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So after I wrote a particularly poorly received answer about variable specific impulse, based on discussion I read here, I realise I may have misinterpreted what was being discussed in that thread. My understanding was that the thread was discussing launch vehicles, and came to the conclusion that matching the exhaust velocity to the current velocity of the vehicle caused the modified rocket equation for that case to be linear (which is quite the improvement!). However, I now suspect I have misinterpreted the maths and comments there, but I do not feel qualified to understand what is actually going on in those equations.

What, then, is the increase in efficiency described in the linked thread actually for? When would it be relevant? If it doesn't mean that $V_{ex}$ matching improves efficiency on takeoff, what does it mean instead?

This is similar to, but not exactly the same as this question, since that asks about what the optimal ratio of thrust/ $I_{sp}$ is, whereas I am asking about the efficiency gains when using an optimal ratio. Additionally, the solution to that question makes the significant simplification that the mass of the vehicle is constant throughout the launch.

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    $\begingroup$ Are you perhaps confusing variable specific impulse (which is hard and usually isn't done, particularly so for launch) with variable thrust (which commonly is done)? $\endgroup$
    – David Hammen
    Feb 15 at 14:42
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    $\begingroup$ All this stuff about variable specific impulse / exhaust velocity doesn't seem to be very applicable to boosters. More like ion drives or some such. $\endgroup$
    – Organic Marble
    Feb 15 at 14:43
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    $\begingroup$ @OrganicMarble Exactly. $\endgroup$
    – David Hammen
    Feb 15 at 14:44
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    $\begingroup$ saying something is "more efficient" or "less efficient" on its own isn't really sufficient in engineering. There are many efficiency metrics, and for launch from Earth we tend to be most concerned with mass-specific impulse, not energy per impulse (not least because no variable specific impulse drives with sufficient thrust to lift a launch vehicle to orbit exist). $\endgroup$
    – Erin Anne
    Feb 15 at 14:53
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    $\begingroup$ Many launchers intentionally reduce thrust (but not specific impulse) near max Q, and also near shutdown. Reducing thrust is easy, but changing specific impulse is anything but easy. Companies have gone bankrupt trying to build variable specific impulse launch engines. $\endgroup$
    – David Hammen
    Feb 15 at 14:54

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