Aside from all the other stuff this is where your calculations fail.
You see how shawn keeps mentioning 1st hour?
This is where the mixing curve starts changing the recovery rate. That's WHY you have 1st hr vs every hour recovery afterwards
clearly
Even though Shawn likes to allude to the fact that I'm a hard headed dumbass who will never change their mind about something
, I will always listen to a valid argument and have an open mind.
I do believe instantaneous has their place. However in Forsyth county, due to the fact that the county water has such a harsh ph to foster scale at a much faster rate (because all of the infrastructure piping along Winston-Salem is failing) I never spec and instantaneous water heater for our area because no one bothers to do the annual flush and maintain the heat exchanger properly and typical failure will happen after 5 years.
I personally have a state 40 gallon gas water heater, For the last 11 years and it has survived 3 teenagers, a 100 gallon Jacuzzi tub and a wife that takes a 20 minute shower before me in the morning and a bath every single night while the kids are usually showering. My set point is at 140゚ And I can count one hand the number of times we have ever encountered any kind of hot water deficit, and that was when my wife was taking a bath at night we were washing towels in hot water, the dishwasher was going and my daughter was taking a shower upstairs.
Keep in mind my son used to take 30 minute showers and both of my daughters wash their hair and usually will take a bath and shave their legs, and THEN a shower immediately after around the same time my wife takes her evening bath.
I personally will never own an instantaneous water heater because of so many experiences with them not working properly, but also will never have a VRF system in my home. Not because they aren't wonderfully efficient and are the absolute most perfect way to individually cool and heat different rooms, but because they are so complex and when one fails you cannot run up to ACR and find a replacement part any day of the week. It's along those same lines why I continue to support tank water heaters.
YMMV Consult a doctor if rash continues, do not use happy fun ball in States that do not allow its packaging. Happy fun ball originated from a space rock that fell from a distant planet.