Physics Can Be Such A Drag.

Lu-Tze can’t think of a funny name asks

I want to go to the west coast of America. But like, really really fast. Of all the stupid inventions of science fiction over the years (Gravity Elevators, Teleporters etc.) what’s actually possibly feasible?

None of them. I can’t deal with science fiction on this blog, which is what gravity elevators, teleporters etc. fall within the realm of. They might be possible using crazy future science, but I can’t reasonably predict that. I have to stick to the world of mundane physics, and in this world there are some nasty limiting factors on exactly how quickly you can get about the planet, the major one being atmospheric drag.

As you travel through the Earth’s atmosphere, you encounter a force caused by Newton’s third law; conservation of momentum means that as you hit air molecules in the atmosphere and move them out of the way, the air molecules impart an equal and opposite force on you that resists your motion through the atmosphere. This is air resistance, and the resisting force is the drag force. Drag force can be calculated by

Where FD is the drag force, ρ is the density of the atmosphere/fluid through which you are moving, v is your velocity relative to the atmosphere, CD is the drag coefficient of the vehicle you’re travelling in (it varies depending on the shape of your vehicle) and A is the cross-sectional area of your vehicle (which can be broadly thought of as the surface area of the vehicle perpendicular to the direction of motion).

It looks complicated, but since the drag coefficient is also dependent on ρ and V and A is going to be as small as you can make it we can boil it down to just saying that FD is proportional to the density of the atmosphere you’re travelling through multiplied by the square of your velocity.

It’s that square that effectively kills any hope we have of faster Earth-based travel using near-future technology. As you go faster, the drag force resisting your movement increases exponentially and the amount of thrust you get from burning fuel gets smaller and smaller. I got this graph from Wikipedia which demonstrates the problem.

Specific impulse is a measure of how fuel-efficient something is. A thing with a high specific impulse will use less fuel to create the same amount of thrust as something with a low specific impulse. You will notice that turbofan jet engines, while only being capable of relatively low velocities, have an incredibly high specific impulse because they can sustain those low velocities on very small amounts of fuel. As you get faster the specific impulse of even the experimental air-breathing engines like ramjets and scramjets decreases exponentially because the amount of atmospheric drag opposing their motion is increasing exponentially.

So, while we can go fast inside the Earth’s atmosphere it’s not very fuel-efficient to do so, and that’s the main consideration we have when we consider mass transit of humans about its surface. What about going outside the Earth’s atmosphere? That would reduce the density term in the drag equation to zero and remove atmospheric drag entirely. This permits spacecraft to achieve much higher velocities than anything could ever manage inside the atmosphere, but there’s a small snag involved. You see that the specific impulse for rockets on that graph is both very small and totally flat with respect to velocity? That’s because rockets, in order to operate at the velocities they do and in order to operate outside an atmosphere, have to cart their own oxidiser along with them wherever they go. This makes them really, really fuel-inefficient.

Still, you asked me what is possibly feasible, not what is likely to happen, and there is a very feasible method of getting to the other side of the planet very quickly. It’s the space plane concept, and the best example of that at the moment is Virgin Galactic. It might seem odd for me to say that since I’ve spent quite a lot of time on this blog tearing Virgin Galactic apart because it’s not a real spacecraft. This is because it goes up to an arbitrary line separating “the atmosphere” from “space” but doesn’t actually go into orbit, which is what really qualifies as space. However, the sub-orbital flights that Virgin Galactic makes would actually be quite handy for getting around the Earth’s surface on short notice, in much the same way that intercontinental ballistic missiles are quite handy for incinerating the capital city of an opposing superpower on the other side of the world on short notice. The US was even investigating the space plane concept fairly recently as a way of delivering a rapid reaction force of marines to anywhere on Earth within two hours. The drawback, as ever, is that sub-orbital flights are still bloody expensive despite not actually going into space. Virgin Galactic costs $200,000 per berth, which is why it’s marketed as a way for the super-rich to experience “space” rather than as a next generation transport mechanism and why I think it’s never going to go much beyond that in a commercial capacity. Maybe I’m wrong, though. Maybe in fifty years we’ll all be flitting around in Virgin Galactic space planes while the embalmed corpse of Richard Branson cackles madly in its life support pod. You never can tell.

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8 thoughts on “Physics Can Be Such A Drag.

  1. Interrobang‽ says:

    I was expecting you to just rip apart the usual tropes and explain how all this crap about “teleporting” particles was a bunch of headline grabbing rubbish, but instead got something way better. A+++ Would Read Again.

  2. hentzau says:

    That was my original plan, but since they contravene basic physical principles it wouldn’t have been very interesting as the post would have consisted of four words: “You can’t do that.”

  3. Smurf says:

    I suggest we dig really long tunnels between places and then suck all the air out to create a vacuum. That way we can get really fast trains. Right?

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