Naruto Shippuuden Episode 55

[Uchiha Barles]

Awww, now look what you've done Yuki, you went ahead officially made into a geek fest something that was only bordering on it....I'm in!

I prefer the simpler explanation for chakra and it's usage. Each person has a certain amount of chakra at any given time. Like, if Naruto and Kakashi have not been using chakra, and Kakashi says "you have four times the chakra I have", then that's how much chakra Naruto has at that moment.

The amount of chakra that can be outputted by a ninja is determined by whatever biological system that transfers chakra out of the body. To illustrate what I mean, take an electrical signal generated by a neuron. The signal is propagated by a change in the concentration of ions along the neuron (very simplistically speaking). Once a signal has been passed, another one cannot pass until until the ion concentrations return to their "pre-signal" concentrations. The speed at which this happens depends on the person (again, simplistically speaking). A similar thing could explain why one person is able to output more chakra than another. Maybe the number of outlets from which chakra can leak differs by ninja. Maybe there's strain associated with leaking out chakra, and the amount of strain that the chakra vessels can take also varies per person. A combination of these two would explain why training on the rasengan made Naruto's hand numb and blistered and what not.

So basically, this takes the X variable you mentioned and makes it static over short periods of time, by making the Y function determine that chakra replenishes at a much slower rate. The Z function would be a determined by the specifics I speculated on in the previous paragraph.

Now, as far as using the fact that this is a shonen story to excuse that these characters get "shonen hero power ups", is not something I sit well with. The reason is, Hunter x Hunters does this crap MUCH better. You are hard pressed to find anything that's happened to any character in the story that doesn't fit into the system they established in the beginning. If you consider Kurapica's eyes, he's an exception, and his exception still makes use of the nen system in a way that doesn't make you call "bullshit". The hero power ups are well there. The hero power ups in this anime leave much to be desired. HxH shows us things don't have to be the way they are. In fact, I'll throw on some twisted sister right now..."we're not gonna take it! NO!"

One more edit: What makes it worse, is that the series gives a pretense of explaining these things to us. If you're gonna bother with an explanation, make it good. Otherwise, DBZ it, you don't hear anyone who like DBZ complaining about a lack of explanation, because the series doesn't even try.