Biking Force, Power and Calorie Estimator

The Biking Force, Power and Calorie Estimator calculates the approximate forces acting on a bike at a given speed, using various different inputs, and uses these to calculate the power output required from the rider, and an approximate estimate of the calories burned per hour and per mile.  It is very similar to the Energy Consumption During Cycling online calculator, although this one is less sophisticated: both use the same physics to model the problem.  There are three natural forces acting on a bicycle in motion, which are used to calculate the total force and the power: I assume that they are exactly balanced by the propulsive force supplied through the drivetrain by the rider that moves the bike forward.  The forces are:

• Gravity "drag": the weight experienced pulling a bike either backwards or forwards, due to the grade;
• Friction: due to the weight of the bike and rider, and the rolling friction coefficient; and
• Drag: the force due to wind and the motion of the bike through the air.

The inputs for the calculator are:

• Road grade (G): enter in percent. Default is 0 % grade. Positive is upslope, negative is downslope.
• Bike speed (v): default is 14 mph
• Wind speed (v_w): positive is a head wind, negative a tail wind.   Default is 0 mph
• Friction coefficient (μ): Used in calculating friction force.  Default is 0.008, which is for narrow, high pressure tires.  Use a larger value for lower pressure or wider tires
• Rider mass (m_r): Mass of the rider.  Default value is 70 kg (about 155 lbs)
• Bike mass (m_b): Mass of the bike.  Default value is 14 kg (about 30 lbs) (Yes, this is high for modern bikes.)
• Rider area (A): Projected frontal area of rider.  Default is 0.4 square meters.  (For those with technical knowledge, I'm assuming a drag coefficient of 1.)
• Body energy conversion efficiency (e): Efficiency of body in converting internal energy to useful work to move the bike.  Enter values in percentage; default is 20%.  Values between roughly 15% and 25% are reasonable.

The outputs are:

• F_g: Gravity "drag" force, due to up or down slope (N)
• F_f: Friction force (N)
• F_D: aerodynamic drag force (N)
• F_t: sum of all forces (N)
• P: Power output required from rider to move the bike at this speed (W)
• C: Net Calories (i.e., kcal) burned in an hour of biking at this speed (kcal)
• W: Net Calories (i.e., kcal) burned per mile of biking at this speed (kcal)

Three notes:

• This calculator is for educational and recreational purposes only!  Values of friction coefficients, projected body areas, and especially energy conversion efficiency are approximations!  If you use the calculator as a basis for an exercise regimen, you have been warned, and I take no responsibility for any results. 
• If the net force acting on the bike is negative (that is, the force due to any downslope or tail wind means that you don't need to pedal), the calculator will not give any results.
• I assume that the drag forces acting on the bike are exactly balanced by the propulsive force the rider supplies.  That is, these calculations are not correct for the typically short periods of acceleration when the bike is changing its speed.