What is the best chemical rocket fuel from a purely specific impulse standpoint?

Question

A variety of different rocket programs use a variety of different fuel types. Researching this, the main fuel combinations I saw were: RP-1 / LOX (SpaceX's Falcon rockets, early stage Atlas and Saturn rockets), methane / LOX (SpaceX's Starship), HTPB (ISRO's PSLV), PBAN (NASA's SLS boosters), LH2 / LOX (upper stage Ariane rockets and SLS) and UDMH/N204 (ISRO's GSLV). Nevertheless, these fuels aren’t used solely for their specific impulse because other factors such as toxicity and cost are considered.

According to Wikipedia

The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 seconds (5.32 km/s) with a tripropellant of lithium, fluorine, and hydrogen. However, this combination is impractical.

Theoretically, what other chemical propellant combinations would yield high specific impulse values and why would those combinations have a high specific impulse?

Edit: Thanks to Organic Marble for pointing out that I missed the LH2/LOX combination and pointing out that I hadn't thought of ion drives (though this question is limited to chemical rockets).

Answer 1

From the historical NASA document Space Handbook: Astronautics and Its Applications, by Robert W. Buchheim (1959).

Super high-energy bipropellants

300 to 385, ISP

• Fluorine-Hydrogen
• Fluorine-Ammonia
• Ozone-Hydrogen
• Fluorine-Diborane

But fluorine is very difficult to handle. Doing a combustion experiment back in the mid 1960s, I had a regulator burn up that was apparently not properly passivated that released a whole bottle of fluorine to the atmosphere. No injuries, luckily.

Answer 2

TL;DR: Pentaborane or LH2/LOX

From a purely specific impulse standpoint, pentaborane is perhaps one of the most potent rocket fuels, providing excellent specific impulse (about 340/365 seconds in atm/vac, see RD-270M) in the atmosphere. In addition, when combined with nitrogen tetroxide (RD-270M again), it can be used as a storable propellant as it is liquid at room temperature. For higher-energy combustion oxygen difluoride could also be used but it is very unstable and reacts with many materials. However, the reason why it isn't used as rocket fuel is because of its high toxicity and deadly exhaust products.

The lithium/fluorine/hydrogen combination does give 542 seconds of specific impulse, which is very good for a chemical propellant, but it is relatively impractical due to the difference of temperatures, with the addition of a toxic exhaust product and poor storability (lithium metal is liquid at 180 C, fluorine reacts with almost everything, and hydrogen liquifies near absolute zero, making the temperature differences near-impossible to fix). Plus, the tankage and properties of such a tripropellant may be a plumber's nightmare.

On the other hand, LH2/LOX (aka hydrolox) is a great rocket fuel for vacuum-optimized engines, providing up to 460-470 seconds of impulse in a vacuum. Many upper stages use this propellant mix, while a few launch vehicles use it as a lower stage (Ariane 5, Delta IV, Space Shuttle) but the engineering for a lower stage hydrolox engine may be more difficult due to expansion of the exhaust.

What about stuff that isn't a chemical propellant?

Again, this is from a specific impulse standpoint and not from practicality. Also this is based upon current to very near-future technology (maybe up to 50 years ahead), so antimatter-powered rockets, fusion drives, and whatnot are out of the question. If you want the best specific impulse here, use ion engines.

Ion engines (and the VASIMR) mainly use electricity (lots of it, up to several MW) and consume very little propellant for very high exhaust velocities at the cost of very low thrust, which only makes it applicable for vacuum operation. These engines can potentially reach up to 20000 seconds of specific impulse, and can operate for years without malfunctioning. However, ion engines are usually only used in small spacecraft as the tiny thrust cannot provide much acceleration for larger payloads.

The similar VASIMR may have applications for larger spacecraft or even manned spaceflight as it can trade efficiency for thrust, ranging from 1000 to 30000 seconds of impulse as thrust decreases. However, this is still in development and has not seen flight yet.

The last form of propulsion that I'll be talking about is nuclear thermal rockets, where a nuclear reactor heats up liquid hydrogen to very high temperatures and ejects it out of a nozzle, potentially giving up to 800-1000 seconds of specific impulse as well as relatively high thrust (up to 250 kN). However, such an engine is very heavy and brings the risks of reactor meltdown/failure and radioactive contamination. Although prototypes were built in the 1960s, they never saw spaceflight.

Hopefully this gives enough details about efficient rocket propellants. If you want me to give details on any other fuel, let me know.

And if you want supreme efficiency, use a kraken drive.

Answer 3

Very theoretically, metallic hydrogen has a predicted Isp of 1700 s.

(Or lower if it has to be diluted to not melt a rocket engine with a 6000 K reaction temperature.)

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Under extremely high pressure, there's some experimental evidence that hydrogen does phase-change into a conductive metallic state. It's a very light atom, and has a lot of energy locked up in chemical bonds in that state, which is ideal for Isp. There are no heavier atoms involved. So this is probably the theoretical max as far as chemical energy propulsion.

It's hypothesized to be metastable, i.e. it may stay metallic if you release the pressure, but AFAIK not confirmed. But with the right nudge, it will release that energy as it reverts to gaseous form. Hopefully stable enough to not be set off by vibration in a fuel tank...

When I say high pressure, we're talking about millions of atmospheres (350 to 600 GPa), produced with diamond "anvils" (article with photo), with tips as small as 5μm in diameter.

So we're not making much metallic hydrogen at a time, to say the least. It's still a big deal when any lab manages to make any tiny amount and do some measurements to confirm that it's actually metallic. In terms of practically being able to produce quantities useful for rocketry, we might be a little closer than with anti-matter, but tech readiness level 1 at best. We're only at a "might be theoretically possible" stage.

And I don't think we've verified that it could maintain that phase if the pressure is released (i.e. metastability), which is necessary unless you want your fuel tanks to be diamond-tipped mountains, way too heavy for a rocket to ever lift.

Nonetheless, a 2010 paper by Silvera and Cole, Metallic hydrogen: The most powerful rocket fuel yet to exist, discusses the possibility. (Other researchers have criticized it as being overly optimistic for discussing rocketry applications when first announcing the possibility of having observed metallic hydrogen. It wasn't until later experiments at even higher pressures that people, including Silvera, were able to confirm metallic hydrogen). Anyway, its abstract includes:

Metastable metallic hydrogen would be a very light-weight, low volume, powerful rocket propellant. One of the characteristics of a propellant is its specific impulse, Isp. Liquid (molecular) hydrogen-oxygen used in modern rockets has an Isp of ~460s; metallic hydrogen has a theoretical Isp of 1700s!

If pure metallic hydrogen is used as a propellant, the reaction chamber temperature is calculated to be greater than 6000 K, too high for currently known rocket engine materials. By diluting metallic hydrogen with liquid hydrogen or water, the reaction temperature can be reduced, yet there is still a significant performance improvement for the diluted mixture.

Answer 4

Ideal specific impulse for a given chemical reaction can easily be obtained from the energy density of the reaction.

If $d$ is the energy released by the chemical reaction per mass of reactants, then the effective exhaust velocity is simply

$$v_e = \sqrt{2\cdot d}$$

And the specific impulse is

$$I_{sp}=v_e / g_0$$

where $g_0$ is the standard gravity, $9.80665 \, \mathrm{m \cdot s^{-2}}$.

(The formula for $v_e$ is easily derived from the kinetic energy formula, $E_K=\frac{1}{2}mv^2$.)

For example, for an ideal engine burning a stoichiometric mixture of lithium and fluorine, assuming the enthalpy of formation is $23.75\, \mathrm{MJ\cdot kg^{-1}}$, we get

$$I_{sp}=v_e / g_0 = \frac{\sqrt{2\cdot 23.75\, \mathrm{MJ\cdot kg^{-1}}}}{9.80665 \, \mathrm{m \cdot s^{-2}}} \approx 703\, \mathrm{s} $$

According to this answer about highest enthalpy of formation, burning beryllium with oxygen (though rather impractical) would release slightly more energy per mass, as the stated entropy of formation of beryllium oxide is $23.96\, \mathrm{MJ\cdot kg^{-1}}$. But this only slightly increases $I_{sp}$ to about $706\, \mathrm{s}$.

In practice, the storage temperature and pressure of the reactants could make a much larger difference in $I_{sp}$ than just the three second difference between these ideal computed values.

See also these notes about ideal $I_{sp}$ for various fuel mixtures.