The analysis in that article is wrong. You can see from the video of his model that the path of the wheelset is sinusoidal.
The wheelset's offset from the center of the track is proportional to the rate of change of the wheelset direction of travel, which is proportional to the rate of change of the offset. Those two "rate of change" relationships are responsible for the sinusoidal form of the solution of the differential equation of the wheelset motion.
The sinusoidal motion occurs on a real railroad, but it is gently damped over many cycles of oscillation by details of the truck configuration that are not considered in a simple analysis. Typically, as the train speed increases, the damping effect goes away and the oscillation begins to grow rather than die out. At this "critical" speed, the train leaves the track. This is one of the most important considerations in designing high-speed trains.
The Bay Area Rapid Transit ("BART") was designed many years ago, deliberately favoring "modern" engineering over traditional railroad practices. One foolish thing that they did was to use cylindrical wheels instead of conical ones. They have been tolerating the resulting very loud noise and rapid wear on wheels and rails ever since the mid-century. There is finally a project under way to change to conical wheels. (Another, harder to fix, mistake was to use the Indian gauge of 5 1/2 feet, making any interchange impossible and rolling-stock replacement expensive.)
I just found this on Wikipedia:
New rail technologies
As one of the first entirely new rapid transit systems built from scratch in the 20th century, the architects of what would become BART intended to design a rail system that could be marketed to other cities and regions. This led to several unconventional design choices for the system.
Tracks were intended from the outset to utilize a broad gauge of 5 ft 6 in (1,676 mm), unusual in the United States. Parsons Brinkerhoff - Tutor Bechtel recommended the gauge for better stability and smoother riding; it was not selected for greater safety in high winds when crossing the Golden Gate Bridge, or for faster trains, contrary to myth. Also, tracks were designed to utilize flat-edge rails and wheels. The railway utilizes an electrical powered at an unusual 1,000 volts of direct current. (Historically, streetcars operated at 600 V and older subway systems tended to adopt this voltage, while new systems contemporary to BART and since usually use 750 V power. Standards BS EN 50163 and IEC 60850 only specify these as well as 1,500 V power.)
The combination of unique loading gauges and unusual rail technologies has complicated maintenance and increased cost of the system, as rolling stock requires custom wheelsets, brake systems, and power systems.
Bob Nelson
3railguy Needle point axles are why modern era trucks roll better than postwar trucks with wheels that rotate on the axel. The angle of the wheel has little to do with it. Atlas O recently put out trucks with squared off wheels. There is very little if no difference in freeness of rolling.
Needle point axles are why modern era trucks roll better than postwar trucks with wheels that rotate on the axel. The angle of the wheel has little to do with it. Atlas O recently put out trucks with squared off wheels. There is very little if no difference in freeness of rolling.
FJ and GInteresting topic.I'm guessing 1:1 trains have fast-angle wheels? Wondering if other scales have them
Rob
Interesting discussion. I've just assumed that fast angle wheels naturally travel with less friction than the flat postwar ones. But, would a (new), properly lubricated postwar wheelset--with it's differentially rotating wheels--actually have equal or maybe even less friction than a fast angle wheelset, everything else being equal?
Carl
Yes, they do, Dave, but not with so severe an angle. The cone shape is there because the wheel wears faster close to the flange. When it wears from a cone to a cylinder, the wheel is condemned. The rails are tilted slightly towards the center of the track by the tie plates, so that new wheels wear the inside edge of the rail, old ones wear the outside and others wear various points in-between, keeping the rail wear roughly evenly distributed over the rail head.
The cone doesn't naturally center the wheelset on the track as is often supposed. Instead, it creates a sinusoidal oscillation from side to side. You can see this if you ever have a chance to ride in a car with a hole in the floor; and it is often visible at the end of a fast-angle model train, waddling down the track.
The reason for condemning a wheel when the tread becomes flat is that the oscillation is replaced by a tendency to hug one rail or the other, greatly increasing the wear on wheel and rail.
Fast angle wheels first came out when MPC took over Lionel. The wheels are not squared off where they ride on the rail. They are angled to the flange. "Fast angle" is a toolmaker's term for adding an angle to a surface so the part can be quickly removed from the tool without marring the surface during manufacture. Hence the term "fast angle wheel" was coined by Lionel employees.
The fast angle did more than benefit manufacture. Because the wheels are fixed to the axel, it benefits them on curved track. The wheelsets can drift to a point where one wheel diameter point touching the rail is slightly larger than the opposite wheel diameter point touching the rail. This reduces friction because the outside rail is longer in circumference than the inside rail. Especially sharp 031 or 027 curves. If you look closely, you can see the cars lean into the curves as the outside wheels drift to a larger diameter.
The only problem I ever experienced with fast angle wheelsets that are fixed to the axel is with postwar 711 072 switches as the wheels sometimes hug the gaurdrails. This has to do with the wheels being fixed to the axel. Not the fast angle.
Our community is FREE to join. To participate you must either login or register for an account.
Get the Classic Toy Trains newsletter delivered to your inbox twice a month