Actually, supersonic airflow at the fan tip is pretty common. Has been for at least 30 years.
RB211-535E4:

• Fan diameter: 1.88m
• Fan RPM at 100% N1: 4500
• Tip speed: 443 m/s

A turboprop is basically a very high bypass turbofan with a lower exhaust velocity. The means its propulsive efficiency is best at lower air speeds. Maximizing propulsive efficiency, in the simplest terms, is simply about using as much of the energy provided by an engine to displace the aircraft forward and as little to displace the surrounding air backward - you want to get the aircraft from point A to point B, not the static air in reverse. Hence, propulsive efficiency is best when effective exhaust velocity is as close to true airspeed as possible. Propeller effective exhaust velocity is lower than for turbofans, so they work better at lower speeds than turbofans do. It actually has relatively little to do with altitude and fairly little to do with how the mechanical power to drive a prop/fan is generated.

But that's not how turbine engines work. This isn't your car. Typically turbine engines operate 85-100% of their rated rpm and in cruise it's closer to 95-100%. Oh and continually stopping and starting turbine engines is one of the worst things you can do to them, because that's when they experience most of their wear.

In that case, job done. You're basically describing the thermodynamic cycle of a high-bypass turbofan or turboprop engine, minus all the electrical efficiency losses in between. Gas generator driving a turbine which produces mechanical power to drive a bypass fan or prop. And you're misunderstanding the reason why we have multiple engines on passenger aircraft. It isn't because we can't build em large enough. It's because everything fails. That's why you have two of everything in aircraft. Two engines, two fully independent electrical systems, two sets of flight control actuators, yes even the two pilots. Heck, it's also the reason why landing gear has least two sets of wheels on each axle.

Let me be clear. I like the idea, but you're describing infrastructure that's just way outside of practicality right now. In 20-30 years? Maybe. But in the next decade. Highly unlikely.

But that's the crucial bit. Getting to any Lagrange point or high Earth orbit is the costly bit. LEO to GTO is 2.5 km/s. And it's another 0.7 km/s to the Moon's orbital radius and that's only at apogee. To circularize at GEO is more than a simple escape & Mars transfer together - that's the power of the Oberth effect. Using the slow spiral-out method, you can almost double the delta-V requirements. That's why even Ad Astra says on their website that for practical human spaceflight, you'd need a nuclear reactor.

Well argued, point taken on the rads.

It's half of what you quoted.

The Hohmann transfer delta-V breakdown is about 3.2 km/s for Earth escape and about 0.4 km/s for Mars transfer. So you'd have already spent around 90% of the delta-V using hydrolox. Why not spend the little bit extra and just do the whole escape burn in one go? Fewer systems, fewer components. And what about the journey back? From Mars, it's about 2/3 of the delta-V requirements to go to Mars (assuming direct re-entry and no capture attempt into Earth orbit), so again another 1/2 year burn to return.

You're gonna get heating in the panels, the electrical equipment, etc. Those need cooling. Hence the rads. I'll admit, it's not going to be very much, but it's there.

That seems a lot more realistic. It's kinda difficult to split the difference here between what of that are necessary because of the panels and how much of it is the spacecraft without a more detailed analysis. Still, even this kind of spacecraft, without any payload or fuel, using electric thrusters would need around 1/2 year of acceleration to get to escape velocity. That's why I think it'll take a lot more dense power source to make it viable for human flight. Now if you could place a 0.5 MW power source in that footprint it starts to become practical for human travel.

Interesting stuff, thanks! However, these are just the solar panels themselves. Not the rest of the on-board components needed to support them. The radiators, the electrical equipment, etc. My guess is, when all is said and done, it'll be a lot more than the manufacturer-quoted 150W/kg figure for just the panels themselves (as they themselves claim only 1/3 mass/W compared to rigid solar panels, not 1/100).

I think you may be misunderstanding what I'm talking about. It's not "heavy" vs "light", it's "highly loaded components" vs "lightly loaded components". A massive design has lower component loading, simply because there's more material to carry the stress. That's why we build bridges out of thick steel girders, not sheet metal. Of course, as long as the component's structural limits aren't exceeded, making it heavier doesn't help.

Oh and about this new claim:

That's not true either. You can't use it as a LIFT stage (i.e. low-atmosphere). But you can certainly use it for ascent (upper atmosphere, circularization) and escape (the aforementioned 3.6km/s). TWR of Delta Cryogenic Second Stage, gross ~30t /w ~20t payload = ~50t. RL-10B thrust is ~11t Earth equivalent, so Earth TWR is 0.22:1. Yes, the burns are long (often over 15 minutes), but if you design your trajectory right, it's doable.

YOU said one of its problems was TWR. Now you're changing the claim by tacking on the "too long to be useful" qualifier. I'm not going to let you get away with that. Quit ducking and dodging. YOU said it's a problem. I showed you it's not a problem.

Are you seriously going to quote a news article interviewing the rocket engine's creator as a source worthy of detailed analysis? Containing gems such as:

Oh hold on to your hats! It *could* take just 39 days? That's practically ready to fly!

I was talking about the concept 200kWe reactor you mentioned. I know TOPAZ were flown, but those were few-kW units. I also kinda doubt the amount of red tape there would be much different to NERVA (high-enriched Uranium either way, so the greenies are gonna go crazy), but I don't really care about it from a technical analysis POV.

I should have been more clear. NERVA wasn't flight-ready. It was mission-ready, in that the system had been tested at full scale and that a detailed plan existed to construct one. Your point on the ressurectability, I will happily yield. Unfortunately, with the state of society today, it might well be very difficult to build a flight-ready engine, as you correctly noted in the environmental concerns.
The rest of your points, I have no problem with. My original contention was simply with you saying that NERVA didn't have the TWR. It did and was pretty straightforward to complete (it was considered for the Apollo upper stage). The real technical killers for a Mars mission, in my mind, are:
a) the environmental regs today make large-scale reactor development pretty difficult
b) the propellant was awful. LH2 is a bitch to work with. For deep-space missions requiring deep-space maneuvers, it's essentially a non-starter.

Source to flight-ready hardware please. I don't buy that the ISS has a very inefficient array.
Overall, I like VASIMR better than NERVA as a future prospect, especially when coupled to a high-power source. But that development is very much in the not-so-near future. If we want to get people to Mars within a decade, it's either biting the bullet and building a flight-ready NERVA or chemical and of the two, the latter seems more doable.

Sources? A single 32kW solar array assembly on the ISS weighs around 16t. I hope you won't try to claim that designers weren't motivated to make it as lightweight as possible, given that the ISS experiences no accelerations of any kind.

Neat, rather than admit you were wrong, you go with insults. I'm going to stoop to your level.
So if NERVA's TWR wasn't a problem, why did you say it was? What's the nature of that problem? Just to illustrate, VASIMR's incredibly low thrust is a significant issue, insofar as it's not really conducive to escape burns. Ideally, main propulsion rocket engines need to provide a short, intense impulse. Not a long, gentle nudge. Even a 20 day burn means you're going to be spiraling out, not burning out, giving much worse delta-V (and consequently lengthening the burn).
Moreover, the proposed nuclear power reactors you describe are merely concepts at this point. No real hardware. By contrast, NERVA was effectively mission-ready in the 70s. It's easy for you to be handwavy that "it'll get resolved somehow", but unfortunately, there's a fairly big step between "concept study" and "mission ready hardware".

Then you shouldn't have said it's a problem. Honestly, quit weaseling. NERVA's TWR wasn't a problem. Period. There were plenty of other problems, but TWR wasn't one of them.

Scrap that latter point about a 200 day burn, I shouldn't be doing math at 12 at night.

Yes, that would be you and I quote:

So make up your mind. Is it a problem, or is it not a problem? Also, don't shift the goal post by tacking on qualifiers like "to be useful". You didn't say that originally. You said it's a problem. I showed you it isn't. TWR of 0.2 on an orbital booster is a non-issue.

I think you may have forgotten to carry a one somewhere. 2400 kg at 5N of thrust gives .0002 m/s^2 of acceleration. So not 20 days, but 200 days! And even if you weren't off by one order of magnitude, even a 20 day burn is no longer a classical Hohmann transfer from down low near the Earth (for maximum Oberth-effect awesomeness), so the delta-V requirements go up tremendously (probably around double). So using the correct acceleration, you're looking at over a year-long burn. THAT'S why even the VASIMR creators envision nuclear-powered spacecraft using VASIMR for interplanetary travel.
Glad to see you at least know the rocket equation.