Rolling Resistance Gradient Split Calculator
Our cycling calculator computes rolling resistance gradient split instantly. Get accurate stats with historical comparisons and benchmarks.
Formula
P_total = (F_rolling + F_gradient + F_aero) x v
Total power equals the sum of rolling resistance force (Crr x m x g x cos(theta)), gradient force (m x g x sin(theta)), and aerodynamic drag force (0.5 x rho x CdA x v^2), all multiplied by velocity in meters per second.
Worked Examples
Example 1: Climbing a 7% Gradient at 15 km/h
Problem: A 70 kg rider with a 8 kg bike climbs a 7% gradient at 15 km/h. Crr = 0.004, CdA = 0.35. What is the power split?
Solution: Speed = 15/3.6 = 4.167 m/s\nRolling force = 0.004 x 78 x 9.81 x cos(4.0) = 3.05 N\nGradient force = 78 x 9.81 x sin(4.0) = 53.43 N\nAero force = 0.5 x 1.225 x 0.35 x 4.167^2 = 3.72 N\nTotal power = 60.2 x 4.167 = 250.9 W\nRolling: 12.7 W (5.1%) | Gradient: 222.6 W (88.7%) | Aero: 15.5 W (6.2%)
Result: Total: 251 W | Gradient dominates at 88.7% of power
Example 2: Flat Ride at 35 km/h
Problem: A 75 kg rider with 9 kg bike on flat ground at 35 km/h. Crr = 0.005, CdA = 0.32. What is the power breakdown?
Solution: Speed = 35/3.6 = 9.722 m/s\nRolling force = 0.005 x 84 x 9.81 = 4.12 N\nGradient force = 0 N (flat)\nAero force = 0.5 x 1.225 x 0.32 x 9.722^2 = 18.53 N\nTotal power = 22.65 x 9.722 = 220.2 W\nRolling: 40.1 W (18.2%) | Gradient: 0 W (0%) | Aero: 180.1 W (81.8%)
Result: Total: 220 W | Aero drag dominates at 81.8% of power
Frequently Asked Questions
What is rolling resistance in cycling and what causes it?
Rolling resistance is the force that opposes the motion of a tire rolling over a surface. It arises primarily from the continuous deformation of the tire as it contacts the road, a process called hysteresis that converts kinetic energy into heat. The rubber compound, tire casing construction, tread pattern, tire pressure, and road surface texture all influence rolling resistance. A smooth, high-pressure road tire on clean pavement might have a coefficient of rolling resistance (Crr) as low as 0.003, while a knobby mountain bike tire on rough terrain could have a Crr above 0.020. Reducing rolling resistance is one of the easiest ways to gain free speed on the bike.
How does gradient affect the power required for cycling?
Gradient has an enormous impact on power requirements because it adds a gravitational component to the forces opposing motion. On flat ground, a cyclist might need 150 watts to maintain 30 km/h. On a 5 percent gradient at the same speed, the gravitational force alone requires an additional 200 or more watts depending on total system weight. The gradient force equals mass times gravitational acceleration times the sine of the slope angle. Unlike aerodynamic drag which increases with the cube of velocity, gradient force is constant at any speed, making it the dominant resistance factor on climbs. This is why lightweight riders and equipment provide the greatest advantage on steep hills.
What is the coefficient of rolling resistance and what are typical values?
The coefficient of rolling resistance (Crr) is a dimensionless number that characterizes how much energy a tire loses per unit of force pressing it against the surface. Lower Crr values mean less energy loss and faster rolling. Top-tier road racing tires like the Continental GP5000 achieve Crr values around 0.0032 to 0.0040 at optimal pressure. Standard training tires range from 0.004 to 0.006. Gravel tires typically show Crr values of 0.006 to 0.010 depending on surface conditions. Mountain bike tires can range from 0.010 to 0.025 on rough terrain. Tire pressure, width, surface roughness, and ambient temperature all affect the actual Crr during a ride.
How do I interpret the power split between rolling resistance, gradient, and aerodynamics?
The power split shows how your total energy output is distributed among the three main resistance forces. On flat ground at moderate speeds, aerodynamic drag typically accounts for 70 to 90 percent of resistance, with rolling resistance making up most of the remainder. As the road tilts upward, gradient force quickly dominates. At 5 percent gradient and 15 km/h, gravity might consume 75 percent or more of your power. Understanding this split helps you prioritize equipment and position changes. On flat terrain, improving aerodynamics delivers the biggest gains. On climbs, reducing total system weight matters most. Rolling resistance improvements benefit both scenarios equally.
Why does tire pressure affect rolling resistance differently for different surfaces?
Tire pressure affects rolling resistance through a complex interaction between tire deformation and surface texture. On perfectly smooth surfaces like a velodrome track, higher pressure reduces tire deformation and lowers rolling resistance. However, on real-world road surfaces with imperfections, excessively high pressure causes the tire to bounce over bumps rather than absorbing them, wasting energy through suspension losses at the rider level. Recent research shows that optimal pressure on typical roads is often 10 to 20 percent lower than the maximum rated pressure. Wider tires at moderate pressures can actually have lower real-world rolling resistance than narrow tires at high pressure because the contact patch shape becomes more efficient.
How do weather conditions affect rolling resistance and overall power requirements?
Weather conditions significantly influence all three resistance components. Temperature affects rolling resistance because warmer rubber compounds deform more efficiently, reducing hysteresis losses by 2 to 5 percent for every 10 degrees Celsius increase. Wet roads increase Crr by 10 to 30 percent due to the water film between tire and surface. Wind directly modifies the aerodynamic component by changing the effective air speed relative to the rider. A 10 km/h headwind at 30 km/h riding speed increases aerodynamic power requirements by roughly 80 percent. Air density decreases with temperature and altitude, reducing aerodynamic drag. At 1500 meters altitude, air drag is approximately 15 percent lower than at sea level.