so I think we are aiming for something like 70-80dB reduction.
It's doubtful that you would need that much. That's a VERY tall order, or a home studio. Even the best professional studios don't usually go to that extreme. A more reasonable goal for a home studio would be around 50 dB. But do some testing with a sound level meter, and also check your local noise regulations, to make sure. If you really do need 70 dB, it IS possible, but youare going to need one hell of a budget to accomplish that.
First thing will be to strengthen the floor joists to make sure the structure of the house can take the extra weight
Right. You will need to hire a structural engineer for that part. He's the only guy who can safely (and legally) design the floor structure.
...then fill the cavity below the floor with soundproofing materials.
Ummm... no, it doesn't work like that. Sorry. That's a common misconception, but there's actually no such thing as "soundproofing materials". There are METHODS and TECHNIQUES that can be used to get good sound ISOLATION, but "soundproofing" is impossible, and no material on it's own could do that, even if it were possible. Instead, you will need to create an isolation SYSTEM, that consists of several individual parts. Those parts do act on their own, individually, to a certain extent, but far more important that that, is how they interact together, as a complete system. Just putting "materials" under your floor will do zero to isolate. Instead your floor needs to be design as an isolation system that includes the floor deck itself, plus whatever is supporting that deck, plus a few other things None of those by itself is any use for isolating, but when put together correctly, they can provide a good amount of isolation.
The room below is quite tall so we will hang a second ceiling below the exisiting ceiling and fill that cavity as well.
... and that would create a "three-leaf system", which will REDUCE your isolation for certain frequency ranges. It will NOT improve isolation. Yes, I know that this is not intuitive at all, but it is the plain truth. Logically, you would think that if having one sound barrier helps a bit, and two sound barriers helps a lot, then three must help even more, but that simply isn't the case. There's lot of things about acoustics that are not intuitive at first glance, but once you understand the principles, it all makes sense.
Here's a diagram that shows the issue. This diagram is for walls, but the same principle applies to floors and ceilings too (as well as doors and windows):
2-leaf-3-leaf-4-leaf-STC-diagram--classic2-GOOD!!!.gif
There are three parts to the diagram. The one on the left shows a typical situation where there is already one wall that consists of a stud frame with a sheet of drywall on each side, and somebody decide to build another identical wall right next to it, to get more isolation. A typical stud wall will get you about STC-33, and as you can see, adding the second wall increased that to about STC-44, which isn't very much! They DOUBLED the entire wall, and only get an 11 point increase. Not what you'd expect, intuitively.
The second image, in the middle, shows what would happen if, instead of building the second wall with drywall on BOTH sides, it would have been built with drywall on just ONE side. In other words, that system uses only THREE sheets of drywall, or 3 "leaves" in acoustic terminology, yet it gets over 50 dB of isolation! So with FEWERE barriers that wll gets MORE isolation! Definitely not intuitive.
The image on the right of that sequence shows what would happen if, instead of leaving the drywall on both sides of the original wall, they would have removed that drywall and put it over the drywall on the OTHER side of the studs, then built the second wall the same way: with 2 layers of drywall on only ONE side of the studs. So now there are only TWO barriers in that wall, yet the isolation took a steep jump, way up to STC-63! That third option has the exact same materials, and the exact same mass, and the exact same side as the first option, yet it is about one hundred times better at blocking sound. The ONLY difference is that there's just two leaves of mass on the best wall, as compared to 4 leaves on the worst wall, and 3 leaves on the intermediate wall.
Not intuitive at all, but very true. Supported by both acoustic theory, and also numerous real-world tests in acoustic laboratories, plus even more numerous actual studio builds, all over the world.
I could explain the technical reasons why it works like this, if you want. But the important point is that your floor needs to be designed like the third image above, with only two leaves, but you are currently planning to design it like the second image, with three leaves, which is a bad choice.
Then we'll build decoupled stud walls within the room,
Once again, refer to the above diagram: first you need to remove any drywall, plywood, OSB, MDF, or other paneling that might be on the inner face of the existing walls, then "beef up" the outer face of those walls with more mass. Then you can build the new wall, with drywall on only ONE side of the framing.
including a triple glazed window,
Very bad idea! For the same reason as above. Triple glazing gives you LESS isolation than a properly done studio window, which consists of TWO panes of glass (one in each "leaf" of the wall) separated by a large air gap.
ceiling on top of the walls,

Right! but once again, the same principle applies. Your entire ceiling and roof system must be two leaves, only.
fill all the gaps with rockwool or similar.

Right! But do make sure you get the right stuff! You can't just use any old insulation. It has to be the correct density for the job, and that density number is different for each type of insulation. One size does not fit all!
Hang a pair of heavy doors with seals round them.

RIght! One door in each leaf, for the same reasons as above.
So I guess we need to include gaps for the aircon and build some kind of baffles to keep the sound from getting out.
Yes, but it's a little more complicated than that.... HVAC is a very large part of studio design and studio construction. When I'm designing a studio, I often spend as much time on the HVAC system as I do on the entire rest of the studio! It's a big deal...
Probably I am posting too early, just trying to find out information before I start so I don't have to tear anything out and re-do it.
Not at all!!! Quite the opposite, in fact: it is NEVER too early to start posting, and even more important; IT is NEVER to early to start designing your studio, and planning. If you look around the forum, you'll find that the only studios that were built successfully, and worked great, are the ones that were based on extensive, careful, detailed design, spanning months. Those builders that didn't bother too much with design, or tried to cut corners, are the ones that ended up with flops, or never even finished their studios...
please can you or anyone else recommend HVACs for this size of room and show me a link to help me install it whilst keeping the room isolated?
You'll have to start working through the math for that! It's not a complicated process, but you'll have to do some learning first, then some calculating, then some designing. Basically, each room in your studio needs one fresh-air supply duct, and one stale-air exhaust duct. Both of those ducts must be dimensioned such that the air is flowing at the correct velocity, AND ALSO the correct rate at the point where it goes though the registers. If it is moving too fast (velocity too high) then the air flow itself will be noisy, and also annoying: you don't want a constant wind blowing on your head! And if the RATE is too low (not the velocity: the velocity can band should be very low, but the rate has to be correct), then you won't be getting enough fresh air into the room. So you start by calculating the total volume of air in the room, then figuring the correct rate by considering that you have to replace that entire volume at least six times per hour, preferably 8 times per hour, while keeping the velocity at the register to less than 300 FPM. Based on that you can dimensions our registers, your ducts, and your silencer boxes. You also need to know how much isolation you need so that you can figure out how to design the silencer boxes: more isolation requires more baffles and thicker wood, plus a longer box. You need one silencer box at each point where a duct goes through a leaf. Once you have all that, then you figure out the total static pressure that your system will create, then you search around for an HVAC fan that can produce the correct air flow volume at the correct velocity when facing that static pressure level.
That's just the ventilation side of things: you also need to dimension the actual air conditioner unit (usually a "mini-split" system in most home studios). You have to determine the sensible heat load and the latent heat load that your studio will produce, for both extremes: with many people in there playing hard on a hot summers day with high humidity outside, and also for just one person in there late at nigh in mid-winter with low humidity. So you do the math to see what BTU/Hr rating you need for those extremes, then look around for mini-split systems that have the right capacity, and can also produce the right flow rate/velocity for the re-circulated air.
That's a rough outline of the process. It's more complicated, actually, but that's the basic idea.
- Stuart -