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In October 2009, Dr. Pete Welcher presented these slides at a Bluesnet Network Advisory Group meeting in Santa Barbara, CA. This presentation covers RF (radio frequency) essentials you need to make Wireless LAN (WLAN, WiFi, 802.11) work well. Click this link to review the RF for 802.11 WLAN (784 KB) seminar PDF.
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The answer is pretty simple. When you estimate the number of AP's by square feet, you are in effect working with non-overlapping AP circles. But deployments overlap! So if you budgeted one AP per 3000 sq ft, for linear placement you have to adjust the square feet per AP number (or the linear distance) upwards, i.e. each AP is going to cover something more like 5000 sq ft, i.e. the spacing is NOT going to be what I have in the linear distance table for a "pure" 3000 sq ft circle calculation. It looks like you need to bump the linear distance up by about 1.3, as another way of approaching it.
The key here is realizing you're best off working it exactly one way: pick linear dimensions (for no less than say my 5000 sq ft number of 57') and then lay out a grid and count. Or work budgetarily with X sq ft per AP, but then come up with linear dimensions that are appropriate when you take overlap into account.