Electrical – How to calculate the maximum cable length of fire detection loop

To send data, the sender first turns each 4-bit nibble into a 5-bit word, which ensures that five straight zeroes is never valid and indicates signal loss

Not exactly. This encoding does much more than just detecting signal loss. It makes sure that the same number of zeros and ones are sent (a.k.a. DC balanced), does some error detection, and has otherwise useful properties for this type of work.

Now, a change in voltage must propagate through the wire; first the recipient will see it, and then the sender themselves will see it on the "undriven" side of the circuit. The sender must see this feedback in order to ensure continuity (doesn't it?).

No. Ethernet has properly terminated signals (the termination is on the other side of the isolation transformers), and so the signal does not reflect back to the transmitter. In Ethernet there is no concept of continuity, only link. Link is established by a handshake type protocol between the two ends of the cable. If device A can send data to B, and B can send data to A, then there is a good link between the two devices.

So, the limit to the total circuit length, assuming the ideal that voltage propagates at c, is how far light can travel in 31.25 microseconds. That distance, given a simplistic c = 3*108 m/s, is 9.6m ~= 31.5 ft. Since that's total circuit length from sender to receiver and back, the actual total cable span is half that, or 4.8m ~= 15.75ft. Beyond this length of Cat5, it is simply impossible for the sender to toggle the voltage fast enough to maintain the fundamental frequency, so the two parties negotiate a lower frequency, resulting in a lower maximum bitrate over the longer cable.

No. Since there is no reflections, there is no relationship between bitrate and cable length. To put it differently, a Gigabit Ethernet cable that is 100 meters long can have up to (approximately) 600 bits worth of data "stored" in the cable.

By the time we get out to 182m, the Cat-5 specification's maximum cable length at which simple resistance of the spec'ed cable will have reduced signal voltage below the threshold of the receiver's distinction between the three states, I calculate that this speed-of-light limitation will also have reduced the maximum sustainable fundamental frequency to approximately 1.65MHz, for a baud rate of 6.6Mb/s and a true data rate of only 5.28Mb/s.

Ethernet spec allows for a maximum cable length of 100 meters, not 182 meters. And this has nothing to do with the bitrate or voltage thresholds. It has everything to do with collision detection and minimum packet size.

I do Ethernet all day long and we are able to transmit 900 Mbps of real data over a 100 meter long cable with absolutely no issues with reduced throughput.

if I have any unk-unks in this, it could be completely off.

Yeah, completely off. Sorry.

Convection does not scale linearly with surface area, it's a fluid dynamics problem rife with Nusselt numbers and Rayleigh coefficients. Since it's not my field, and since I'm more likely to use CFD than first principles in such a situation anyway, I'll point to a calculator that might allow some feel for the problem here (assuming it's actually implemented correctly, of course).

If I stick in reasonable numbers like 100°C for the wire 1, 2, 10mm for the wire diameter then I get total heat loss scaling with roughly the diameter (and thus the surface area) to the power of 2/3.

Preece was looking at fusing current, which would be at a much higher temperature than typical operation of an electrical wire.