I consider the rails of a railroad and the steel wheels turning on it much like a marble on a glass table. There is not a lot of friction there. I suppose that’s why diesel-electric locomotives achieve such efficient fuel economy.
Once that momentum starts rolling with the weight on top of it, it doesn’t take too much to keep it rolling and on the other side of the coin, very hard to stop.
The amount of contact of a glass sphere on a glass table is very little. The same amount of contact of a steel wheel on a steel rail is very little. Not much friction on either.
To put it in layman’s terms, if you came home and took a marble out of your pocket and set it on the glass table, in most houses the floor is not completely level. The marble will find its way to the lowest end of the table even though the slant is not much.
Introduce a grade and of course everything wants to roll down hill. Introduce a radius on a grade the marble will string line to the inside of the curve uphill but to the outside of the curve downhill.
The only difference between the marble on the glass table and the wheels on a rail is the train wheels have flanges.
Flanges dig down on radius when string lining in or out of a curve thus causing extra friction and drag.
Everyone understands this. I’m not coming up with some kind of New Concept here.
I can’t find the math. I am very good in math but I can’t find the math.
A grade uphill with a radius compounds the grade but there is so many different radius.
friction doesn’t depend on contact area, it simply depends on weight. While the friction coefficient for steel is around ~0.6, railroads typically use 25% of the adhesive weight as the MAX tractive effort (TE) or drawbar force. While a locomotive could exceed this force, it would slip.
the charts below indicates the drag on a moving train, lbF / ton for both empty and loaded cars. Using ~5 lbF/ton for a train moving 10-20 mph, a 1000 T train requires 5000 lbF to overcome friction moving on level grade.
the force required up a grade is proportional to the sin of the angle. For typical grades, the sin of the angle is the grade as a %. A 1000 T train going up a 1% requires a force of 10 T or 20,000 lbF, significantly exceeding the friction of the train.
if it matters, on real trains the flanges do not add resistance because they seldom , if ever, touch the rails themselves … the tread is tapered to keep the wheels centered
The railroads have quite a bit of time and money invested in flange lubricators. Some mounted on the locomotives themselves, others that lubricate the entire train’s flanges before entering a curve.
This would lead me to believe that the flange contacts the rail more often than seldom, if ever.
Simple physics flanges are what keeps the Train on the tracks
Uphill grade the flanges rub on the inside of the rail
Downhill grade the flanges rub on the outside of the rail
Simple physics it’s what keeps the Train on the tracks… just like a flat spot on the wheel from wear, when you hear a thump thump thump when the train rolls down the track… it wore, it has a flat spot from breaking too many times in the same place
Sorta, no. If the trains are going at the rated speed of the curve and superelevation then, no, the flanges do not rub the rails. If the speed is above or below the speed of the curve and elevation then yes the flanges will rub the rails. If the train is going slower than the rated speed then they will run the inside rail. If the train is going to faster than the rated speed then it will rub the outside rail.
curves have elevation. The raised outside rail which raises the center of gravity produces a force pulling the car toward the lower rail. the centrifical force of the car tracking a curved path pushes the car outward or in a straight line.
At one particular speed, the two forces balance and the flange do not touch (or at least not with much force).
For those who did not watch the video Greg posted, the tappered wheels do two things.
They allow gravity and forward motion to center the car keeping the flanges off the rail as discussed above.
And they change the effective diameter of the wheels in curves to cause the outside wheel to travel farther than the inside wheel, which it must do to avoid slippage.
As Dave explained, if the train is traveling at the design speed of the curve, the wheels shift up the outside rail enough to cause the outside wheel to travel the farther distance and the inside wheel to travel less distance, while still keeping the flanges off the rail.
Too much slower, or too much faster and there is some flange contact.
OR, when curves are simply too sharp, and reach the limits of the wheel tapper, there is flange contact and speeds are highly restricted.
And all of this physics is why trains require such large radius curves, and is why we should do our best to run our models on the largest possible radius curves…
There are several kinds of friction, in two basic categories - external and internal. External is, at it’s simplest, the friction of contact between two separate bodies. These may be two “rigid” bodies, like steel wheels and rails, or one or both may be non-rigid bodies, like airplane skin and air. Internal friction is generated mostly by the deformation of a body, like a rubber tire with an obvious flat contact spot with a road.
There are two types of external friction - static and dynamic. Static friction requires some level of force to make one body begin to slide past another (described mathematically by the coefficient of static friction), while dynamic friction requires some generally lesser level of force to maintain the sliding (described mathematically by the dynamic coefficient of friction). The difference between dynamic and static friction is why traction control and anti-lock brakes provide better control over a vehile - a properly tuned traction control system provides faster acceleration of a vehicle because it does not let the wheels break free and spin, while anti-lock brakes stop a vehicle in a shorter distance than locking up the wheels and letting them slide actoss the contact surface.
Contrary to what one person said, external friction is dependent on much more than just the weight of the moving body. It also depends on the properties of the materials and the contact area between the two materials. If the latter were not the case, even the heaviest vehicles would have the narrowest possible tires. But take a look at a dragster - huge tires, to maximize contact area and thus friction with the strip.
Most interestingly, the friction a vehicle deals with in dry conditions (ignoring atmospheric friction) is primarily internal friction of the materials in contact. In an overly-simplified explanation, the wheels (steel or rubber) are in static contact with the surface (steel or asphalt or convrete or gravel or dirt) they’re tr
The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:
Amontons’ First Law: The force of friction is directly proportional to the applied load.
Amontons’ Second Law: The force of friction is independent of the apparent area of contact.
Coulomb’s Law of Friction: Kinetic friction is independent of the sliding velocity.
Look at the Wikipedia link you provided. It contains a table of coefficients of friction. If friction was dependent only on weight, the coefficient of friction would be the same for everything.
For something more in-depth, get a copy of this ASM International handbook and study it:
The laws you state are more rules of thumb than actual laws. They were not derived from an understanding of mechanical properties, but rather from experimentation and observation (as were many engineering principles). Like the ideal gas law, they are generally “good enough” (they’re actually first-order approximations), but they break down under many circumstances. Superfluidity is one example.
