A significant portion of a car's fuel is used to overcome this force. Designing low-resistance tires is a key strategy for improving fuel efficiency.
Railways
Trains are highly efficient largely because of the very low rolling resistance of steel wheels on steel rails. Understanding this allows for the design of transportation systems that can move massive amounts of freight with minimal energy.
Bicycle and Sports Performance
In competitive cycling, minimizing rolling resistance is critical for performance. Tire pressure, material, and width are all optimized to reduce this force and allow for greater speeds.

Common Misconceptions and Correct Methods

  • Is Rolling Resistance Constant with Speed?
  • The Effect of Tire Pressure
  • Ignoring Power Calculation
There are several common misunderstandings about rolling resistance. Clarifying these is key to accurate analysis.
Speed's Influence on Crr
While our basic model assumes a constant Crr, it can actually vary slightly with speed. For most everyday calculations, this effect is negligible, but it can be a factor in high-performance applications. Our calculator uses a simplified model that assumes Crr is independent of speed.
Tire Pressure is Key
It's a common myth that a softer, under-inflated tire provides better grip and lower resistance. In reality, under-inflation increases the contact patch and tire deformation, which significantly increases rolling resistance and wastes fuel.
Force vs. Power
It's important to distinguish between the rolling resistance force and the power required to overcome it. The force is independent of speed, but the power (energy per unit time) is directly proportional to it. A higher speed requires proportionally more power to counteract the same resistance force.

Mathematical Derivation and Formulas

  • The Core Formula
  • Calculating Normal Force
  • Deriving Power from Force
The Rolling Resistance Force Formula
The fundamental equation used by the calculator is:
Frr = Crr * N
Where:
- Frr is the rolling resistance force.
- Crr is the dimensionless rolling resistance coefficient.
- N is the normal force.
Calculating the Normal Force (N)
The normal force is the force perpendicular to the surface of travel. On a flat, horizontal surface, it is equal to the object's weight:
N = m * g
Where 'm' is mass and 'g' is the acceleration due to gravity.
The Power Calculation
Power is the rate at which work is done. It is calculated by multiplying the force by the velocity:
P = Frr * v
Where 'v' is the velocity of the object.