(I've also always enjoyed the parallels of this story with "From the Earth to the Moon")
What that means in practical terms is that the harder you push something to go through the air, the harder the air pushes back. If you plot the air resistance as a function of energy applied, you see that the long before your payload has achieved orbital velocity + the amount you expect to slow down going up through additional air, you are dumping so much energy into the air that your payload vaporizes.
"But we'll shoot it straight up to minimize the time in the air!" Now you'll have an orbit who's perigee intercepts the earth again (aka highly elliptical).
The ideal trajectory can be calculated, (easiest at the equator but there are solutions for latitudes above and below the equator, to accelerate into an orbital plane such that on your first orbit you can "bounce" (trade excess velocity for altitude) into something that is lies entirely out of the atmosphere. But in that trajectory you spend more time at lower altitudes and that means more energy to get past that air and that makes you vaporize that much more quickly.
"We'll start from a higher altitude!" is another avenue to explore, the ideal altitude to start from is > 65,000' (20 km) which is defined as 'near space' but still 80km from the Kármán line. And we're still unable to build a 20km tall tower.
Lots of various solutions to various problems. Sabot-type rounds, ablative coatings, small rockets to add the horizontal element of orbit, longer, mass-driver-like launchers, and so forth.
The thing is, none of this, pardon the expression, is rocket science. (It's tough, but there's not a huge amount of new ground to be covered and/or new technologies to develop). If you can accidentally shoot something outward at multiples of escape velocity, you can certainly do so on purpose.
ADD: In reference to GP's comment, with the right trajectory it's completely feasible to shoot something into lunar orbit. Maybe Verne wasn't so far off!
The Air Force was heading down the road of airplane-to-orbit back in the 50s, but everybody decided that rockets were the way to go so the X-Plane (at least in terms of rocket-planes pushing the envelope of manned flight) program was abandoned.
Who knows where we would be had we kept going? If nothing else, we could have seen major improvements in heat management.
Yes on the modeling but the consensus was 'not physically possible'. Not a solution to the problem. In a single impulse launch[1] the amount of energy that is dumped into the atmosphere around the mass you are accelerating results in temperatures that convert that mass into vapor. Any additional energy just moves it closer to being a plasma.
> If you can accidentally shoot something outward at multiples of escape velocity, you can certainly do so on purpose.
The point here is that the 'cover' in the case of the article did not get into space. A hypothesis that the cover went into space was proposed, but that hypothesis was shown to be false (or untenable) after additional calculations were made. At no time, even "by accident", has anyone sent something into space on a single impulse launch. And the math and models all say it isn't possible, these days you could run the CFD analysis yourself on a high end desktop if you had the software.
In the 80's when Reagan's "Star Wars" program was promising a huge market for launch capacity to LEO, a dozen or more companies sought to get into the launch business. The key feature they were shooting for was "single stage to orbit" but all sorts of things were contemplated, including single impulse ideas. Even for impractical (from a cargo perspective) long skinny javelin type shapes do not reach orbit before vaporizing.
I also have a faint memory of even an ASAT system (trying to 'shoot' things in orbit) that failed to do so due its inability to change the laws of physics. (that would have probably been an Aviation Week article, I haven't subscribed for nearly a decade so early 2000's?)
On the moon without an atmosphere it is a great idea, on earth it just doesn't fly (pun intended :-).
[1] The term "Single Impulse Launch" describes a launch system where all of the energy that is applied to a mass it done at once (and typically by a system attached to the departure point) such that once the mass and the energy system separate, no additional energy is added (post impulse, the mass is ballistic. During ballistic flight it is only being acted on by air resistance, gravity, and sometimes geomagnetic forces)
Just spent about an hour poking around the internet. Fun subject! I believe you are stating this as far too certain of a thing when it's not. But hey, an hour doesn't mean much :)
There are three issues. Issue #1: without some way of correcting orbit, all you could ever get is some crazy long ballistic orbit (Which is another way of saying an elliptical orbit which intersects the ground). Solution? A sabot with standard space-capable gear inside.
Issue #2: hard acceleration needed. Solution? Not as big of a problem for cargo as you would think. Bull encased his gear in wet clay and it worked in a cannon setup. Some proposals calls for a 2km track with a 100G load, which is fine for a lot of cargo.
Issue #3: the atmosphere is basically a brick at the speed required. This sounds like much more of a problem than it is. Think about it: we have capsules re-entering Earth's atmosphere all the time, sometimes as fast as 12km/sec -- and that's at an very slight angle. Shooting more directly into space, the atmosphere would be mostly cleared in an extremely small amount of time. Bull was working with about 1/4 escape velocity decades ago. Even with gear like the Navy's new railgun, you're in the ballpark.
On my cusory search, I couldn't find other commenters as pessimistic as you are. If you have links, please share! I'd love to learn more. In the meantime, here's a paper that studies the issue. https://research.lifeboat.com/ieee.em.pdf
ADD: I by no means intended to imply this problem is easy or trivial, just as far as I can tell, it's nowhere in the neighborhood of being as open-and-shut as "the math doesn't work out"
At high enough speeds, does the atmosphere supercavitate? Could you use a double-shot, with the first projectile basically ablating away and creating a "wake" for the second to fly through?
Space elevators would be preferable from a footprint perspective caveat the seemingly infinite tensile strength cables.
Also, I see that there are improvements in that part of the design: the cables could be replaced with counterweights, and those counterweights could be accelerated upwards and dropped, in order to dampen the waves generated by the release of vehicles.
http://launchloop.com/Counterweights
I don't see why this has a flattened middle segment at all - wouldn't it work better if it was a continuous parabolic arc, like an elliptical orbit that intersects the Earth at the locations of the base stations? That way, the working mass wouldn't have to make sharp turns wherever support cables are pulling on the loop.
https://en.wikipedia.org/wiki/Mass_driver
BTW, they seem to be a staple of sci-fi anime, Gundam shows in particular, and look quite a bit like a roller coaster with an abrupt upward ending.
If anybody has the time, many years ago I wrote a simulator for various launch concepts. It's a project that can start off quite simply -- and can get as complex as you'd like. I ended up with an earth-moon model that could handle various rocket/mass-driver/payload combinations.
It's both fun and educational. Great for trying out new languages.