# Unevenness and slopes

## Unevenness and slopes of a route. Positive, negative and accumulated unevenness.

The difference in level, by definition, is the difference in height between two or more points. The zero level point will be the point where we start the route, regardless of the height of that point at sea level.

The accumulated difference in altitude will be positive if the final height is greater than that of the starting point (we have accumulated meters by ascending) and negative if the final height is less than that of the starting point (we have accumulated meters by descending). If the starting point and the end point coincide, the accumulated difference will be zero.

Strictly speaking, to calculate the accumulated gradient of a route, we will add the positive gradient and the negative gradient. For example, on a circular route that climbs a 500-meter pass and has the same departure and arrival point, the positive difference in altitude will be 500 meters and the negative difference in altitude will be another 500 meters, so the accumulated difference in altitude will be 1000 meters. On any route with the same starting and finishing point, the positive accumulated gradient will be equal to the negative accumulated gradient.

As the routes usually do not usually only go up or down, but there are concatenated ascent sections and descending sections, the positive accumulated difference will be the sum of all the height gains and the negative one will be the sum of all the height losses. Therefore, it will not coincide with the height gained or total altitude gain, which is the difference between the highest level and the lowest level of the route.

Example: We leave point A with an altitude of 500 meters above sea level and end at point F with an altitude of 600 meters above sea level, passing through intermediate points B, C, D and E.

We add all the altitude gains in the ascending sections:

A-B: 600-500 = 100

B-C: 1000-600 = 400

D-E: 1300-700 = 600

Positive cumulative difference: 1,100 meters

We add all the altitude losses in the descending sections:

C-D: 700-1000 = -300

E-F: 600-1300= -700

Negative accumulated gradient: -300 – 700 = -1,000 meters

Total accumulated slope: 1,100-1000 = 100 meters.

In cycling, when we talk about “accumulated slope”, we usually refer to the positive slope, as it gives a better idea of the difficulty of the route.

## Slopes of a track

To determine the difficulty of a route, as important as knowing the unevenness is knowing the slopes of the different ramps. The slope is the relationship between the distance ascended vertically and the horizontal distance traveled to ascend it. A quick and simple formula to calculate the average slope of a section would be the following as long as the vertical distance and the horizontal distance to the point of ascent are known:

Slope (%) = Vertical distance x 100 /Horizontal distance

According to known data: distance traveled, elevation angle, vertical distance, etc. There are other methods in which trigonometric calculations are applied.

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