I need help calculating races for my cub scout pack. Can I get some help/advice? (X/post from AskReddit)

A week from today I am in charge of the pack's space derby. I am estimating about 16 boys should attend and I would like to have each boy race each other boy once and only once. The track holds up to four rockets at a time. By my estimates I can accomplish this task in 20 races- each racer has 15 competitors, and racing 3 competitors each race, 5 races per rocket to acheive this and four groups in each round (I hope I am using the terms right).

I've been trying to puzzle out a combination that leaves no duplicate racers and lets everyone race everyone else once, but I can't break the code. Any race experts or math whizzes that know the formula to do this, please help.