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Use a maglev railgun for initial acceleration - in a new, hyperbolic tunnel facing eastward - this exits from the burrowed -undergrade- track to Equadors' Mt. Chimborazo peak - (a mountaintop both 6 km high, and closest to equator / hence shortest distance to Space),
exiting vehicle through the higher atmosphere at hyperspeed. No structure needed, tunnel is surrounded by rock. Simply stated, seven reasons why I think this is viable :

  1. Location: application of max. earth rotation to assist both vector forces and velocity to transport vehicle to orbit
  2. close to equator launch provides “Closest to Space” distance though atmosphere. (2 km closer to Space than Everest)

  3. Atmospheric density clearance: lowest density of atmosphere to accelerate through.

  4. substantially lower energy expended: the “tyranny of Rocket propulsion” is fuel weight and use. This eliminates over 75% of standard rocket propulsion energy usually expended. (@ 61 km altitude Saturn V has expended over 80% of its weight, 2 million kg fuel load at slower velocity, 2.3 km/s )
  5. With railgun tunnel interior near vacuum - and a hi-speed mountain peak aperture for vehicle egress, (and Bull’s large cannon calcs about orbital projectile speed @ 7.2 km/s) are efficiently achieved with minimal rocket energy propulsion. conventional, off the shelf technology applications
  6. Realistic, controlled railgun acceleration over 4 km within tunnel - and an almost unlimited earth-based energy supply.
  7. Tunnel boring machines, magnetic railgun, large mass and volume of space transport vehicle.

What are largest technology obstructions required for such a launch system?

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    $\begingroup$ en.wikipedia.org/wiki/Project_HARP - Check this out, you may enjoy this read. $\endgroup$ – Magic Octopus Urn Jan 30 at 13:24
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    $\begingroup$ You say "almost unlimited energy supply is assumed" and then ask "what are largest tech problems?" But you have just said that you assume that the hardest part -- supplying the millions of amps of current required to scale a railgun beyond "tabletop" size -- has been solved. That problem has not been solved; we do not have materials that withstand the necessary sustained currents. $\endgroup$ – Eric Lippert Jan 30 at 20:31
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    $\begingroup$ Remember, the problem is not the electrical energy per se; you are right that we have plenty of electricity available. The problem is concentrating that electrical energy so that there is an enormous amount of it moving extremely quickly through an extremely small space. It's similar to designing a hydraulic system and saying "we have plenty of water". Sure, we have an ocean of water but we cannot increase its pressure or flow in a narrow pipe to an arbitrary degree given our current materials available. $\endgroup$ – Eric Lippert Jan 30 at 20:35
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    $\begingroup$ Mt. Chimborazo may be 2km further from the centre of the earth than Mt. Everest, but that doesn't mean it is 2km closer to space. The atmosphere is oblate, just like the earth is -- its thickness at the equator is just about the same as its thickness over Nepal. $\endgroup$ – TonyK Jan 30 at 22:42
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    $\begingroup$ Why on earth would you spend hundreds of billions to potentially trillions to build one of these rather than investing a relatively small pittance in reusable rocket tech? Best case scenario, a rail-gun system could put an extremely limited payload into a specific orbit and it would still cost you a ton of money. These things belong on the moon where they could easily inject small objects into a earth return trajectory, and they are totally non-viable on any planet with a thick atmosphere. $\endgroup$ – eps Jan 31 at 17:12
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What you're describing is (more or less) the StarTram "gen 1" design.

The reference design has:

  • 40 tonne unmanned cargo projectile, 25 tonnes of payload, ~2 m wide, ~13 m long.
  • A 130 km maglev acceleration tunnel, evacuated.
  • An exit point 6000 m up, on a mountain.
  • A plasma window to allow projectile egress into atmosphere without repressurising the entire tunnel.
  • Muzzle velocity of ~8.78 km/s and 10 degree elevation.
  • ~.63 km/s delta-V rocket for orbital injection.
  • Launch into a polar orbit with multi-thousand-km of ocean downrange so accidents don't drop hypersonic debris onto inhabited countries.

(There used to be a nice ebook available from their website, but it is no longer free. I got a free copy, and it has some technical information in it... more than the Wikipedia page, but not nearly as much as I'd have liked.)

The slight increase in exit speed compared to your suggested design isn't particularly interesting, but the much, much longer acceleration tunnel points to the StarTram folk being somewhat more conservative about a) the ability of their magnetic accelerators and b) the ability of the cargo carried in the projectile to survive acceleration forces. Power switching for a big coilgun, and handling rail wear and arcing in a railgun will vastly increase the cost of the system. Compared to that, the StarTram authors believe that building a 130 km vacuum tunnel will be cheap.

They suggest that a suitable projectile (and contents) will undergo a 30 g acceleration along the barrel, and then a brief ~10–20 g deceleration when it leaves the barrel and hits the atmosphere. There's a heat-to-drag tradeoff here... blunt nose projectiles heat less, but slow down more. Heat rejection seems like it might be a challenge, perhaps requiring some sort of open-cycle water cooling system, for example. They seem confident that it'll have enough excess speed to push through the rest of the atmosphere without substantial losses so only a little booster will be needed to stick it into an orbit.


I think that the major technological hurdle that they looked at was the power supply (and remember that their accelerator is a bit more gentle than yours, so they can get away with a power supply with a lower peak power output). They suggest that Superconducting Magnetic Energy Storage (SMES) would do the job... 60 superconducting storage loops, each 250 m in diameter with 10 MA currents to store ~50 GJ each, and taking up about 50 km of tunnels all by themselves. Large-ish SMES units do exist, but not as many that are this big and provide that much power. The switching equipment will probably be formidable, and between that and the power storage systems probably makes up the bulk of the project cost.

Everything else just seems to be a "simple matter of engineering": no-one has made a giant plasma window, but the design seems like it should scale up OK. No-one has made an 8 km/s maglev, but prototype sled launch systems have managed 3–4 km/s without the benefit of big vacuum maglev tubes. Long underground tunnels exist. Some, like in the LHC are even filled with magnets and superconductors. And so on.

No, the biggest hurdle will be persuading someone to pay for the damn thing, and that seems likely to be a far more difficult challenge than any of the engineering concerns! The major part of the StarTram ebook is basically talking about all the lovely things you could do with your spacegun once you'd ponied up enough cash to build it. The estimated cost in 2006 was about 20 billion dollars, and everyone knows how optimistic such things are...

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    $\begingroup$ I enjoyed reading this, +1. There are some technical papers linked from the "resources" section of their website. I particularly like how they describe the 100 km evacuated acceleration tube as "short". $\endgroup$ – Organic Marble Jan 30 at 18:51
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    $\begingroup$ still cheaper than SLS $\endgroup$ – Everyday Astronaut Jan 31 at 15:39
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    $\begingroup$ As you say, that cost estimate was laughably low -- probably closer to a trillion than a billion. In reality these engineering challenges are utterly massive problems, any one which could be project ending on its own. And even if you get it all correct your payloads would still be extremely limited; I doubt even starlink sized sats could survive. But really, the biggest hurdle is that reusable rockets have solved the problem this (and the space el) were trying to address and are a better solution by every metric. $\endgroup$ – eps Jan 31 at 17:03
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Many novel launch schemes need some amount of help from rockets. What kills a lot of them is doing a tradeoff study of just enlarging the rocket part and getting rid of the non-rocket part. Surprisingly often, that works out to be better and cheaper. --Henry Spencer

This is a system that needs a rocket part, as one of these two cases would necessary have to be true:

1) The spacecraft exits the maglev tunnel at significantly less than orbital velocity, in which case it needs a rocket part to get it up to orbital velocity

or

2) The spacecraft exit the maglev tunnel at nearly orbital velocity, in which case it would need a rocket to keep up with the massive atmospheric drag.

In either case, the Henry Spencer rule of thumb applies.

While the air at a mountain top is thin, it's still thick enough to breath. Spacecraft encountering that part of the atmosphere at such high velocities currently need heavy heat shields.

Even with today's "slow" launch rockets, the peak dynamic pressure they experience is a tough problem, and with a much higher start velocity, the problem becomes much worse.

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    $\begingroup$ to #1.) agreed, massive drag. YES, vehicle exits at far lower than orbital velocity, with attached rocket & fuel. At specific altitude, rocket fires, then accelerates to LEO. If inertia carries vehicle to 48-50k ft altitude, then ignites rocket, there are huge fuel/mass launch savings. #2. impossible. Who is Henry Spencer? $\endgroup$ – Quentin Parker Jan 30 at 9:56
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    $\begingroup$ @QuentinParker Who is Henry Spencer? You may search this group and the internet for the name. Or read wikipedia. $\endgroup$ – Uwe Jan 30 at 16:14
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    $\begingroup$ Spacecraft encountering that part of the atmosphere at near-orbital velocities tend to break apart. Aerobraking for re-entry usually occurs at an altitude of 50+ kilometers. $\endgroup$ – Mark Jan 30 at 23:47
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    $\begingroup$ @Uwe : Air being barely not thick enough to breath might still be 10 times thicker than what can break apart your spacecraft if it's going too fast. $\endgroup$ – vsz Jan 31 at 9:54
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    $\begingroup$ @aroth The very act of "pushing the atmosphere out of the way" will make the first projectile decelerate rapidly, so your real payload (which isn't encountering that much drag, so not slowing down nearly as much) will smash into it. $\endgroup$ – TooTea Jan 31 at 15:28
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The length of the tunnel is going to be, IMO, the biggest factor.

Acceleration

According to Wikipedia, the escape velocity of Earth is 25,020 mph (40,270 km/h), or 6.951 mi/s (11.186 km/s). Even if we reduce that to, say, 16,000 mph (25,750 km/h) (as suggested by Alexander Vandenberghe in comments) to compensate for the height of the mountain, it's still a considerable speed.

https://en.wikipedia.org/wiki/Escape_velocity

We can use a combination of a couple of online calculators (linked below in the Resources section) for some "simple" calculations. If we start at 0 for speed and 16,000 mph for a final speed. We can plug in different accelerations to find out how long it'll take to get to that speed in the acceleration calculator. Then we use the average speed of 8000 mph (assuming we increase speed linearly, instead of exponentially or something else), we can put in the time from the first calculator to get the total distance it takes to get the length of the tunnel using the velocity calculator.

If we put in a "modest" acceleration of 5 G's, we get a tunnel length of almost 325 miles (523 km). Even if we drastically bump that acceleration up to 17 G's, we're still looking at a tunnel over 95 miles (153 km) long. For reference, the worlds longest tunnel is 85.1 mile (137 km) long and is only 13.5 ft (4.1 m) wide.

The most acceleration a human has been able to provably withstand is 46.2 G’s, done by Air Force officer John Stapp. This would still be a tunnel over 35 miles (56 km) long. Also, we have to consider that cutting off oxygen to the brain for over 1 minute will kill people. This requires at least 12.5 G's for 59 seconds, if we don't care about brain damage and only death. This would require a tunnel 131 miles (211 km) long.

Air resistance

Even though we would have reduced air in the tunnel due to the only opening existing at the top of the tunnel, we still have to deal with many miles worth of that air before we even exit the tunnel. There's 2 basic options to deal with that:

  1. Push all the air out in front of the craft because it fits exactly in the tunnel with no room for air to go around the craft as it's accelerating.
  2. Leave room around the craft for the air to flow around it.

Option 1 is a bad idea, since that creates the most amount of drag, as well as potentially creating hurricane forces as the craft pushes air out of the tunnel in front of it. It also leaves a vacuum behind it, creating suction against the forward motion of the craft and also sucking air back into the tunnel when it leaves. There's just too many reasons why this is a bad idea.

Option 2 has it's problems, since air will have a tendency to build up in front of the craft causing more drag, unless there's enough room around to prevent it, which would have to increase the size of the tunnel as the speed increases.

There's a third option, seal the end of the tube and create a vacuum inside the tunnel, then break the seal just before the craft exits the tunnel. This would create a pressure differential that would shred the craft to pieces. This is part of why the Hyperloop is having issues.

Intrusions

There would have to be some way to prevent any kind of breach to this tunnel. People, animals, and birds may be curious as to what this big opening is and enter it to see what it is. If they were there for a launch, it would be a major disaster, and not just for the unsuspecting sparrow that built a nest on the rail. The craft would likely be seriously damaged, if not mortally crippled by this kind of impact.

But also consider something as small as a drop of water. At approximately 0.05 grams in weight, if it hits the craft as it exits the tunnel at 16,000 mph, it hits with almost 1300 Joules of force. That's almost twice the force of a .357 magnum handgun at 790 J and almost as much as a .45 Colt at 1600 J. Even if the craft is "only" going 1000 mph, it's still hitting the craft at almost 5 J, which isn't much in itself, but would still not be desirable. Hitting multiple drops like this would likely create enough impacts and noise to make Launch Control seriously consider an abort.

This means the tunnel would have to be completely sealed along it's length to prevent any kind of breach, even against water leaks. And because rock is still permeable, it would have to be sealed against air, so that it could still maintain the low air pressure granted by the opening at the top of the mountain. After years of operation, enough air and other gasses would eventually leak in to significantly increase the air pressure of the tunnel. Sealing it would considerably increase the cost of construction and it would have to be constantly monitored and maintained/repaired, further adding to the cost.

Other consideration

I'm sure there are other reasons why a tunnel this long will be a major determining factor in why it won't likely get constructed. Initial and running costs are definitely a major factor, but there's other's I'm sure I haven't considered. Time to build and the amount of materials are considerable, and would take more time and effort to guesstimate than I have time to consider right now.

And there's plenty of other considerations that aren't related to the length of the tunnel, but I'm not going into those, since I just wanted to focus on the length of the tunnel. I'll let others look into those.

Resources

https://www.omnicalculator.com/physics/acceleration

https://www.omnicalculator.com/physics/velocity

https://www.omnicalculator.com/physics/kinetic-energy

As we’re just standing at sea level, a standard 1 G of G-force is acting on us. The record for highest G-force on a roller coaster is 6.3, and it’s only manageable because it lasts just a few seconds. Fighter pilots may have to endure up to 8 or 9 Gs while wearing special compressed suits, designed to keep blood in the upper body and prevent fainting.

It’s difficult to calculate the exact level of G-force that would kill a human, because the duration of exposure is such an important factor. There are isolated incidents of humans surviving abnormally high G-forces, most notably the Air Force officer John Stapp, who demonstrated a human can withstand 46.2 G’s. The experiment only went on a few seconds, but for an instant, his body had weighed over 7,700 pounds, according to NOVA.

Check out the video below for an interesting example of lethal, high-intensity G-forces from a design project called the Euthanasia Coaster. It would, hypothetically of course, kill anyone who rode it by cutting off oxygen to their brain. This particular design places the lethal exposure level at one minute of 10 Gs.

https://www.medicaldaily.com/breaking-point-whats-strongest-g-force-humans-can-tolerate-369246

Water supply Delaware Aqueduct United States New York State, United States 137,000 m (85.1 mi) 1945 4.1 m wide. New York City's main water supply tunnel, drilled through solid rock.

https://en.wikipedia.org/wiki/List_of_longest_tunnels

If a breach ever occurred, the air would rush in supersonic speeds with the force of 30,000 kilograms over the entire cross section.

The air would continue to race down the track with explosive force until the pressure equalizes or until it slams into an object - most likely, into the train capsules.

At just 3 PSI (pounds of pressure per square inch), air can cause significant damage to a human body with the potential to result in the loss of human life. At 5 PSI, buildings would begin to collapse and fatalities would be widespread. With 10 PSI, reinforced concrete buildings become severely damaged or can collapse entirely. Most people would be expected to die.

In the case of the Hyperloop, air would enter the tube at 15 PSI (!) equivalent to one atmosphere or 10,000 kg per square meter. As it enters any perforation, the atmospheric pressure would tear open the tube like a tin can. Any and all capsules that stand in the way would be instantly shredded apart. The results would almost certainly be deadly.

https://interestingengineering.com/biggest-challenges-stand-in-the-way-of-hyperloop

A drop of water is 0.05 mL of water, so its mass would be 0.05 grams.

https://www.thoughtco.com/atoms-in-a-drop-of-water-609425

A 180-grain (12 g) bullet fired from .357 magnum handgun can achieve a muzzle energy of 580 foot-pounds force (790 J). A 110-grain (7.1 g) bullet fired from the same gun might only achieve 400 foot-pounds force (540 J) of muzzle energy, depending upon the manufacture of the cartridge. Some .45 Colt ammunition can produce 1,200 foot-pounds force (1,600 J) of muzzle energy [...]

https://en.wikipedia.org/wiki/Muzzle_energy

IK08 - Protected against 5 joules of impact (the equivalent to the impact of a 1.7kg [3.7 lbs] mass dropped from 300mm [1 ft] above the impacted surface)

https://lumascape.com/ik-ratings

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