The Maths

Pedestrian Eco-town

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

Alternative Design #1

Outer Districts

The area of an outer district is given by ∏r² where r, the radius, is 300m.

From this we must remove the extra space required for the bus lanes.

Area of bus lanes	= 16 × 600
	= 9,600m²

Building area per outer district	= area - bus lanes
	= 282,743 - 9,600
	= 273,143m²

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

Population	= building area × F.A.R / floor space per capita
	= 273,143 × 0.9545 / 70
	= 3,724

Central District

The area of the central district is given by ∏r² where r, the radius, is 300m.

From this we must remove the extra space required for the bus lanes.

Building area of central district	= area - bus lanes
	= 282,743 - 19,200
	= 263,543m²

If the central district has a F.A.R of 1.5, and allowing 70m² per capita for housing, work, services etc., this gives a population of:

Total Population

Adding the populations of the 12 outer districts and the central district we get:

Public Transport

Longest Journey

The longest journey is 7 stops and does not require a transfer.

With trolleybuses running every 5 minutes, the average wait is 2.5 minutes.

Now we need to calculate how long it takes to travel from one station to the next.  We will assume a top speed of 30mph, or 13.33m/s, an acceleration of 1.33m/s², and a dwell time of 20 seconds.

Distance covered during acceleration/braking	= ½ × a × t²
	= ½ × 1.33 × 10²
	= 66.66m

Distance covered at top speed	= total distance - acceleration and braking distance
	= 600 - 2 × 66.66
	= 466.66m

Time spent at top speed	= distance at top speed / v
	= 466.66 / 13.33
	= 35s

Using this data, together with the dwell time, we can calculate how long it takes for the bus to travel between stations.

Total time	= dwell + acceleration time + time at top speed + braking time
	= 20 + 10 + 35 + 10
	= 75s

or 1.25 minutes.

This gives us a longest journey of:

or just over 11 minutes.

Capacity

In the morning rush-hour, how many people can the trolleybus network transport to the town centre?  With trolleybuses running every 90 seconds, and using double articulated vehicles with a seating capacity of 90, then the total capacity for the morning rush-hour is:

or just under a third of the 45,000 residents of the outer districts.  The 5,000+ residents of the central district are, of course, already there.

Note that this is just seated capacity.  The double articulated buses in Curitiba, for example, can carry up to 270 people at full load.

Also, trolleybuses could run every 60 seconds if needed, increasing rush-hour capacity to almost half of the outer districts' 45,000 residents.

And, since work places are spread throughout the town, rather than being concentrated at the centre, not everyone will have to travel through the town centre to get to their place of work, reducing the necessary rush-hour capacity.

Size of the Fleet

How many trolleybuses are needed for the whole town?

Each trolleybus does a complete circuit in 14 × 1.25 = 17.5 minutes.  Thus to provide service at 90 second intervals, 12 buses are needed per direction.  So 24 are needed in total, plus spares.

These 24 trolleybuses replace the 10,000+ private cars that would be needed in a conventional town.

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