First, i hope you're not annoyed by such "trivial" balance reports like this - one of the things i try to do in-game is to build cost efficient rockets, so i do sometimes notice things like this.

Having unlocked the J-2X some time ago, i noticed it was much more expensive than the J-2, more so than what i expected from the increase in stats. I also noticed the very good sea level I_sp, even though this is an upper stage only engine (irl and according to in-game description). I've googled a bit but couldn't find any info on the irl I_spSL, but according to the nozzle area ratio and chamber pressure i'd assume a sea level I_sp more in line with a typical upper stage only engine.

Today i took the time and did some basic plots, containing the J-2X with current and with adjusted price, the latter denoted by the asterisk:

As can be seen, the J-2X is easily the most expensive upper stage hydrolox engine per vacuum thrust or vacuum thrust * I_spvac, even quite a bit more expensive than the clearly better and irl very expensive RS-25. If the sea level isp/thrust get toned down, i suggest a cost of around 7200-7300 (i used 7250 in the plot for the asterisk variant).
Even if it gets to keep the high sea level performance, it should probably cost around 8000 to not be overpriced compared to the RS-25.

I found some info, NASA says the J-2X would be destroyed if started on the ground in flight configuration (= with nozzle extension) and that a ground-startable version with a shorter nozzle extension would have less vacuum I_sp, around 436s. This post basically says the same for the non A5 RL-10 variants.
This probably means that the J-2X along with the non A-5 RL10 sea level I_sp should all be nerfed to merlin-xV levels, ≤ 10s!?

@MikeOnTea the issue with that is that simply putting the SL Isp very low would give the wrong numbers in the upper atmosphere. The problem with starting a vacuum engine at sea level is that the exhaust flow separates from the nozzle. But if you take the variation in Isp through the operating range and extend it down to sea level, it would be about the same as if it worked at sea level with no flow separation. So I think what you really want is a curve which is straight through the operating range and then abruptly drops to almost zero.

Yeah, admittedly the information you need to do this right is not widely available. Depending on what sources you use, is appears that flow will separate when the exit pressure drops below somewhere between 10% and 40% of ambient. But then you also have to know the exit pressure, which isn't usually available and can't really be calculated without simulating the engine.

Good point and idea, blowfish. I don't know though whether we can find infos about roughly where that cutoff-point should be and how the curve should look above that in the operating range, but i'll try googling for infos.

I've long thought that the SL-ISP of 'vacuum' engines should be... non-existent. There are often no published numbers, and from my understanding of the physics involved, the performance would range from 'non-existent' to 'likely to just explode'.

However @blowfishpro brings up a good point -- while the usability of these engines at sea-level is a big 'no' due to instabilities, the 'theoretical, by-the-numbers' ISP is probably not 'that low' either (100-200'ish? entirely guessing). At the point where the exhaust stabilizes the ISP is certainly greater than zero, and probably a good portion of the vacuum ISP.

I would think that a decent curve could probably be found for these engines that gives them unusable thrust/ISP at sea-level, but returns them to decent performance in their intended use range. Probably start at 10% V-ISP for 'sea level' stats, slowly climbing for the first bit, say up to ~20% at ~5k alt, but then very quickly going up to >80% by 10k alt. The intent would be to make them useless as a lifter, but perfectly viable for 2n'd/upper-stage use, by simulating this point of 'start of stability'. (entire proposition is guessed at; a better model could be determined with a bit of statistical analysis with regards to atmospheric pressure and particular engine)

@MikeOnTea -- if you would like to take a stab at this, I'm willing to adjust some engine curves if a decently generic 'vacuum-engine' ISP curve can be derived.

In regards to cost -- I'm fairly open to cost adjustments. Currently they should all be mostly consistently cost-balanced based on their thrust output... but some engines might have been missed during the recent cost-balance pass. (the spreadsheet I use determines the engine cost based on thrust and a constant scalar applied to all engines; a couple receive further hand-tuning such as the extra-expensive RS-25).

Some good news, i found a rocket thrust simulator from NASA. With it, i think we are able to estimate nozzle exit pressure, and it even warns you when the ambient pressure is so high that there's a shock in the nozzle. It also gives you the I_sp at various ambient pressures.

So, i used that tool to model curves for the RL10A-4 and the RL10B-2 as examples, using the shock warning pressure as the pressure above which the I_sp of the engine is zero.

RL10A-4 curve:

	key = 0 451 0 -478
	key = 0.823 57 -478 -57000
	key = 0.824 0 -57000 0

RL10B-2 curve:

	key = 0 465.5 0 -1503.5
	key = 0.281 43 -1503.5 -43000
	key = 0.282 0 -43000 0

With these curves i plotted the I_sp against the altitude on kerbin:

Zoomed in to low altitudes:

I think these results look quite good. Particularly nice to see that the RL10B-2 really has to pay for that huge nozzle/expansion ratio in low altitudes.

The cutoff point has to be determined for every engine individually as it depends on expansion ratio and chamber pressure, but as it only needs to be done for upper stage engines, i guess it's manageable.

Thoughts?

About the cost of the engines - yes, the hydrolox engines i plotted above all look pretty balanced, except for the J-2X, so might very well be possible that it was missed during the last balance-pass.

While modeling the J-2X curve, i realized i have to set the cutoff point higher – the warning from the simulator i used previously was at nozzle exit pressure below 5% ambient pressure, which would've made the J-2X almost ground-startable. After researching some more i found out that they ground test the J-2X with quite a reduced-length nozzle, and an intermediate-length nozzle together with a diffuser to simulate higher altitudes, but not at all with the real nozzle.
So, i set the cutoff point now at 10% ambient pressure – if the engine exit pressure is below that, thrust/I_sp is zero. This is still a fairly low pressure/cutoff point and i'm a bit unsure if we should increase it even more. For the currently plotted engines it's enough to prevent their ground use though, i guess.

Plots:

A small detail: As i've been trying to get a curve for the J-2X and checked the tool against the J-2, i realized the sea-level I_sp was too high. After some digging around i found a second, lower chamber pressure value for the J-2 – i assume that to be a sea level value, because with that put in the simulator, i get the correct sea level I_sp – and it can make sense as the J-2 has an open gas generator cycle, and the generator/turbine has to fight the ambient pressure as well. I've thus assumed that the J-2X also has an equally lower chamber pressure at lower altitudes, which might or might not be true, but it shouldn't reduce low-altitude-performance too much. I've not assumed the same for the Merlin 1DV, because that seems to use the same hardware as the 1D which does seem to have the full chamber pressure at sea level.

Feedback welcome.
If we can agree on those curves, i'll try to do the rest of the upper stage engines. Should i open a new ticket for the curve rebalance, by the way, as it is not only J-2X related anymore?

Yeah, it's tricky. Also, how does KSP deal with non-vacuum Isp on worlds other than Kerbin?

Vac engines on Mars/Duna are not so troublesome.

What they likely need is a failure mode (maybe this will standardize once the add-on is a thing) such that at an ambient pressure >X, they blow up.

The curves are all pressure based, so the engines should work fine on mars/duna at surface altitude while you're out of luck on venus/eve. :)

@MikeOnTea Can leave the vacuum-engine rebalance stuff in this ticket. I'll update the name appropriately, and split of the cost-updating to a new ticket (err...how bout I just fix it now and call it done... :) -- updated to 7250 for now).

For reference, here is the full engine-stat sheet... which may or may not have some holes in it (note the cost specified in the sheet differs greatly from those in the parts... I may have not even done the last cost-update pass at all...).

EngineData.xlsx

As to the proposed curves -- they seem about appropriate to me, though I'm not sure how well KSP will cope with the 0's for ISP below certain altitudes.

Have you tried using any of the new curves in-game?

The one adjustment I might make would be to come up with a slightly more gradual setup -- rather than having strictly 0 ISP below a specific altitude, setup the tangents/keys in such a way as to have a much more gradual lead-in; so the ISP is non-zero at low altitudes, but effectively useless.

I would agree with @taterkerman that this would be a prime candidate for a failure mode for these engines. I'm generally not a fan of 'random' part failures... but player-induced failure through misuse of the part is perfectly acceptable. I suppose in the absence of failure modes, having zero ISP would effect mostly the same outcome (minus the explosions...and retaining a functional engine that could be used later).

I made a short test flight firing 2 RL10 engines and SRBs as lifters from the ground to the operating range of the RL10s, and it seemed to be working fine.
Can think about/try a slight lead in though.

If the 0's work, then it seems fine to go with that.

Any idea how RO handles the vacuum engines? There has generally been quite a bit of research behind the values they use, and I'm kind of curious as to how they have set them up. Might give you a few more data points to work with.

I don't recall RF/RO having any special handling for flow separation.

Hehe, before doing any work on this, i actually checked ROs I_sp curves hoping they might've already done the work, but not so – their vacuum engines seem to work fine on the ground, unless they have some different feature like part breakage. I might ask them about the matter and see what they think, and i will run some further tests with the 0s.

A few observations:
Engines with 0 I_sp use their fuel and get hot, but don't have any exhaust plume.
KER displays 0 delta-v and NaN for the first mass value (second works though) for mixed stages containing 0 I_sp engines.
Stages with only 0 I_sp engines aren't shown in KER's stage view in flight while at 0 I_sp altitude.
As you wouldn't want to mix upper and lower stages anyway with the new curves, nothing of that should really matter though, i guess.

The side effects such as those where why I was concerned with the strictly 0 isp.

• Effects - the effects are scaled based on currentThrust/maxThrust -- so it would make sense that with zero thrust output, there would be zero plumes.
• Fuel use - fuel flow rate is calculated from max thrust and vacuum ISP, and is constant regardless of thrust.
• Heat - determined by fuel flow * config-specified heat multiplier (or is it a divisor?)
• Thrust - determined by currentISP/maxISP * maxThrust * throttle
• Delta-V - stages with a 0 ISP should logically have zero dV. However, the ISP is not strictly zero, but merely zero below a specific pressure.

I think many of those oddities may be reduced or eliminated by specifying a non-zero low-point (e.g. substitute 10ISP for the 0ISP in your graphs) -- this would give KER/MJ/etc -some- value to play with for the 'sea level' performance, while still rendering the engines 'all but completely useless' while at/near sea level.

Well, i guess i gonna use 10 I_sp as a baseline then, easy to adjust the curves to that, and you get at least small engine visuals and no more NaNs.
When i'm done, i guess a PR is preferable to posting the curves here?

If you are familiar/comfortable with the PR process, yes, please. Otherwise with something like this it is probably simple enough for me to patch it in manually if needed.

Yeah, I think the ~10 ISP is a good compromise to keep things stable from a code/calculation perspective, while still giving the desired effect concerning usability.

Sorry, got a bit busy and forgot to respond to your post on the PR re: the cutoff altitudes:

I'm fine with just adding a quick blurb to the engines stating 'vacuum-optimized, not startable at sea level' or similar. The altitudes you had posted for the few engines you calculated all seemed to be way below where I would expect the engine to be used anyway, so not really worth the trouble for now.

I'll work on getting this info added over the next few releases; no need for you to worry about it.

Yep, all the engines should work fine on second and higher stages, they just won't really work on first stages anymore, so most users probably won't even notice any change, which is good. :)

Just a quick documentation of the process i used to create the curves:

• In the NASA nozzle simulator set to known engine values:

  • Geometry -> Aex/Ath (expansion ratio)
  • Propellants -> fuel and mixture ratio if available
  • Flow -> Pto (chamber pressure)
  • Flow -> Pfs (ambient pressure, first use 0 for vacuum)
  • Flow -> Tto (chamber burn temperature, adjust to match published real vacuum I_sp)

• Pex is the nozzle exit pressure

• Multiply Pex with 10 to get cutoff ambient pressure (if using 10% cutoff)

• Set Flow -> Pfs to cutoff ambient pressure (10 * Pex) to get Isp at cutoff point

• Divide cutoff ambient pressure by 101 to get the cutoff point on the curve, set to cutoff I_sp

• Set cutoff point + 0.001 to baseline I_sp (10).

• Calculate tangents for them to be straight lines (simple with other curves as examples)