Calculate rolling resistance force (F_rr = Crr · N), power loss (P_rr = F_rr · v), normal load, specific energy consumption (Wh/km), and tire pressure adjustments with the free in-browser Rolling Resistance Calculator.
5.48 HP • Rolling Force: 147.1 N (33.07 lbf) • Energy Rate: 40.86 Wh/km
33.07 lbf
4,086 W
mg·cosθ
65.8 kWh/100mi
Crr · g
v² / (2 · Crr · g)
Rolling resistance (also known as rolling friction or rolling drag) is the retarding force opposing the motion of a rolling wheel or tire along a surface. Unlike static or kinetic sliding friction, over \(90\%\) of rolling resistance in pneumatic tires is caused by viscoelastic hysteresis—the repeated compression and relaxation of the tire tread and sidewalls as the contact patch rolls over the ground:
Polymer chains in tire rubber do not return \(100\%\) of the energy absorbed during compression at the leading edge of the contact patch. The unrecovered energy dissipates as heat.
Microscopic slip between the flattened tire tread elements and the road surface creates localized shear friction, wearing tread blocks and consuming kinetic energy.
On compliant terrain (gravel, grass, sand), the wheel actively pushes a bow wave of displaced material forward, significantly elevating the effective \(C_{rr}\).
Deriving the governing equations for rolling force, power dissipation, and specific energy rates:
| Physical Quantity | Mathematical Formula | Engineering Description |
|---|---|---|
| Rolling Resistance Force (\(F_{rr}\)) | $$F_{rr} = C_{rr} \cdot N = C_{rr} \cdot m g \cos\theta$$ | Net retarding force opposing forward travel |
| Rolling Resistance Power Loss (\(P_{rr}\)) | $$P_{rr} = F_{rr} \cdot v = C_{rr} \cdot m g \cos\theta \cdot v$$ | Continuous power required to overcome tire drag (kW / HP) |
| Energy Consumption Rate (\(E_{\text{rate}}\)) | $$\text{Wh/km} = \frac{F_{rr}}{3.6} \qquad \text{kWh/100mi} = \frac{F_{rr} \times 0.1609344}{3.6}$$ | Electric vehicle specific battery consumption per distance |
| Flat Coast-Down Stop Distance (\(d_{\text{coast}}\)) | $$d_{\text{coast}} = \frac{v^2}{2 C_{rr} g}$$ | Theoretical roll-out distance purely from rolling drag |
Input the curb weight plus cargo/passengers in \(\text{kg}\), \(\text{lbs}\), or metric tonnes.
Choose from standard presets (passenger car, EV low-rolling-resistance, bicycle, train, heavy truck) or enter a custom \(C_{rr}\).
Provide cruising speed (\(\text{km/h}\) or \(\text{mph}\)) and any hill slope angle (\(\theta\)) in degrees.
Inspect dynamic power loss in \(\text{kW}\) and \(\text{HP}\), specific energy consumption in \(\text{Wh/km}\), and the step-by-step LaTeX proof.
Standard empirical \(C_{rr}\) values measured across automotive, rail, and cycling applications:
Sub-millimeter deflection yields ultra-low energy loss
High-TPI supple cotton/silk casing at 80 psi
Silica-infused tread compound maximizes battery range
All-season radial tire on smooth asphalt road
Why maintaining manufacturer cold tire pressure saves energy and fuel:
Under-inflation increases the contact patch area and causes excessive cyclic flexing of the tire sidewalls, elevating hysteresis energy loss:
A \(20\%\) drop in tire pressure (e.g. from \(35\text{ psi}\) to \(28\text{ psi}\)) increases rolling resistance by approximately \(12\%\), reducing overall EV battery range by \(3-5\%\) and accelerating uneven shoulder tread wear.
Accurately models passenger cars, EVs, heavy semi-trucks, road bicycles, and steel rail locomotives.
Accounts for road grade angles (\(N = mg\cos\theta\)) during uphill climbs and mountain descents.
Displays power in \(\text{kW}\) and \(\text{HP}\), force in \(\text{N}\) and \(\text{lbf}\), and energy in \(\text{Wh/km}\) and \(\text{kWh/100mi}\).
Calculates theoretical flat deceleration rates (\(a_{rr} = C_{rr}g\)) and coasting stopping distances.
Renders clear algebraic derivations showing live variable substitutions.
Executes instantly on client device without server latency or data collection.
Understanding which retarding force dominates at different road speeds:
Total vehicle driving resistance equals rolling drag plus aerodynamic air drag:
Because rolling resistance is linear with speed (\(P_{rr} \propto v\)) while aerodynamic drag grows cubically (\(P_d \propto v^3\)), rolling resistance dominates at speeds below \(75\text{ km/h}\) (\(45\text{ mph}\)) (city driving), whereas aerodynamic drag dominates at highway cruising speeds.
Enables EV drivers and engineers to calculate exactly how much battery power is consumed by tire hysteresis per kilometer.
Assists freight fleet managers in calculating return-on-investment (ROI) when retrofitting semi-trucks with SmartWay-verified low-resistance tires.
How low-rolling-resistance tires extend battery range on heavy electric vehicles:
Because battery packs add \(400-600\text{ kg}\) of mass, electric vehicles experience higher normal contact loads (\(N = mg\)). For a \(2,100\text{-kg}\) EV cruising at \(100\text{ km/h}\), standard tires (\(C_{rr} = 0.010\)) consume \(5.72\text{ kW}\) of continuous power (\(57.2\text{ Wh/km}\)). Switching to EV-specific silica-infused tires (\(C_{rr} = 0.007\)) cuts rolling power loss to \(4.01\text{ kW}\), saving \(17.1\text{ Wh/km}\) and adding up to \(40\text{ km}\) (\(25\text{ miles}\)) of range per full battery charge.
How competitive cyclists minimize mechanical power losses:
Fine 320 TPI corespun cotton and silk casings deform over road irregularities with minimal internal shear, cutting \(C_{rr}\) below \(0.0030\).
Eliminating butyl inner tubes removes friction between the tube and tire casing, saving \(3-6\text{ Watts}\) of rider output per wheel at \(40\text{ km/h}\).
How Class 8 semi-truck fleets reduce diesel consumption across 18 rolling tires:
A loaded \(36,000\text{-kg}\) semi-truck traveling at \(90\text{ km/h}\) expends approximately \(53.0\text{ kW}\) (\(71.0\text{ HP}\)) overcoming rolling drag at \(C_{rr} = 0.0060\). Reducing fleet average \(C_{rr}\) to \(0.0048\) through SmartWay low-drag tires reduces continuous rolling resistance power demand by \(10.6\text{ kW}\), saving over \(2,400\text{ liters}\) (\(630\text{ gallons}\)) of diesel per tractor-trailer annually.
How factory robotics engineers calculate wheel torque and battery requirements:
Solid polyurethane wheels on smooth warehouse epoxy exhibit \(C_{rr} \approx 0.015-0.025\), requiring steady tractive effort under heavy pallet loads.
For a \(1,200\text{-kg}\) AGV with \(100\text{-mm}\) radius wheels (\(r = 0.10\text{ m}\)), rolling resistance force is \(F_{rr} = 235.4\text{ N}\), requiring total continuous motor torque of \(T = F_{rr} \cdot r = \mathbf{23.54\text{ N}\cdot\text{m}}\).
Why vehicle energy consumption spikes in sub-zero winter temperatures:
Tire rubber polymers become stiffer at low ambient temperatures (\(0^\circ\text{C} / 32^\circ\text{F}\)), shifting the rubber loss tangent (\(\tan\delta\)) and elevating hysteresis loss by \(20\%\) to \(30\%\) until driving friction warms the tire carcass to operating equilibrium (\(45^\circ\text{C}-60^\circ\text{C}\)).
How automotive testing standards model high-speed tire drag:
At autobahn velocities (\(v > 130\text{ km/h}\)), centrifugal standing waves form in the tire belt package, causing non-linear increases in \(C_{rr}\) that automotive engineers capture using quadratic velocity coefficients (\(c \cdot v^2\)).
Comprehensive answers to common questions about rolling resistance formulas, Crr coefficients, EV range optimization, and tire pressure physics.
