Propellant efficiencies?

[jedidia]

There's something about propellant efficiency I don't quite understand (kind of orbiter sdk related too, as you can specify an efficiency of your propellant resource).

The massflow of my thruster is given by thrust and Ve. if I throw a kg of mass at a certain velocity out the nozzle, the thrust will always be equal. It doesn't matter wheather it's "a kg of lead or a kg of feathers", as the saying goes in switzerland. So what does propellant efficiency actually mean?

 

[Urwumpe]

The massflow of my thruster is given by thrust and Ve. if I throw a kg of mass at a certain velocity out the nozzle, the thrust will always be equal. It doesn't matter wheather it's "a kg of lead or a kg of feathers", as the saying goes in switzerland.

That is absolutely correct.

So what does propellant efficiency actually mean?

It means how high this velocity is at which you can eject it. It is not propellant efficiency, but specific impulse: The impulse you get by consuming one unit of mass. It is a measurement of your propulsion technology.

The propellant efficiency is best described by the property "characteristic velocity" for chemical bipropellants. It fails of course for nuclear or electric engines, since these have different demands on the propellant to be effective.

Characteristic velocity depends only on three values:

• mean molecular mass of the exhaust
• Combustion temperature
• Ratio of specific heats (of the exhaust).

These are independent of the engine (only mixture ratio).

It has two definitions, one external by the nozzleless engine performance (only throat conditions), one internal by the combustion properties with perfect nozzle performance

[math]C^\star = \frac{p_c A_t}{\dot{m}} = \sqrt{\left ( \frac{2\kappa}{\kappa-1} \right ) \left ( \frac{R T_c}{M} \right ) \left ( 1 - \left ( \frac{P_e}{P_c} \right ) ^\frac{\kappa - 1}{\kappa} \right ) } = \sqrt{\left ( \frac{2\kappa}{\kappa-1} \right ) \left ( \frac{R T_c}{M} \right ) } [/math]

 

[jedidia]

It means how high this velocity is at which you can eject it. It is not propellant efficiency, but specific impulse: The impulse you get by consuming one unit of mass. It is a measurement of your propulsion technology.

So basically it is a measurement for how difficult the propellant is to accelerate?

 

[Urwumpe]

So basically it is a measurement for how difficult the propellant is to accelerate?

No, it is a measurement how much impulse one kg of exhaust gets by the propulsion process. Or, how much force you act against the exhaust for every kg burned per second.

For chemical engines, where all energy is stored in the propellant, it means how much energy is stored in the propellant and how much of it gets used for propulsion by the engine. The characteristic velocity on the other hand explains this all without knowing the engine, it only says how much energy stored in the propellant can theoretically be turned into kinetic energy by the combustion process (How high your chamber pressure is, how much energy is used for pumping fuel or how you expand it, is ignored).

 

[jedidia]

No, it is a measurement how much impulse one kg of exhaust gets by the propulsion process. Or, how much force you act against the exhaust for every kg burned per second.

Ah, now I get it. I think. So, in the end, this would only really apply to engines with actual combustion? It's how much of the combustion product actually gets out the nozzle at the desired speed?

In an NTR or a VASIMR the exhaust velocity of all particles should be about the same, since you usually have a uniform gas that gets accelerated by expansion or magnetic acceleration. Is that correct?

 

[Urwumpe]

In an NTR or a VASIMR the exhaust velocity of all particles should be about the same, since you usually have a uniform gas that gets accelerated by expansion or magnetic acceleration. Is that correct?

Pretty much yes. In a NTR for example, the "combustion" temperature would be defined by the reactor power heating the mass flow.

Or for VASIMR, you would have fuel getting accelerated by electromagnetic fields, instead of propelling by heat machine concepts, like a NTR still does.

It must not be the same, as you can see, but it has different dependencies. Maybe you have a relation to beam power in your exhaust (P = F * Ve), keeping beam power relatively constant and thus dropping specific exhaust at higher thrust levels.