But I'd like to look at an innovative transportation system Mr. Johnson designed in 1990, called the TRANS System. It involves "pods" in pneumatic tubes travelling cross country at 200 m.p.h., and locally at 60 m.p.h. and 30 m.p.h. The idea is to turn the "drag" concept upside down, the pod being propelled through concrete tubes by the drag force of air being pumped by at 230 m.p.h. Johnson also envisions elimination of wheel drag by lift provided by the Bernoulli effect. He ultimately envisions a system wherein people and goods can be transported to within two blocks of 98% of possible destinations in the U.S. at prices about 20% of today's and costs of 10% (the difference being used for reduction of the national debt).
There's no math in the linked page, though not because Mr. Johnson doesn't have abilities in that discipline - he's a graduate from the University of Chicago in "nuclear physics." There's lots of claims about the price to move a pound of freight or a pound of passengers. But there's no explanation of how those figures were derived. Beyond capital costs, of course (which Johnson also estimates), the primary operating expense would seem to be keeping hundreds of thousands of miles of air moving at 230 m.p.h. There are also costs associated with the various control systems he envisions.
While the state of research on such systems is not highly active, it's also not non-existent. A brief article with further references of the use of so-called "PCP" (pneumatic capsule pipeline) systems for freight transportation by Dr. Henry Liu of the International Freight Pipeline Society can be found here. It's clear from reading this article and others that Johnson's system represents a large jump in sophistication, particularly with respect to the velocities involved (over 100 meters/second vs. approximately 20 meters/second). Johnson also discusses a "linefill ratio" (the proportion of the tube occupied by freight or passengers) of 50% where the state of the art using blowers is about 3% and the hope is to use linear induction motors to increase this to 15%. There is also an extensive article on utilization of a PCP system for freight transport in New York City here.
Let's think about the power involved in such a system. We'll ignore any change in potential energy required for elevation change. Using the D'Arcy-Weisbach equation and estimating things like the surface roughness of the inner surface of Johnson's concrete tube (he suggests a teflon lining and believes that, even with a Reynolds number on the order of 1.7*10^6, laminar flow can be maintained) and the operating pressure of the system, I can calculate a pressure drop of about 21.8. Pascals/meter. This is a loss of one atmosphere every approximately 4.6 kilometers. So, ignoring the mass of the cars (not particularly accurate since, according to Johnson's design, at peak capacity they might occupy on the order of one half the volume of a tube) we need enough power to provide a pressure boost of 21.8 Pascals in a distance of one meter and a diameter of two meters, or a volume of 3.14 m^3. This should be an amount of work of 21.8*3.14 or 68.5 joules. At 230 miles per hour, it needs to do this in 0.097 seconds. So the power required for that meter is 68.5 joules/.097 seconds, or about 704 watts.
Running some quick numbers for drag, lifting and moving the capsules would require another 440 watts for a subtotal of 1144 watts. Then, assuming a 3 meter long capsule with a mass of, say, 250 kilograms, accelerating it to 89.4 meters/second in maybe 30 seconds will take about 745 newtons. It will take 1340 meters to get to speed, so the power used in accelerating is 745 newtons*1340 meters/30 seconds or 33.3 kilowatts. Just as a rough estimate, in 100 kilometers, maybe 150 such accelerations are taking place, so the system must provide 150 capsules*33,300 kilowatts/100,000 meters or 50 watts/meter. Thus, the total estimated power required is, in round numbers, 1200 watts/meter. The energy requirements are starting to look "scary big." Does this level of power usage make any intuitive sense? Well, I have a vacuum cleaner that uses 11 amps at 110 volts for a power of 1210 watts. The vacuum cleaner is simply moving air, albeit turbulent even at much lower Reynolds number but through a much smaller area and over a shorter distance.
In any case, if I'm even close, a 100 kilometer tube would use 120 megawatts. Assuming that it's half full of capsules, and each capsule is 3 meters long, there are 16,600 capsules. Comparing this to cars, let's assume that 16,600 cars are moving at 55 m.p.h. and getting 25 m.p.g. These cars would use 10.1 gallons/second, each gallon containing 120*10^6 joules or 1.22*10^9 joules/second or watts. This is 1.22 gigawatts or 10.2 times as much power as the Trans system.
Now, there are many, MANY considerations beyond these factors. For example, no accounting of the primary energy (well to wheel for the cars, primary source to generator to fans for the Trans system) was done. And the system would use the energy to move the air regardless of whether there was a single capsule or the tube was filled to capacity whereas cars only use fuel when in use. But let's assume only 10% capacity utilization. The cars would still use about as much energy as the pods, and the pods would be almost four times as fast. Mr. Johnson may have a good idea from an energetic point of view. I wonder, though, how people would take to being in a fully enclosed capsule in a sealed tube?
*Edited to correct factor of 10 error. The advantage of the TRANS system is diminished considerably by this correction and likely constrained to be used in areas where high load factors are expected to be the norm.