Computing Climbing Effort

We now have the pieces to produce a cycling climbing model we can use to analyze our own abilities to perform. Scenario Modeling is done in two phases. The first computes the total effort to make the climb independent of the time it takes, while the second asks whether a given cyclist could make the climb in a given amount of time. This page is concerned with computing the first. This number effectively replaces a scenario like the Alpe d’Huze by a single number.

What data do we need?

Ascent scenario modeling requires just five pieces of data:

  • Ascent – Elevation Gain and Cycling Distance
  • Cyclist – Weight and power output levels
  • Cycle – Weight

To model the climb itself,

Ascent Modeling

Mont Ventoux France (https://www.macsadventure.com/us/biking-tours/)

Ascent modeling computes the effort to make a climb,  independent of the time it takes. Just two numbers would seem too few, but we catch a break because of the nature of gravity and rolling resistance. Aerodynamic drag is usually ignored because ascent speeds are low, and serpentine routes tend to alternate head and tail winds.

The total effort is computed by adding the following two simple calculations:

WorkAgainstGravity = Cycle-Cyclist Weight * Elevation Gain

WorkAgainstResistance = Cycle-Cyclist Weight * Resistance Coefficent * Cycling Distance

This single number provides a complete description of the climb.

Ascent Model Examples

Here is the Alpe d’Huze computation of the total work effort. We assume an elevation gain of 1071 m and a cycling distance of 13.2 km. Next we assume the surface is Asphaut with a coefficient of 0.002. Finally we assume an Elite Marco Pantini is making the climb. He weighs 126 lbs and his cycle is 16 lbs. Converting to kgs, this yields a combined weight of 631.6 newtons or 142 lbs.

WorkAgainstGravity =631.6 Ntws * 1071 m = 676,444 Joules

WorkAgainstResistance = 631.6 Ntws*0.002 * 13200 m =                     21,063 Joules

TotalEffort = 695.507 KJoules

This single number is a representative model of this:

https://pedalworks.wordpress.com/2014/04/17/alpe-dhuez/

Computing Climbing Effort

This brings us to one of the most surprising simplications when computing the total work in performing an ascent. Again using the Alpe d’Huze, we know their is a total elevation gain of 1071 m or little over a kilometer.

You could find data that brings up the climb into sloped segment, compute the work needed given the slope, and then total up. Or you can simply compute the change in potential energy. In this case, the work needed to make the ascent is

WorkAgainstGravity = weight * Elevation Gain

Again using Marco Pantini as the cyclist, the work he needed to complete in his record ascent against gravity was:

WorkAgainstGravity = 631.6 Newtons * 1071 m = 676,443.6 Joules

We caught a break

In climbs, gravity is the most significant force we have to deal with. So we have certainly caught a break in that because it is conservative, we can compute the total climbing effort against it by such a simple formula.

Next Topic:   Assessing Climbing Abilities