Have you ever been working on a wireless design for a project and just couldn’t figure out what the coverage area of a particular external antenna would be? Have no fear, trigonometry is here!

I for one never thought that working in wireless would require use of advanced math. No, we aren’t talking about calculus or differential equations. The more arenas and high density conference centers I design, the more I rely on trigonometry to help me. In large, high density venues, it is nearly impossible to design a proper WLAN solution without the use of external antennas. Before you stop reading, note that I said “nearly impossible” 🙂 Now I wouldn’t recommend using only omnidirectional antennas to cover an arena when the antennas are mounted over 17-18 meters, but some will argue it can be done.

I recently was working on a project, trying to map out AP placements to provide coverage for the floor area of a large arena for a customer. The venue is a 9000 seat multipurpose arena, with a 25,000 square foot center floor that is used for sporting events and conferences. Normally in a VHD environment, I don’t provide for overlap in cells, as we are more concerned with high capacity cells than we are with high quality roaming. In this case, I had to design for roaming and high density since the venue floor is used for trade shows that sometimes see upwards of 1500-2000 people in the area at the same time. We’ll talk about VHD seating coverage for the rest of the arena in another post.

So everyone knows (or at least I hope they do) that an AP with any antenna does NOT produce a truly circular coverage pattern. When we design, we use circles as it makes visualization of the coverage plan much easier. You can see a typical depiction of a design in the image below.

Design Document Drawing

However, what we get in real life from the output of the antenna is more like this:

More Accurate Coverage Pattern

With that in mind, what’s the best way to get a rough idea of what the coverage cell size will be without any fancy predictive survey tool like Ekahau? This is where good old trigonometry comes in.

Start out by using a laser measure to quickly determine the height above the floor that your antennas will be mounted. Once you have that measurement, we can calculate a rough coverage area based on the antenna height and beamwidth of the antenna. Lets take a look at an example here:

55 feet antenna height + 30 degree beamwidth antenna = approx 31 foot coverage radius

So how did we get that approximate radius? Utilizing a triangle calculator the trigonometry can be quickly computed to give us the output needed as shown here:

Side 1 is our distance from the floor to the antenna, and the 30 degrees comes from the beamwidth of our antenna. With just these two values, we can determine our approximate coverage radius from Side 3 in the drawing above. After doing the math, I placed the antenna at this distance and took measurements to determine the actual coverage area. Sure enough, the actual measured coverage was around 32 feet (when measured to -70dBm with my Aircheck G2. This was perfect for the design I was working on, as each of the APs providing service in this area needed roughly 15-20% overlap to provide for good roaming.

So if you find yourself in a pinch and need a quick way to calculate the approximate coverage area from an external antenna, use the triangle calculator!

Always remember, math never lies! 🙂

-Scott