In theory the RDRE would improve chemical rocket efficiency by about 10%. There is a finite amount of energy in any fuel/oxidizer combination set by the chemistry. Regular rocket engines use a turbopump to push the ingredients into a combustion chamber at high pressure. The expansion of the resulting hot gas is what turns into thrust.

The RDRE feeds the ingredients at lower pressure, and uses a detonation to create the high pressure for expansion. The energy otherwise used to run the turbopumps is then directly used for thrust. Turbopumps generally tap off some of the fuel and oxidizer flow to power themselves.

Those are the same thing if you have the same thrust. More efficient means less fuel mass means more acceleration from a given thrust.

uhh looks like i have to do some research and math here soo..

The rocket engine, according to the plan, worked for 3.2 s, accelerating the rocket to a speed of about 90 m/s, which allowed the rocket to reach an altitude of 450 m.

The detonation shockwave travels significantly faster than the deflagration wave leveraged by today's jet engines, Trimble explained: up to 2,000 meters per second (4,475 miles per hour) compared to 10 meters per second from deflagration.

i am gonna use the second one (but i don't know if it is talking about the vehicle or the wave.)

distance from mars (130,000,000 km)

speed of detonating engine = 2km/s

so, 130000000/2= 65000000 seconds = 752.31481481 days or 2 years and 22 days.

not sure don't quote me on this.

edit: YES I knew it i was right that i was wrong!

Yes, that part is completely wrong. Nuclear rockets still use propellant. Nuclear thermal rockets use about half as much by mass as the best chemical rockets, but they only get their peak performance with LH2, which takes up about 5 times as much volume for the same amount of mass. A nuclear thermal spacecraft will be a big pile of propellant tanks (likely drop tanks so you don't have to carry empty tank mass around) strapped together with a nuclear rocket engine at the back and a small payload tacked onto the front.

The "45 days" claim appears to be in reference to the "wave rotor" stuff that's been getting massively overhyped. Basically, as described, they propose sticking a widget between the nuclear reactor and the nozzle that somehow doubles the specific impulse while halving the flow rate.

This means doubling the power output of the reactor. Since the power output of the reactor is already limited by the need to keep it from melting, and the reactor is cooled by the propellant flow which you've just cut in half, it's not clear how this doesn't result in the reactor, well, melting. Also, even if it worked, doubling the specific impulse isn't nearly enough of a gain to allow a 45 day trip to Mars.

They then throw in nuclear-electric propulsion, which requires heat exchange loops, many megawatts of electrical generation capacity, giant radiator arrays, and arrays of ion thrusters. They assume all this can be done "with minimal addition of dry mass", and this is how they double the performance again to get their 4000 s number. However, it doesn't actually appear to have anything to do with the wave rotor.

NASA's giving one guy $12500 to look at it. It's not taking anyone to Mars any time soon.

The thermal nuclear engine has propellant, technically not fuel. It's not combusted, just ejected backwards at high speed. It's gets used up, but it's not a source of energy.

The detonation engine still uses both fuel and oxidizer. It isn't nuclear. The nuclear engine was just mentioned at the end as another engine being worked on.

No, Orion is a nuclear pulse drive, not a nuclear thermal rocket. Bombs vs. a reactor.

NTRs have not only been designed, but actually built and tested for full-duration firing.

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My kids are bored after 30mins in the car. I won't be sailing them on a 6 year round trip to Neptune

Eh, there are other electric engine options that are better than ion engines, such as plasma engines or mass drivers. And if power isn't a limiting factor the ultimate in propellent efficiency is a photon rocket, aka a light bulb. No need to carry propellent, though you need 300 megawatts of photons to get a pathetic newton of thrust, so whatever reactor is powering it will need a shit ton of fuel. Though if you're using a laser array to push a mirrored sail that power plant can remain on the ground.