Contour Interpolation Calculation

Q: How is the location of a contour computed along a radial?

A: Based on the contour level you specify (in dBu) and the contour percentage you specify, the location of the contour along each radial is determined from the field strength computed at points on that radial.

For example, suppose you compute the field strength along a radial and you want to locate contour that defines 39dBu coverage for 90% of the locations, and a second contour that defines the 39dBu coverage for 95% of the locations.

The illustration below shows the points along the radial colored green if they are above 39dBu, and red if they are below 39dBu.

For each location along the radial, the number of "acceptable" points (above 39dBu) to that distance is compared to the number of total points to that distance. The contour is placed at the farthest location where the specified percentage value is maintained.

For example, on the 39dBu, 95% contour location shown above, the acceptable to total points ratio is 29/30, or 96.7%.

Moving to the next point on the radial (a red point, below 39dBu) would yield a ratio of 29/31, or 93.6%. This is below the requirement of 95%, so the contour specification would not be met at this point along the radial.

If you continue to compute the ratio to the end of the data computed on this sample ratio, you will see that no other location farther out on the radial meets the 95% criterion. Therefore the 95% contour is placed at the location shown, the farthest along the radial where the percentage of acceptable points is at least 95% of the total number of points.

On the other hand, using exactly the same radial and computed field strength data, the 90% contour in the example above is much farther out on the radial. That contour is placed at the point where 45 of the 50 points (90%) meet the 39dBu requirement. Note that the contour can never go beyond the computed data on the radial. In this case, if you specified the 39dBu and 85% contour, it would also be located at the end of the radial, at the same location as the 90% contour. In this case, you may want to compute another study and specify a greater distance for the radials from the transmitter site.

Consider another example shown below.

This represents a different radial, with different field strength values computed along the radial, again shown in green and red.

In this case, the 90% contour is determined by the ratio of 27/30, or 90%.

These examples illustrate that when the contour for 39dBu is drawn for the 90% or 95% location value, there may still be points outside of the contour that meet the field strength requirement. The contour defines the area where 90% (or 95%) of the locations meet the requirement. In many cases, a region of "un-acceptable" points close to the transmitter site (due to terrain shielding, etc.) can severely limit the range of the contour, even when substantial coverage exists farther out.

Note also that if only the contour is shown, there is no indication where the "unacceptable" points (below the required 39dBu) are located. Plotting the radial coverage is necessary to more clearly define the areas of acceptable and un-acceptable signal.

Be aware that certain conditions can provide a contour that is not representative of the actual coverage.  For example, if a radial has a number of points close to the base station that are obstructed by terrain or other surface features, those points can distort the contour distance on that radial:

This problem usually can be corrected by specifying longer radial lengths.

Be cautious about using contour percentage values that are lower than about 90%.  The following illustration of an extreme case shows how lower percentage values can give distorted results of the coverage actually computed for the radials:

This is another example where adding the radial coverage to the map along with the contour can give a more complete picture of where the contour is a good representation of the coverage, and where the interpolated contour distance may give a wrong idea of the actual coverage.

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