Copyright ©2011 by Paul Niquette. All rights reserved.
the World's Fastest Train
puzzle will recognize the photograph on the right as
that of the V150,
train that set a world record speed of 574.8 kph
(357.0 mph) on April 3, 2007, as recorded in this video.
the view is from the rear of the train can be confirmed
by the red lights and by the unoccupied cab. There is a
third clue: The pantograph
has been deployed. Whereas the V150 has a power
car at each end of the consist,
each with its own pantograph, the pantograph only at the
rear of the train is used to collect power from the overhead
system for distribution throughout the train.
Pictured above are two examples of
modern pantograph design:
on the left and the Faiveley
on the right. Both are designed for high speed
trains, featuring integrated pneumatic controls,
individual suspension of carbon collection strips,
vertical head guidance and fast lowering
Most people will recognize these devices, for they apply the same pantograph design as those simple spring-loaded assemplies atop modern light rail trains placidly plying their streetcar services on trackways embedded in the middle of city boulevards.
Unchanged in concept for decades, the standard configuration is shown in Sketch 1 on the right, with its main components called out: stabilizing arm that keeps the pantograph head level and control arm that actively moves the head vertically to keep the force on the contact wire within a narrow range. In high-speed trains, the practice is to lock the lower arm in a fixed position, which reduces the inertial mass that has to be raised and lowered in real-time.
Overcoming wind resistance of the pantograph would seem to be a minor challenge for any train developing thousands of horsepower. Still, the V150 deploys only the rear pantograph on each consist and has roof fairings over the idle pantograph stowed in front.
Meanwhile, automatic controls in the pantograph system must maintain the requisite contact force, adjusting rapidly for variations in the track, overhead wire, and swaying of the train as indicated in Sketch 2.
Finally, under emergency conditions, the control system must be designed to drop the pantograph abruptly. Watch this clip for an example of what can go wrong.
The Pantograph Design puzzle will address another issue -- aerodynamics -- which is receiving plenty of attention in the high-speed rail industry. Let us first take notice of the fact that modern Z-shaped pantographs are not symmetrical with respect to direction of train travel: Going one way, the "knuckle" between the pantograph arms will be facing forward, which means the carbon strips are being drawn along the wire. In the opposite direction, the "knuckle" will be facing backward and the carbon strips will be pushed along the contact wire. For light-rail vehicles operating no faster than, say, 50 mph, there are no significant aerodynamic effects resulting from the train's direction. At speeds over 100 mph, though, one direction must surely be preferable.
Have a look at the picture of the Acela below, which is a view from the front of the train, and we can see the "knuckle" is facing backward, so that the contact strips are being pushed along the contact wire. The picture on the right shows a close-up of the pantograph. It shows something else, too...
On Acela trains, each power car is equipped with two pantographs. They face in opposite directions. Unlike the V150, which distributes traction power to all cars in the consist from the rear pantograph, the Acela applies traction power only in the power car itself collected from overhead by one of its own pantographs -- always the pantograph selected for its "knuckle" facing the rear of the train.The rationale for the rear-facing "knuckle" will become clear to solvers of the Pantograph Design puzzle using a hypothetical train. Let the upper arm on its pantograph be six feet in length. When deployed at a nominal level, the pantograph reaches upward from the 'knuckle" a distance of three feet to the contact wire.
The frontal areas of the contact strips and their holders are held perpendicular to the relative wind and dominate the aerodynamic drag of the structure. As shown in Sketch 3, with the "knuckle" facing aft, drag imposes an upward component of force ("lifting force") on the head. Solvers will observe that traveling in the opposite direction, the force will be pointing downward.
What are your estimates for the
following table entries: