Potential to Kinetic Energy

Cycling Energy and Descents

We have discussed the concept of cycling energy and how Physics quantifies the degree to which a CyclistCycle can coast or make descents. Kinetic energy quantifies the degree to which pedaling has produced cycle forward motion. Potential Energy quantifies the degree to which pedaling has changed the CyclistCycle elevation.

KineticEnergy = ½mv²

PotentialEnergy = mgh

Transforming Potential to Kinetic Energy

As you descend, your potential energy decreases as your height decreases until you reach the bottom. So what happened to it? Potential Energy is what overcomes rolling resistance, aerodynamic drag, and with whatever is left over, provides downhill acceleration.

We will eventually get to looking at a descent model that includes all three, but first, we only focus on descent and ignore resistance and drag.

becomes kinetic energy as observed by your increasing speed.

You are at the crest of an ascent. As you push yourself towards the downhill, you know that because you are now at an angle determined by the slope, that while some of your weight is still into the road, a portion is directed downwards and it is this that is pulling you into your descent.

But we also know that gravity is one of a select group of forces which are called conservative which means we can use an energy perspective to characterize the descent rather than solving a Force differential equation. This allows us to make some initial observations about a descent from how the energy is converted from potential to kinetic energy during the descent.

Using energy to track descent dynamics

We know at the crest of a hill and assuming we are starting at rest, we have no kinetic energy and potential energy equal to the CyclistCycle weight multiplied by the current elevation. As we make the descent, our elevation is progressively being reduced and as a result, the potential energy is also being reduced. At any given point, it is still the weight multiplied by the current elevation.

So what happen to the potential energy difference from the crest of the hill? We know the answer. It has been converted into motion. If you ignore rolling resistance and aerodynamic drag, that difference would have been transferred completely into kinetic energy.

When we add in resistive forces, we will find that they bleed off some of the potential energy and result in important characteristics to a descent. The analytics to do this require using the force equation which we will do on another page presenting the final results rather than going through the math. In the meantime, let’s see what just tracking energy in the absence of resistive forces can tell us about the descent.