Hot weather warning 25th July 2019

[whole diary]

[Adrian]

Presumably the overhead wires are also heated a bit by resistance losses caused by the current flowing. This would be very variable according to amount of traffic, not a constant.

Regardless as to the details, it is well known that the wires expand in the heat, and means to compensate for this are readily available.
So what went wrong ? Was the temperature greater than the maximum planned for ? If so that sounds like a basic error in design or installation. The temperatures though reaching a new record were still only about 1 degree higher than those previously achieved. I would expect infrastructure to function correctly up to at least 5 degrees higher than the previous record.

Or were the multiple failures not due to simple expansion of the wires, but something else related to the heat.

A few more quick calculations.  Contact wire has cross-section of 120 mm2, copper has resistivity 1.7 x 10-8 so 1.4 mOhm per metre.
If a train is drawing 10000 kW at 25kV, that's a current of 400 A, which would cause heating of 23 W per metre.

Heat capacity will be about 400 J per K per m, so rate of heating would be roughly 1 degree every 20 seconds.

Of course, I've ignored the heat generated at the point the pantograph touches the contact wire.  I've no idea how to estimate that, though any heating effect must surely affect the pantograph more than the wire.  Do pantographs get hot?

[stuving]

Some people are never satisfied ... but here is the official reckoning of the maximum current capacity of Series 1 OLE^▸ (Overhead Line Equipment, more often "OHLE") (some of this will flow in the catenary wire, but not a lot as it's smaller and less conductive):
 

Ambient temperature 28o C Solar gain 980 W/m2 Wind speed 0.45 m/s (1 mph) Current 531 A Resulting wire temperature 56o C Notes:    That applies for a conductor wire at end-of-life wear - 25% gone (so presumably down to 90 mm2). The limit is for continuous current, and for 10 minutes or less it can be raised by 15%. Under those conditions the wire itself can cope with 964 A, reaching 80o C, if the run is short enough for expansion to be less than 1 m. If the wind is just a little higher - 3 m/s (6.7 mph) - at 30o C ambient, the current limit becomes 964 A. I don't think starting current is a big issue -  nothing like the headache it is for 1500 V DC▸ (Direct Current) OLE, anyway (think of a big goods loco in the south of France on a hot day, for example).