Mass transit makes two contributions to energy efficiency.
1) When ridership is high enough, mass transit moves people more miles on less energy than cars do.
2) When other conditions are right for high population density, mass transit encourages and enables high density, which, in turn, is a major source of energy efficiency.
The cost of transportation, of course, is one place where higher population density contributes to lower energy use per capita. You can get more in a closer distance, so -- even if you drive there -- you expend less energy. And, often, people in high-density areas walk there instead of driving there. Or they take very high efficiency, because of high ridership, mass transit.
But people in high-density areas also live in apartments which leak heat only on exposed walls, not on four sides and a top. (If you want to be terribly technical, as much heat leaves an apartment room as a house room; it's just that more of it goes to another room which is leaking heat back.) And less energy is expended on cutting grass and purifying water to potable quality for spraying on lawns.
Low density areas not only use more energy per capita during their occupation, they also require more energy to construct, as well. Roads, sewers, power lines, water lines, all require energy. A little of this is charged -- at the regular, subsidized, rate for energy purchase -- to the builder or the homeowner. A lot of it is paid by the government or all utility customers.
When traffic frequently gridlocks, that discourages population density. We may be fairly certain that other forces would produce a greater density if the traffic congestion weren't working against it. Under those circumstances, mass transit reduces traffic congestion and encourages greater density. And, when the greater density occurs, the results are benefits which promote even greater density -- closer shopping with a greater variety of products, for example. (The September Scientific American includes an article which also proposes that social progress advances more rapidly in large cities, as well.)
There is no discernable reason for mass transit to encourage higher density if you don't have traffic congestion. If you see one, please note it in a comment.
I'll examine contribution (1) after the jump.
Mass transit vehicles, buses, Els. streetcars, cost a good deal of energy to move, more than the average car. (They also consume the labor of a driver and, of course, the energy and labor to construct.) If they are reasonably full, then they use less energy than the cars for which they are the alternative. Clearly, one major requirement for them to be full enough on average is to have a reasonable population density. (A smaller population density might fill buses at rush hours if those buses only ran at rush hours. I know of no location, however, where this program has been tried. One problem is that the drivers, equipment, managers, etc. must be provided even if they aren't used most of the day. School buses, as an exception, do behave similarly to this.)
On another post of mine, a commenter suggested that if we had electricity that had been generated in a green fashion and if low-density suburbs were served by trackless trolleys on a frequent-enough schedule to attract riders, then we could have mass transit with a zero carbon footprint in those suburbs. The answer sounds a little like "If we had sugar, then we could have lemonade, if we had lemons." Certainly it doesn't speak to the question of extending mass transit in the present situation.
(Trackless trolleys are -- or were -- electric-powered, rubber-wheeled vehicles. The current that powers a streetcar comes from a single overhead wire, then powers the motor, and then flows into the tracks and -- from there -- into the ground. The current that powers a trackless trolley flows from one of a pair of overhead wires, then through the motor, and then back through the other wire. The trolley has the advantage over a streetcar of a [limited] ability to steer around obstacles in the road, and, of course, no tracks to bump car tires. It has the disadvantage of two wires to install and maintain and which overhang the street. They were mildly popular once; I don't know of any place where they still exist. Before embracing the idea, I'd ask why they weren't kept.)
The problem of schedule frequency is a real one. Any reduction of scheduling frequency will be met by a drop in utilization. One would expect a greater drop where car usage is more convenient. On the other hand, when ridership isn't filling the vehicles sufficiently, a greater frequency will reduce ridership per vehicle.
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A personal note:
I have a replacement hip that has become infected. I shall have surgery two weeks from today which will probably replace that hip with a third one with special antibiotic properties.
Since I post from the library instead of home, I expect to be off the Internet for something like 6 months. I may be able to post once or twice more before the surgery, but they will be sporadic. I'm not ignoring your comments, if you make them.