Regarding Antenna gain for reception 10 km away.
Wireless communication range/distance is reduced often by a factor of 2-6 due to multipath and normal range calculations get difficult/impossible.
Assuming that your wireless communication doesn't have multipath and is 500 feet with normal zero dBi antenna gains, everytime you double your distance you need 6 dB (factor of 4) more antenna gain in your receiver to keep the same signal strength. 10 km is 6 miles = approx. 30,000 feet. So to see how much extra gain you need, here is some basic math.
dist (feet) vs. antenna gain (dBi)
500 = zero (original antenna having 500 foot range)
1000 = +6
2000 = +12
4000 = +18
8000 = +24
16000 = +30
32000 = +36 dBi gain or 4000 gain.
Gain = 40,000/[(beamwidth azimuth) x (beamwidth elevation)]
or beamwidth = sqrt(40,000/4000)= sqrt(10)= 3.3 degrees.
at 2.4 ghz wavelength = 11.803"/2.4 = 5 inches.
3.3 degree beamwidth is approx. 20 wavelengths, so your antenna would be about (20x5")or 100" x 100" in size. That's pretty big.
KCH.