A balanced second stage should require less effort than an unbalanced second stage all things equal.
incorrect.
Think of a seesaw which is essentially what this is.
@halocline even more simplified, but trying to get conceptual understanding vs. actual ;-)
In an unbalanced reg
put a 135lb weight on one side, and a 137lb weight on the other
Requires 2lbs to move it because 137-135=2
135 being the IP, and 137 being the spring pressure. When you breathe, you are lifting up on the 137lb side
in a balanced reg
2lb weight on one side, 0lb weight on the other
2-0=2, so still 2lbs to move it, and again, breathing is lifting up on the 2lb side
That is cracking effort, the force required to change the state of the valve from closed *seesaw down*, to open *seesaw up*
now, in an unbalanced reg, when you start to lift that seesaw up, that 135lb weight starts to lose weight and goes to 130lbs. You started the motion with 137-135=2, but to continue to keep it up, you now have 137-130=7lbs. The faster you move it, the more weight is lost. Area under the curve increases as you start to inhale which is why in the graphs posted you see a rapid increase in work of breathing as the RMV goes up because the regulator doesn't have time to rebound properly and as gas density increases, the IP drop also increases.
In a balanced reg, there is theoretically no change, so it stays at 2lbs regardless of how fast or how much you moved the seesaw so the area under the curve is pretty flat.
In an unbalanced servo-assisted upstream reg *i.e. Poseidon Jetstream and Xstream*, the 137lb weight is the one that gets lighter as you pull on it and that is why their breathing curve is so different than a normal downstream regulator