Theoretical maximum ISP from chemical rockets

[Kurveball]

So I've been googling around a lot lately and wanted to know what you guys thought about this. There are obviously a lot of factors such as chamber pressure, propellant, bell diameter etc. that determine a rocket's final isp.

But I wanted to know if anyone had ever worked out how high it could reasonably go.

[Jonfliesgoats]

I seem to remember something aru No 450 or 500 seconds, but I am not sure why I have that number in my mind.

[James Kerman]

The best ion drives get about 5000isp.

Theres a good website that lists atomic engines and their stats here:http://www.projectrho.com/public_html/rocket/enginelist.php

If you're talking about chemical rockets then tripropellant engines might be the answer.  In the 1960s Rocketdyne fired an engine using a mixture of liquid lithium, gaseous hydrogen, and liquid fluorine to produce a specific impulse of 542 seconds, likely the highest measured such value for a chemical rocket motor.  This would be very difficult to engineer into an actual rocket because of the toxicity and differences is storage temperatures.

There is this thread about hydrolox with some great information:

 

[shynung]

You can work it out, at least in theory. Look at the propellants used, determine the reaction products and energy liberated, and assume this energy goes wholly to accelerating the reaction products. Then, knowing the reaction product's mass and kinetic energy, you can work out the 'short-hand' theoretical exhaust velocity, which becomes specific impulse after divided by standard gravity. I read somewhere that if you do this with the hydrogen-oxygen mix, you'd get a specific impulse well above 500 s.

I say short-hand, because even with a perfect engine design that's 100% efficient at converting chemical energy to kinetic, the exact chemical composition of the exhaust need not necessarily be the same as what a chemical textbook would tell you; burning 2 molecules of hydrogen with 1 of oxygen does not produce 100% water, even at stoichiometric ratios. Some of the exhaust could be stuff like HO, H, O, or other rarer combinations. These reduce the chemical efficiency, as some of the reaction products have not fully liberated their chemical energy by the time they leave the nozzle.

Then there are the physical issues. Exhaust particles impart momentum directly opposite of their direction of travel onto the engine. Excluding ion thrusters, rocket engine exhaust doesn't always travel towards the same direction as the nozzle points. These tangentially-leaving exhaust particles impart less forward momentum, reducing effective specific impulse.

All this, before considering the mechanical efficiency of the engine design itself. Older engines use what's called a gas generator cycle, where part of the propellant is used to run the propellant pump, then thrown away. Newer designs attempt to improve specific impulse by routing this propellant back into the main chamber, at the cost of reduced thrust, and needing to run the turbine at uncomfortably high temperatures, requiring either heat-resistant materials, extensive cooling systems, or both.

Edited December 30, 2016 by shynung

[wumpus]

Also remember that the formula for ISP is pretty much based only on exhaust velocity and acceleration in "1g".  So increasing the ISP means increasing amount of heat in your exhaust, which is pretty much already pushing the limit of what materials science can survive (although switching to closed loop effectively "increases" ISP by avoiding losses).

For more extreme ideas:

Nuclear engines have similar heat issues, so expect *less* efficiency from a water-fed nuclear rocket than a hydrox chemical rocket (which is why they traditionally only use hydrogen).

Even if the "em-drive" doesn't work, you can get the same effect (at lower efficiency) by shining a light in a single direction.  You could also crank the Isp of an ion drive arbitrarily high by means similar to a cyclotron.  Such a thing would be pointless for interplanetary voyages (the Isp isn't the limiting factor) and probably equally silly for interstellar voyages (I would suspect that any such design would get *more* thrust from the black body radiation (with materials chosen to emit preferentially in one direction) used to cool the nuclear reactors...).

[todofwar]

1 hour ago, shynung said:

You can work it out, at least in theory. Look at the propellants used, determine the reaction products and energy liberated, and assume this energy goes wholly to accelerating the reaction products. Then, knowing the reaction product's mass and kinetic energy, you can work out the 'short-hand' theoretical exhaust velocity, which becomes specific impulse after divided by standard gravity. I read somewhere that if you do this with the hydrogen-oxygen mix, you'd get a specific impulse well above 500 s.

I say short-hand, because even with a perfect engine design that's 100% efficient at converting chemical energy to kinetic, the exact chemical composition of the exhaust need not necessarily be the same as what a chemical textbook would tell you; burning 2 molecules of hydrogen with 1 of oxygen does not produce 100% water, even at stoichiometric ratios. Some of the exhaust could be stuff like HO, H, O, or other rarer combinations. These reduce the chemical efficiency, as some of the reaction products have not fully liberated their chemical energy by the time they leave the nozzle.

Then there are the physical issues. Exhaust particles impart momentum directly opposite of their direction of travel onto the engine. Excluding ion thrusters, rocket engine exhaust doesn't always travel towards the same direction as the nozzle points. These tangentially-leaving exhaust particles impart less forward momentum, reducing effective specific impulse.

All this, before considering the mechanical efficiency of the engine design itself. Older engines use what's called a gas generator cycle, where part of the propellant is used to run the propellant pump, then thrown away. Newer designs attempt to improve specific impulse by routing this propellant back into the main chamber, at the cost of reduced thrust, and needing to run the turbine at uncomfortably high temperatures, requiring either heat-resistant materials, extensive cooling systems, or both.

Does it matter where the reactions take place? Thinking about what you would make in hydrolox aside from water, none of them will be stable and your number two product will probably be peroxide, which will then act as a monopropellant but it would probably persist long enough to not go off in the main reaction chamber.

[shynung]

@todofwar Definitely. Rocket engines work by using de Laval nozzles, which are designed to convert gas pressure to velocity. This design works by making sure gas pressure and flow rate makes the gas go supersonic at the throat/choke point of the assembly. If the reaction happened after the propellants go past the throat, pressure generated there won't be converted to velocity as efficiently as if it happened before the throat.

This figure shows the cross-section of a typical de Laval nozzle. Exhaust nozzle to the right, combustion chamber to the left.

Edited December 30, 2016 by shynung