Set in the year 3000, the series Futurama features one of the most interesting forms of personal travel: pneumatic tubes. Pneumatic tubes were used primarily in the late 19th to the early 20th century to transport small packages over short distances, typically within a building or city. Though use is very limited today, the idea has renewed interest with Elon Musk's Hyperloop is a conceptual high-speed transportation system in which pressurized capsules ride on a cushion of air.
Is a Futurama type tube travel possible, and can science answer the question? Turns out, it can!
Riding a Column of Air
Futurama travel likely works by sucking people through the tube. A vacuum pump sucks the air out inside the tube. If the difference between the pressure from the outside to the pressure inside the tube is great enough, the resultant force can push someone along the tube.
We are going to assume we are sending an "average" man through the tube (kicking and screaming if we have to). His mass, m, is about 70 kg (154 pounds) and his effective area, A, is about 0.135 square meters (1.45 square feet). The k is the drag coefficient or how much friction there is.
We really do not know how fast someone is going through the tube but we can figure it out. We will assume the maximum speed or terminal velocity is the same as a skydiver. There are some differences here, as the skydiver is falling vertically with his arms and legs out and tube travelers travel lengthwise but the terminal velocity gives us an upper limit to work with. For this, we turn to the terminal velocity equation.
We could solve the second equation but instead, we just plug it into the first. This makes things easier.
This gives us a new equation that we can use to determine if tube travel is possible. This gets rid of most of the other variables and makes calculation less problematic.
The pressure at the entrance of the tube, P1, is open to the atmosphere and is just atmospheric pressure, about 101 kilo Pascals (14.6 pounds per square inch). From what we know, P2, the pressure inside the tube is about 91.1 kilo Pascals or 13.2 pounds per square inch. As it turns out, from an engineering perspective, this is an easy pressure to attain and it is possible to move a human being along a tube.
This "back of the envelope" calculation only considers a person traveling horizontally through a tube and, as we can see, Futurama's tubes are far more complex; travelers can change direction and move from one tube to another to get to their destination. This will require a system of valves to quickly push a person into a new tube. Controllers will have to constantly monitor traffic to ensure accidents don't happen.
What may be a more feasible form of tube travel is Elon Musk's Hypertube, the same type of travel that was seen on Kingsman: The Secret Service. It just connects two points but it will do so quickly. The real question is, if Futurama style tube travel was invented, would you use it?