“rolling resistence varies with the weight of the car, being considerably more for a ton of empty than a ton of load. it also increases gradually as speed increases.” (the railroad : j.h. armstrong, 1998)
i am assuming “rolling resistence” is rolling friction. friction is directly proportional to the normal force present, so why is it that a heavily loaded car has less friction than an empty?
thank you
cbt141
its not so much an issue of less friction… as it is more mass…the more mass something is…the more force it takes to stop it…as well as getting it started…its pysics 101
csx engineer
I think the term we seek here is INERTIA, not friction. Newton’s laws cannot be violated.[swg]
What an odd statement.
this is my initial reaction as well, however, the question is “rolling friction” and there is a wrinkle here which makes “force equals mass times acceleration” the wrong tool to answer this question.
the quoted author, mr. armstrong, is very clear in his intent. he later says, “the formulas usually used for estimating train resistence gives 4.2 pounds per ton for the loaded car, and almost three times as much per ton for the empty.” (the railroad. page 20,paragraph#3)
this statement seems to be counter intuitive. does any one have a lead on how to explain it?
thank you.
cbt141
My understanding of physics and trains may not be perfect, but I can think of two places where we might find friction in this context. The first is between the wheel and the rail, that is not obvious but if it didn’t exist the wheels would behave as if they were on ice, and simply slide.
The second may be more what Mr Armstrong is referring to. That occurs at the wheel bearings of the trucks. They have to support the weight of the car and the load, and that may have an effect on the amount of effort required to start the car in motion. The bearings might be less efficient unloaded, than when loaded.
It could be referring to the total drag force of a train which is made up of three components.
There’s a constant rollong resistance which is the sum of the rolling resistance at the wheel rail interface and the rolling resistance of the bearings. This force is independant of speed
There’s a viscous rolling resistance caused by the lubrication in the bearings. This term rises linearly with speed. Double the speed double the force.
There’s an aerodynamic resistance which is based on the shape of the vehicle. This is proportional to the square of the speed. Double the speed and the aerodynamic drag goes up by a factor of 4.
These three terms are added togeher to produce a grapf of the total train resistance vs. train speed, and is referred to as the Davis Equation. R = A + Bv + Cv*v
Now, certain vehicles will have and increased aerodynamic drag when they are empty because of the difference in shape. Coal cars and bulkhead flats for example.
This could be what he’s on about.
Hugh’s explanation is essentially correct.
To elaborate, rolling resistance is a aggregation of forces that oppose the movement of a train, vary with speed, and must be overcome by the tractive force of the locomotive. It does NOT include grade resistance, which dwarfs rolling resistance for any appreciable gradient.
A. Elements of rolling resistance that vary with axle loading include:
B. Resistance that varies with the square of the velocity .
C. Other resistances include wind resistance (not to be confused with quiet-air resistance), acceleration resistance, and starting resistance (inertia).
The Davis formula is fairly reliable at low speeds, but not at high speeds. It doesn’t seem to work very well with very heavy cars, either. Moreover, its values are empirically derived, so it’s not truly a mathematical formula like one of Newton’s laws of motion.
Back to the original question. You asked how
bigboy, hugh, mark,
very helpful. thank you.
cbt141
…“Quiet air resistance”, probably has another variable…and I believe that would be what altitude the train would be operating at…Thicker and heavier air pressure at sealevel. That is, if we’re splitting hairs.
To expand on Mark’s comments a little, if you have watched unit trains pass, the loaded train runs past much more quietly, but with “heavier” sounds at switches and rail joints. An empty train has drumming sounds from the empty carbodies, and sometimes more flange squealing in curves.
The trucks oscillate more on empty cars, and can “hunt” oscillate wildly from side to side. All the energy to generate the noise and oscillation, as well as the added wind resistance, is coming from the locomotive.
I hope this mental image helps explain the difference.
Peter
I feel like I’ve flashed back to last fall, when we studied all this in school![(-D][(-D][oops]
i slep throught physics class in high school…lol
csx engineer
A practicle illustration
You can pull 28-32 loads up 2.78% having 10 - 18 degree curves with 5 SD9’s at 7 MPH. The number of empties is 49 for the same track. Dry rail numbers with full sand.