1. Originally Posted by Helmholtz
My layman's approach would be like this:

Speaker power rating is determined by its max. voice coil temperature. The voice coil gets heated by the power dissipated in its DCR and is cooled via heat radiation to the surrounding structure and by convection.

An example: An 8 Ohm/50W speaker can take 20Vrms. This means a current of 2.5Arms. It DCR is typically 6.4 Ohm (80% of 8 Ohm), so the max. dissipated thermal power is 40W.
Everything else being equal, the 4 Ohm version of the speaker needs to have a DCR of 3.2 Ohm for a thermal power of 40W and a rated apparent power of 50W.

Everything else being equal means that both voice coils should have the same surface area and (thermal) mass. Realization (including achieving the necessary inductance to get a Z of 4 Ohm) will require a heavier wire as well as less turns for the 4 Ohm version. The optimization process probably requires some iteration.

I am aware that I ignored radiated acoustical power, but this is assumed to be the same for both versions.

Surely JMF knows better.
So in simplest terms what I said is correct "Same gauge fewer turns means less power handling." Which anchor took offense to.

nosaj

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2. Originally Posted by Helmholtz
- - -. The voice coil gets heated by the power dissipated in its DCR and is cooled via heat radiation to the surrounding structure and by convection- - -
Yes. And in addition some speakers are designed to pump a little air thru the gap as the voice coil moves.

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3. Originally Posted by Helmholtz
- - -. The voice coil gets heated by the power dissipated in its DCR and is cooled via heat radiation to the surrounding structure and by convection- - -
Yes. And in addition some speakers are designed to pump a little air thru the gap as the voice coil moves.

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4. Originally Posted by nosaj
So in simplest terms what I said is correct "Same gauge fewer turns means less power handling." Which anchor took offense to.

nosaj
Things are complicated because parameters are interdependent.
Max. speaker RMS current at middle frequencies (ca. 300..500Hz) is determined by its power and impedance ratings. The thermal power is given by I² times DCR. So in principle less DCR means less voice coil heating. Same gauge half turns number would meet the 3.2 Ohm DCR requirement for equal thermal power. But this would decrease voice coil volume and surface causing excessive VC temperature, in other words: less power handling.
Also to meet the 50% inductance requirement, turns number must be decreased by only 30%.
This means that wire gauge must be increased to get a DCR of 3.2 Ohm with 70% turns and to get enough voice coil volume and surface.

Most surprisingly my measurement on 16 Ohm and 8 Ohm Celestions confirmed the 2:1 ratio of DCRs but the inductance ratio was only 1.6:1 (@1kHz). This shows that there is some leeway regarding actual number of turns.

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