The Maths

Density

F.A.R is a measure of density, and is found by dividing the total areas of all the floors by the area of the ground occupied (including the building plots, gardens and streets.)  The higher the F.A.R, the higher the density.

Assuming that each resident requires 40m² of living space at a F.A.R of 0.75, then the ground space required per person for housing is given by:

And assuming each resident requires 30m² for non-residential uses at a F.A.R of 1.5, then the ground space required per person for non-residential uses is given by:

Now we can calculate the average F.A.R:

Town for 24,000

The area of the town is given by ∏r² where r, the radius, is 750m.

With an average F.A.R of 0.9545 and allowing 70m² per capita (40m² for housing, 30m² for work, services etc.) this gives a population of:

Population	= building area × F.A.R / floor space per capita
	= 1,767,145 × 0.9545 / 70
	= 24,097

Or over 24,000 people.

Assuming a walking speed of 75 metres per minute, the walk from the edge of the town to its centre is given by:

Town for 35,000

The area of the town is given by ∏r² where r, the radius, is 900m.

This gives a population of:

Population	= building area × F.A.R / floor space per capita
	= 2,544,690 × 0.9545 / 70
	= 34,700

Or just under 35,000 people.

And the walk to the centre is given by:

Sample Blocks

2.5 Storey Row Housing

Ground area	= (8 + 84) × (8 + 10 + 12 + 8 +12 + 10)
	= 5520m²

F.A.R	= total floor area / ground area
	= 4200 / 5520
	= 0.76

4 Storey Block

Ground area	= (10 + 48 + 2 + 10) × (10 + 48 + 2 + 10)
	= 4900m²

F.A.R	= total floor area / ground area
	= 7680 / 4900
	= 1.567

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