...scba tank that is 1/3 the size of standard tank but holds same volume of air...
The math behind most of this is not terribly difficult. The design must be a composite, as it would otherwise be a nightmare weight wise.
SCBA cylinder range widely in size and pressure rating. From as small as 1.1L to 9.0L and 150bar to 379bar. As your post lacks more specifics, I will assume the "S80" of the SCBA world, which is a 6.8L composite cylinder charged to 310bar in the US or 300bar in Europe. This is the most ubiquitous cylinder in use world wide for fire departments etc.
Unfortunately air does not behave like ideal gas at higher pressure and models badly as an ideal gas above 140bar at room temperature. Thus you have to treat the gas as a real gas and include the corresponding formulae.
The air volume a 6.8L cylinder charged to 310bar holds is roughly 1859L. Luxfer specifies the amount this cylinder holds at 1840L, which is due to them using a different compressibility model then I used above, but those 19L shouldn't bother us for an armchair calculation.
Your design occupies a third of the size. I will assume a third of the volume and disregard material sizes, which are already very thin on modern composite cylinders. I know this is not entirely correct/fair, but again probably good enough for an armchair calculation.
This means we are looking at for a composite cylinder with a
2.27L volume, holding
1859L of air, charged to an unknown pressure. If you plug in the numbers, you end up with a pressure of
4750bar. At 4750bar the Z-Factor for air is roughly 5.7130.
Luxfer has H
2 composite cylinders on the market today which are rated to 520bar. To my knowledge these are one of the higher rated composite cylinders under the TPED.
I'm not saying what you have been proposed to invest is impossible on an engineering scale, but it is an order of magnitude above what is on the market today. As others pointed out, just this new cylinder won't do, you need compressors and regulators to handle these very different pressures. I do not see that this is a serious or viable project. The benefits seem very small to the downsides.
Compressibility considerably diminishes with higher pressure, negating the gained benefits by these higher pressures. Do not let yourself be fooled by ideal gas law computations, as these do not apply here at all.
The above has been calculated with MiniREFPROP and Coolprop. If you really want better numbers, obtain REFPROP or ESS.