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Comparing the cross-section of modern high-speed trains to old train waggons, which had straight walls and were limited to speeds around 200 km/h, I notice that most of them have curved outer walls. The width of the cabin decreases with height (and at heights occupied by passengers) and this obviously reduces space and comfort inside the cabin. So my question is, what are the main benefits of this? I am thinking of:

  1. lower cross section of the train, i.e. reduced aerodynamic drag.

  2. lower center of gravity. This is not bad with strong side winds!

  3. lower moment of inertia for rolling around the longitudinal axis between the wheels for driving with high speed trough curves.

So what are the main benefits of curved outer walls? Is a circular shape the best?

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  • $\begingroup$ Tunnels are mostly round - curved sides help improve clearance, people are smaller at the top - head is smaller than bidy (for most...) $\endgroup$ – Solar Mike Jan 19 '19 at 7:56
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    $\begingroup$ Curved panels fixed to a frame around the edges are also "stiffer" than flat ones in resisting low frequency vibration, and hence reduce noise levels inside the vehicle. $\endgroup$ – alephzero Jan 19 '19 at 11:37
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All the three items you said are correct. And what Solar Mike said is correct too. Here are the list of the other items.

1- with manufacturing an design advances they can build ideal shapes more easily than the old times when a box was default structure for trains and cars.

2- cylindrical shapes are ideal for longitudinal torsion caused by the vibration due to suspension and turbulence created by the wake of train itself. Also the entire car acts as an integrated structural pipe and is inherently stronger. While the old train cars would warp and crumble easily.

3- economy in material, for the same volume a cylinder has less surface.

4- structural efficiency, round surfaces share and transfer stresses much better than the rectangular ones which have stress concentration on the corners and rattle and suffer fatigue damage.

5- cross winds and stormy gusts go around the round cross sections more easily.

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Old carriage design relied upon 4 surfaces which meant that velocity was restricted. With an increase in velocity there is a fourfold increase in structural stresses, generally. Just as early tunnels were built with rectangular cross sections it was only with my great great grandfather's invention that tunnels became cylindrical tubes under London. This was possibly due to Alfred Ely Beach's suggestion in 1840 that a circular section would be more efficient. See James Henry Greathead for further info. Early airframe design was based on box but now is elliptoid.

Rectangular design has 4 corners that have to resist the combined stresses transmitted by 2 concurrent surfaces in maintaining structural integrity. This flaw is eliminated with elliptiod shapes and removes potential pinion points which are weak and heavy.

Centroids of trains are taken axially through their length and due to lightweight materials in the carriage, the CoG is usually $\frac {1}{3}$rd from the bottom of the carriage. The onion points removed allow increased velocities due to better structural strain management in fabric of the train.

A key issue also is removing opportunity for strain hardening to occur and thereby increase mechanical safety of materials used.

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