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Rolling Rersistance

 

Rolling Resistance with Weight Formula

\( F_r \;=\;  \dfrac{ C_r \cdot w }{ r }\)     (Rolling Resistance with Weight)

\( C_r \;=\; \dfrac{ F_r \cdot r }{ w }\)

\( w \;=\; \dfrac{ F_r \cdot r }{ C_r }\)

\( r \;=\; \dfrac{ C_r \cdot w }{ F_r }\)
Symbol English Metric
\( F_r \) = Rolling Resistance \( lbf \) \( N \)
\( C_r \) = Rolling Resistance Coefficient \( dimensionless \) \( dimensionless \)
\( w \) = Object Weight \( lbf \) \( N \)
\( r \) = Radius \( in \) \( m \)

Rolling rersistance, abbreviated as \(F_r\), is the force that opposes the motion of a tire as it rolls along a surface.  It's one of the factors that affect the energy efficiency and fuel consumption of vehicles.  When a vehicle's tires make contact with the road or any other surface, there is a deformation of the tire's rubber, and this deformation results in a resistance to motion.

Rolling Resistance with Gravity Formula

\( F_r \;=\; C_r \cdot m \cdot g \)     (Rolling Resistance with Gravity)

\( C_r \;=\; \dfrac{ F_r }{ m \cdot g }\)

\( m \;=\; \dfrac{ F_r }{ C_r \cdot g }\)

\( g \;=\; \dfrac{ F_r }{ C_r \cdot m }\)
Symbol English Metric
\( F_r \) = Rolling Resistance \( lbf \) \( N \)
\( C_r \) = Rolling Resistance Coefficient \( dimensionless \) \( dimensionless \)
\( m \) = Object Mass \( lbm \) \( kg \)
\( g \) = Gravity \(ft\;/\;sec^2\) \(m\;/\;s^2\)
Factors Contribute to Rolling Resistance
Tire construction  -  The design and construction of the tire, including its tread pattern, materials, and internal structure, can significantly impact rolling resistance.  Tires designed for higher fuel efficiency often have lower rolling resistance.
Tire inflation pressure  -  Underinflated tires can increase rolling resistance because a larger portion of the tire's surface area comes into contact with the road, leading to more deformation and greater resistance.
Road surface  -  The type and condition of the road or surface on which the tires are rolling can affect rolling resistance.  Smoother, well maintained roads generally result in lower rolling resistance compared to rough or uneven surfaces.
Load on the tire  -  Heavier loads placed on a tire can increase rolling resistance, as they cause more tire deformation and contact with the road.
Speed  -  Rolling resistance tends to increase with higher speeds due to the increased deformation of the tire at higher velocities.

Reducing rolling resistance is important for improving the fuel efficiency of vehicles.  Many modern vehicles are equipped with tires designed to minimize rolling resistance, and proper tire maintenance, such as maintaining the correct tire pressure, also helps reduce this resistance.  Lower rolling resistance means that less energy is required to keep the vehicle moving, which can result in improved fuel economy and reduced greenhouse gas emissions. 

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