Hi there, they use the first nap as an extension of night sleep...it's mostly REM that first nap and most restorative. Sets you up nicely for the day. There is great explanation in the Weissbluth book "Healthy Sleep Habits, Happy Child". Although that book advocates CC it also gives great information about sleep.
I think I have found the magic morning A this week for Finn at 6 months is 2 hr 30. So I wind down at exactly 2 hr 30 and he is asleep by 2 hr 45 and I get a 1.5 hour nap. It's hard to calculate but you have to ensure that the time it takes them to fall asleep has to be included in that A (eyes open to eyes close). I think this is where I fall down a lot of the time. He never seems to be consistent on the time it takes him to go to sleep. Today I caught the first yawn and plunked him down at 2 hr 30 and there was a bit of mantra and then nothing 5 minutes later.
If that first nap is good, I find that he can be pushed to 2 hr 45 for his following A. And then back to 2 hr 30 for the next A (and pray I can get a CN in) and then he can do sometimes 3 hours leading up to bed if I really drag out the bedtime routine.
It is entirely possible that your LO is on the shorter end of A's. Some are just working on different things, milestones at different times and aren't following any averages per se.