Here’s where I left it in Sky Rectangle – a proposal for interlocking back-to-back apartments arranged in rows half-stacked and half-terraced, with both the apartments and access corridors illuminated and ventilated by 4m x 8m shafts open to the sky and corridor.

And this is what that proposal is going to be inserted into – five levels of shopping mall floor-plate, each with an area of approximately 35,000 square metres and with the long sides oriented approximately east-west. Within that floor-plate are atriums, openings for escalators, and cores for elevators, fire-escapes and utilities. There are also double height cinemas, a double height ice-skating rink and a swimming pool, all of which I’ll ignore. Conditions on the periphery are not uniform. Unusually, the north and east side also have three levels of external deck access while the western corner has five levels of externally linked terraces. I’ll ignore these special features because I’m attempting to derive general principles.

Basically, the problem is one of inserting a regular spatial system into a structural one that’s regular only in parts. I don’t know how this is going to turn out. Disjunctions between the two systems will occur on the periphery, around the atriums and around the cores where they ought to be of most benefit to the most people.

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It was a worthy idea, and all the disjunction space was indeed around the periphery, the atriums and the elevators but, as you can see from the Level 2 layout below, there was just too much of it. I was only getting about 100 dwellings per floor. [At this time, I was still assuming an ice-skating rink in the middle on the lower side.]

The area of the floor-plate minus openings is about 30,000 m2. The footprint of each pair of apartments is 128m2, but another 64m2 needs to be added for the access corridor (on one side) as it is be shared by adjacent group of dwellings. The total built footprint for 100 units is therefore 12,800 – a little over one third which is not great. This is largely the result of the basic (paired) residential unit being 8m x 32m. This length creates much disjunction, particularly at the short ends and around elevators. Having occasional unpaired units 24m long instead of paired ones at 32m length also reduces efficiency. Staggering alternate floors doesn’t make much difference as what one gains on the even-numbered levels is lost on the odd-numbered ones. Despite that, or perhaps because of that, the overall environment doesn’t look bad.

This proposal has the views out that I’d envisaged but the best possible situation shown in the image below doesn’t occur often enough or for long enough as the longest “street” has only four units each side.

This next plan is sufficient as proof of concept but I’d like to increase the floor-plate efficiency from one third to at least one half. There are about 600 units here and this doesn’t seem enough for the project to go forward. I’ve identified four problem spots and each of them are caused by the long basic unit encountering an edge or an obstacle. Alternate levels will have the same problems but in different places. Not unrelated is the fact that getting more units in is a bit like designing a car park in that the more double-loaded roads you have, the more efficient it will be. Even looking at this image below, there clearly aren’t enough of those double-loaded access streets shown in the image above. The vertical pattern of streets should be more apparent.

1 The levels above and below have the best fit for the units and this edge condition is the direct result of staggering alternate floors. This can be solved by fitting half-bay (approx. 4m x 8m) two story units between the voids. These units would have no outdoor space save for the void outside their habitable room windows.

2 A different variation could make use of some of the space to the left of the elevators between situations 1 and 2. Nothing can be done about the 16-m spaces either side of the elevators in 2. It might be helpful to have a variation with the standard for unit one half and shortened (by one bay) for the other, interlocking half.

3 This area is isolated by voids and is not large. This suggests breaking the pattern of voids and having standard three-bay units as well as specially designed two-bay units stacked every level.

4 The same might have to be done for all of this sector as none of its areas are large.

The differing overall lengths of these variations account for instances where there are sufficient columns but insufficient length for five-bay paired unis. These variations tidy up the edges and fill in some of the spaces (that would still be necessary even if the unit and corridor positions didn’t alternate). There’s no point rotating the direction of voids and units 90° because larger (longer) areas won’t occur anywhere except the leftmost edge in the above image. Moreover, the streets would be terminated by elevator cores while the same number of variations would still be needed.

On levels 4 and 5 is a two-storey ice-skating rink supported by beams on level 3 but it now makes sense to build over this to provide approximately 24 additional units. Each of the elevator and stair cores is in reality different but I want to keep them generic at this stage and not indicate the internal arrangement. My only conditions are that there be four metres of space on all sides and that their positions not be hidden any more than they currently are.

For now, I’ll design those more compact variations that ought to squeeze some more efficiency out of the floorplate.

If I don’t reach 50% efficiency, then I’ll scrap the staggering and instead design a typical floor along the lines of the above with units facing outwards, units facing inwards towards the atriums and inner units lit and ventilated only by light wells. The units will still follow the column grid but in the other direction. As a solution, I don’t like having a horizontal hierarchy of light as well as a vertical one. If I adopt this arrangement then, in most instances, the ends of these inner access corridors will have elevator cores and, because of that, indirect light from both inside and outside.

Rather than pursuing that Plan B, I did this.

The yellow units are the main unit type but there are now also five other variations. There will be about 180 units per level which is almost 1,000 not counting the basements. I can still see five instances where paired half-bay units could fit but it’s approaching as good as it gets for its premises. It is now easier to see the long double-sided streets that make most efficient use of space.

I won’t bother doing something similar for the alternate floors as, in the above, you can see there are three different conditions for how the units “meet” the elevator cores. Although the situations for the same core will differ, the principle of using the variations to account for shortfalls in length will still apply, only in different positions.

Another option is to start again, and use this study and the one before as the basis for an optimized Mat-rix House with a primary structure FF of 5.5 m and a column grid of 5.5 x 5.5 m. This would (just) be large enough to to arrange a car park (if required) and would also allow either steel or mass timber structure. This structure would be more regular and, since there is no need for atriums to bring light and air, or to add “incident” for the sake of it, elevators and stairs would best placed on the periphery. This will be for some other time.

Conclusion

The demonstration mall is on the left in the image above, and has approximately 1,000 two-bedroom apartments. The two levels of basement car parking extend two bays past the building’s east and west sides so, if B1 and B2 were opened to the outside by removing the slabs in these extensions, it would be possible to have another 400 additional units, bringing the total to 1,400.

To the right of the mall is a typical high-rise residential complex with each half of a paired tower having 4 apartments x 30 storeys = 120 apartments. Let’s say the mall’s width is equal to three and a half tower halves, and that its length is equal to four rows of three half towers. There are approximately 1,440 units.

The spatial efficiency is about the same but the mall has six 5.5 metre levels (approx. 30 metres) and already exists, while the generic towers have thirty 3.0 metre levels (approx. 90 metres).

The cost of purchasing an abandoned mall and inserting lightweight apartments into the existing megastructure has to be weighed against the (financial and environmental) cost of acquiring and clearing a similar area of land and building anew. Purchasing an abandoned mall, demolishing it and then building a conventional residential development makes no environmental sense and is unlikely to make any financial sense either.

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Sky Rectangle

Mallville

Modest Megastructures