What is the official definition of first-hour delivery of hot water tanks?

Question

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

Answer 1

From the energy.gov page on sizing water heaters:

To properly size a storage water heater for your home -- including a heat pump water heater with a tank -- use the water heater's first hour rating. The first hour rating is the number of gallons of hot water the heater can supply per hour (starting with a tank full of hot water). It depends on the tank capacity, source of heat (burner or element), and the size of the burner or element.

The EnergyGuide label lists the first hour rating in the top left corner as "Capacity (first hour rating)." The Federal Trade Commission requires an EnergyGuide label on all new conventional storage water heaters but not on heat pump water heaters. Product literature from a manufacturer may also provide the first hour rating. Look for water heater models with a first hour rating that matches within 1 or 2 gallons of your peak hour demand -- the daily peak 1-hour hot water demand for your home.

If you want the gory details (such as the outlet temperature of 125°F used in the tests), by the way, you can find them in 10 CFR 430, Subpart B, Appendix E, section 5.3.