It is obvious that I need an expansion tank, but I am not sure that the increased pressure in the closed system is making the noise.
The question is why is it only happening a 4:45 and for only 15 min and no other time.
Also since the system is supposedly a closed system with the prv Then why when I turn off the water to the house does the noise stop. The increased pressure should be kept in the system when the house supply is off.

Could the PRV be defective? Allowing the hammering noise to be transmitted from the main.

Thanks for all the advice I have learned quite a bit about my plumbing system by researching this problem here and in the archives.