An analysis based on linear distance fails the essential geometric test:
> Humans walk at roughly 2.1-3.0mph. "European cities" are listed as having bus stops 984-1476 ft apart, which would imply you'd typically walk half that to reach the nearest one (492-738 ft), which for a fit 3.0mph person is 2-3 minutes, and for a frail old 2.1mph person is 3-4 minutes.
> Of course, people can be further away than that (they live orthagonally to the bus route), but you get the point. If you doubled bus stop distances to 1476ft apart, it would not add many walking minutes for the users.
Given four "bus stops" spaced at the corners of a square of dimension d, and a linear relationship of distance and time such that d == t, the distance to a stop along the edges of the square is at most d/2 == 0.5d. As the crow flies (straight line) the distance from the center of the square to any of the corners is sqrt(2*(d^2)) / 2 or (approximately) 0.71d.
But people don't fly, rather geometric physical reality is something sometimes called "manhattan distance" which essentially means that they need to walk to the edge and then along the edge (or zig-zag block by block, which amounts to the same thing just repeated at smaller scale). In this case the distance walked to any of the corners from the center is exactly d. Unless you live in the middle of a park (with stops at the corners) d is the best outcome. In a physical environment other obstacles may present which require backtracking; indeed, the bus routes (and hence stops) are likely optimized to avoid backtracking, acknowledging this physical reality.
> Humans walk at roughly 2.1-3.0mph. "European cities" are listed as having bus stops 984-1476 ft apart, which would imply you'd typically walk half that to reach the nearest one (492-738 ft), which for a fit 3.0mph person is 2-3 minutes, and for a frail old 2.1mph person is 3-4 minutes.
> Of course, people can be further away than that (they live orthagonally to the bus route), but you get the point. If you doubled bus stop distances to 1476ft apart, it would not add many walking minutes for the users.
Given four "bus stops" spaced at the corners of a square of dimension d, and a linear relationship of distance and time such that d == t, the distance to a stop along the edges of the square is at most d/2 == 0.5d. As the crow flies (straight line) the distance from the center of the square to any of the corners is sqrt(2*(d^2)) / 2 or (approximately) 0.71d.
But people don't fly, rather geometric physical reality is something sometimes called "manhattan distance" which essentially means that they need to walk to the edge and then along the edge (or zig-zag block by block, which amounts to the same thing just repeated at smaller scale). In this case the distance walked to any of the corners from the center is exactly d. Unless you live in the middle of a park (with stops at the corners) d is the best outcome. In a physical environment other obstacles may present which require backtracking; indeed, the bus routes (and hence stops) are likely optimized to avoid backtracking, acknowledging this physical reality.