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It was pleasant this morning in NYC 77F/25C: I did not break a sweat walking to the station. In contrast, the platforms of the #6 train at 42nd and 77th felt 15F/8C degrees hotter. I was not the only one sweating.

What causes the appreciable temperature increase in the station?

gatorback
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  • This seems off-topic, but it's probably due to the heat generated by the trains themselves and the fact that the further down you go the temperature is more and more constant throughout the year. The heat from the sun just doesn't penetrate deep enough. – Guido Aug 01 '18 at 14:28
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    I'm voting to close this question as off-topic because it's focus is not travel. – Augustine of Hippo Aug 01 '18 at 14:33
  • When reading this question I wondered why the temperature would be below the freezing point of water (which is +32°F, which is clearly higher than +15°F). 'Took me a minute to realize that "+" means "than elsewhere" here. – DCTLib Aug 01 '18 at 14:52
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    A why question like this is probably better-suited to [Physics.SE]. It's hot because you're underground and the air pressure is higher, and because the trains are throwing off a tremendous amount of energy when they brake. – choster Aug 01 '18 at 14:59
  • I was sort of hoping that some of the interesting travel-related facts thrown up in finding the answer (I didn't know the length, mass, speed, or capacity of a Circle Line train until I tried to answer this question) might bring the question back into relevance. But I will of course bow to the will of the community! – MadHatter Aug 01 '18 at 15:01
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    @choster Higher air pressure doesn't cause increased temperature. Sure, if you take air and compress it, it will heat up, but that's in a dynamic situation. In the static situation (where the air has already been compressed and you're not compressing it any more), it will equalize its temperature with its surroundings, just like anything else. – David Richerby Aug 01 '18 at 15:35
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    @MadHatter The mass, length and speed of Circle Line trains are not travel-related in the sense of this site: a traveller doesn't need to know any of those things. – David Richerby Aug 01 '18 at 15:37

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An S7 underground train, as used on the Circle Line, weighs 213.7 tonnes empty, and carries up to 1045 passengers at speeds of up to 100km/h. A train carrying 500 passengers of average mass 60kg decelerating from 80km/h (22m/s) to stationary must get rid of 60MJ of energy via its brakes, which will be dissipated as heat into the environment.

If the platform is 120m long, and is of semi-circular cross-section with radius 5m, that energy is dumped into at most 5,000m^3 of air. My faithful old Science Data Book says that average air has a density of 1.293 kg/m^3 and a specific heat capacity of 993 J/kgK, so each train's energy causes a temperature rise of around 9K (9C, ~16F) in that air.

There are lots of confounding variables; you asked about New York, for a start. S7 stock has regenerative brakes that are able to shunt about 20% of that energy back into the network, trains on short inner-city runs probably don't get up to 80km/h between stations, the passage of the trains pulls air in and out of the tubes, most platforms have ventilation systems, the brakes are unlikely to cool to ambient temperature in the short time it takes to let passengers on and off, and so on. But on the face of it, trains do provide a significant heat source to the platform environment.

Edit: because comments threads can disappear around these parts, particularly on closed questions, I wish to link to an excellent article on the subject, drawn to my attention by Patricia Shanahan, to whom much thanks. It provided a much more detailed analysis of the contributors to heat in the system, and helpfully confirms that braking is the dominant contributor. It also discusses in much more detail how heat is removed from the system, and concludes that the battle can only be won by decreasing dissipated brake heat.

MadHatter
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  • And also, all the bodies that are in the station and the train give quite a bit of heat themseves, too. – SJuan76 Aug 01 '18 at 22:04
  • @SJuan76 my wife raised that point, so I ran some numbers for that, and got less than 10% of the braking heat dissipation. But your figures may differ - do feel free to show them! – MadHatter Aug 01 '18 at 22:51
  • Let’s add the fact that NYC subway rolling stock has air conditioning. Cooler inside means hotter outside. – jcaron Aug 01 '18 at 22:56
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    The London Underground deep tunnels are a special problem. They run through clay that does not conduct heat well, and some have been running for over 100 years. See Cooling the tube – Engineering heat out of the Underground – Patricia Shanahan Aug 02 '18 at 06:17
  • @PatriciaShanahan losses to the surrounding cold sink are indeed another confounding variable, though as you point out poor thermal conductivity will hinder that. And thank you for that link - fascinating! (SJUan76, note that they also conclude that passengers aren't a significant heat source, and that braking is the dominant one.) – MadHatter Aug 02 '18 at 09:42
  • @MadHatter The cold sink effect may be negligible as long as it is a cold sink. The London Underground problem is that even a tiny excess of heat released from the trains over heat dissipated by the ground can build up if it goes on decade after decade. – Patricia Shanahan Aug 02 '18 at 10:30
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    @PatriciaShanahan this may not be the place for this discussion, but there may be a misunderstanding. As long as the clay was cool, the cold sink it provided was non-negligible - it provided a significant cooling effect in the early days (see, eg, The deep tube tunnels section of your marvellous article) and so provided a significant confounding variable to the back-of-an-envelope heat calculation I did above. As the clay has warmed up, it is less useful as a cold sink because it is no longer cold, and so its confounding effect has become negligible. – MadHatter Aug 02 '18 at 10:45
  • @MadHatter You are right. – Patricia Shanahan Aug 02 '18 at 14:21