Given the integral of the power over time, that amount of power is not likely to be an issue as I said in my post. My reference to the 47 Ohm resistor is in reference to the 47 Ohm series resistor.
That transformer is likely to be okay with a time limited surge current in the the range indicated. Again it is not uncommon for the transformers in our gear to be subjected to 5 to 10 times their nominal ratings at turn on.
That heating spike when cold is why I advocate current limiting heaters to prolong their lifespan, but that's a separate issue. (Light bulbs fail in this fashion. Temporary thermal runaway why heater flash occurs.)
The important issue here is that the isolation transformer, like any transformer, must be designed to survive overloads; I do not know if an isolation transformer is designed for overloads of five times operating current lasting for tens of seconds, maybe even ten times the rated current. This is not a very robust transformer, it appears to be designed to power small analog circuits.
A filament transformer, to contrast, would, of inherent necessity, be designed to for that startup load; how could it not, given its intended application?
Triad is closed for the weekend or I would call and ask.
In the this application we are not worried about the integral of the wattage over time at turn. We are concerned about one of the windings of the transformer acting as a fuse if its maximum current is exceeded.
It's not purely the fuse aspect that's the problem. High current causes spot heating. If the winding has any weak spot in the wire, that can fail over time, not in the same way as a fuse, but because it gradually is eroded and the maximum current load drops to the point that it fails. The junction of the two pieces can be higher resistance which has current forced through it and this causes spot heating. Light bulbs fail in this manner. The insulation also fails from heat and can short. That wire can get very hot before it burns, and that heat can damage the insulation.
Using components beyond their maximum ratings leads to failure.
This, by the way, is why selenium rectifiers fail in vacuum tube equipment. They're reliable until stressed and then it all goes kablooey. I've read the papers and databooks from the 1940s and 1950s where the rules are relaxed for consumer items with a short expected lifespan. Welders and elevators used selenium rectifiers and these are still working decades later because they weren't abused.
For example lets look at fuses. Lets say that a 1 amp fuse will blow when the current reaches 1 amp, although that is not exactly correct it makes for a simple example.
Not exactly. Fuses are governed by time-current curves. So the greater the magnitude of overload, the faster it blows. We're not guaranteed that a 1 A fuse actually blows at 1 A, or that it doesn't take many minutes to blow at that rating.
See, for example, LittleFuse's guidelines:
The problem is that a fuse can carry many multiples of its maximum current for some time. Resistors also do this, which is why they make poor fuses.
This is the big problem with fuses. I learned that the hard way many years ago. Relying on a fuse to save you only works in the case of a high-current short.
I understand why you might do this to build in a numerical fudge factor, but this can be confusing for those that are following this thread and trying to learn how things work. You indicated that the total current draw would be 0.6 amps and would exceed the rating of the transformer. Again this could be confusing for those trying to learn how things work.
Yes, I already acknowledged the incorrectness of that miscalculation and it's clear earlier in the thread. Again, I typically deal in parallel heaters, not series, and went with the typical without thinking. This is why we have design reviews. It is 150 mA, since it is series.
BUT the fact remains that on startup the load can be many times the normal load. I've seen numbers of as much as ten times, depending upon the heater construction. Expecting three to five woud not be unreasonable.
To be clear, all of this is just my OCDness attacking the keyboard on my laptop computer.
It's not OCD.
It actually matters. When engineers stop analyzing reliability and considering points of failure in designs everything falls apart: planes fall out of the sky, buildings and bridges fall down, tunnels start dropping concrete on cars, the electric grid collapses, spaceprobes malfunction, spacecraft are nearly lost or actually lost, and motherboards start rebooting for inexplicable reasons when one has not yet finished saving one's work.
BTW, if one is really worried, the inclusion of the correct CL-XX type NTC (negative temperature coefficient) current limiter would be cheap and easy.
An excellent idea. This is not perfect, because the inrush limiter it is of shorter duration than the heater startup, but it will prevent the worst of the overload.
The more I think about it, the more I prefer
battradio's suggestion of back-to-back filament transformers. They're designed for this sort of overload. That would totally solve the problem in the most elegant and cost-effective way.