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How much fuel did JWST save due to an accurate Arianne 5 launch, and how much fuel will be remaining after JWST L2 orbital insertion? And how many years is that fuel expected to last?

According to https://en.wikipedia.org/wiki/James_Webb_Space_Telescope "Eight smaller thrusters are used for attitude control—the correct pointing of the spacecraft.[74] The engines use hydrazine fuel (159 liters or 42 U.S. gallons at launch) and dinitrogen tetroxide as oxidizer (79.5 litres or 21.0 US gallons at launch).[75]"

"It was designed to carry enough fuel for ten years,[172] but the precision of the Ariane 5 launch and the first midcourse correction were credited with saving enough onboard fuel, that the observatory should be able to maintain its orbit for "significantly more" than this."

But it doesn't say how much of this fuel was expected to remain after L2 orbital insertion assuming the expected less than perfect Arianne5 launch which was planned for; lets call this number e for expected fuel and lets call the number a for actual remaining fuel with the much better launch than expected. And it doesn't say much fuel is expected to be used annually for JWST orbital maintenance and momentum dumping; call this number y for expected yearly orbital maintenance. These numbers could be used to compute how many years the more efficient Arianne 5 launch increased the JWST lifetime. $$\text{years_gained} \approx \frac{a-e}{y}$$

I think I've read that the expected planned mission of 10 years was gated by the annual orbital maintenance which would imply: $$\text{planned_lifetime} \approx \frac{e}{y}\approx 10\;\text{years}$$ The actual fuel limited lifetime would be: $$\text{actual_limited_lifetime} \approx \frac{a}{y}\;\text{years}$$

https://arstechnica.com/science/2022/01/all-hail-the-ariane-5-rocket-which-doubled-the-webb-telescopes-lifetime/

Mike Menzel, said the agency had completed its analysis of how much "extra" fuel remained on board the telescope. Roughly speaking, Menzel said, Webb has enough propellant on board for 20 years of life.

Sheldon
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    I clarified the numbers I'm interested in. – Sheldon Jan 09 '22 at 06:55
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    It won't run out of fuel after 10 years. 10 year design lifetime means "there is no chance of running out of fuel, no matter how bad things go (within reasonable assumptions)". I.e. worst possible injection, many missed correction maneuvers, more momentum unloading etc. Under nominal conditions that should last at least 15 - 20 years. (no citation, so not an answer). – asdfex Jan 09 '22 at 10:00
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    @asdfex: Mike Menzel (Lead Mission Systems Engineer for James Webb Space Telescope) is quoted by numerous sources as confirming that thanks to the precise insertion by Ariane 5 and the two correction burns, Webb has enough fuel for its maximum design life of 20 years. I have not found a first-party source, unfortunately, but Arianespace has re-tweeted several of those third-party sources, which indicates they agree with the assessment. Here's just one example: https://twitter.com/ariane5/status/1479923663881256966 – Jörg W Mittag Jan 09 '22 at 10:24
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    Yes... 20 years correspond to roughly 6 m/s per year (at 120m/s remaining after 30 m/s for the MCCs). If we assume momentum unloading at 2 m/s/year and take the public 2-4 m/s/year for station keeping there's still a huge range of possible lifetimes. – asdfex Jan 09 '22 at 10:35
  • Also note, it didn't actually "save" any fuel. It just didn't use any of the assigned contingency and stayed at nominal consumption. It could have saved some fuel if Ariane slightly overperformed. – asdfex Jan 09 '22 at 10:37
  • The quoted numbers seem to apply to the bi-propellant thrusters only (because of the ratio of mass of fuel to that of oxidizer) - see answer to How to convert bi-prop to delta-v for JWST. The momentum unloading uses hydrazine only, which budget is not accounted for in these quotes, logically. W/o this info, it is impossible to estimate the additional life-time, as it may be capped by the momentum unloading, even assuming that there is a single tank of hydrazine. Frustrating! – Ng Ph Jan 09 '22 at 11:11
  • @asdfex The worst case (but still realistic) assumptions led to the five year lifetime that NASA guaranteed to the US Congress. A really bad launch, or a really bad MCC1a would have resulted in a congressional inquest. The ten year lifetime design goal used nominal assumptions, but still with some dispersions. Apparently things went so well with launch and with MCC1a that even that ten year design goal are expected to be exceeded. As is the case with your comment, no citation, so not an answer. – David Hammen Jan 09 '22 at 12:17
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    @Sheldon You quoted the wikipedia article out of context, and the wikipedia article itself quoted the NASA sources it used out of context. The two thrusters used for MCC1a and MCC1b used hydrazine and dinitrogen tetroxide, as will the two thrusters that will be used for orbit insertion and orbit maintenance. The eight thrusters used for attitude control and momentum dumping are mono propellant thrusters that use hydrazine only. It's the four large thrusters that are bi-propellant thrusters. – David Hammen Jan 09 '22 at 12:37
  • @DavidHammen I remember seeing a table that suggested all launch parameters where in fact very close to nominal, so I don't see how fuel could have been saved compared to a nominal consumption. – asdfex Jan 09 '22 at 12:43
  • @asdfex As I wrote, "The ten year lifetime design goal used nominal assumptions, but still with some dispersions." Only a fool assumes everything is going to be perfect in mission planning. There's a difference between "perfect" and "nominal". From what I've read, the launch was nearly perfect, as was the MCC1a burn. No sources with numbers, which is what the OP wants. – David Hammen Jan 09 '22 at 14:25
  • @DavidHammen, others, seems like 6m/s per of which 2-4m/s per year is for station keeping and uses both fuels. But the momentum unloading gets penalized by using only one fuel, and probably has a smaller $v_e$ as well since as well since using only hydrazine should be less efficient. Thanks for the info! – Sheldon Jan 09 '22 at 14:50
  • @DavidHammen We both mean the same thing, but we use the terms differently. When I say "nominal [point]", it's your "perfect [point]" which lies within your "nominal [range]", which I would call "expected variation". – asdfex Jan 09 '22 at 14:55
  • I assume momentum unloading can be minimized by creatively choosing JWST's observation targets and orientation to take advantage of solar radiation pressure to remove some momentum buildup??? – Sheldon Jan 09 '22 at 15:02
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    Your assumption that momentum unloading can be optimized (depending on the scientific tasks and their sequencing in time) may well be correct, but it doesn't help answering your question. Your question is how much extra lifetime have they (NASA) won, as a result of actual launch and correspondingly mid-course correction (MCC) executions. Of the budgeted 66.5 m/s for MCC (out of 150m/s total budget), the published burn times indicate that ~ 20 m/s only was used. This is indicative of how much margin they have, to exceed the 10y requirement, concerning propellant for orbit maintenance alone. – Ng Ph Jan 09 '22 at 15:33
  • @asdfex (and David Hammen), correct me if I am wrong, but when you are required to design something that shall meet X and you have a $\sigma$ of uncertainty, then as an engineer you size your something at X+$\sigma$, at least, or X+$\sigma * 3$ if you are a "concencious" engineer. – Ng Ph Jan 09 '22 at 15:49
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    @NgPh Stacking up worst case upon worst case ... upon worst case, and doing so in the worst possible way easily results in a launch vehicle that cannot launch or a spacecraft that cannot reach its objectives. What we do instead is lots (and lots and lots) of statistical analyses (e.g., Monte Carlo, Markov Chain Monte Carlo, bootstrap, jackknife, ...) to determine behaviors at, for example, the three sigma level. Non-space industry has gone far beyond this and is moving toward six sigma processes. Space exploration is nowhere near six sigma. – David Hammen Jan 09 '22 at 17:05
  • @David Hammen (and adsfex), I agree, but that's not my point. My point is that the 150 m/s (or approximately 280Kg) of fuel that was factually loaded, is not for a "nominal" 10y. It corresponds to 10y + implementation margin. So, even w/o the actual accuracy of Ariane launch, the 10y quote, as it is a user's requirement (ie not to the appreciation of the implementers), is neither a "maximum", nor the the center of the uncertainty bracket. This is how people work in space (I don't have experience with other indusries). If you "shall meet X", then nominal=X+margin. – Ng Ph Jan 10 '22 at 10:10

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The three MCC course correction burns, which are listed In this NASA blog and and this NASA blog have totaled 24.4$\frac{m}{s}$ fuel used so far, in burns totaling 79.5 minutes.

  • Dec 25th, 20$\frac{m}{s}$, 65 minutes
  • Dec 27th, 2.8$\frac{m}{s}$, 9.5 minutes
  • Jan 24th, 1.6$\frac{m}{s}$, 5 minutes

JWST started out with 150$\frac{m}{s}$ worth of thruster fuel James Webb telescope; limits to propellant lifetime?, of which 2-4$\frac{m}{s}$ are expected to be used annually for station keeping. A Monte Carlo simulation estimate was: 2.43$\frac{m}{s}$ annual station keeping usage; James Webb telescope; limits to propellant lifetime?, and Stationkeeping ... James Webb Space Telescope

By my math, this leaves JWST about 125$\frac{m}{s}$ worth of fuel remaining for both station keeping and momentum dumping, which is good enough for 20 years of fuel limited lifetime given a reasonable upper bound annual fuel usage of 6$\frac{m}{s}$.

Finally, there is this quote, "The first, MCC-1a, is expected to be a long, continuous burn (potentially up to 3 hours) performed approximately twelve hours after launch"; JWST Mid-Course Correction. If the total of the three MCC burns had turned out to be 190 minutes instead of 80 minutes, then by my math the accurate Arianne launch saved 110 minutes worth of MCC burn, which equates to 34$\frac{m}{s}$, which increased the JWST lifetime by at least six years, and maybe as much as ten years. Of course, a 3 hour burn would probably be worst case, but given the unpredictability of launch vehicles, such a scenario had to be considered realistically possible...

One final NASA link I found also states that JWST has 20 years of fuel instead of 10 years worth of fuel. NASA: Webb arrives in orbit of L2. JWST's lifetime is probably not going to be fuel limited...

Sheldon
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  • I concur. My answer to your linked question is "Bottom line: My best guess is currently 150 - 67 = 83, and 83 / (2 to 4) = 41 to 21 years." – uhoh Jan 24 '22 at 21:59
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    what blows my mind is how small the station keeping maneuvers really are. Today's burn amounts to only 1.6$\frac{m}{s}$, or 3.4 mph, and the total annual station keeping might only be 2.5$\frac{m}{s}$, which is only 5.6mph. These are tiny tiny numbers compared to the $\Delta_V$ from the Guiana spaceport to L2 which might be 12.5$\frac{km}{s}$ or 28000mph when including the atmospheric drag. – Sheldon Jan 24 '22 at 23:12
  • Yes, every two weeks for ~six months means twelve nudges per orbit, but they are certainly relatively small nudges. I wonder how much lower it could be if they forgot about it being an astronomical observatory and went for the absolute minimum delta-v plan. Perhaps with the sunshield more active as an additional propulsive, it could get really low. – uhoh Jan 25 '22 at 00:14