The steady state energy efficiency of a rocket needs to consider all inputs (combustion thermal energy, gas generator/pressurization for the propellant feed system, electrical for ion engines, et cetera) and losses (mechanical shock, thermal, ionization, erosive). The best way to understand this conceptually is to draw a bond graph of all system inputs and outputs and then calculate the dependencies and ultimate losses (energy leaving the propulsion system by various means) compared to the useful kinetic energy in the expelled propellant.
Most chemical combustion thermal rockets lose about 30% to 50% of the energy in thermal losses alone; that is, the hot plume carries away energy that does no work. An ideal rocket would spit out a very fast, very cold propellant that is fully expanded by the time it leaves the exit plane (or in the case of an aerospike nozzle, the isobaric minimum surface). Our most ideal practical propellants are hydrogen and oxygen, which still has an exhaust temperature well in excess of 1000 K even in a vacuum with an extendable nozzle, representing lost potential energy. Other significant losses occur within the pumping of propellants for high pressure engines, hence why the most efficient propellant feed and pressurization systems use the complex staged combustion rather than gas generator or pressure fed systems, albeit with the complexity and reliability issues that come with those.
While many non-engineers like to focus on engine specific impulse (I[SUB]sp[/SUB]) and engine thrust-to-weight ratio (TWR) as the parameters to describe engine efficiency, the characteristic exhaust velocity (usually written as C*) is really more useful in comparing the relative efficiency of different engine designs independent of the nozzle parameters. I[SUB]sp[/SUB] is a useful parameter in rocket vehicle design as it is a measure of propellant utilization efficacy and gives you a scaling factor for propellant load, and hence ties directly to mass fraction, but the engine designer is more interested in C*, maximum thrust output, and combustion stability at ignition and steady-state throttled levels.
Not that using I[SUB]sp[/SUB] as a comparison between different types of engines, like combustion, nuclear thermal, nuclear or solar electric, nuclear pulse propulsion, et cetera, tells you almost nothing about the actual efficiencies or practicality in a specific application because of how different the system requirements for each are. Although a nuclear thermal rocket (NTR)has substantially higher specific impulse (800-900 seconds versus a maximum of about 460 s for chemical rockets) and ion is higher still (1200 s to 3000 s), both require very large and heavy energy production systems, and generate an enormous amount of waste heat that has to be rejected by a large and heavy heat transfer/radiator system, which increases the scale of the entire vehicle relative to the payload. NTRs have been suggested for a crewed Mars mission but provide efficiency only above a certain mass threshold and have the added complexity of being too large and heavy to be launched as a single unit by any existing or proposed space launch vehicle.
The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) has been suggested as a magnetically confined RF heated plamsa rocket with specific impulse advertized at an order of magnitude above chemical rockets at good power throughput efficiency (~60%) but thus far the largest proof of concept operated at 200 kW and a thrust level measured in single digits of netwons. The size of the powerplant needed to provide high levels of thrust would be enormous. NASA had proposed to mount a pair of VASIMR rockets on the ISS to test for stationkeeping but Ad Astra failed PDR back in March due to technical maturity and safety issues.
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