Re: voltage drop calculations
I infer that the two gates are fed from the same circuit, with 18 amps flowing the first 450 feet to the first gate, and with 9 amps flowing the final 95 feet to the second gate. If that is not correct, then please clarify.
With that configuration, I calculate a voltage drop of 5.01 volts to the first gate, and an additional 0.53 volts to the second gate. The total VD is 5.54 volts, or 4.61%. Since you didn?t give us the details of the feeder to the panel that in turn feeds the gates, then I can only guess that the total VD exceeds 5%. That is not a code violation, but you might want to re-think your choices.
Now to answer your question, let me again presume that one circuit carries both gates. You can use this process with appropriate changes, if your actual configuration is different.
The total current of 18 amps cannot be more than 80% of the branch circuit?s ampacity. So you need 22.5 amps worth of conductor. The next larger overcurrent device is 25 amps. The minimum acceptable conductor for 22.5 amps (before considering VD) is a #12 (here presuming a 75C copper conductor). The required EGC for a 25 amp breaker is a #10 copper.
Now turn to Table 8. Because of voltage drop, you are upsizing from #12 (6,530 CM) to a #4 (41,740 CM). That is an increase in size by a factor of about 6.392. You need to upsize the EGC from a #10 (10,380 CM) by that same factor. 6.392 times 10,380 is 66,349 CM. The smallest size conductor that is at least 66,349 CM is a #2 (66,360 CM). (This one was close!)
So my answer to your question is a #2.