Ken Larsen's web site - Light Rail math
People won't use light rail unless it is convenient. In order to be convenient, a person must live within a quarter mile of a station, and their destination must also lie within a quarter mile of a station. What is the probability of both being true for the proposed Durham-Chapel Hill Light Rail line? Astonishingly, the answer is less than 0.1%. Here is the math:
There will be 18 stations.
The total area within a quarter mile of a station is 0.2 square mile (based on the formula for the area of a circle).
Therefore, the total area for all 18 stations is 18 x 0.2 = 3.6 square miles.
The total area for Chapel Hill is 21.3 square miles. [The area of Orange County is 401 square miles.]
The total area for the city of Durham is 96.6 square miles. [The area of Durham County is 298 square miles.]
Therefore, the total area for both is 117.9 square miles. [The total area for both Orange and Durham counties is 699 square miles.]
Therefore, the percentage of Chapel Hill and Durham that lies within a quarter mile of a station is 3.6/117.9 = 3% [If you count all of both counties, it's just 3.6/699 = 0.5%.]
The probability that a trip's origin and destination both lie within a quarter mile of a station is found by multiplying 3% by 3%. That equates to a microscopic value of just 0.09%. [If you do this math for all of both counties, it's just 0.5% by 0.5% = 0.0025%.]
0.0025% = 1 chance in 40000
This math doesn't even count cars which are passing through ... starting or ending their trip outside of Durham or Orange county. If you add these cars, the probability becomes even lower than 1 chance in 400.
You can increase the coverage area by providing ample bus service to drive people to and from stations. However, the downside of that is that people will have to take one or more buses to get to a station and then take one or more buses to get to their final destination. Add in the expense of tickets and the travel time and many people will conclude that cars are far more convenient.