Problem is that we do not have any information on the actual production rate, though I attempted to give the best possible estimate:
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Okay this bit strikes me as a particularly puzzling bit of reasoning
"It is also confirmed by their being over 600 Lunar class in a Segmentum fleet (specifically, that of Segmentum Obscurus). There are 6 other cruiser and 8 light cruiser classes in a fleet – assuming a minimum of 200 and maximum of 500 ships per Segmentum per class, Imperium would have a minimum of 17 000 and a maximum of 41 000 cruisers in the Imperial Navy. "
Your line of thought, if I understood it correctly, is to assume that because one Segmentum has 600 of a particular class then not only does every segmentum has the same but every cruiser must also be represented in comparable, almost identical numbers on the higher end of your assumption.
Both of these assumptions I find to be unwarrented.
The first is if there's one thing the Imperium is consistent about is that its not consistent with even the quote speaking of the "typical" sector fleet specifying systems are going to fluctuate from the stated figure based upon importance and threat level. And while not explicitly stated in the quote, we can logically assume simply available resources since the Imperium is almost always painted as being short of all resources except warm bodies. So assuming the Segmentum Obscurus is a perfect represenative benchmark for the Imperial navy as a whole is problematic.
Secondly is the whole point of mentioning the number of cruisers, it being a mainstay of the Segmentum Obscurus fleets, ease of being built ect are establishing what makes the Lunar class special. That having half a thousand or more of a single cruiser class is exceptionally rare in a Segmentum. So much so that the Lunar class being an exception is numerous enough to become the mainstay at least within the Segmentum Obscurus. Obviously any estimates are going to be very loose but I would guess in the ballpark of the Lunar's 600 being a third to a half of the total cruisers in Obscurus so 12,000-18,000 total cruisers
Chambers' word however is contradicted by
Battlefleet Koronus. Specifically...There are five Major Segments, and each has "thousands" of sectors. At minimum of 2 000 sectors for "thousands", this means that absolute minimum number of sectors in the Imperium is 10 000.
Well there are ways to bring the quote more in line with the Word of God statement, assuming said statement is canon, to prevent a contradiction. There could be many sectors in out of the way, unimportant sections of the galaxy that are badly understrengthed. That would fit with the theme of the Imperium being constantly short of material and borrowing from itself just to maintain its demand.
It is possible the "
substantial volumes" around Holy Terra don't actually include thousands of sectors focusing on smaller, more fortified territory.
The combined merchant fleets comprise almost 90% of all interstellar spacecraft in the Imperium" and consist of "millions" of ships.
Would be interested in what quote this from but an Imperial fleet 10% of their total merchant fleets would be in the ballpark for Chambers' "official" fleet numbers.
Assuming at least 4 system defense boats per civilized world and 32 per hive world or forge world (of whom there are "hundreds" – assuming 500)
Would be curious as to the quote pertaining to "hundreds" and the full context of what its referring to.
Loss rate would have to be above 99% for fleet to be at or below 2 million. However, number of warships cannot be significantly above the 2 million either, as the Imperial Navy is consistently portrayed as overstretched.
That's a really crucial point. Its more or less a plot point that the Imperium is chronically short on manufactured supplies and equipment. It doesn't seem to be attrition that is the issue since we have numerous examples that Imperium equipment can and frequently does last. Indeed the implication is one of the reasons the Imperium industry can meet its demands is because lasguns, plasma guns and Leman Russ tanks can be maintained in the field with the poorest level of maintenance for centuries. So the equipment isn't breaking down from wear and tear and isn't being destroyed.
Obviously the real answer is 40k is a fictional universe that was never meant to be taken too seriously and is governed by whatever sounds cool in the moment but if we are trying to apply a rigorous analysis of the universe is that, for various reasons up to and including Sci-Fi writers have no sense of scale, Imperium industry is anemic.
We do get this quote from "For the Emperor", page 162, in regards to going to war with the Tau and an implied industrial disparity :
'Which is why we're so desperate to avoid a full-scale war over this miserable mudball,' Amberley said. 'Keeping it would tie up our naval assets from at least three sectors just to secure our supply lines, and we'd be funneling Guard and Astartes units in from all over the Segmentum. Putting it bluntly, it's not worth the effort.
Basically the Imperium would require "at least" three sector fleets just to secure their supply lines, presumably the total for the whole operation would be larger, against a foe they have faster FTl than and whose ships they are equal if not superior to in comparison.
We can gleam, pound for pound, the Tau are far more industrialized than the Imperium able to equip a fleet far beyond their size in a fraction of the time the Imperium had to build their navy. That the Imperium advantage is simply that they have a wider reserve to draw upon not that their forge and hive worlds are spitting out godly amounts of material.
Against the Galactic Empire, a million world empire with tens if not hundred of thousands of warships, all sizes, at their disposal, such a reserve would be smaller in comparison.