# A comparison of average speeds between flatter and steeper rides By Bike North Member John Constandopoulos

I have often heard riders refer to their average speed to determine how well they did on a particular ride and I wondered how good of an indicator average speed by itself is without taking into consideration the elevation gain? So I tried to investigate this by looking at the various elements that make a ride harder and which also considers power output.

My starting point was the equation that describes the three key elements of a ride.  The total power  = the power required to overcome rolling resistance + the power required to overcome wind resistance + the power required to overcome the gradient. The equation describing this is: Power = krMs + kaAsv2d+ giMs  Ref: http://theclimbingcyclist.com/gradients-and-cycling-how-much-harder-are-steeper-climbs/ , where

• P = power required
• kr= rolling resistance coefficient
• M = mass of bike + rider
• s = speed of the bike on the road
• ka= wind resistance coefficient
• A = the frontal area of the bike and rider
• v = speed of the bike through the air (i.e. bike speed + headwind or – tailwind)
• d = air density
• g = gravitational constant