Analytic Cycling Logo Forces on Rider

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 m2.  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  m2 
Coefficient Wind Drag  0.50  dimensionless 
Air Density  1.226  kg/m3 
Weight  75.0  kg 
Coefficient of Rolling  0.004  dimensionless 
Grade  0.030  decimal 
Wind Resistance  9.8  kg m/s2 
Rolling Resistance  2.9  kg m/s2 
Slope Force  22.1  kg m/s2 
Cadence  100.  rev/min 
Crank Length  170.  mm 
Pedal Speed  1.78  m/s 
Average Pedal Force  156.5  kg m/s2 
Effective Pedaling Range  70.  degree 
Effective Pedal Force  402.3  kg m/s2 
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