rec.puzzles Archive

The left and right wheels on a train car are welded to the axle to make one solid wheel-axle-wheel combination.

physics/train.wheels New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

The left and right wheels on a train car are welded to the axle to make
one solid wheel-axle-wheel combination.  There is no 'differential'
such as found in automobiles to allow one wheel to turn faster than the
other when the vehicle is turning.

When the train negotiates a curve in the track, obviously the outer
track is longer than the inner track.  A simplistic wheel/track design
would result in friction as one or both of the wheels slip to
compensate.  What really happens when a train travels around a curve to
minimize or (possibly) eliminate slippage?

-- John Vriezen <vriezen@millcomm.com>
Show solution
The wheels are tapered such that when the train slides toward the
outside of the curve the effective diameter of the outer wheel
increases and that of the inner wheel decreases.

-- Ed Foster <erfoster@netcom.com>

[ Editor: a hint posted with the problem, a reply to it, and a
diagram of the tapered wheels, August 1995. ]

Hint follows -

Neither the train 'trucks' nor the axles are rigid.

-- The Flash <goodwim@elec.canterbury.ac.nz>

Um, the axles and trucks bend to compensate.

[ Editor: the quoting in the collected posting is mixed; the hint
appears to be The Flash's, and this reply is unattributed. ]

I believe the wheels are kind of cone shaped (inner radius is larger).

  /|             |\
 / |             | \
|  |             |  |
|  |-------------|  |
|  |             |  |
 \ |             | /
  \|             |/

^                 ^
|                 |
Track positions in a left turn (seen from the back).

-- Tomas <y94tombl@isy.liu.se>