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Humanity has found a way to travel to another dimension (kinda like Asgard in the MCU). There they have found boulders of a wonderful substance. It is light, strong, has a high melting point, it hardly weakens at elevated temperatures, and it is virtually nonreactive. It has a pure white colour with a mat finish. Due to it's appearance it has been dubbed "Cloudbark". The material is amazing for a lot of high-stress situations. The only downside is that it is a nightmare to work with. The only way it can be made workable is by bathing it in HF for days. Then during smiting it slowly off-gasses the HF it had absorbed quickly becoming unworkable again. Much like how a smith works with steel.

An rocket-engine manufacturer wants to use this material in the combustion chamber of a new engine. Withstanding a lot of force at incredibly high temperatures would allow for a boost of the nozzle velocity. Increasing the specific impulse of the rocket propellant.

Limiting the use of this Cloudbark material to only the area's exposed to a high temperature. How much more specific impulse could this new rocket-engine give to a rocket like the Saturn V?

Material properties of this "Cloudbark"

  • yield strength 9470 MPa
  • ultimate strength 12190 MPa
  • fatigue limit 4730 MPa
  • shear modulus 311 GPa
  • young modulus 927 GPa
  • compressive strength 80 MPa
  • specific weight 2.593 kN/m^3 (293,15 K)
  • thermal expantion 0.6×10^−6 * K^-1
  • melting point 10721 K
  • thermal conductivity 0.01 W/mK

ps. To make the answer useful to others. Which property of these (if any) would be the limiting factor for increasing the specific impulse further?

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  • $\begingroup$ Can you say how specific impulse is related to heat-resistant material, or not? $\endgroup$ Commented Jul 16, 2022 at 21:50
  • $\begingroup$ @RobbieGoodwin specific impulse is directly related to the temperature achieved in the reaction chamber. better heat-resistant material can help achieve those temperatures without the whole thing exploding. $\endgroup$ Commented Jul 16, 2022 at 22:02

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Specific impulse (Isp) is closely related to exhaust velocity. A reasonably detailed formulation of exhaust velocity can be found here, and gives this equation:

$$V_e^2 = {{kR_{gas}T_c \left [1 - \left ({p_e \over p_c} \right){(k-1) \over k} \right]} \over k-1}$$

I'll gloss over most of the details there as being more or less uninteresting, so the key bit you should care about is $V_e^2 \propto T_c$, or altenatively, $I_{sp} \propto \sqrt {T_c}$: specific impulse is proportional to the square root of the chamber temperature.

The chamber temperature in something like the Space Shuttle Main Engine is a little over 3100K, and it is kept that low by careful tuning of the reaction and regenerative cooling of the chamber and nozzle by cryogenic fuels. If it got much higher, everything will melt and blow out of the back of the rocket and You Will Not Go To Space Today. Chamber pressure is more awkward to reason about, but even substantial increases in pressure don't affect the exhaust velocity much given that pc is already pretty high in modern rockets. Rgas is related to the molecular weight of the exhaust gases, and if you're using a rocket that combusts its fuel you're never going to get a whole lot lighter than the steam that comes out of a hydrogen/oxygen rocket, like the SSME

Your cloudbark rocket motor could withstand triple the temperature of the SSME, and so you might expect an Isp about 1.7 times higher. The SSME had a specific impulse of 453 seconds, so a ballpark figure for a cloudbark motor might be ~785 seconds, a pretty respectable value. You could make a SSTO with that, certainly.

How much more specific impulse could the Saturn V rocket get

Thats sort of a weird question, because the Saturn V was engineered around the limitations of materials and manufacturing of its time. You've just upended rocket motor manufacturing (and many other things besides... power stations suddenly get a lot more efficient, and smelting of exotic high-temperature metals and ceramics is now much easier, for example) and so whole new rockets would be made around the new technologies instead.

Which property of these (if any) would be the limiting factor for increasing the specific impulse further?

The fuel, and that's something you can't get around by changing your rocket material. If you can't make your exhaust gas lighter, then you can't raise your Isp further.

One option here is to dust off solid-core nuclear rockets, like NERVA. Nuclear rockets were never used for actual spacecraft, but they did exist and were even test fired... the Kiwi atmospheric tests were done at almost the same time that Apollo 11 was launching, so it matches your Saturn V technology level and timeline. Nuclear rockets are non-combusting, so the exhaust can be pure H2, which is 9 times lighter than the H2O from a hydrogen/oxygen motor. NERVA would have managed 841 seconds vacuum Isp with chamber temperature somewhere between 2400K and 3100K, so assuming your cloudbark has appropriate physical characteristics to be used as fuel cladding then you could run your rocket at triple the temperature and get an Isp of over 1400 seconds at high thrust... that starts to sound like the sort of crazy performance that gets you a single stage to Mars rocket.

If you handwave the properties of cloudbark appropriately, nuclear rocketry could be made both highly effective and nonpolluting. Real-world solid core rockets tended to huff out a distressing amount of radiation in their exhaust, but if you settled for a two stage rocket using conventional fuels to lift your cloudbark-NTR into orbit and then run that in space you've got an excellent platform for exploring and developing the inner solar system.

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