For those of you that don't know, the HyperLoop is a secretive idea, hinted at by Elon Musk, which essentially proposes international travel at an amazing speed and efficient cost. The proposed transportation method will hypothetically take roughly thirty minutes to go from San Francisco to L.A. Now, my personal guess on the technology which he claims is going to be the "fifth mode of transportation" is that is actually a technology with has been in question for many years and is only based on one scientific premise: Newton's law of universal gravity from 1687 - though, in practice, it would be very difficult and take huge engineering feats to implement. Allow me to explain.

1. Gravity and Force Vectoring

Consider the following image:

Imagine that the blue circle is Earth, while the grey dot is it's center point. Now, image the red and purple lines as tunnels through the surface of the Earth. Before we go further with the current illustration, though, lets talk about gravitational pull through a massive body. Assuming no friction and wind resistance, you can, theoretically, travel strait through a massive sphere using nothing but gravitational energy. How? The core of the sphere would accelerate you toward it at a high rate of speed, the rate of acceleration decreasing as you get closer. Once you passed the center (you're going fast as hell, remember), it would start to accelerate you against your current velocity (decelerate, really). However, because you gained that velocity from the same gravitational energy, it will take exactly the same distance to slow you to a stop: stopping you at the surface of the sphere - on the opposite side! Now, it would start to pull you back again, but that would obviously be counteracted using other technology. Don't take my word for it, though. Let's look at the math.

This equation, where G is the gravitational constant and p is the average density of the sphere, describes the time it would take for that phenomenon to occur:

t = root(3Pi / (4Gp))

This equation, using the same constants and R as distance from the center at which we begin to fall, shows the maximum velocity you would reach:

v = R root(4/3 PiGp)

Now, if we put in the constants for Earth and allow Wolfram Alpha to work it out for us, we get the following results:

Time: Roughly 42 minutes

Speed: Rouyghly 17,750 miles per hour

Now we can go back to our diagram. Assuming we go exactly through the center (a line not plotted), our math tells us it would take 42 minutes. How about for the purple line? Or the red line? Surely it's not the same? Actually, it is. The deference in force, calculated byF * sin(theta) is proportional to the difference in distance, calculated byD * cos(theta)[F = force on a strait path, D = length of a strait path, theta = corresponding angles of a vector between the bisected deferred path and the center-point of the strait path]. This means that any cut through the sphere would work out to have the same exact travel period and a maximum speed calculated byv * sin(theta).

2. Friction and Drag

While this method seems like it could be great, friction highly offsets the gravitational pull and would result in significantly different results (one's which I don't know the math to calculate, in fact). However, we can use magnetism to counteract the friction.

Consider this image:

What is happening here? According to zelmerszoetrop on Reddit, it is a process called "induction heating." Essentially, the alternating electrical current inside the coils is causing a quickly changing magnetic field, essentially suspending the object in place. While this does cause the object to get significantly hot, we can counteract this very effectively (what you're looking at is, essentially, how a motor works). Now, my theory of an easy way to counteract the drag against the air would be to use the spin induced by the magnetic suspension to our advantage by making our capsule essentially a giant propeller, helping to accelerate itself forward as it spins.

There are problems with this, however. For one, I have absolutely no idea how much energy this would take. The whole point of this system would be using gravity to do the work - does this outweigh the benefits? I'm not sure, so let's try another alternative. This second option would be to use permanent magnets to suspend the capsule inside the tunnel. Ideally, it would not spin and would stay perfectly suspended inside of the tunnel. There could then be some sort of on-board propulsion to counteract the drag. We may also have a method of "vacuuming" the tunnel to keep drag minimal.

3. Current Technology

This idea seems very feasible for the far future, but what about today? Physicists have talked about this for years but it has never been anything serious due to many factors:

- The absence of capable drilling tech
- Seismic anomalies and our lack of understanding of tectonics
- No sponsorship
- The inertial forces acting upon passengers
- etc

4. Conclusion

Has Elon Musk found remedies to our problems with this technology, or is HyperLoop something completely different? The price tag of $6 Billion might say it is, though everything else makes me feel like this is what he is talking about. Regardless of what technology is in the works, though, I'm sure it will be great. What do you guys think it could be?