Originally Posted by

**spare_wheel**
Originally Posted by

**Jaywalk3r**
Gravity is a conservative force. The net elevation gain between the starting point and ending point is what matters most, and for any loop, the net elevation gain is zero.

You might (or might not) find this paper interesting.

An excerpt:

*Elevation gain requires extra energy. But during the descent to the starting elevation, all of this extra energy is recovered. So, in the long term, by the principle of conservation of energy, the net energy consumed by elevation gain / loss will be zero; only the air drag and tire rolling energies need to be minimized. In other words, hill force is a reactive load, and hence, does not dissipate energy.*

At first, the notion that ascending and then descending a hill is an energy-neutral activity seems to be at odds with observation. Of course, one gets more tired on a hillier course. To explain this phenomenon, we must discern where the energy loss occurs. For this purpose, we explore the path of the energy through reactive and resistive loads in a time trial that includes hills.

In a time trial without electric assistance, the athlete is going as fast as possible all the time. Therefore, when going uphill, speed is reduced; a relatively large portion of the athlete’s energy is used against the reactive load (hill force) and stored as potential energy. During the descent back to the starting elevation, all this stored energy is returned to help the athlete; hence the descending speed is higher than the ascending speed. But because air drag and tire rolling resistance increase with speed, the amount of energy that was stored during the (slow) ascent is less than the extra energy dissipated during the (fast) descent. This energy deficit is covered by the athlete working out for a longer time due to the slower average speed. So, while it is true that a hilly time trial consumes more energy than a flat one of the same length, the extra energy is consumed during the descent. And provided that the starting and ending elevations are the same and no braking is involved, the total energy can be accurately computed from the speed profile with no regard to the elevation profile. In other words, if the uphill and downhill speeds and distances were reproduced on a flat course, the total energy would be exactly equal to that on the hilly course.

This has an important implication: It means that if the athlete had enough power to climb the hill at the same speed as descending it, then, a hilly time trial would have consumed exactly the same energy as a flat one of the same length and finishing time.

If we want to accurately describe the difficulty (with respect to energy required) of a ride, knowing the variation associated with the riders ground speed and air speed is more important than knowing the elevation gain.