The external height at the top of the slope is about 3.6m.
... and how do you plan to support that?
Even if your trusses used raised collar ties, or are scissor trusses, you'll still get nowhere near 3.6 m at the peak of your inner-leaf ceiling. Not sure what your span is, but rule of thumb says that a raised collar tie should go no more than one third the pitch of the roof, so the lower chord would be at maybe 2.8m, perhaps 2.9m max, if you can get an excellent design that really can transfer the loads and tensions in that configuration. But that's your outer leaf! You still need account for your inner-leaf.... I don't see you being able to get much more than about 2.6 or so as the peak of the actual acoustic inner-leaf ceiling.
Please post your truss layout, so I can take a look at that, and see if there's any way of optimizing it for better height.
As the roof deals with rain water better if it's sloped I just increased the slope to be 12degree,
Also Rod's book seems to show live rooms without parrallel ceilings in his photos, and he says asymmetry is better in live rooms.
Asymmetrical shape is fine for live rooms, rehearsal rooms, tracking rooms, even isolation booths and vocal booths. But not for control rooms. You can't mix in a room that is not symmetrical. You did say that you want to mix in this room, therefore it cannot be asymmetrical...
That said, you could still have a sloped ceiling if you want, as ong as you arrange the room so that the ceiling slopes symmetrically about the left-right axis, and rises to the rear. In other words, the ceiling would have to be low over the front of the room, where the speakers are are, rising up towards the rear of the room.
But a parallel ceiling is of course not an issue if it's a better idea in this case.
If the ceiling can be symmetrical and also sloped, and that would help to increase overall room volume, then it's probably worth doing.
I was trying keep this system simple with a portable system,
Portable air conditioners still need to dump the waste heat somewhere! It doesn't disappear into nothingness inside the box: Normally there's a rather large flexible duct on the rear of the unit that has to go out of the room, through an open doorway, or window, or a huge hole in the wall... So even a portable A/C unit is still a ducted system, in that sense. They are also extremely noisy, because the compressor itself is inside the box. With a mini-split, the compressor is outside, in the external unit, so it is much less noisy. And the pipe bundle that links the two units is way, way smaller than the huge duct of portable unit.
Well to match the walls they acheive around STC 63 in rods book
Careful with STC.... In fact, forget STC! It is no use at all for telling you how well your studio will be isolated. STC was never meant to measure such things. Here's an excerpt from the actual ASTM test procedure (E413) that explains the use of STC.
“
These single-number ratings correlate in a general way with subjective impressions of sound transmission for speech, radio, television and similar sources of noise in offices and buildings. This classification method is not appropriate for sound sources with spectra significantly different from those sources listed above. Such sources include machinery, industrial processes, bowling alleys, power transformers, musical instruments, many music systems and transportation noises such as motor vehicles, aircraft and trains. For these sources, accurate assessment of sound transmission requires a detailed analysis in frequency bands.”
It's a common misconception that you can use STC ratings to decide if a particular wall, window, door, or building material will be of any use in a studio. As you can see above, in the statement from the people who designed the STC rating system and the method for calculating it, STC is simply not applicable.
Here's how it works:
To determine the STC rating for a wall, door, window, or whatever, you start by measuring the actual transmission loss at 16 specific frequencies between 125 Hz and 4kHz. You do not measure anything above or below that range, and you do not measure anything in between those 16 points. Just those 16, and nothing else. Then you plot those 16 points on a graph, and do some fudging and nudging with the numbers and the curve, until it fits in below one of the standard STC curves. Then you read off the number of that specific curve, and that number is your STC rating. There is no relationship to real-world decibels: it is just the index number of the reference curve that is closest to your curve.
When you measure the isolation of a studio wall, you want to be sure that it is isolating ALL frequencies, across the entire spectrum from 20 Hz up to 20,000 Hz, not just 16 specific points that somebody chose 50 years ago, because he thought they were a good representation of human speech. STC does not take into account the bottom two and a half octaves of the musical spectrum (nothing below 125Hz), nor does it take into account the top two and a quarter octaves (nothing above 4k). Of the ten octaves that our hearing range covers, STC ignores five of them (or nearly five). So STC tells you nothing useful about how well a wall, door or window will work in a studio. The ONLY way to determine that, is by look at the Transmission Loss curve for it, or by estimating with a sound level meter set to "C" weighting (or even "Z"), and slow response, then measuring the levels on each side. That will give you a true indication of the number of decibels that the wall/door/window is blocking, across the full audible range.
Consider this: It is quite possible to have a door rated at STC-30 that does not provide even 20 decibels of actual isolation, and I can build you a wall rated at STC-20 that provides much better than 30 dB of isolation. There simply is no relationship between STC rating and the ability of a barrier to stop full-spectrum sound, such as music. STC was never designed for that, and cannot be used for that.
Then there's the issue of installation. You can buy a door that really does provide 40 dB of isolation, but unless you install it correctly, it will not provide that level! If you install it in a wall that provides only 20 dB, then the total isolation of that wall+door is around 20 dB: isolation is only as good as the worst part. Even if you put a door rated at 90 dB in that wall, it would STILL only give you 20 dB. The total is only as good as the weakest part of the system.
So forget STC as a useful indicator, and just use the actual TL graphs to judge if a wall, door, window, floor, roof, or whatever will meet your needs.
So I'm trying to bring the silencer box design as close as I can to that within reason.
You say you want each leaf of your walls to have two layers of 16mm drywall on each leaf. That works out to a surface density of around 24 kg/m2. Therefore you will need one silencer box made of materials totaling 24 kg/m2 where the duct goes through the outer-leaf, and another silencer box made of materials totaling 24 kg/m2 where the duct goes through the outer-leaf. That's two silencer boxes on the duct. And since you will have two ducts (one for bringing in fresh air, one for removing stale air), you will need four silencer boxes, each of which is made with walls that have a surface density of 24 kg/m2. If you use plywood to make them, then taking into account that the density of plywood is only about 80% of the density of drywall, the plywood will need to be 20mm thick, 2 layers.
Then you will need to check that the insertion loss of the final unit will be high enough, and that the static pressure will not be too high for your fan to handle.
What static pressure can your fan deal with? What flow rate do you get for that static pressure?
= 182.85 CFM.
Sounds about right. Call it 200 to be safe.
A bit too high a velocity. I'd be looking for less than 300FPM and nearer to 100FPM would be great.
You've been listening to Rod!
Yup, those are good goals to shoot for... but that's about air speed AT THE REGISTER! The speed that the air is moving as it moves through the registers going into and out of the room. The duct speed can be higher.
Rod in his book says you can reduce the velocity by increasing the size of the ducting.
Yep! Simple math: If you increase the cross sectional area, then for any give flow rate, the speed MUST be lower.
Not only that, but you MUST change the cross sectional area, several times, in order to get the benefit of the impedance mismatch, which is a great help in reducing the intensity of low frequencies moving down the duct. Those changes must be sudden, for maximum effect.
Mount the fan on the exterior wall.
The same diameter round ducting runs through the walls to the isolated internal wall.
So where is the silener box on the outer leaf? You didn't mention that one....
A grille/register is mounted on the exterior wall (should this be the same size as the fan, or same as double size outlet?)
Ducting runs through the wall into another baffle box attached to this soffit. This baffle box also has a register/grille on it.
You seem to be forgetting the silencer box on the inner-leaf, in this case.
The fan would be controlled by a speed controller and set to a lower RPM to provide the desired CFM.
It's always good to have a speed controller, yes, but do check that your fan can handle the static pressure that the system will present to it.
Should the fan push new air into the room or extract it out? Or does this entirely make no difference
There's pros and cons both ways. You can make good arguments for having a fan pushing air in, and you can also make good arguments for a fan sucking air out. Personally, I usually prefer to put the fan at the far end of the exhaust duct, sucking air through the room.
Of course, if you chose to use a ducted AHU outside the room, then you can recirculate a lot of the air through that, save money, etc. and use smaller ducts for the make-up air coming on from outside, and the corresponding exhaust air going overboard....
- Stuart -
Ummmm... I don't think so! That's just the amount of make-up air that you need! According to ASHRAE guidelines, you need about 6 room changes per hour. Your room will measure about 4.1 x 5.2 x 2.75, as far as I can figure out from what you say, so that's about 59 m3, which is 2100 ft3 very roughly. Six changes per hour gives you 12,600 ft3/hr, which is 210 CFM. 
Also Rod's book seems to show live rooms without parrallel ceilings in his photos, and he says asymmetry is better in live rooms. But a parallel ceiling is of course not an issue if it's a better idea in this case.