Average Isp of an engine during launch?

[Streetwind]

I've been wondering how I should be rating my liftoff stages in terms of dV. Obviously the Isp sits at its ASL value when the rocket is on the launchpad, but this changes very very quickly. Most engines get within 1 point of vacuum value at 10,000 meters, and all engines hit vacuum value at 20,000 meters. So for practical purposes, 80-85% of the climb is done at vacuum Isp as far as height traversed goes.

But rocket velocity isn't uniform, and to top it off, there's also the gravity turn constantly changing the climb rate.

Has there ever been a discussion on this topic, about how to estimate the average Isp of a rocket engine across the entire climb from launchpad to X meters, while traveling at terminal velocity and executing a normal (leveling off between 70-80km) gravity turn?

Edited February 12, 2014 by Streetwind

[capi3101]

There have been discussions of this topic before; bottom line is that it's too dependent upon the design of your craft and the way that you fly it to answer definitively.

Myself, when I want to estimate how much delta-V a rocket utilizes during the launch stage, I just use the atmospheric Isp rating. It means I underestimate the amount of delta-V the booster has available to it, and if I've calculated that it will make it, then it should definitely make it. The same cannot be said when you go with the vaccum Isp (i.e. if you overestimate it).

EDIT: Somebody will suggest "just use KER" or "just use Mechjeb"; I use KER, and I still go with the method above.

[Silverchain]

As capi says, I go with the atmospheric value and trust that the overall performance will have a level of reserve in practice. It's interesting to look at the corrected specific impulses at sea level at Duna and at Laythe, too.

[Lord_Zord]

I can help you on this one.

There was a thread some time ago regarding Isp and altitude, I can not remember which one it was and it is probably buried deep by now. Fortunately I copied most of the valuable things in it and can explain them back.

In KSP (unlike the real world) Isp is dependent on surrounding pressure according to this equation:

Where Isp_v is engine Isp in vacuum and Isp_s is engine Isp at Kerbin sea level.

And furthermore you can get the pressure at a given altitude by this equation:

Where -Alt is the negative of the given altitude in meters and 5000 is the scale hight of Kerbin (change this to make the equation work on other planets).

Combining these two equations and you get:

And there you go, just plug in the altitude and get current Isp back.

Note that for pressures over 1 atm Isp is not significantly further reduced.

Hope this helps someone.

[arq]

It comes up much closer to the vac ISP in most cases. Usually I find 4500m/s of vac delta-V is sufficient with proper TWR management. You could use something like protractor or any other utility that has a dV counter to see how much you've expended, then compare that to a calculated value.

[yaur]

I handle this a couple of way. first i assume vacume and build in some extra because as you've noticed isp gets pretty close to vacume in the first 10k meters or so. Second, i do a test launch with mechjeb to make sure i'm happy with the dV in orbit.

[Streetwind]

There have been discussions of this topic before; bottom line is that it's too dependent upon the design of your craft and the way that you fly it to answer definitively.

Myself, when I want to estimate how much delta-V a rocket utilizes during the launch stage, I just use the atmospheric Isp rating. It means I underestimate the amount of delta-V the booster has available to it, and if I've calculated that it will make it, then it should definitely make it. The same cannot be said when you go with the vaccum Isp (i.e. if you overestimate it).

I see... that's unfortunate. I suppose I will just have to keep estimating.

The issue with using the sea level Isp is that that may work fine for stages that only burn for 10-20 seconds; but if you have a stage that goes all the way (or almost all the way) to orbit, you would vastly overestimate the amount of fuel needed.

And there you go, just plug in the altitude and get current Isp back.

That's an interesting equation - unfortunately not what I was after, though. I'm looking for the average Isp across the entire flighttime of a stage. The formula given shows only a snapshot of a given moment. It basically gives me the same I can see ingame by right-clicking on the engine.

I suppose if I integrated this equation I would get a better result... but for that I would need the duration of atmospheric flight as well as make the assumption that the climb rate is uniform over the entire integral. Can MechJeb do something like that - hold a craft at (for example) exactly 100 m/s for a fully vertical 20km climb?

[Lord_Zord]

I see... that's unfortunate. I suppose I will just have to keep estimating.

Found it. It was newer then I thought.

http://forum.kerbalspaceprogram.com/threads/54196-Specific-impulse-as-a-function-of-atmospheric-pressure-density

I suppose if I integrated this equation I would get a better result... but for that I would need the duration of atmospheric flight as well as make the assumption that the climb rate is uniform over the entire integral. Can MechJeb do something like that - hold a craft at (for example) exactly 100 m/s for a fully vertical 20km climb?

You could do a numerical solution by taking the Isp say, every second, and making a table and/or graph out of it, and get an average. Recording the values could possibly be done with a mod, MechJeb or maybe Telemachus. Failing that recording a video with the stats showing on screen during assent is an ugly but fool-proof way.

PS. Found this thread while looking around the forums, maybe it can help

PPS. I have no idea if I am doing this right

[thereaverofdarkness]

I find that with a two stage to orbit launcher, with approximately the same dV in both, basic LiqF/Ox rockets will get an Isp about halfway between launchpad and orbit, and in the second stage you get basically perfect Isp.

[How2FoldSoup]

I see... that's unfortunate. I suppose I will just have to keep estimating.

The issue with using the sea level Isp is that that may work fine for stages that only burn for 10-20 seconds; but if you have a stage that goes all the way (or almost all the way) to orbit, you would vastly overestimate the amount of fuel needed.

That's an interesting equation - unfortunately not what I was after, though. I'm looking for the average Isp across the entire flighttime of a stage. The formula given shows only a snapshot of a given moment. It basically gives me the same I can see ingame by right-clicking on the engine.

I suppose if I integrated this equation I would get a better result... but for that I would need the duration of atmospheric flight as well as make the assumption that the climb rate is uniform over the entire integral. Can MechJeb do something like that - hold a craft at (for example) exactly 100 m/s for a fully vertical 20km climb?

It's funny I read the first few lines of your reponse saying that it only calculates that moment and I was going to suggest you integrate the equation..but it appears you've already come to that conclusion. I know there are mods that record flight information and I'm sure you could do a few test flights, average the results and integrate over that equation to give you a pretty good approximation(especially if you let mechjeb do standardized flight paths)

[technion]

I wonder how this plays into the question of "when does hauling a nuclear engine off Eve's surface justify its efficiency vs its weight" ? It's a heck of a lot to bring, say, 10km into the air, but if it becomes worthwhile at that point, it may just be altogether a good move.

[Streetwind]

Eve has a much thicker atmosphere than Kerbin so you need to haul it up further than 10km.

For me it was honestly more a question of "I have this SSTO rocket and I want to calculate its delta-V by hand". For this I need an Isp value that averages the entire climb from 0 to 70km. But the question can be generalized for any rocket stage across an arbitrary height band.

Edited February 12, 2014 by Streetwind

[KerikBalm]

I think for EVE, given both its atmosphere, which is very bad for the nuke, and its high gravity, which is again very bad for the nuke (its TWR is terrible), aerospikes are pretty much the only engine you'd want to use.

I also figure that a mk1 command pod with an FL200 and an lv909 gets more dv than the same with a nuke (due to the nuke's weight). For upper stages of equal weight, the nuke doesn't seem to get more dv until you're feeding the lv909 with an fl800 tank.

Realistically, all you want your craft to do is get to orbit around EVE. The upper stage, the one operating at low atmospheric pressure, should be so light, that I doubt its worth carrying a nuke up from the surface, because the nuke won't do much better for your stage that should just get a command pod/mk 1 lander can into orbit.

Eve is so hard to get to and back from, that if you are trying the "direct ascent" approach, rather than the "oribital rendevous", you're a masochist.

Heck.... you can even put on 2 RCS thrusters on the lander can, jettison everything and just push the lander can alone with RCS (you can get some significant dv from just 0.01 weight of RCS thrusters), and then bail out and jet pack your way into a stable orbit.

Then you rendevous with your interplanetary stage that you left up there in orbit.

Do not bring the interplanetary stage down to Eve's surface, its a huge waste.

[Dispatcher]

Back to the OP, you could shift from the idea of using an average iSP at a given altitude/ pressure for a simpler (and crude) approach: using the average of the two published iSPs of an engine, with no regard for altitude/ pressure. Example: LVT30 320 345 370; the average being the middle value. For air breathers (or that mode), an example such as Turbojet 800 1000 1200 should be understood in the light of the fact that since an air breather does not actually continue to function in vacuum, the vacuum value is not a practical value, although the maximum functional value approaches it. In a sense, this makes the average value (in this case 1000) a reasonable approximation of the maximum functional value for an air breather.

However (and as others have suggested), I go with the initial (surface) iSP when considering dV since I tend to have a little reserve of dV at each stage of the flight.

[UmbralRaptor]

For a (Kerbin) SSTO: 0.2 atm (Call it 0.21 if you're at the low end of useful TWR)

For a (Kerbin) 2STO where both stages are relatively similiarly sized: 0.5 atm for the first stage, ~0 atm for the second. (may need adjusting)

[Streetwind]

Interesting. How did you come to these numbers, UmbralRaptor? Is that based on simple examination of time spent reaching various heights, or is there math involved?

[UmbralRaptor]

MechJeb's ÃŽâ€V recorder, and noting burnout altitudes, mainly. They're very much rules of thumb.

More detailed examinations require numeric simulations of ascents, and I'm actually unsure of how to best do that.

[Streetwind]

Well, it's a workable approximation. Looks like I wasn't too far off in eyeballing the average of the 350-400 engine at 390

I'm going to mark this as answered for now, since we're probably not going to get much more detail than this.

[numerobis]

I think for EVE, given both its atmosphere, which is very bad for the nuke, and its high gravity, which is again very bad for the nuke (its TWR is terrible), aerospikes are pretty much the only engine you'd want to use.

The 48-7S is better than the aerospike on Eve, because of much better TWR. It's pretty much a tossup between the T30 and the aerospike. The LV-N might, maybe, be useful for the top stage, but I have my doubts -- even on Kerbin it's marginal.

[Streetwind]

The 48-7S only works so well on Eve because a.) it's broken beyond belief and b.) KSP neglects to actually continue scaling Isp beyond 1 atmosphere worth of pressure. If it wasn't clamped to that, we would likely see sub-100 Isp on the 48-7S on Eve's surface, while the aerospike would still be around 380.

Honestly this should be implemented, because the aerospike could really use that niche. I'm probably going to use a mod to make it happen if I ever get around to visit Eve...

[technion]

The 48-7S is better than the aerospike on Eve, because of much better TWR.

I've had quite a few runs at sea level Eve ascents and vehicles, and whilst I often put 48-7S's in upper stages, that's the only place I've been able to use them. The ascent requires enough fuel that those FL200 and similarly small tanks just don't push enough dv no matter what they are outfitted with. You can asparagus stage a certain number of these, but you reach a point where your outside stage is good for all of about one second and pushes negligible dv. To address that, you migrate to larger tanks. You can put those little radials around but at an FL800 in size, the TWR just gets frustratingly low and you fall back on Aerospikes.

[undercoveryankee]

The radial isn't as overpowered as the inline 48-7S.

A trick you see a lot is to put several inline 48-7S on the same tank by hanging the off-center ones on cubic octagonal struts.