One other way to think about this is to step back and consider the cable as a heated cylinder - the heating comes from the resistive dissipation - so I2R Where the first I and the R give the voltage drop, and the second one gives you heating in watts. The cooling is proportional to the surface area available to lose heat though,  and what that in turn is surrounded by.

So as surface area rises more or less as the diameter, but cross-sectional area, and therefore 1/ resistance) rises as the square of diameter, we see that the amps per square mm obey something close to a 1/r sort of rule. - a cable of half the cross sectional area  has twice the resistance but 70% of the area to sweat heat off through. So it can carry rather more than half of  the current. However, as soon as you bundle cables together all of this goes out of the window, as the idea of being able to lose heat all the way round is lost, as there will be heating from one side and cooling from another.

The same thinking allows yo uto estimate the extra temperature rise from an overload, and to see if it is catastrophic - insulation at well over 100C,  or just life limiting.
A few years ago now the IET did a publication looking at cable lifespan versus temperatures  by accelerated life testing (i.e running cables too hot to make them age faster)  and that showed that the occasional flight up to 100C does very little to PVC, but doing it for months at a time is not wise. It was a bit more scientific than that and used the Arrhenius Equation to show that above a certain point life span halved with every 8-10 degree rise. I suspect a copy is on-line but if not I will see if I can find it at home this evening.

Mike

One other way to think about this is to step back and consider the cable as a heated cylinder - the heating comes from the resistive dissipation - so I2R Where the first I and the R give the voltage drop, and the second one gives you heating in watts. The cooling is proportional to the surface area available to lose heat though,  and what that in turn is surrounded by.

So as surface area rises more or less as the diameter, but cross-sectional area, and therefore 1/ resistance) rises as the square of diameter, we see that the amps per square mm obey something close to a 1/r sort of rule. - a cable of half the cross sectional area  has twice the resistance but 70% of the area to sweat heat off through. So it can carry rather more than half of  the current. However, as soon as you bundle cables together all of this goes out of the window, as the idea of being able to lose heat all the way round is lost, as there will be heating from one side and cooling from another.

The same thinking allows yo uto estimate the extra temperature rise from an overload, and to see if it is catastrophic - insulation at well over 100C,  or just life limiting.
A few years ago now the IET did a publication looking at cable lifespan versus temperatures  by accelerated life testing (i.e running cables too hot to make them age faster)  and that showed that the occasional flight up to 100C does very little to PVC, but doing it for months at a time is not wise. It was a bit more scientific than that and used the Arrhenius Equation to show that above a certain point life span halved with every 8-10 degree rise. I suspect a copy is on-line but if not I will see if I can find it at home this evening.

Mike