Crosstown Traffic
All you do is slow me down
And I got better things on the other side of town
How is capacity determined in traffic analysis?
Congestion will slow you down. The travel time in congestion is defined as a function of the capacity of a road. The closer that the demand, volume, on a link comes to that capacity, the worse the congestion. However the capacity that is used in those calculation is often misunderstood. If it were better understood perhaps no one would ask questions like “How can you even have a Volume to Capacity ratio that is greater than 1.0?”
Traffic flow theory says that traffic moves like a compressible fluid. While my auto insurer of course doesn’t want me to compress my car, the compression as it is being used here, and by extension the capacity of that compressible traffic, refers not to the physical bumper to bumper capacity. It refers to the operating capacity of the car. And that operating capacity incudes not only the car itself, but also the spacing to the car ahead. It is that spacing between cars that is compressible, not the car itself.
In a compressible fluid, the flow is expressed as the product of the speed and the density. Because flow is typically expressed as cars per hour, and speed is typically expressed as Miles per Hour, this means density would have to be expressed in cars per mile. The space consumed by an auto would be the bumper to bumper car length plus the spacing to the car in front, feet per car, or converting the units, miles per car. It should then be apparent that density of traffic as a fluid has to be the inverse of the operating length of a car, i.e. the bumper to bumper length plus spacing.
When I took Driver’s Ed, the rule of thumb for the safe spacing to the next car was a function of driving speed. That rule of thumb from the safe following distance to the next car was one car length for each 10 MPH of your speed. This has since changed to a 2 or 3 second gap, which says that the spacing between cars should be the length to travel those seconds at the speed of the car. In any event both the old time rule of thumb and the newer gap time rules, make the operating length a function of speed. If the bumper to bumper car length is 20 feet, and the operating speed is 70 MPH, then the space “occupied” by the car is 20 feet plus 7 car lengths, 70 MPH/10, or 160 feet. The density would thus be 1 car/160 feet, or 33 cars per mile. This means that the flow at 70 MPH and a density of 33 cars per mile would be 2310 cars per hour. This is just about the standard capacity in passenger cars for a freeway with a design speed of 70 MPH.
For the 2 or 3 second following rule you would get much lower capacities, but the Maximum Flow Rate its actually a transition between laminar and turbulent flow of fluid, which is way beyond what I wanted to discuss here. So when the LOS is F and the Volume to Capacity, v/c, ratio is greater than 1.0, the spacing between cars is less than the one car length per 10 MPH rule. Safety suffers, but this v/c ratio is still physically possible. The maximum density is of course one car length, but since that occurs at 0 MPH, the flow rate is zero anyway.
