Where do you get this from?
The information I have from the
SRD:
To fire the catapult, the crew chief makes a special check against DC 15 using only his base attack bonus, Intelligence modifier, range increment penalty, line of sight, and successive shots (from a table). This is the "Fire" Action.
Loading requires a DC 10 Strength Check to wench the arm down, then a DC 15 Profession check to Latch the Arm, then a DC 15 Profession Check to load the ammunition. It then takes 2 1 round actions to aim. Heavy catapults need a bit higher strength check and have wenches so up to 2 others can "aid other" in the strength check.
I BELIEVE that you can do all these checks in one round. The aiming you can. That is why it says a "crew" of #. The Crew is how many people to aim it in 1 round. Assuming you can do all the loading actions in 1 round, that means a crew of 3 can fire a light catapult every 2 turns. A crew of 2 every 3 turns. Assuming that you cannot do the checks in sequence to get it all one turn to load, it would take 5 turns to fire the catapult with a crew of 2.
There are some obvious tricks to "share" a extra hand and get higher rates of fire out of them for fewer people.
A Ballista requires 1 full round action to load, 2 for small characters. This means a medium sized person can fire it every 2 rounds. I don't see where 3 came from, unless we are setting the Kobold on it?
So where do your guy's figures come from?
Also Mainiac, as Edio pointed out, there are some other methods of locomotion that Ballista aren't as good at dealing with. This is why we have a little diversity.