~350cm³ for a tape, ~375cm³ for a 3.5in HDD, With HDDs being able to extend past the 18TB of LTO-9 tapes.

I am too lazy to measure them right now, but your numbers must be wrong.

Visually, an LTO cartridge cannot have much above a half of the volume of a 3.5" HDD and it must be at least 3 or 4 times lighter.

Carrying a suitcase with twenty LTO cartridges is as easy as carrying any other typical suitcase, but carrying twenty HDDs would not be easy at all, due to the great volume and weight, and the volume in a real situation would be greatly increased by the need of adding some serious padding, in order to avoid catastrophic damage if the suitcase were accidentally dropped.

More importantly, the price per TB of tapes is much lower, and when you consider the ratio between the expected lifetimes, the price per TB and per year is much, much lower.

Of course, tape drives are extremely expensive, so you need to store at least a couple hundred TB to break even with the price of HDDs.

You are right. double checked, I think it might have been some site listing the box size for some unknown reason, 260cm³ should be the correct size.

Your analysis ignores cooling.

LTO-9 can cram 18TB uncompressed data onto a tape. A 3.5" HDD is a bit smaller, but we already see 25TB drives. They are much heavier though, so LTO has an edge on density per mass, while HDDs have an edge on density per volume. Tapes (specially in tape library) have a huge advantage in density per dollar as capacity increases linearly with the number of tapes.

OTOH, HDDs have much better latency, as even a powered down hard-disk will power up and retrieve data faster than the time it takes to load a tape and read it. I can imagine a number of ways to partition a HDD pool in ways that the access patterns allow for most drives to be unpowered at any given time.

Having been responsible for several multi-petabyte storage projects, my experience is that TCO over a 20-year archive lifespan (LTO's design spec is 30, but boundary-pushing is not a good idea in the long-term storage game) is much lower for tape. Indeed you can't generally get reliable parts and support for disk shelves beyond about seven years, which means a full-solution refresh at least twice as often as with tape.

Most of the time the right answer is most of the storage in tape, with a couple of petabytes of disk in front of it to deal with hot data. Even in that circumstance you have to carefully manage the disk storage and filesystem or you wind up with client devices too new to access the supported fs version, another problem that basically does not exist with tape.

That's a good point - there is no such thing as a tape-only data storage system - you'll need RAM, flash, and HDDs to help ingest large quantities of data so that tape drives can have data ready to write.