If enviromental concern was not taken into account, could you use a nuclear thermal rocket such as NERVA or Pewee to take off from Earth's surface into low Earth orbit?
If not why?
Is a launch failure the only enviromental concern?
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You'd need something with a better thrust-to-weight ratio than NERVA for that. But that might be within the realm of possibility. The NERVA engine mass was about 20,000 lbm, and the thrust about 75,000 lbf, which doesn't leave near enough for the rest of the vehicle and propellant. It was really designed for an in-space stage, where the benefit would be substantial.
As for environmental, use of NERVA in Earth's atmosphere does pose a problem even if there is no accident. In normal operation, bits of the reactor fuel come out in the heated hydrogen thrust, leaving a radioactive trail in the atmosphere. You would need to do this very far from populated areas (perhaps a sea launch), and do analyses of the distribution and eventual fate of the radioactive material to show, hopefully, that it would not significantly increase health risks to humans.
I would say it's a bad idea even without taking environmental impact into consideration.
For vertical ascent from earth's surface, a good Thrust to Weight ratio (T/W) is desirable. Else gravity loss can inflict a big delta V penalty.
According to Kirk Sorensen NTR's T/W isn't that great. See SSTO is a bad idea, but NTR SSTO is worse.
"Could" is such a tricky phrase. Do you mean near-term and economically viably, or eventually, after a 50-year technology maturation? Assuming you mean within 20 years, my answer is "Probably yes, but the system would be less attractive due to financial and other considerations than evolved chemical rockets." The big challenge from a performance perspective is thrust-to-weight, or T/W. Yes, a NERVA-class NTR with its ISP of 700-1000 uses each kg of fuel twice as efficiently as a chemical rocket, but when launching from the ground that doesn't come close to making up for its lower T/W (7 vs 70 for chemical rockets, per Wikipedia). Project Timberwind designed a pebble-bed (more granular-bed) NTR in the 80's and got to a claimed (design) T/W of 23 at sea level and 30 in vacuum. However the Wikipedia article doesn't mention the flow instabilities (read: Localized hot spots leading to failure) that were confirmed when they built a partial test article and flow tested it with inductive heating to simulate nuclear heating of the simulated fuel elements. So a near-term achievable result lies between NERVA's proven T/W of 70 and Timberwind's pushed-too-far goal of 30. Meanwhile, Aerojet said "What if we inject extra mass to improve T/W at the cost of ISP during the first 1-2 minutes, called LANTR? T/W climbs impressively, but still not where you want it to compete with chemical rockets for a first stage. http://www.nss.org/settlement/moon/LANTR.html ; http://www.dtic.mil/dtic/tr/fulltext/u2/a454590.pdf
NASA looked over NTRs at the behest of Bush Sr for his mars project and said a fresh program to develop a mars-transfer NTR (still not for ground launch but to improve our throw weight to mars) with modern environmental controls would cost a cool \$1B. Applying that number to your problem, I think we can say that a near-term \$1B investment and adding LANTR would give us a functional but underperforming first stage. And considering what's going on with SpaceX and Blue Origins, that $1B could buy a LOT of kerosene and methane.
BUT crunching the numbers might yield a kick-ass second stage/mars transfer injection vehicle.
By the way, be careful reading claims of Dumbo and Timberwind fans. When you make your fuel passages smaller (small channels for Dumbo, or a granular bed for Timberwind) your heat transfer coefficients go up dramatically. That's great for T/W (less reactor size and weight needed to transfer the same amount of energy to the fuel) but moves you into the territory of Laminar Flow Instability. That's a pesky problem where the hydrogen flows more slowly the hotter it gets. And since the engine is generating energy at a constant rate, hot spots rapidly become hotter spots and then you get sort of a whistle-boom effect.
Also, you can get your fuel hotter (thus improving ISP and thrust) if you use metallic fuel elements. Hooray! Hotter exhaust! Oops, the elements weigh twice as much as the lower-performing carbon elements; you improved ISP but reduced T/W. How about an NTR that does the initial 2/3 of its heating with relatively light carbon elements then runs the fuel through a second stage with metallic elements to reach peak exhaust temp? Do you have any idea how much of a nightmare the neutron modeling would be for that? Now you're probably looking at a $2B project, easy.
So if we decide to colonize an outer planet on a massive scale - say a $500B+ investment over 20 years - AND it's enough of a social imperative to disregard the sprinkling of radioactive exhaust - then second-stage NTR + LANTR would be worth looking at, especially as a second stage/MOI engine. But even then NTRs probably won't make sense as a first stage or SSTO until we achieve a technological leap to gas-phase.
Sorry for the lack of math.