Car, motorcycle and bicycle energy comparison graph using Matplotlib

     Everytime I met bike enthusiasts there's a lot of fuss about the bicycle being more efficient than cars and motorcycles. So I thought in making a graph comparing cars, motorcycles and bicycles . Of course here Is shown a mechanical stand point about the subject.

     The simplest energy equilibrium equation goes like this:

     F_t is the traction force 

     F_r is the resistance force

     F_i is the inertial force

     F_a is the aerodynamic drag force

     F_r is the rolling resistance force

     F_g is the gravitational force

     V is speed

     The power that makes the vehicle goes forward equals the speed times the its traction power. That power has to overcame the resistance forces in the opposite direction of the traction. 

     The resistance forces can be model as, inertial forces, aerodynamic drag forces, rolling resistance forces, and gravity resistance forces.  Roughly the inertial force deals with speed variations, the aerodynamic drag is the drag imposed by the air, the rolling resistance is deals with the mechanical friction between parts and the gravitational forces is the tangential forces caused by gravity, helping you in downhill, and making your life harder in hillclimbs. Mathematically they can be written as bellow. 

      C_d is a dimensionless parameter called drag coefficient.

     C_r is a dimensionless paramenter called coefficient of rolling resistance.

      I is the steepness of the hill (rise/run)

      To plot the graph I'm using an amazing python library called matplotlib. See the script.

    
     And here is the graph plotted:

     One final word, a very cool site doing an interactive version of this calculations only for bike) can by found in Mr. Steve Gribble website.

http://www.gribble.org/cycling/power_v_speed.html 

Once again, thanks for reading. 

Eddie.