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I've already described a combination of existing technologies that would provide a dramatic leap. The key is to get out of the atmosphere; as Robert A. Heinlein said, "Once you are in orbit, you're half way to anywhere." So the key is to get into orbit.

After Apollo, NASA worked on a fully reusable space shuttle. Their design was Two Stage To Orbiter (TSTO): a lifting body orbiter, and a fuselage and delta wing booster. The orbiter had heat shields, the booster did not. Both were piloted, in the late 1960s and early 1970s they didn't have good autopilots or remote piloting yet. Unfortunately Nixon was elected president, his plan to end the Vietnam war was to raid NASA's budget. He also told the military that they and NASA couldn't have separate launch vehicles, either work together or neither get anything. So the space shuttle had to be all things to everyone. The military wanted something to launch big spy satellites, so the cargo bay was expanded from 11 metric tonne to 400km orbit inclined orbit (over Cape Canaveral) to 27 metric tonne to 185km polar orbit. Actually the larger design could lift 16 metric tonnes to 400km inclined orbit. But polar orbit capability meant it required a long glide path; there are runways dotted all over the planet at temperate latitudes, but nothing over the poles. So that meant a fuselage and delta wing orbiter, which is heavier. And the slashed budget couldn't afford the piloted fly-back booster, so they used a "drop tank"; something the military is quite familiar with. NASA calls that the "external tank". Then a senator from Utah said he has a company that builds segmented solid rocket boosters for Titan III missiles, where are the segmented solid rocket boosters going to go on this new shuttle? NASA said a solid rocket booster that big isn't safe for human space flight, especially not with rubber O-ring seals right next to a liquid hydrogen tank. Looking back, I think the families of Challenger astronauts would agree. But the senator wouldn't authorize funds for the shuttle without it, so the shuttle got the solid SRBs. The shuttle was supposed to fly 50 missions per year, the factory for the first stage of Saturn V rockets was converted to external tanks, and sized for 50 tanks per year. The factor for SRBs was built with multiple casting pits, sized to fill 100 boosters per year (50 launches). The flight schedule called for a peak launch rate of 66 launches in one year. But the shuttle never did better than 6 launches per year. Now it's scheduled to be scrapped once ISS is complete.

So the big trick to space flight is not some fancy in-space propulsion, but a reusable system to get into orbit. A shuttle designed to fly through atmosphere will have wings and heat shield and stuff for atmosphere, so it won't be optimal for in-space operation. So the shuttle should only go to low Earth orbit, such as the orbit of ISS. Once you to LEO then transfer to a dedicated in-space ship. Once you commit to a shuttle that barely gets out of the atmosphere, you can design it to make use of the atmosphere. So how do you do that?

In the 1950s the US military developed something called Project Pluto. It was a cruise missile that used an unshielded plutonium reactor as the heat source for a RAM jet. It didn't use any other fuel, just plutonium. A RAM jet requires mach 1 to ignite the engine, but the unshielded plutonium reactor would spew radiation out its tail pipe. It was designed to drop big thermonuclear bombs, so the radioactive exhaust was considered minor. Besides, it would be air-launched over the ocean from a B-52 bomber. It used radar mapping of the terrain, and an autopilot that flew low knap-of-the Earth. Amazing they got that to work in the late 1950s.

So, adapting this technology for civilian use, we need a nuclear fission jet engine. To take off from a runway we need a turbine engine, not a RAM jet. The reactor has to be shielded, protecting it's passengers from hard radiation and containing fission fragments (nuclear waste). Plutonium is chemically highly toxic while uranium oxide is not, so the reactor has to be uranium fuelled rather than plutonium. Uranium-233 is much more fissile (easier to react) and a richer fuel (more energy per fuel weight) than uranium-235, so use uranium-233 as fuel for this jet. Uranium-233 isn't as fissile or as rich as plutonium-239, but it's much safer. Uranium-233 is extremely rare in uranium ore, but can easily be made by exposing thorium-232 to neutron radiation. The Maple reactors that will make medical isotopes to replace the NRU reactor at Chalk River work by exposing samples of material to neutron radiation, and each reactor is sized to produce 110% of the entire world demand for medical isotopes. That means one reactor can be worked on for maintenance while the other produces isotopes. However, it also means while neither is under maintenance, the other can be used to make U-233 for jet engines. Heat from the reactor has to be transferred to air passing through the jet engine very quickly; before the air leaves the engine. Heat shields of the space shuttle are designed to transfer heat to air flowing at hypersonic speed, so the same heat radiating material can be used to transfer heat from the reactor to air inside the jet engines. Then it's just a matter of designing a turbojet engine; something engineers know how to do.

Such a fission jet engine would be able to take off from a runway, accelerate to greater than mach 20 at the edge of space, then a rocket engine would have to take over. Another nuclear reactor (or the same one) could heat liquid hydrogen to serve as a solid core nuclear thermal rocket. That would provide final thrust into orbit. The space shuttle enters the atmosphere at mach 25, so leaving at mach 25 would be enough to reach orbit altitude. Another rocket burn would be required to circularize the orbit, but that gives you an idea how much speed is involved. Existing manoeuvring thrusters could be used to orient the spacecraft.

Current heat shield tiles are fragile, but they work well enough. The problem is foam from the external tank ripping off and hitting the tiles. A shuttle without any external tank could use current heat shield tiles without worrying about damage. Actually, the heat shield has been improved; white tiles have been replaced by thermal blankets that are cheaper, protect against more heat, and are much more durable. Another generation of thermal blanket has been developed called DurAFRSI, but hasn't been used on the shuttle yet. It handles even more heat than the AFRSI blankets currently in use and is more steam lined, but doesn't handle as much heat as black tiles or the grey material on leading edges of the wings. So use the new stuff we have now; once you get rid of the external tank current heat shield technology is enough.

Another advantage to the nuclear fission jet engine is that it can be air-started before landing. That permits a powered landing, rather than just gliding. If something goes wrong the shuttle can fly around and try again. Much safer than a glider.

Dedicating this new shuttle to inclined orbits only, not polar orbits, would mean you can use a lifting body design. Especially if you have a nuclear jet engine with plenty of fuel. A lifting body design like the X-38, or even better the HL-20, would dramatically reduce weight of the shuttle.

Another technology is for the windows. Current windows are made of glass, which gets pitted by micrometeorites. They grid those pits out before every flight. They don't even use a power grinder, the hand grind the windows each time. That consumes a lot of time, at high salary expense. The US army developed a new material in the 1980s for windows of tanks. It's highly impact resistant, much more so than glass. Aluminum oxynitride is known by its chemical formula: AlON. AlON is correctly spelled with a lower case "L" and the rest upper case. It's 1/4 the thickness of armoured glass and consequently 1/4 the weight. More importantly, it can withstand much more heat, and withstand impacts better without pitting. Eliminating pitting would eliminate the necessity to hand grind windows. That would reduce cost and turn-around time.

Oh, did I mention that when I was a kid I wanted to be an aerospace engineer? There wasn't an aerospace engineering program anywhere in Manitoba and my parents could afford to send me out of province, so I took computer science instead. If I was rich I would like to quit work and take an aerospace engineering degree. Hmm, engineer or politician? Sometimes I think going into politics is going over to the dark side. Then I realize how many things in government are fundamentally screwed up, that if I don't fix them no one else will. Never the less, I have studied space technology quite extensively.

   

ion engines does look spacy too

   

Actually, NASA has done a lot of work on Ion engines. The Glenn Research Center developed the NSTAR ion engine that was used on Deep Space One. They have further developed that technology.
http://www.grc.nasa.gov/WWW/ion/

One reason it's important, at least to the military, is that the Russians have been using Hall Effect thrusters on their military satellites since the 1960s. NASA thought Hall Effect only had a specific impulse of 1700 seconds while ion engines could do 3000 seconds or better. That meant NASA's ion engines were twice as fuel efficient as Russian engines. Then the Soviet Union broke up and Russia sold everything that wasn't nailed down. NASA bought their technology, hired their engineers to tell NASA engineers everything they know. The Thruster Anode Layer (TAL) version of Hall Effect thrusters that Russia developed were just as fuel efficient as NASA's ion engines. In fact, NASA management for a while thought Russian engines were better. Glenn engineers didn't like that, but grudgingly learned everything the Russians had to teach. They then improved their own engines, got the new ion engines even more fuel efficient. New high power ion engines got above 8,000 seconds and they hope to do more. Of course everything comes with a price, the high power high efficiency engines require a lot of electric power. It turns out you can crank the Russian engines up with just as much more power and get the same performance. Physics doesn't care which country you come from, same power and same fuel results in same thrust and same fuel efficiency.

Of course I have a bit of an advantage. In 2001 I asked NASA if I could get information about their ion engine. I wanted to use it for a real probe to Mars. The Mars Society has some NASA scientists and engineers on their board of directors, so NASA was willing to listen. The director of the small shuttle payloads project told me how much it would cost to launch a very small space probe on the shuttle, and how to get NASA to sponsor the mission. When I asked the Glenn Research Center if I could get information on the ion engine, it turned out be the time their engineers were learning from Russians so they were pleased someone was still interested in their engine. I spoke to one of the lead engineers who developed the engine. He gave me the technical engineering reports on the ion engine used for Deep Space One, in-space performance reports, schematics, photographs; as he put it, everything short of the blue prints. That was everything authorized for export to Canada. And no, I won't give you copies. They were given to me in trust so I'll keep them. I used that information in 2002 to submit a bid when NASA asked for proposals for their Next Generation Ion Engine. I got on NASA's short list, they liked me, but unfortunately the fine print said anyone outside the US wouldn't get paid; so that killed it. I asked the Canadian Space Agency to fund me, but they weren't interested at that time. Oh well.

So you see I do know something about this subject.

The link above has information available to the public. It is the website of NASA's Glenn Research Center.

   

Maybe I'm reading it wrong but it appears you are basing your calculations on a constant speed with out taking into account that most of the time the craft would either be accelerating or decelerating, which would add quite a bit of time to the duration of the trip.

   

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