Wind resistance, rolling resistance,
and gravity are forces acting on a rider. Power is needed to overcome these
forces and move a rider at a given speed.
Wind Resistance, Fw,
is the force in newtons on the rider and bike caused by wind drag. Variables
affecting drag are effective frontal area of bike and rider, A, drag
coefficient, Cw, air density, Rho, and speed, Vmps.
See also Air Density.
Note: Frontal Area, A,
is hard to measure. Often it's calculated from some form of a coasedown
test or from speed verses power data. Typical values are around .5
m^{2}. A large rider
may have a larger frontal area.
Rolling Resistance, Frl,
is the force in newtons on the rider and bike caused by the rolling friction
on the road. Variables affecting rolling resistance are the coefficient
of rolling resistance, Crr, and the weight of the rider and bike,
Wkg.
Gravity Forces, Fsl,
pull the rider and bike down the slope, GradHill. The slope
of a hill is defined here as rise divided by horizontal run. This
is expressed as a decimal number.
Power is the work required
per unit of time to overcome the net forces acting on the rider and bike.
The speed of the pedal, Vp, depends on the
cadence, Cd, and the crank length, Cl.
The average force on the pedals, Fav, during
a revolution is related to power and the speed of the pedal, Vp.
The effective pedaling force, Feff, gives
the force in each of two legs that is required to give the same average
force, Fav, while pedaling in only a portion, Eff, of a full
rotation of the pedals.

Wind Resistance 
Fw = 1/2 A Cw Rho Vmps2 

Rolling Resistance 
Frl = Wkg 9.8 Crr 

Gravity Forces 
Fsl = Wkg 9.8 GradHill 

Power 
RiderPower = (Fw + Frl + Fsl) Vmps 

Speed of Pedal 
Vp = Cd Cl 2 Pi /(60 1000) 

Average Force on Pedals 
Fav = RiderPower/Vp 

Effective Pedaling Force 
Feff = Fav 360 / (2 Eff ) 
Example:
Forces On Rider
Frontal Area 
0.50 
m^{2} 
Coefficient Wind Drag 
0.50 
dimensionless 
Air Density 
1.226 
kg/m^{3} 
Weight 
75.0 
kg 
Coefficient of Rolling 
0.004 
dimensionless 
Grade 
0.030 
decimal 
Wind Resistance 
9.8 
kg m/s^{2} 
Rolling Resistance 
2.9 
kg m/s^{2} 
Slope Force 
22.1 
kg m/s^{2} 
Cadence 
100. 
rev/min 
Crank Length 
170. 
mm 
Pedal Speed 
1.78 
m/s 
Average Pedal Force 
156.5 
kg m/s^{2} 
Effective Pedaling Range 
70. 
degree 
Effective Pedal Force 
402.3 
kg m/s^{2} 
Speed 
8.00 
m/s 
Power 
278.5 
watts 
Power required at various speeds for given rider parameters.
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© 2001 Tom
Compton 