Supposing I were to have a parabolic, high gain, directional Wi-Fi antenna such as this one
( http://antennas.com/pdfs/ARC-DA5834SD1_DS_090711.pdf ) that had 34 dBi of gain and was transmitting without any obstructions, how far could it reach?
Sam: With clear line of sight, it can probably go many miles. It is a 5Ghz band antenna, and very, very directional. You have to point that antenna within 4 degrees of the target, else you will lose signal quickly to the sides.
This antenna is designed for point to point links, like ones mounted on towers, each pointed to each other. In those cases, they can probably go 10-20 miles, depending on terrain. They must have clear line of sight between the antennas to work properly.
The distance is not related directly to the gain of the antenna. The WiFi protocols assume a certain guard time, and if you exceed a certain distance, the transit time of the radio signal will exceed the guard time leading to a severe loss of performance. To go more than a few hundred feet reliably you need special microwave links to get reasonable operation. These links do not rely on WiFi protocols.
If you are lucky, about a quarter mile. Unless a bird flies through its' path.
50 yards, approximately.