# Are nuclear thermal engine designs limited to about twice the Isp of existing chemical rocket engines? If so, why; what's the limiting factor?

Discussion below With Ultra Safe Nuclear engines and hydrogen propellant, how far to Mars could you get and still be able to return to Earth in an emergency? including a comment that suggests that the following quote makes it sound like a "solid core nuclear thermal rocket", and that it is likely to have similar performance "as every other solid core nuclear thermal rocket."

From their October 19, 2020 press release Ultra Safe Nuclear Technologies Delivers Advanced Nuclear Thermal Propulsion Design To NASA:

NTP systems achieve expanded payload mass capabilities due to their two-fold increase in specific impulse compared with chemical propulsion systems.

From kerolox to LOX LH2 Isp's range from roughly 360 to 440 seconds.

Quesiton: Are nuclear thermal designs in the ballpark of roughly 700 to 900 seconds? If so, what is the limiting factor? Why can't they easily go higher?

For solid core engines, yes, that's their limit.

If so, what is the limiting factor?

The exhaust velocity (and hence specific impulse) is linked to the heat of the propellant. The propellant can't get any hotter than the fuel elements.

Why can't they easily go higher?

Cos your fuel elements would melt and blow out of the back of the rocket in an embarassing way.

As you mentioned in your question itself, an important figure of merit is the "characteristic velocity":

$$c_* \propto \sqrt{\frac{T_t}{M_w}}$$

where $$T_t$$ can be taken to be the exhaust temperature, and $$M_w$$ is the molecular weight of the gas species in the exhaust. If you'd like a source for the equation, you can see it mentioned here, along with a load of related notes. It is equation 9.

What this basically boils down to is that both chemical engines and NTRs have the same ultimate operating limits... they can only get so hot, before critical bits melt and the whole thing goes poof.

Unlike a chemical rocket, however, an NTR can produce exhaust which has much lighter gasses, such as neat H2. At the same exhaust temperatures, those light molecules will be travelling much faster than, say, the heavier H2O coming out of an LH2/LOX rocket.

An NTR filled up with water would have pretty much the same Isp as that LH2/LOX rocket, though it would have somewhat smaller and more convenient reaction mass tanks, and is a bit easier to fill up.

There are various solutions that have been proposed to deal with this.

Liquid and gas-cored NTRs are the obvious ones, where you pre-melt-down your reactor core deliberately, though of course they have their own formidable technical challenges.

There's an add pulsed reactor design that relies on neutron heating of the reaction mass that allows for hotter exhaust by relying on neutron heating of the reaction mass, which sounds a little technically farfetched but someone obviously believes in it.

The most plausible solution seems to be to build a decent NEP rocket instead. Certainly that's within our technical capabilities at this time.

• @uhoh it does just seem to boil down to temperature and molecular weight of the exhaust products. An NTR could have neat H2 flowing out of the back, whereas a chemical rocket has to make do with hefty H20 instead. – Starfish Prime Feb 26 at 9:17
• @uhoh if you'd like a source for the $\sqrt{T/M}$ thing, it pops up in all sorts of places, such as here: web.stanford.edu/~cantwell/AA103_Course_Material/… – Starfish Prime Feb 26 at 9:18
• Super; thank you! (or Super-thank you, both apply) – uhoh Feb 26 at 9:34
• – uhoh Feb 26 at 9:48
• @uhoh that'll be the heavy lifting by by the $\propto$ ;-) exhaust gas chemistry isn't something I know anything about. – Starfish Prime Feb 26 at 10:26