I first learned about the P-TDY opportunity through a supervisor in 2015. I was in Minot, ND at the time, low on leave, and itching for a fun trip. I looked up the reg (36-3003) and noticed item 12 allows P-TDY: "to participate or train in sports, recreation and talent events officially conducted or sponsored by elements of the Air Force, inter-Service organizations, or DoD". After a quick search I found the Navy-Air Force Half Marathon was still accepting registrations and was an official DoD sponsored event. I wrote and submitted an MFR (Memorandum For Record) for my Commander to officially sign granting me 5 days of P-TDY for the race (2 for travel, 1 before the race to acclimate, 1 for the race, 1 for recovery). My wife did the same and got hers approved to. We covered all of our expenses but didn't have to burn leave (which is extremely valuable as a 13N since it was a 24/7, 365 duty - you want Christmas off? Gotta take leave bro) Unfortunately, as of 2020, it looks like the Navy-Air Force Half Marathon is indefinitely cancelled. If you want to do a similar event I recommend the Air Force Half/Full Marathon (Dayton, OH), Marine Corps 10K or Marathon ( D.C.), or the Army 10 Miler (D.C.).