The Mass Law of sound insulation provides a guide by which the level of transmission loss (TL) of a structure (how much sound energy it inhibits) can be predicted. It tells us that, in a single leaf wall or partition, TL increases by 6dB with every doubling of mass at a given frequency (this is a theoretical figure – in the real world it’s nearer to 5dB) and with every doubling of sound wave frequency, TL also increases by 6dB. This illustrates two important facts that we need to bear in mind when designing a studio. Firstly, low frequencies are harder to control than higher frequencies and if you intend to control low end frequencies with a single leaf construction, it will need to be dense and very, very heavy. That also means it will be extremely expensive to build and, given that the ceiling needs to be the same density as the walls, incredibly difficult to construct.

Fortunately, there’s a way to dramatically improve TL without hugely increasing cost, time spent and effort. This requires building a ‘room within a room’ structure, sometimes referred to as a MAM (mass air mass) or MSM (mass spring mass) system. It’s important to know that in order for a MSM partition to work effectively, the two leaves must be completely separate from each other structurally i.e. they cannot connect at any point. If they do, this will form a ‘flanking path’ which will turn the structure (at least partially) into a resonator rather than an isolator. Look at the cross-sectional wall diagram below. This represents a top down view of wooden framed, stud walls of varying construction, clad with plasterboard and shows the rather contra-intuitive way in which MSM isolation works. The STC (Sound Transmission Class) measurement is used in the building industry to quantify isolation in houses and offices etc. It’s not very useful in music applications because it only considers a limited range of frequencies but is illustrative in this instance.

The addition of insulation in the example second from left (rock wool or fibre glass flock) in the cavity of a basic wall (far left) improves the sound isolation by providing ‘damping’ of the plasterboard cladding (i.e. it reduces vibration). Notice how doubling the mass of the wall in the same configuration (third from the left) produces only a modest improvement (STC 40) and removing one inner layer of plasterboard increases this to STC 50. Better still, removing both inner layers increases this to STC 57 (second from right) and doubling up the plasterboard on the outside faces of the wall (far right) gives a rating of STC 63. The materials used are identical to those in the STC 40 wall but by arranging them differently in the STC 63 wall, insulation is massively improved at exactly the same cost. The take away from all this is that if you want a reasonable level of sound insulation, build an air-tight, two leaf MSM system of appropriate mass with loose cavity insulation for the best, most cost effective result.

So far so good! But there other factors to consider (this is often the case in acoustics). Strictly speaking, mass law applies directly to non-rigid partitions or ‘limp mass’ (insert your own single entendre here). Building materials invariably have an inherent rigidity, so mass law is only really an indicator of possible T/L. The actual sound insulation of a given structure depends on the interaction of the mass involved, the stiffness of the materials and how effectively they are damped. As well as this, mass law is subject to resonance at lower frequencies (we already know that low frequencies are harder to contain) and losses at higher frequencies due to the coincidence effect or coincidence ‘dip’.

Every panel you build will have a natural range of of frequencies at which they will vibrate more easily than others. These are called resonant frequencies and consist of a fundamental frequency and multiples of this known as harmonics. The critical frequency of a wall is that at which the bending waves within the wall match the frequency of a sound wave impacting on it. When this coincidence happens it enables more efficient transfer of sound wave energy across the partition. The effect of resonance and coincidence dip can’t be eliminated but you can engineer your design to have the lowest possible fundamental frequency and highest possible critical frequencies. The algebraic formulae for calculating these effects on transmission loss are listed on the table below this paragraph if you want to do your own calculations. The link below that is for an online transmission loss calculator. It was built by ‘Gregwor’ who is a moderator of The John Sayer’s Recording Design Forum and I recommend that you subscribe to it if you have any interest in building your own studio. The moderators and senior members of the forum have a great deal of sage advice on this and other related topics and I’m very grateful to Greg for his permission to use the link.

TL = 14.5*LOG(M*0.205)+23dB

where M = surface density of leaf

F0 = C((m1+m2)/(m1*m2*d))^0.5

where C = constant for empty or insulated cavity

where m1 and m2 are mass of each leaf (kg/m^2)

where d = cavity depth in metres

F<F0 = 20LOG(f*(m1+m2))-47

F0<F<F1 = R1+R2+20LOG(f*d)-29

F>F1 = R1+R2+6

where f = frequency you want to check TL of

where m1 and m2 are mass of each leaf (kg/m^2)

where d = depth of cavity

where F1 = 55/depth of cavity

MASS LAW = 20LOG(f*(m1+m2))-47.2

http://johnlsayers.com/phpBB2/viewtopic.php?f=1&t=21770

© John Steel 2020

(Heating, ventilation, air conditioning)

As I have already mentioned, this is the aspect of studio design that is most complex and time consuming (at least for me). I recently realised the way I have been thinking about it is mostly wrong!! More about that in a paragraph or two but this is a subject that gets complicated very quickly. In essence, what you are trying to do is ensure that:

• Sufficient fresh air is brought in to your insulated space
• Humidity is controlled in order to make heating & cooling efficient and
• Exhaust air is vented properly
• Transmission loss is maintained throughout the ventilation system

Broadly speaking, there are two types of HVAC systems you can choose from. The first type is a ducted, forced-air system that circulates via a heat exchanger and can include a dehumidifier unit. The total volume of air in the system is cycled 6-8 times an hour and is ‘topped up’ with 30% fresh air. The boiler will need to be housed in a separate room, the ducting will need to be large and the silencers even larger!

The second type is a ‘ductless’* mini – split system. This is where air circulation and heating / cooling are separate and only needs to move 30% volume of air compared to a forced air system (the fresh air you need to breath). This type of HVAC is less efficient and will require a drain pipe to be installed from the AC condenser unit through the inner & outer leaves to the outside, but has the significant advantage of being cheaper to install and requiring smaller silencers.

My studio is a single room, so adhering to the KISS maxim (“keep it simple stupid”), I have opted to build a ductless HVAC system. Please note that when I say “cheaper to install” it’s still actually fairly costly – it’s a relative term to describe money well spent.

The first step is to calculate the volume of your room or rooms. The quantity of supply air needed to ventilate the room adequately in cubic feet per minute (CFM) is: 30% of 6 x room volume (in cu feet) ÷ 60. (6 = the minimum number of air changes per hour).

In my instance this works out to be: 30% of 6 x 1600 ÷ 60 = 48 CFM (It took me 3 years to properly understand this and I’m eternally grateful to Gregwor from Alberta, Canada [designer of the MSM calculator and moderator of the John Sayers’ Recording Studio Design Forum] for making the penny drop with one of his many clear, concise posts on the subject).

Once you have this figure, you have to consider the velocity of the air entering the room. Why? – because if the air velocity is too great when it arrives at the supply register for the inner leaf, you will hear an audible ‘whoosh’ due to turbulence which, obviously defeats the whole project. Conventional wisdom has it that air velocity as it comes into the inner leaf must be no more than 300 cubic feet per minute, ideally it should be even less. The only way to control this is by adjusting the dimensions (specifically the cross sectional area) of the duct and silencer boxes you are going to build. *(Yes, ‘ductless’ mini-split systems do, confusingly, often have an amount of ducting in them).

You will be intuitively familiar with the general principles involved here. What helped me was to visualise using a garden hose. We all know that if you partially block the flow of water with your thumb, the speed of the jet (velocity) increases. When you un-block the hose (increase the cross sectional area or CSA) the speed of the water falls. This is the effect we’re looking to achieve in our HVAC silencers.

Making sure the dimensions of all the elements of your HVAC system are correct is critical! We already know our desired air volume (in my case 48 CFM) and we also know that we have to keep the velocity to under 300 feet per minute. The maths for calculating the minimum CSA of your supply is:

CSA = CFM ÷ 300 [48 ÷ 300 = 0.16 ft (1.92 inches)]

Remember, we really want the air flow to be slower than this, so let’s metaphorically take our thumb further away from the flow and increase this to 4 inches (100mm).

Great! I know the minimum CSA of my system and with that figure, now I can scale all the other parts of the path. Starting at the beginning, I’m going to need an air intake something like this – often referred to as a ‘louvre’ (nothing to do with the Parisian museum).

Something to keep in mind is that louvres have a defined ‘open’ or ‘free’ area. This refers to the unobstructed region of the grille which is typically between 35% – 60% of the total area. I’m going to connect my louvre to a filter box and then a short length of round steel ducting – so the maths goes like this:

50mm x 50mm (duct radius) = 2500mm²

x 3.142 = 7855 mm²

multiply by 2 to give double the surface area (assuming 50% open area):

= 15710mm² (square root of this will give the louvre size)

= 125.339539mm

Filter Box without lid.

Filter Box with latched lid.

So let’s round that up to 150mm. This is connected to the filter box which in turn, connects via a circular flange to a short run of round steel duct where it feeds into the outer leaf silencer. In order to slow the airspeed, the CSA of the silencer must be twice the CSA of the supply duct. For round duct this area = 3.142 x r(adius)² (Pi x r squared).

My duct has a 5cm radius: 5 x 5 = 25cm² 25 x 3.142= 78.55cm² (CSA)

So doubling and rounding up gives us a silencer CSA of 160cm². Remember that this is the space for the air to flow through, not the over all dimensions of the silencer. The silencer has to be made of materials that match the surface density of the leaf that it’s attached to so they’ll need to be fairly massive and include three or four internal baffles for adequate insulation. At the point that the silencer goes through the outer leaf it should be via a sleeve of identical density. Inside the void, the connection to the inner leaf silencer can be made with conventional ducting.

The CSA of an inner leaf silencer should be greater again than the outer leaf silencer (thumb well and truly away from the end of our imaginary hose). So I intend to build mine with a cross section of 324 cm² (18cm x18cm). The attached sleeve goes through the inner leaf and into the room through a diffuser grille directly above the intake of the AC condenser unit. This will help to mix the fresh air with room air and maintain an even temperature.

Outer leaf silencer (open).

The exhaust side of the ventilation system is almost identical – only in reverse. It should be located on the opposite side or end of the room to avoid the re-circulation of stale air. The one extra component needed is a fan to pull air through the path. The fan can be fitted on the supply side to ‘push’ instead. The main difference is that this will create positive air pressure in the room and locating the fan on the exhaust side will cause negative pressure. The advantage of having negative pressure in your room is that it acts on the doors (I’ll cover doors and windows in another post) and helps to increase insulation by pulling them into the seals.

The fan has to be powerful enough to meet the airflow requirements of your room and also overcome the static pressure inherent in any HVAC system. Every component added to the path will add a small amount of resistance to airflow or static pressure. This can be cumulatively significant and is tricky to work out although there is a very helpful app available from ASRHAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) which helps to detail static pressure for specific HVAC components. Static pressure is usually measured in inches of water column, which is often shown as an abbreviation such as “in. wc,” “in. wg” or “in. H2O”. Even experienced designers will concede there is at least a small element of educated guessing involved in calculating the static pressure of a sound insulated HVAC system. This is partly because of the requirement to maintain transmission loss. If you were simply installing ventilation and AC, you would keep the ducting as straight as possible to lower static pressure and turbulence, but we need to include baffled silencers which are made up of 90° & 180° turns. The method I used to estimate the static pressure of my silencer design is called “equivalent duct length”. This asserts that a 90° turn in ducting is equivalent to the duct diameter x 60. If you are using a combination of round and square ducts, you can use this online calculator to work out the equivalent diameters:

https://www.engineeringtoolbox.com/equivalent-diameter-d_205.html

For my design I calculated that the small silencers would have an equivalent round duct diameter of 14.2cm and the large ones 19.9cm.

Equation for converting a sharp 90 degree bend into an equivalent length of straight duct is:

Duct Diameter x 60

14.2 x 60 = or 852cm for each 90 degree turn x 8 for each silencer = 68.16 metres (223.622ft) of straight duct for each outer leaf silencer

and

20 x 60 = or 1200 cm (3.937008 ft) for each 90 degree turn x 11 for each inner silencer = 132 metres (433.0709 ft) of straight duct for each inner leaf silencer.

Using the engineeringtoolbox.com friction or head loss calculator for air ducting this results in:

Friction Loss (inH2O): 0.072
Friction Loss (inH2O/100 ft): 0.0302
Air velocity (ft/min): 282
Air velocity (ft/sec): 4.6899999999999995
(Outer leaf silencer)

and

Friction Loss (inH2O): 0.0216
Friction Loss (inH2O/100 ft): 0.005
Air velocity (ft/min): 138
Air velocity (ft/sec): 2.29

(Inner leaf silencer)

Giving a combined loss for all 4 silencers of 0.1872 (inH2O) or 46.63 pascals and apparently achieving an air velocity of 138 ft/min at the point it enters the inner leaf.
Using the ASHRAE app I added in the losses for 2 outer louvres with filters [2x 0.05 in.wg], 2 plenums[2 x 0.01in.wg] and 1 metre of additional 4” ducting[0.02 in.wg]
Total = 0.3272 in.wg or 81.5 pascals.

So, in short, I know that a fan that will move up to 300 CFM through 100mm duct against a static pressure of 0.35 in.wg will be fine.

© John Steel 2020

By February 2020 I was finally ready to start building. There was a fair amount of tedious preparation work such as removing rawl plugs, screws, nails and other fixings from the brickwork / woodwork. I was careful to mark where I need to back fill holes with chalk circles as they’re not that easy to see and failing to block them with mortar will affect sound insulation. I moved on to stripping out the old wiring and neon lighting and a temporary power supply was rigged up by an electrician.

I commissioned a steel flitch plate to reinforce the existing beam and the work was carried out by a local fabricator (to an excellent standard I might add – it was engineered to millimetre accuracy).

To build the flitch beam, I hired a local carpenter called Sean Butler (www.seanbutler.co.uk), who I already knew was great, very easy to work with and reliable. Because of the weight of the additional beam and steel plate, he brought his father Alan (also a very experienced carpenter and dry humourist – seeing the numerous chalk circles on the wall, he said he felt as though he was working at a “crime scene”) as well as an assistant. Before it could be fitted the supporting ‘pier’ needed attention because it wasn’t quite as tall as the one at the opposite end of the room. When the beam was originally installed it was leveled by packing the gap with blocks of wood(!!). So props were placed under the beam and the packing removed, meanwhile engineering blocks were cut to size and cemented in place. By the next day the mortar was firm enough to take the props away and the main structural reinforcement done! Next I set about sealing the outer leaf walls. To do this, I intended to fill the numerous drill holes in the brickwork and then apply two thick coats of masonry paint. Then, just as I was getting started, I encountered the first big setback. I had assumed that because the garage is built in to the earth at one side, this was a good thing. It has to be, doesn’t it? WRONG!!!!!! For the six months up to February, SE England had seen very high rainfall (for the previous 3 months it had been 155% of average and for February it was 250% of average). It seemed to rain non-stop, almost with no let up. Overnight on the 4th of March it was particularly bad, really knocking down to the point that the ground surrounding my house was completely saturated (there was standing water on the lawn). Inevitably, rain water found it’s way into the garage between the bottom of the wall facing the hill and the concrete floor. The chalk line in the photos indicates roughly where the ground level is on the outside of the wall.

I arranged for a drainage contractor to visit with a view to installing a French drain (named after it’s inventor rather than the country) and was waiting for the quote when the next big setback – covid-19, arrived. The resulting shut-down meant that it was impossible to buy materials for the project, although given the significance of world events, this didn’t actually seem very important at the time.

Fast forward to May 2020 and I had used the enforced delay to refine my design (largely as a way of occupying myself) and also gathered some very useful information about combating damp. I was in touch with a studio builder in Bristol called Tom, who built his studio on heavy clay soil next to a river which has been known to overflow. He recommended tanking the garage, whatever else I decided to do. So, as building materials became available again, this was the first job I tackled. I applied a coat of Construction Chemicals tanking slurry (as far as I can tell it’s a mixture of cement and glass fibres) up to one metre above ground level (said to be the limit of capillary rise in brick walls). Then added a wedge of mortar (or ‘fillet’) around the perimeter of the room where the slab meets the wall. When the mortar had hardened sufficiently, I painted on a second coat and left it to cure (the manufacturer recommends a full week). Not my tidiest work, but at least it will be hidden! Meanwhile I raised the two joists nearest the gables to make room for the inner leaf silencers, moved another one other to create more space between the rafters and pinned the others with M12 bolts. The raised joists will be reinforced (or ‘collared’) before any increased load is placed on them. Then I started to make a framework from softwood batten inside the gable timbers which is set in 30mm from the edge. I’m going to attach the Cement board and OSB3 cladding to this (after caulking it of course). I originally intended to pin the boards directly to the gable but doing it this way will increase the inter-leaf cavity by the thickness of the cladding.

A side-note that may be of interest to other project builders is that you can save a considerable amount of money on materials by bulk ordering. I found suppliers that beat trade prices by quite a large margin (£4 per sheet of OSB3, nearly £5 per sheet of MDF and over £6 per sheet of cement fibre board).

© John Steel 2020

It’s been a fair while since I updated my build diary, so here’s what I did this Summer. I continued framing between the rafters up to the level of the joists on the N.W. & S.E. facing walls. This was trickier than the gables because the framing has to be contoured to the same angle as the rafters.

The next step was to begin cladding the framework, first with 12.5mm cement board then a layer of 18mm OSB. I was careful to thoroughly caulk all the seams of the frame and after the sealant cured I fixed the individually cut panels to the frame using star drive screws.

I fixed the OSB panels to the rafters after applying green glue to the side that will be in contact with the cement board. I don’t have pictures of the green glue being applied as I was concentrating too hard on the task to remember to take any. I have a few more panels to fit and I’ll try to capture this when I do.

I added ‘collars’ to the raised joists so they’ll be reinforced and rigid enough to support the outer leaf silencers and supporting framework.

With the help of Kate (spouse, musical collaborator, song-writer and percussionist of the first order) I applied two thick coats of masonry paint to the brick walls and piers in order to seal them.

The next step was to make the outer leaf silencers as they needed to be raised onto the joists before the middle leaf decking is fitted (I have actually installed two short runs of decking already, one at either end of the room, forming a platform on which the silencers can rest while I build the framing to hold them). I made them out of two layers of 18mm MDF incorporating 3 x 180 degree turns.

As I cut the pieces, I clamped them together to make sure they were going to fit (I’ve heard this referred to as ‘dry fitting’). I learned very quickly that it’s incredibly easy to over-work and damage MDF so I was careful to pre-drill and countersink the inner layer of the box.

As well as (gingerly) using 30mm screws I used a thin bead of wood glue along the joining edges.

Then I added a bead of caulk along the inner and outer seams.

By this stage, they were beginning to get fairly heavy (even without the extra layer of boards which would eventually more than double the weight) so I decided to take the opportunity of adding the foam lining while they were still relatively easy to move around. I used a class ‘O’ acoustic foam, supplied in 25mm thick sheets with an adhesive backing. It’s important to use this type of product as it’s mould resistant, fire resistant as well as being acoustically rated (even though it’s eye-wateringly expensive) and given that, once the boxes are sealed up, air tight, there will be no chance of modifying them, it doesn’t make any sense to use inferior materials.

I found through trial and error that the best way of cutting this type of foam was to use an old (but still fairly sharp) bread knife. Using as much of the blade as possible and cutting slowly produced fairly clean cuts.

I discovered that the adhesive backing wasn’t quite as sticky as I’d hoped and overnight, where it had been shaped around the baffles, the foam had begun to separate.

The solution I found was to buy some 52mm plastic washers to hold the foam in place where it was being deflected. They’re actually surveyor’s markers but are perfect for this application as they have beveled edges and while they will add a small amount of drag to the airflow it will help avoid the foam completely springing loose when the glue completely dries out.

When the silencers were completed they weighed 64 kilograms each, so the next challenge was to raise them up to the middle leaf decking ( a three metre lift). For this I used an inexpensive (£10) cable pulley set along with three locking carabiners, two load straps and an old security chain. All of these components have a load capacity of at least 200 kilograms.

The nylon rope supplied with the pulley set looked very flimsy and as if it would untwist very rapidly under the load so I replaced it with marine grade, double braided rope. The lift was pretty straightforward and the finished boxes are on the decking and sealed to keep out insects, dust and other unwelcome guests (apologies for the poor picture quality – it was the end of a long day). The next part of the build is making the frame for the silencers – more to follow and thanks for reading.

© John Steel 2020

I must confess that the rate of progress slowed down quite a bit over the Autumn and Winter months. This was partly due to the fact that when it’s cold, damp, freezing or windy, it’s not that much fun to work in the garage. Also, I have found it difficult to source certain materials recently. I ordered a few cases of caulk in December (I am getting through a large amount of it) and it arrived in mid – February. The supplier told me this was because the manufacturer simply couldn’t import sufficient quantities of the raw materials needed to make it following Brexit. That said, I have actually achieved a fair amount for an old-timer. I continued fixing the first layer of OSB in the middle leaf decking until it was completed.

Now the only gaps in it are where the raised sections are (these will be completed after the inner and outer leaf silencers are in position) and an opening for a triple sealed hatch door which will mirror one on the inner leaf. I built the two frames which are going to support the outer leaf silencers and form part of the enclosure for the inner leaf silencers at opposite ends of the room, incorporating the joists I raised last year.
I made sure that the OSB sheets met over the existing ceiling chords and / or were overlapped with a plank of the same material after being caulked.

I think I should mention that the task of caulking has been made considerably easier since I bought a battery powered caulking gun. I started off using the hand operated type and quickly realised that it would result in severe repetitive strain injury given the amount of sealing I had to do. When researching studio building, you often read maxims like, “if in doubt – caulk it!” and variations thereof. It’s true and before you start building, you can’t imagine how much time and effort you will spend doing this simple task. I’d go as far as saying that the caulking gun is probably the most labour saving tool I have.

Then I began fitting panels of 12mm cement fibre board on the underside of the decking, in between the joists. This combination of cement board and OSB is actually the opposite way round to the cladding on the walls where the cement board was attached first, with battens, between the rafters and OSB (with green glue) attached directly to the rafters. This is because OSB forms a better weight bearing platform (it’s far less brittle) and also cement board is pretty unpleasant to work with; the less I have to cut up, the better. I used the usual, liberal amounts of green glue on the cut panels which, according to the manufacturer’s instructions, should be applied in a ‘random pattern’. In the interests of personal amusement, I based many of these random patterns on short phrases . . .

Rhetorical questions . . .

. . . and inspirational quotes in the style of elusive studio designers!

When the panels were properly glued (I actually applied the green glue more like this) . . .

. . . I lifted them up into position and locked them in place using two panel supports. These can be operated one-handed, so I could easily support the boards with my other hand while adjusting them.

I added a stripe of caulk along each edge and using another support, fixed pre – cut lengths of batten into the joists to hold the cement boards in place.

Now this layer of cement board is in place, it’s almost time (after yet more caulking) to start on the inner leaf structure. Covid 19 allowing, this will involve getting outside help as I don’t have the joinery skills to build and fit sealed windows and doors. Still, it’s starting to feel like I can at least see the destination that I’m heading towards. Thanks for reading – best wishes, John.