Low-Isp second stage

[DanP]

Hi!



Looking at the Falcon 1 and Falcon 9 specs, I started wondering.

They both have RP-1/LOX second stages, which are rated with relatively low Isp (less than 350s).

Usually, a second stage ignites in the upper atmosphere and is supposed to bring the payload into orbit, or nearly so. Therefore, you would want to use a high-Isp engine, probably H2/LOX, like on the Delta IV, Atlas V, Ariane 5 ECA, and the future Ares I, Ares V and Angara.

How come they use RP-1/LOX on the Falcons then?

Sure, they simplify design a lot, since they can borrow stuff from the first stage which is also RP-1, and becasue they don't have to worry about the plumbing and tanks required for LH2 (complicating things on the pad and adding wight to the rocket). But shouldn't you end up with a far less capable launcher?

It doesn't seem that they have, judging by the planned payload capabilites of the Falcons. Does the lighter weight of an RP-1/LOX system compensate for its lower Isp? On the other hand, wouldn't the low Isp mean you have to carry a lot more propellant compared to an H2/LOX system?



Dan.

 

[RocketMan_Len]

Therefore, you would want to use a high-Isp engine, probably H2/LOX, like on the Delta IV, Atlas V, Ariane 5 ECA, and the future Ares I, Ares V and Angara.

How come they use RP-1/LOX on the Falcons then?

It doesn't seem that they have, judging by the planned payload capabilites of the Falcons. Does the lighter weight of an RP-1/LOX system compensate for its lower Isp? On the other hand, wouldn't the low Isp mean you have to carry a lot more propellant compared to an H2/LOX system?

It depends on which figure-of-merit you want to go by. Hydrogen is 'better' because of the high exhaust-velocity and light combustion products... but when you factor density into the equation, kerosene gives *double* the performance of hydrogen.

I did a little 'back-of-the-envelope' calculations, using a program called ProPEP (it's a rocket-performance calculator...) Under identical chamber conditions, a LOX/H2 rocket has a *theoretical* Isp of 414 seconds, but a Density-Isp of 130s. An identical motor, burning kerosene, has an Isp of 311 seconds, and a D-Isp of over 320s!

Yes, you lose a bit of payload... and the 'wet' weight is greater. But - you use smaller tanks, no insulation, so you get a more robust vehicle.

(You don't use nitromethane in a truck... )

 

[Linguofreak]

It depends on which figure-of-merit you want to go by. Hydrogen is 'better' because of the high exhaust-velocity and light combustion products... but when you factor density into the equation, kerosene gives *double* the performance of hydrogen.

I did a little 'back-of-the-envelope' calculations, using a program called ProPEP (it's a rocket-performance calculator...) Under identical chamber conditions, a LOX/H2 rocket has a *theoretical* Isp of 414 seconds, but a Density-Isp of 130s. An identical motor, burning kerosene, has an Isp of 311 seconds, and a D-Isp of over 320s!

How are you calculating density ISP? DV per unit volume?

 

[Urwumpe]

Still, there is also the external efficiency, which tells how much kinetic energy stays at the rocket (and how much gets lost for fuel). This phenomena has the effect, that a hydrogen+oxygen rocket engine can operate effective at higher velocities relative to Earth, while others are more effective at lower speeds.

Maximum effectivity is at velocity = exhaust velocity, effectivity becomes negative at velocities higher than two times exhaust velocity. Negative means: More kinetic energy is ejected with the exhaust. While this has no impact on the payload, it has an impact on the rocket.

 

[RocketMan_Len]

How are you calculating density ISP? DV per unit volume?

If I'm reading the derivation right... it's Isp multiplied by the average density of the propellants.


-----Double Post Auto-Merged 3/8/2008 at 05 : 07 : 39-----

Still, there is also the external efficiency, which tells how much kinetic energy stays at the rocket (and how much gets lost for fuel). This phenomena has the effect, that a hydrogen+oxygen rocket engine can operate effective at higher velocities relative to Earth, while others are more effective at lower speeds.

That's a new one on me... any more specifics...?

 

[Andy44]

Still, there is also the external efficiency, which tells how much kinetic energy stays at the rocket (and how much gets lost for fuel). This phenomena has the effect, that a hydrogen+oxygen rocket engine can operate effective at higher velocities relative to Earth, while others are more effective at lower speeds.

Maximum effectivity is at velocity = exhaust velocity, effectivity becomes negative at velocities higher than two times exhaust velocity. Negative means: More kinetic energy is ejected with the exhaust. While this has no impact on the payload, it has an impact on the rocket.

I'm not sure I follow. In the inertial frame, who cares what the propellant's velocity relative to Earth or any other body is?

 

[Urwumpe]

I'm not sure I follow. In the inertial frame, who cares what the propellant's velocity relative to Earth or any other body is?

you have to remember that the launch of a satellite is a maneuver relative to earth. in that case it has an effect. but you mostly notice it for multistage rockets, in single stage cases, the effectivity is equal to the effects of the better ISP and mass ratio.

 

[DanP]

Thanks for your replies fellow orbinauts.

Maximum effectivity is at velocity = exhaust velocity, effectivity becomes negative at velocities higher than two times exhaust velocity. Negative means: More kinetic energy is ejected with the exhaust. While this has no impact on the payload, it has an impact on the rocket.

I'm not sure I have my head around this one.

What does having an impact on the rocket mean, contrary to having an impact on the payload?

 

[RocketMan_Len]

If I'm reading the derivation right... it's Isp multiplied by the average density of the propellants.

(Forgot to mention - the value is expressed in kilogram-seconds per litre...)

 

[BrianJ]

I'm not sure I have my head around this one.

Me neither! :blink:

The Rocket Equation
dV = ISP*ln(initial mass/final mass)
implies that the dV available from a rocket is independent of it's velocity.

On the other hand, I can see that unless
rocket velocity (relative to launch site) = exhaust velocity
then the exhaust will have some velocity (relative to launch site) and thus some kinetic energy(which has not been transfered to the rocket).

So what exactly is Urwumpe's "external efficiency" measuring?

Surely the relevant quantity is how much dV you can get in a given time - which is independent of the velocity of the rocket, no?

Confused? I am :lol:

BrianJ

 

[Linguofreak]

Me neither! :blink:

The Rocket Equation
dV = ISP*ln(initial mass/final mass)
implies that the dV available from a rocket is independent of it's velocity.

On the other hand, I can see that unless
rocket velocity (relative to launch site) = exhaust velocity
then the exhaust will have some velocity (relative to launch site) and thus some kinetic energy(which has not been transfered to the rocket).

So what exactly is Urwumpe's "external efficiency" measuring?

Surely the relevant quantity is how much dV you can get in a given time - which is independent of the velocity of the rocket, no?

Confused? I am :lol:

BrianJ

Basically, it's a question of how much energy goes into producing a given amount of DV. If your Isp is higher than your mission DV, you end up wasting alot of energy in your exhaust. If Isp is lower than mission DV, you end up wasting energy and propellant because the propellant that gets burned last has gotten accelerated with the rocket before being used (which took energy and propellant to do), and the higher you mission DV is over your Isp, the more propellant you need per pound of rocket.

 

[BrianJ]

Thanks Linguofreak, but I'm still rather hazy about this. I need to work through some examples with pen and paper - tomorrow (it's late and my brain feels like porridge).

I found some info about this on the web, so I'll do some reading

Cheers,
BrianJ

 

[DanP]

Thanks Linguofreak, but I'm still rather hazy about this. I need to work through some examples with pen and paper - tomorrow (it's late and my brain feels like porridge).

I found some info about this on the web, so I'll do some reading

Cheers,
BrianJ

Could you share some links?

Linguofreak, wouldn't the propellant that gets burned last get accelerated with the rocket before being used anyway, nothing to do with Isp being higher or lower than dV ? I don't think I got your point here.

I think I finally got the energy aspect of it, though.

Dan.

 

[BrianJ]

Could you share some links?

Here y'go Dan
http://www.hq.nasa.gov/pao/History/SP-4026/noord12.html
http://www.moonminer.com/rocket_physics.html
http://www.answers.com/topic/rocket-1
http://www.answers.com/topic/propulsiveefficiency-gif-1

The idea that there is an optimum ISP for a given mission dV is counter-intuitive for me, my brain wants to stay with the "Higher ISP = Better" idea!

All the best,
BrianJ

 

[Linguofreak]

Could you share some links?

Linguofreak, wouldn't the propellant that gets burned last get accelerated with the rocket before being used anyway, nothing to do with Isp being higher or lower than dV ? I don't think I got your point here.

I think I finally got the energy aspect of it, though.

Dan.

Of course, but it's a matter of degree. If apply all of your mission DV in a single straight line burn, and ignore the effects of gravity, then when DV=ISP, the last drop of propellant used ends up at rest in the reference frame you started out in. When DV>ISP, the last drop of propellant used actually ends up traveling in the same direction as the rocket at a speed equal to DV - ISP. So if DV is significantly greater than ISP you end up wasting a significant amount of effort in the first part of the burn just on accelerating the propellant for the later parts of the burn.

@BrianJ: Well, alot of it depends on how important energy efficiency is to you. If energy is a significant limiting factor, then yes, there is an optimal exhaust velocity for minimizing the amount of energy that goes into the exhaust. If propellant, however, is your most significant limiting factor, as it very often is, then higher ISP = better.

 

[joeybigO]

One thing to remember is
Ve = G * ISP this wouldn't mean a whole lot unless you were like landing on the moon, or another rotating body.

 

[DanP]

Aha! Got it. Thanks Linguofreak.

 

[Linguofreak]

One thing to remember is
Ve = G * ISP this wouldn't mean a whole lot unless you were like landing on the moon, or another rotating body.

Well actually, Ve = g * ISP, when ISP is measured in seconds. Capital G is the universal gravitational constant, lowercase g is (in this case) Earth's surface gravity, though g in other contexts just means the local acceleration due to gravity.

ISP is often measured in m/s, and in this case there is no difference between ISP and exhaust velocity. (Orbiter uses m/s as its units for ISP)

 

[joeybigO]

Well actually, Ve = g * ISP, when ISP is measured in seconds. Capital G is the universal gravitational constant, lowercase g is (in this case) Earth's surface gravity, though g in other contexts just means the local acceleration due to gravity.

ISP is often measured in m/s, and in this case there is no difference between ISP and exhaust velocity. (Orbiter uses m/s as its units for ISP)

Yikes... sorry... should have been g, little error there, I knew the difference but I seem to have choked on the operation.

 

[BrianJ]

OK, I've got my head around the maths (thanks!).

But I still can't visualize the circumstances where you would choose a fuel/engine combination with a lower ISP over one with a higher ISP, even if the energy efficiency is greater overall for the lower ISP.

Any examples from real life?

Cheers,
Brian