Why does Specific Impulse increase in space?

[Sarxis]

I never thought to ask this question before, but why exactly does the ISP of engines increase in space over what it is in atmo? 

[Draalo]

In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber.

 

from: https://en.wikipedia.org/wiki/Specific_impulse

 

[Firemetal]

Well, I assume that due to the... You know what? I don't know.

https://en.wikipedia.org/wiki/Specific_impulse

Anyway, I believe it is because the specific impulse means the amount of acceleration per fuel used and as the atmosphere pushes you back less and less, more fuel is consumed easier. But I could be wrong.

Fire

Edit: Ninja'd.

Edited March 30, 2017 by Firemetal

[Sarxis]

Ahh yes!  I should have thought that quite simply, it's the atmosphere itself.  Thanks!

[Loren Pechtel]

Fundamentally, because engine first must push the atmosphere out of the way before it can actually exhaust and push the rocket.

[Gaarst]

I wonder if you could obtain the opposite effect by using an extremely over-expanded nozzle...

[OhioBob]

The total thrust of a rocket is made up of two separate components.  The largest of the two is momentum thrust, which is what we get by throwing reaction mass out the back of the rocket.  Momentum thrust is unaffected by the atmosphere.  The second part is pressure thrust, which is the result of unequal pressure forces at the nozzle exit.  The pressure of the exhaust gas at the exit plane of the nozzle is higher than the outside air pressure, so that pressure difference times the area of the nozzle exit produces thrust.  As we rise through the atmosphere, the outside air pressure decreases, so the pressure differential at the nozzle exit increases and we get more pressure thrust.  Specific impulse is just thrust divided by the flow rate of weight ejected, so I_SP is proportional to thrust.

[SYDWAD]

Now that u think about it, it doesn't make much sense. In space you are pushing off of a explosion that is moving in the other direction, in atmosphere you are pushing off of an explosion that is moving anywhere from away slower or towards you. In any case you would think you would have more to push off of and get better thrust in atmosphere.

[septemberWaves]

6 hours ago, Gaarst said:

I wonder if you could obtain the opposite effect by using an extremely over-expanded nozzle...

That's an interesting thing to think about. I imagine that an engine optimized to work at the surface of Venus (with its 90atm surface pressure) might lose I_sp as altitude increases beyond a certain point.

[Allocthonous]

8 minutes ago, eloquentJane said:

That's an interesting thing to think about. I imagine that an engine optimized to work at the surface of Venus (with its 90atm surface pressure) might lose I_sp as altitude increases beyond a certain point.

Which is probably why the ISP on some engines is set to the numbers it is. You'll notice that the space-optimized engines (the terrier, the poodle, the rhino, and if you squint, the puff) have terrible in atmosphere ISP values. The only one that doesn't is the Aerospike, and its flavor text specifically mentions its designed for that specially.

[Blaarkies]

8 minutes ago, eloquentJane said:

That's an interesting thing to think about. I imagine that an engine optimized to work at the surface of Venus (with its 90atm surface pressure) might lose I_sp as altitude increases beyond a certain point.

No, Isp for closed-loop reaction engines are always highest in vacuum. Cody's Lab has an excellent video about this

Rockets How They Work and Why I Havent Used nozzles yet
 

[Sarxis]

9 hours ago, SYDWAD said:

Now that u think about it, it doesn't make much sense. In space you are pushing off of a explosion that is moving in the other direction, in atmosphere you are pushing off of an explosion that is moving anywhere from away slower or towards you. In any case you would think you would have more to push off of and get better thrust in atmosphere.

Giving this some thought, I think the difference is if you could literally throw your foot extremely fast (supersonic), then you would generate more momentum than pushing with your foot off of the ground.  The ground would just end up getting in the way of you throwing your supersonic foot, and not help you generate more momentum.  I think this runs along the line of why we use propeller equipped planes at lower speeds, turbofans at medium speeds, and pure jet engines at higher speeds.

Edited March 31, 2017 by Sarxis

[Spricigo]

10 hours ago, SYDWAD said:

Now that u think about it, it doesn't make much sense. In space you are pushing off of a explosion that is moving in the other direction, in atmosphere you are pushing off of an explosion that is moving anywhere from away slower or towards you. In any case you would think you would have more to push off of and get better thrust in atmosphere.

But you are not only pushing against the part of the atmosphere behind you, if fact don’t matter how hard you are pushing against the atmosphere because you are pushing in all directions.

 

[OhioBob]

10 hours ago, eloquentJane said:

That's an interesting thing to think about. I imagine that an engine optimized to work at the surface of Venus (with its 90atm surface pressure) might lose I_sp as altitude increases beyond a certain point.

All engines will perform better in a vacuum than in an atmosphere.  But an engine can be made to work better in one environment than another engine.  For example, say we have engine A that is optimized to perform at sea level and engine B that is optimized to perform in a vacuum.  Engine A will have greater specific impulse at sea level than engine B, and engine B will have greater specific impulse in a vacuum than engine A, both engines will have greater specific impulse in a vacuum then they have at sea level.  The difference is that engine A has a flatter I_SP curve than engine B, and at some point in the middle the curves cross.

This can be seen in the basic thrust equation,

F = ṁ * V_e + (P_e - P_a) * A_e

where F is thrust, ṁ is the mass flow rate, V_e is the exhaust gas velocity, P_e is the pressure of the exhaust gas at the nozzle exit, P_a is the ambient air pressure, and A_e is the area of the nozzle exit.  The term ṁ * V_e is the momentum thrust, and (P_e - P_a) * A_e is the pressure thrust.

In normal engine operation, ṁ, V_e, P_e, and A_e are all constants.  The only thing that changes on the right side of the equation is the air pressure.  And as you can see from the equation, P_a has a negative sign, so increasing air pressure lowers thrust.

We can adapt an engine to work in either an atmosphere or a vacuum by adjusting the expansion ratio of the nozzle.  Increasing the expansion ratio, i.e. making the nozzle longer with a bigger exit diameter, increases V_e and A_e, and lowers P_e.  By making P_e small and A_e large, we increase the negative effect of P_a, but if the engine is to work only in a vacuum, we don't care.  In a vacuum P_a = 0, so there is no negative effect.  For an engine that's going to work only in a vacuum, we want to make V_e as large as possible to increase the momentum thrust as much as we can (the contribution from momentum thrust is larger than that from pressure thrust).  We do this by making the expansion ratio as large as practical.

When working in an atmosphere we have to try to offset the negative effect of P_a.  In this case we lower the expansion ratio, i.e. make the nozzle shorter and smaller.  This increases P_e and lowers V_e and A_e.  By making P_e large and A_e small, we've mitigated the negative effect of P_a, but we don't want to go too far.  Remember that we're also decreasing V_e, which lowers the momentum thrust.  We want to offset P_a but not at the expense of lowering V_e too far.  It works out that the maximum total thrust that can be obtained at a given value of P_a is obtained when P_e = P_a.  Therefore, for a given value of P_a there is an optimum expansion ratio.  Trying to optimize the nozzle for the particular environment in which it will perform is the job of the designer.

Note that V_e increases when we enlarge the expansion ratio of the nozzle because the gas pressure and temperature decreases as the gas expands.  The expanding gas loses internal energy, in the form of pressure and temperature, which is converted into kinetic energy.  Greater kinetic energy means the gas velocity increases.
 

Edited March 31, 2017 by OhioBob

[Kryxal]

I looked up some stuff on Wikipedia, and it seems that not only are engines less efficient if designed for a lower pressure than used at, you can encounter problems if it goes to an extreme.  Given KSP's handwaving of turbulence, though, I don't expect to see inconsistent thrust anytime soon...