How far is the transmitter site that you want to receive? Is it Line-Of-Sight (LOS)? First you need to make sure that a Yagi antenna will be effective for what you want to receive. Then you need to take the Effective Radiated Power (ERP) that is authorized by their license (unless you know the actual ERP) to calculate how much gain you need. There is always the possibility that the Yagi antenna will not work. I have simplified the process to correctly design the receiver antenna system. But you get the idea that some math is involved.
The site is 17 miles (16.96) south/southwest of me.
No line-of-sight to the site, I have a mesa behind my property that by RF mapping would require my antenna to be at 53 feet height to have line of sight.
This is the first time I have ever heard the term ERP. I would just guess off the top of my head that you are talking about that sites output power? If that's correct, that site is very powerful and picks up talkgroups 3 counties away (roughly 60 miles southeast).
I get signal, with issues, and due to the valley I'm in and the mesa, and after talking with many, it has been determined that I'm getting the signal with my current antenna, an omnidirectional dpdproductions vertical 800 base antenna, due to what seems to be refraction. I won't bore you with all the talk on that right now.
Ultimately, with the refraction situation, my antenna only 18 feet high currently, it has been strongly advised that due to the mesa some jackwagon put in my way of the site and needing to be at 53 feet to have line of site, that I use a directional Yagi with high gain to get the best signal quality, and remedy the issues I have had.
Oddly, I don't know why my sds100 has a remtronix 820s antenna and has almost no issues like my sds200 is having with the outdoor antenna, but that's what numerous people who are seasoned and knowledgeable have advised me to do. They also say the other site I monitor ( thats the opposite direction of the site im speaking of) that's local and a much smaller range shouldnt have any problems receiving on a Yagi that's pointed the the site as its signal should be strong enough to still receive. Don't know as Yagi is directional, but no knowledge with a yagi.