One of the topics that is always discussed in structured cabling installation courses is how to calculate horizontal cabling distances. I've heard many points of view, such as:
* Consider the cable at the longest point.
* Consider the average of the longest cable and the shortest cable.
* Consider the half-length (?) of the longest cable and the shortest cable
etc., etc., etc.
I personally prefer to first have updated plans and second, visit the site to verify them (in case they aren't "fully up-to-date"). To further contribute to this topic, I'm publishing and commenting on an article by Santiago Beron, which appeared in previous editions of BICSI News magazine: "Coverage Circle of a TR"“
The BICSI TDMM-12th Edition Manual states that a TR can cover up to 929 m2, However, this area can be represented by many different shapes and sizes. Additionally, in large buildings, several TRs (transmitter relays) may be necessary; in these cases, determining the TR coverage is critical. It is the responsibility of the Telecommunications Designer to verify the TR location to ensure coverage of the area within the specified boundaries.
One way is to verify that the distance to the furthest outlet does not exceed 90 meters. However, in many cases this method requires multiple measurements and verifications. A simple method is to draw a circle around the TR and determine the coverage area. The question is, what should the radius of the circle be?.
Intuitively, we might say it's 90 meters, which is the maximum length for horizontal cabling. However, we must consider that there may be vertical runs and changes in cable path, including rises and falls, raised floors, and suspended ceilings. The average vertical run varies from project to project. Furthermore, a good practice is to allow for cable slack at the rack and outlet. The net length of horizontal cable that we consider in my projects is Hn = 85 meters.
This Hn Will it be the radius of the coverage circle? Not really. My experience tells me that diagonal runs in the suspended ceiling, for example, are not recommended. Changes in the cable routing should be at 90-degree angles. This way, changes in the cable path will be variations along the X and Y axes.
Mathematically, the distance to the outlet will be D (x,y)= X + Y
In reality, there are multiple 90-degree changes in the cable's path, but we can assume that these are always variations along the X and Y axes.
So the mathematical problem is to calculate the radius of the coverage circle.
First, we establish an equation based on Pythagorean theory:
Where R is the radius of the circle and X can have a range of 0 ≤ X ≤ R. .
The next step is to find the maximum distance of X within the range. Once we calculate this value, we can return to the previous formula and calculate the value of Y and the total horizontal cabling distance to the outlet, keeping in mind that we cannot exceed the maximum horizontal cabling distance H.n.
Calculating the distance function is not straightforward. To estimate the maximum value of this function, we must determine the function's inflection points and its value at the two extremes of the range (where X = 0 and where X = R). Inflection points are the points where the slope of a function is equal to zero (the points on the graph where the function changes from increasing to decreasing values or vice versa). Therefore, we need to calculate the derivative of the distance function.
Solving we get:
Therefore, the distance function has an inflection point at the indicated value. This inflection point should have a maximum and a minimum, but by quickly comparing the function's value at the extremes of the range and this inflection point, we conclude that this is a maximum point.
When we solve for Y using the Pythagorean equation, we also obtain the inflection point:
This means that exactly at point X = Y (or a 45-degree angle), the cable run is at its greatest distance. This might seem intuitive, but without mathematical support, it's just a hunch. Therefore, the mathematical equation for the cable run in the worst-case scenario (inflection point) is:
The final step in the process is to ensure that the worst-case scenario does not exceed the maximum net horizontal cabling distance and to find the radius value.
Dxmax = √2R = Hn
Solving for R in the previous equation, we obtain:
R = 0.71 Hn
The conclusion is that the radius of the circle that determines the coverage area of a TR is equal to 71% of the maximum net horizontal cabling length. For most cases Hn = 85 m. Therefore, we can conclude that R can be approximately 61 m, an easy number to remember.
In some projects, cable runs will be short and in the opposite direction to the outlet, due to the building's characteristics. In these cases, the coverage circle radius method can lead to errors; however, it can be used as a starting point for the designer, who can then refine the calculation according to their own criteria.