Friis Calculation for CC1310 at 868 Mhz:
Two dipoles at 2.1 dBi, 10 dBm TX power level, 10 Kilometers range: -97.0 dBm at the receiver. Ti claims -110 dBm RX sensitivity.
Going to "boost mode" nets 4 dBM more at the RX, for -93 dBm
Friis in this case is assuming perfect free space conditions of course. The TI sensitivity figure -110 dBm is a bench test with no thermal noise and perfect RF matching, and I note there is no noise figure spec for the front end in the data sheet, at least that I can find.
Wiki claims the average height of an Adult Ewe to be 70 cm at the withers. Running a UHF line of site calculator I get 3 Km line of site for the Ewe in perfect terrain. With the Human holding the antenna on a stick at 3 meters, I get 10 Km LOS for the human in perfect terrain. If the receive antenna is on a portable tower, and was a gain antenna such as a YAGI, or stacked dipoles, you'd do much better. At 6 meters for the RX antenna height, you start to have a 10 kM receive bubble.
I like to use a rule of 50% degradation at UHF/VHF in rough terrain, so a 1.5 kM range bubble for the sheep if the receiver is near ground. The limiting factor being the sheep's height.
HF near field propagation starts looking really, really, good at this point. Unless you can build a tower for the receiver, or get the antenna onto a flying platform. Reducing frequency to 150 Mhz for example, results in a much better -65 dBM at the receiver.
All of the above assumes very good VSWR match at both antennas.
This also makes a strong point for development of a really good antenna pattern on the sheep's collar. Boosting Sheep TX power to a modest 23 dBM really would help with the signal to noise ratio at the receiver. Your operating in a region where antenna gain at the sheep does not buy you much increase in range, but where modest power increases help your bit error rate immensely. The modest power increase gives you a chance of some reflected paths aiding in rough terrain, but you do not want to increase TX power to the point you start getting severe multipath propagation.
Friis calculator:
https://www.pasternack.com/t-calculator-friis.aspxThe classical Java range calculator, which uses simplified equations worked out by two way radio companies in the 1960s...
http://www.hamuniverse.com/lineofsightcalculator.htmlThere are more sophisticated freeware radio propagation programs out there that use actual terrain data, but the first order approximations here will hold if there are not tall rocks or severe vegetation.
http://www.nautel.com/wp-content/uploads/2013/05/Radio-Coverage-Tool-NAB-2013.pdfThe ever so useful chart from MiniCircuits:
http://www.minicircuits.com/pages/pdfs/dg03-110.pdfSteve