Thursday, September 20, 2007

Rail Blues

Greetings, Takers of the A-train,

Last night I went to a show in the big city. As you know, I don't own a car, so I took a subway car back, and noticed how very odd it was that about 100 rich patrons waited with me for over 20 minutes for a train. (My metropolitan area has notoriously infrequent trains, especially at night.) It got me wondering: how crazy is it (financially) to run trains infrequently at night?

Extra Costs

It's easy to say "Let's just run trains every minute," but the whole reason why public transit systems work is that many people going the same way can use just one vehicle and driver. Let's figure out the cost of splitting one infrequent but long subway trains into two shorter trains.

If the run lasts two hours and the driver costs $40/hour (including overhead, training, etc.) the personnel expense is $80. The necessary force (hence electricity cost) of pushing an additional train front through the air can be calculated using:

F = .5 A D p v^2,

where A is the area of the train front, D is a drag coefficient (usually about .25 for aerodynamic shapes), p is the density of the medium and v is the speed. Using A D = 4 m^2, p = 2kg/m^3, v = 20 m/s, electricity costs $.15/kWh and the distance traveled is 100 km, we see the extra energy costs is a measly $7. Let's round up and say an extra $100 would be needed to run an extra train.

Extra Benefits

So, how much shorter a commute would there be if an extra train came? The trains come every 24 minutes, and by the time a train came last night there were over 100 people waiting at my station and over 100 at the next station (the two busiest, mind you); let's lowball the estimate and say 250 people would be able to catch a train on average 6 minutes sooner if train frequency were doubled. Doubling train frequency means 25 commuter hours would have been saved at a cost of $100 to the system: $.40 per passenger or $4/hour of passenger time saved.

However, increasing service might increase ridership, so it's possible that the extra train would (at least partially) pay for itself. Increasing ridership eases burdens on parking and roads too; public transit is overall a good bargain.


It's time commuters got vocal about being willing to pay a fair amount for their time that gets wasted by sluggish schedules. I wish we'd get a consistent metric of how much our time is worth, and use it to make policy decisions. Check out my post on machine wages for equivalent cost-time comparisons; this concept may evolve into a wiki page soon.

Keep on track!


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