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This doesn't make much sense, Webb was deliberately underboosted for L2 orbit because it has thruster only on one side and cannot correct for any overboost [0], so if Ariane performed as expected there should be exact calculated amount of fuel left. If there would be more fuel left in Webb than predicted it would actually mean that Ariane overboosted from programmed trajectory, which is bad thing. I think this is just NASA doing its usual underpromise-overdeliver rather than better-than-expected performance from launch vehicle.

[0] (supposedly it cannot rotate its cold side to the Sun, though I don't know what difference it makes when it's not taking images at the time?)

> there should be exact calculated amount of fuel left

Nothing is exact :) Ariane upper stage boosts JWST on a certain trajectory +/- some error in all directions, and then detaches. Along the way, they figure out the error and JWST corrects it with trajectory correction burns. This is somewhat independent of any fuel left for the "underboosting" you're talking about.

A mission designer looks at the performance specs/error distribution for Ariane and tries to include enough fuel so that, 99.X% of the time there will be enough for trajectory correction maneuvers AND a 10-year lifetime. When the (Ariane) burn is precise, errors are small, and less fuel is wasted on TCM, leaving more for the mission itself.

What this (10->20 year lifetime adjustment) really means is that NASA's left quite a lot of margin for TCM here... Which, for something this expensive, was a good thing :)

The point is, if Ariane slightly overboosts requested trajectory it increases JWST lifetime, but it's not indicative of exceptional Ariane performance. In other words, perfectly precise Ariane burn yields shorter lifetime than slight overboost, thus I'm surprised that article attributes increased lifetime to especially precise launch vehicle.
An overboost would have been catastrophic for the mission.

JWST has thrusters on only one side, and to correct for an excess of velocity it would have had to rotate such that its instruments faced the sun, ruining them instantly.

As such, the mission design called for a deliberate underboost, to be made up for by JWST's own precise thrusters. But a more precise launch vehicle means that the error bars are smaller, and they can use a much smaller underboost than would be required from a less precise launch vehicle.

Your point is, if it had a bunch of error (but not too much!) in one particular direction, the lifetime would be even further extended. This is true, and is probably worth a mention in the article as it is an interesting fact of the mission. My point is, the 10-year lifetime was designed with the worst-possible underboost (opposite) error scenario in mind, so it's not at all untruthful to say that the accuracy of Ariane extended the mission.

Ariane performed remarkably well, and that fact should be recognized and praised in the media. It's not exactly wise to hope for "errors in your favor" - much better to be more-precise-than-expected, as it allows them to plan more daring maneuvers with less margin in the future :)

It's not just velocity, it's angular accuracy. In other words, where are we pointing?

When you're course correcting, it's more like "steer this way" or "steer that way", not "dammit we're not going fast enough".

Getting the wrong velocity would have been a complete disaster.

True, but I think most of course correction delta-v budget is due to velocity rather than direction changes, especially with that deliberate underboost. Additionally direction is controlled during burn which is several minutes long, while velocity depends on precise timing of shutting down relatively big thruster.
After reading the article I learned the reason why Ariane 5 rocket performed better than expected. Really cool.
It's unfortunate that, at least in the mind of almost anyone who has taken an embedded systems course, Ariane 5 is associated with that very expensive overflow bug.