How to calculate the speed of a commuting bicyclistEquationsCyclist reach a steady speed when the motive power that they produce balances the rolling and air friction; in other words when the friction drags balance the motive power. The air drag is given by the well known equation:Here A is the frontal cross section area, Cd is the drag coefficient, ris the density of air, The air drag is proportional to the velocity v squared. The dependence on the cross sectional area should make intuitive sense; its harder to shove a big object through the air than a thin object. The density comes into the air friction because the moving object has to shove the air out of the way.The rolling drag is given by the equation:Here M is the mass of the rider and bike, g is the acceleration of gravity, and Crr is the coefficient of rolling friction. This is simply the weight (mg) of the rider and bike times the coefficient of friction.The total drag is the sum of these two drags:The power required to overcome these drags is the velocity times the drag:Thus the power required to overcome the drag scales as the velocity cubed.To calculate some actual values, we need to know the values of constants. The density of air and the acceleration of gravity are well known.The rolling coefficient is more obscure, but various sources give it as approximatelyCertainly one can due better than this with a tuned racing bicycle, but the average commuter bike isn't in great shape. Fortunately the exact value doesn't matter much because the air drag is much more important than the rolling drag at high velocities.The drag coefficient is commonly take to be 0.9The cross sectional area is more problematic. Most of the measurements have been taken for racing cyclists, not 
commuters. Typical values quoted are 0.4 to 0.6m^2. Since a commuting cyclist 
rarely crouches, and is probably more upright than a racer using the top of her 
handlebars, I will use 0.67m^2. 
Finally, we need the mass of the cyclist and 
bicycle. Take a 150lb cyclist, with a heavyish bike of 
28lbs.
Velocity vs. Power 
curves
Using these equations, we can easily 
calculate the speed of a cyclist as a function of the power the cyclist is 
putting out. For example, if the cyclist puts out 
100w
Here are two graphs of the power that a 
cyclist has to put out as a function of the cyclist's 
velocity.
Thus much over 20mph (10m/s) is very 
hard.
There are many calculators on the web that 
will tell you the power for any given velocity. Be aware that they do not always 
state the constants that they are employing. Two such calculators are 
at:
http://www.me.psu.edu/lamancusa/ProdDiss/Bicycle/bikecalc.htm
http://www.exploratorium.edu/cycling/aerodynamics1.html
A very good shareware program to calculate 
the power, (and many other things) is at
http://www.xsystems.co.uk/machinehead/
Stop signs and 
bicyclists
Frequent stop signs dramatically decrease 
the average speed of bicyclists. For instance, it turns out that the to maintai