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Fri 11 Nov, 2005 07:01 am
I have a situation where we can design a housing scheme, but is is required to be a certain distance away from a chemical storage tank.
Two hypothetical concentric circles originate from the tank, which are essentially hazard topography lines, and in each zone created by the two circles (inner, middle, outer) there are restrictions on the type of development allowed.
In the middle zone we can design housing to a density between 28 and 70 people per hectare as risk decreases across the zone. What I want to know is the the average density achievable in the zone. Is it 49? or is there an more mathematical way of working this out? Surely on the outer edge of the zone there is higher density and more of it area wise which would drag the average up. Does anyone know how I work this out?
Thanks
So at R1, the allowed density is 28 people per hectare and at R2 it is 70 people per hectare? Is the density allowed linear between R1 and R2?
Let's say I have it right. To find the total number of people allowed, you would integrate the area function times the density function, then divide by the total area to find the average density.
Area Function = 2*Pi*R*dr
Linear Density Function = (42)*(R-R1)/(R2-R1)+28
Multiply these together and integrate from 28 to 70 to get the total number of people allowed. You can get the area using the typical circle area formulas.
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