May 7, 2016
I recall once figuring that the capacity of a single track of subway was substantially higher than a lane of traffic. This is how that is calculated for a real live subway (the MBTA Red Line, also roughly applies to Orange and Blue lines which run similar equipment.)
redline_cars_per_train = 6
Source: Wikipedia red line article
redline_trains_per_hour = 60/4.5 = 13.3
Source: 2014 MBTA Blue Book, page 17.
Headway is 8 or 9 minutes at rush hour on each of the Alewife/Ashmont and Alewife/Braintree lines, or 4.5 minutes on average on the shared portion of the line.
redline_ppl_per_car_policy = 167 redline_ppl_per_car_crush = (267*74+260*58+277*86)/(74+58+86) redline_ppl_per_car_seated=(63*74+62*58+52*86)/(74+58+86)
Source: 2014 MBTA Blue Book, page 18.
167 is the policy people-per-car. Seated and crush capacities are averages over the red line fleet.
seated_rush_cap = redline_ppl_per_car_seated * redline_cars_per_train policy_rush_cap = redline_ppl_per_car_policy * redline_cars_per_train crush_rush_cap = redline_ppl_per_car_crush * redline_cars_per_train seated_rush_cap * redline_trains_per_hour => 4,671.5596 policy_rush_cap * redline_trains_per_hour => 13,360 crush_rush_cap * redline_trains_per_hour => 21,526.6055
Compare this with a lane of traffic. Rule of thumb is that you get one car every two seconds, or 1800 cars per hour, and an average of 1.2 people per automobile, or 2160 people per lane per hour. Simple seated subway capacity at rush hour is double that, so-called “policy” capacity is 6 times that. Crush capacity, which I’ve seen and not much liked (“nobody takes the subway, it’s too crowded”) is just shy of 10 times the capacity of a lane of traffic.
And understand, this is far from the theoretical capacity of a subway line, it’s just what is actually obtained on a real subway in a real city at rush hour. Run longer trains (requires longer platforms, a completely doable thing) and you can add capacity. Run trains more frequently, and you raise capacity – the London Underground appears to manage 24 trains per hour at rush hour on the Northern Line or not quite double the Red Line’s frequency.
Re-doing the numbers at the London Underground’s rate for scheduling trains:
seated_rush_cap * underground_trains_per_hour => 8,408.8073 policy_rush_cap * underground_trains_per_hour => 24,048 crush_rush_cap * underground_trains_per_hour => 38,747.8899
At the Underground rate, “policy” train packing carries 11% more people than “crush” packing in the current system. And the theoretical “crush” capacity is the equivalent of 18 lanes of traffic.