7:26 PM

Basic Dynamics

Picture 9142

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
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