# The Climb

7:26 PM

## Basic Dynamics The following equation serves for analysis of the relative importance of the resistance forces and the benefits of equipment modification: m(dv/dt) = T – [WSin(ArctanG) + WCrr1Cos(ArctanG) + NCrr2V + ½CdAρ(V + Vw)2] m = mass of the bicycle + rider dv/dt = acceleration rate T = propulsive thrust at the tire contact patch W = wheel weight Crr1 = rolling resistance coefficient G = fractional slope (rise/ horizontal distance) N = number of wheels (bicycle = 2, tricycle = 3) Crr2 = coefficient defining rolling resistance variation based upon velocity (0.0505N*s/m based upon empirical data from General Motors test drum) V = velocity of the bicycle system (bicycle and rider) Cd = aerodynamic drag coefficient A = frontal area ρ= air density (1.2 kg/m3 or 0.00233 slugs/ ft3 are reasonable values) Vw = headwind or tailwind velocity headwind value is +, tailwind value is - The first term = inertial force due to acceleration The second term = rider generated net thrust after the losses through the chain, gears, and rear wheel The third term = force component of gravity (ascending or descending) The fourth term = rolling resistance of the tires + bearings The fifth term = velocity dependant drag from wheel bearings + tires + wind The sixth term = aerodynamic drag of the bicycle system (bicycle + rider) The way to improve acceleration (a) is to increase force (F) or decrease mass (m). Therefore, when comparing two riders of equal ability a 1 kg difference in the equipment weight will make a significant difference. If bicycle system (bicycle and rider) #1 weighs 80 kg and can accelerate from a stop to cover 100 m in 10 seconds, then bicycle system #2 weighing 81 kg will lose about 0.06 seconds in 100 m. This represents a gap of approximately 0.8 m against an equal opponent of the lighter bicycle. The effect of mass/ inertia in the wheels has approximately triple the effect of the frame, fork, and handlebars. Therefore, a similar outcome will result comparing two wheel sets with a mass difference of approximately 312.5 grams. Taken from the technical papers from Reynolds regarding their RZR rims: RZR Technical Guide