Set in the year 3000, the series Futurama features one of the most interesting forms of personal travel—pneumatic tubes. These 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 it is in very limited use today, there has been renewed interest with Elon Musk's Hyperloop as a conceptual high-speed transportation system in which pressurized capsules ride on a cushion of air.
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.
Let's assume we will be 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 in the equation is the drag coefficient which tells us how much friction there is.
We really do not know how fast people can travel through the tube in Futurama but we can figure out their maximum speed or terminal velocity based on the physics of skydiving. There are some differences to consider. For one, skydivers tend to fall vertically with arms and legs spread out. Tube travelers travel lengthwise but the skydiver's terminal velocity gives us an upper limit to work with. Here's 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. It also gets rid of most of the other nasty variables and makes calculation less problematic.
The entrance of the tube, P1, is open so the pressure is just atmospheric pressure, about 101 kilo Pascals (14.6 pounds per square inch). We can work out P2, the pressure inside the tube, using our new equation to find this 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, making it is possible to move a human being along a tube.
Other Considerations of Tube Travel
Before we get excited and start building our own Futurama-style tube network, we need to keep in mind our "back of the envelope" calculation only considers a person traveling horizontally through a tube. 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 requires a system of valves to quickly push a person into a new tube, as well as the need for controllers to constantly monitor traffic and ensure accidents don't happen.
A more feasible form of tube travel might be found on Kingsman: The Secret Service. In fact, this is pretty close to Elon Musk's Hypertube as it just connects two points; a person can travel between the two points very quickly. The real question is, if Futurama style tube travel was invented, would you use it?