Specific impulse as a function of atmospheric pressure / density

[BaBene]

Hello,

I'm currently working on a little program which outputs detailed information of the flight trajectory of my rocket. It's basically just numerical solving of the differential equation composed of all the forces affecting the rocket. During the creation of the differential equation I've come across a problem relating to the specific impulse. As most of you know the specific impulse is not constant for all altitudes, reaching it's maximum in vacuum.

So my question is what is the specific impulse as a function of atmospheric pressure / density? I searched the wiki and forums but haven't found an answer as all calculations presented in the wiki use the ISP at sea level or in vacuum for the sake of simplicity.

I wasn't sure where to ask this question but i hope i used the right forum

Hope that someone has an answer to this question.

Regards

BaBene

Edited October 20, 2013 by BaBene
Question has been answered

[Hodo]

This sounds like a question for Farem he would know.

[numerobis]

It's linear in the pressure for all the rockets.

It is nonlinear for the jets; internally it's implemented using a Unity FloatCurve, and I'm not sure what those really are (the unity docs kind of gloss over the details).

[BaBene]

It's linear in the pressure for all the rockets.

It is nonlinear for the jets; internally it's implemented using a Unity FloatCurve, and I'm not sure what those really are (the unity docs kind of gloss over the details).

Ok, do you have any more details on the actual function? Where is the upper end of the altitude at which the ISP reaches it's maximum value? How do you know its linear? Observation or do you have any source for this?

Thanks and Regards

BaBene

[Specialist290]

I've done a little looking into this subject myself. Here's what I found from my own tests:

Javascript is disabled. View full album

The scale height equations that I used to derive the values on the chart can be found on the individual planet and moon pages on the KSP Wiki.

Of course, I don't know anything about how jet engines work, since I don't do much spaceplane building.

Edited October 20, 2013 by Specialist290

[BaBene]

I've done a little looking into this subject myself. Here's what I found from my own tests:

...

The scale height equations that I used to derive the values on the chart can be found on the individual planet and moon pages on the KSP Wiki.

Of course, I don't know anything about how jet engines work, since I don't do much spaceplane building.

Ah, so it's really just

I'll use that for my equations and see what happens, thank you very much (Maybe someone should put this formula in the wiki?)

Best Regards

BaBene

[numerobis]

Ok, do you have any more details on the actual function? Where is the upper end of the altitude at which the ISP reaches it's maximum value? How do you know its linear? Observation or do you have any source for this?

Thanks and Regards

BaBene

The vacuum Isp is realized at 0 pressure. The atmospheric Isp is realized at pressure of 1 atm (or higher). The atmosphere height of each planetary body you can look up on the wiki; just shy of 70 km on Kerbin. But since the atmosphere thins out exponentially, you've already got the vast majority of the improvement by 5 km on Kerbin.

You can experiment easily: right-click on an engine, launch, note altitude and Isp all the way up. Then land on Eve, throttle up a tiny bit as you hurtle down, and note Isp all the way down. Then convert altitude to pressure via the wiki and see the linear correspondence.

Or, write a plugin. Look up a ModuleEngine on your spacecraft, notice the atmosphereCurve member, call Evaluate, and assume that the parameter is pressure in atmospheres from 0 to 1 (with testing to see that this is apparently a valid assumption).

[Specialist290]

Ah, so it's really just

I'll use that for my equations and see what happens, thank you very much (Maybe someone should put this formula in the wiki?)

Best Regards

BaBene

Pretty much. From what I've heard, though,* it effectively ignores atmospheric pressures over 1 atm, so you'd get the same Isp readings at 11km on Eve as you would at sea level, were you to send a rocket to its surface.

* I haven't managed to test this myself, but it seems to be consistent with other people's reports on the forums and elsewhere.