By Bill Davis
The weight comes into the formula as a component of the grade – the force applied to the pedal moves you in the horizontal or ‘x’ direction until there is a hill. Then the force applied to the pedals is divided into an x and y component – Fx and Fy where Fx is the pedal force that propels you forward in the flat horizontal direction and Fy moves your ass up the hill. This formula then becomes P = Feff*V where Feff is Fx*cos(hill angle) + Fy*sin(hill angle). The grade is y/x which is the Tan(hill angle) and if I factor out cos(hill angle), rearrange the equation and substitute weight for Fy, then
P = (Fx – W*% grade/100)*cos(hill angle)*V. So now the force that propelled you in the x direction on the flats at a given power level has to go up due to the weight
Fx = P/(V*cos(hill angle) + W*% grade/100
To make the long story short, the Pedal Force required to keep the same power level on the flats goes up by your weight x the percent grade/100 and also by a factor of 1/cos(hill angle). So a rider that weighs 10 lbs more on a 6% grade will require .6 more lbs of effort to maintain the same cadence and power output. If you consider that on the flats the rider is only applying about 2.6 lbs of force to maintain a cadence of 90 rpm for 235, this is a 23% increase in effort.