I am looking at getting a new hot water tank. In deciding between a 40 gallon and a 50 gallon, I discovered that the 40 gallon has a higher first-hour delivery rating than the 50 gallon (see this spec sheet). I got curious and am doing the math on how this works, but I'm having trouble finding a precise, official, technical definition of the first-hour delivery rating. The closest thing I can find is this Rheem / RUUD Technical Service document:
First Hour Rating
The calculated amount of hot water a fully heated water heater can deliver in the first hour period. The output on a water heater is normally given in gallons per hour at a 100°F temperature rise. It is the quantity of water that the heater will deliver at 140°F, when the cold start temperature is 40°F. All water heaters are stamped with this output rating in gallons per hour.
I have come across other sources that say it's how much hot water the tank can deliver in a certain temperature range above the inlet temperature in an hour starting from a fully-recovered state, but I can't find those references back now.
Can anyone provide an official, technical reference for this?
Update: Here's another possibility:
The First Hour Rating (FHR) in gallons, is determined by running a Department of Energy specified test with the outlet temperature of 125°F (+/- 5°F). A draw of three gallons per minute starts and then discontinues once the hot water outlet temperature drops 15°F. The water heater is then allowed to recover and the process continues repeatedly until one hour elapses. The sum of the amount of hot water drawn during the test is the First Hour Rating