Range Reality Check

by Rob Flickenger

I had some fun with math tonight.

According to Cisco, you can shoot an 802.11b signal 25 miles at 2Mbps on the AIR-ANT3338 using solid dishes.

According to Encyclopaedia Britannica's entry on "horizon":

"The higher the observer, the lower and more distant is his visible horizon. To one 5 feet (1.5 m) above the surface, the horizon is about 2.8 statute miles (4.5 km) away; and for one at 10,000 feet (3,048 m) altitude, it is about 126 miles (203 km). The distance in statute miles equals 1.224 times the square root of the height, in feet, above the surface."

So, how high would the antennas have to be in order to see each other, before they fall off the edge of the horizon?

Since we'll have two towers, let's assume (for simplicity) that they're the same height and elevation. In order to see each other over the rise in the earth between them, they'd both have to be able to see a spot at the midpoint, 12.5 miles away.

For height x (in feet)

12.5 = 1.224 * sqrt(x)

12.5 / 1.224 = sqrt(x)

10.21 = sqrt(x)

104.29 = x

...So, your antennas would have to be at least 104 feet above the surrounding terrain, separated by 25 miles, pointed directly at the ground 12.5 miles away, with no intervening ground clutter.

But it's worse than that. If we were trying to point a laser beam on one tower at a target on top of the other, we'd be finished. But radio waves expand as they radiate outward from the antenna. For maximum coverage, you'll want to allow space for the fresnel zone at the midpoint. Using this handy fresnel zone calculator, it looks like the fresnel zone is about 70 feet at the midpoint. Grand total: 174 foot towers (or 104 foot towers, with a 70 foot drop in altitude between them, if you're shooting across a big hole). All that with no intervening trees, buildings, highways, or hills.

Right. And they really push 11Mbps, too.

So, how far out can you realistically expect to get with an antenna on your roof, before the curvature of the earth becomes a factor? Well, it naturally depends on how tall the antenna is, how high the other point is, and what's in between... Let's assume you mount a dish on top of your 25 foot high roof, and are trying to hit a neighbor with the same configuration. According to the calculator, the fresnel zone drops to 25 feet at about 3 miles. You can probably push it a bit further, but the further you go, the less efficient your link is likely to be.

Vince Hurst
(a Comm Tech here in Sonoma County) suggests:

If point to point coverage proves difficult over long ranges, and it will, really your best solution would be to repeat from a high site that is visible from both low site locations. A high site with an access point would be able to serve a wide area, yet range will depend your gain, pattern, and terrain.

The moral: don't expect to get the listed "optimal" range by rigging up a dish on your roof. Shoot what you can see, and try to think "up". There's a reason why those big telco microwave dishes sit on top of 200 foot towers in the high hills...

Special thanks to Vince, Ron Wickersham, and others for reminding me of the fundamentals of radio and basic geometry!