QUOTE: Originally posted by trainjunky29 How is a steamer's power curve related to a Gaussian Curve? 1.) A Gaussian curve returns to 0 as the x-component increases, a steamer's does not 2.) A steam locomotive has nothing to do with probability nor with quantum physics 3.) A steam locomotive's power curve has no points of inflection 4.) I plotted feltonhill's data, and it looks nothing like the curves shown in the above link or a "classic Gaussian distribution curve." Sincerely, Daniel Parks
QUOTE: Originally posted by trainjunky29 QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 Dear GP40-2, What exactly do you mean that a steamer's power curve is exponential in nature? I presume you don't mean b^x like in calculus class, nor do you mean x^p. Sincerely, Daniel Parks I mean that a steam locomotive's power curve follows the classic Gaussian Distribution Curve (i.e "the Bell Shaped Curve"). If you plot Feltonhill's data, you will see what I mean. Of course, if you had recorded data at say every MPH from 0 to 80 mph, you would get a real nice Gaussian distribution. Dear GP40-2, I presume this is what you're talking about: http://en.wikipedia.org/wiki/Gaussian_function. I have never seen a locomotive power curve that is a bell-shaped curve. For one thing, a bell-shaped curve is used in probablilty, quantum and atomic physics, and mathematic theory (as stated on the above website). Locomotive horsepower is not at all related to probability, and the Big Boy is a long way from the quantum. To use some big words: The "Bell Shaped Curve" is concave up at the beginning, but has a point of inflection on the way up. It then returns to y where the limit of y as x aproaches infinity is 0 (sorry about having to write that out--it's hard to type in mathematic notation). The locomotive horsepower vs. velocity curve on the other hand is usually always concave-down without a point of inflection, and as speed increases after peak horsepower, the horsepower tends to approach a limit somewhere toward the middle of the horsepower range, rather than returning to 0. In theory, because of friction, air resistance and such, this "post-max" horsepower limit would tend to dictate a maximum speed for the locomotive. In practice, other factors, such as counterbalancing, prescribe a lower maximum speed limit usually. The locomotive horsepower curve might in part be exponential, but were we to work out an exact equation, would almost certainly have trigonometric and probably power components as well. Add to that a ton of constants for friction and steam flow, and you'd get a graph resembling a measured locomotive horsepower curve. Sincerely, Daniel Parks
QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 Dear GP40-2, What exactly do you mean that a steamer's power curve is exponential in nature? I presume you don't mean b^x like in calculus class, nor do you mean x^p. Sincerely, Daniel Parks I mean that a steam locomotive's power curve follows the classic Gaussian Distribution Curve (i.e "the Bell Shaped Curve"). If you plot Feltonhill's data, you will see what I mean. Of course, if you had recorded data at say every MPH from 0 to 80 mph, you would get a real nice Gaussian distribution.
QUOTE: Originally posted by trainjunky29 Dear GP40-2, What exactly do you mean that a steamer's power curve is exponential in nature? I presume you don't mean b^x like in calculus class, nor do you mean x^p. Sincerely, Daniel Parks
QUOTE: Originally posted by trainjunky29 Dear GP40-2, Please clarify on what it is that I don't understand. If you would be so good as to point to a specific statement with which you have an issue, I'd appreciate it. As for the locomotive horsepower vs. boiler pressure: You yourself stated that the Big Boys had smaller piston strokes and diameters than other locomotives. In part, the larger force on the piston from the greater cylinder bore on the Yellowstone, and the greater Mechanical Advantage from the larger stroke on the Allegheny, made up for the decreased boiler pressure. Also, if you give an engine large (wide) steam ports and large valves, it will increase horsepower, as long as you have a boiler to match. Do bear in mind that the lower boiler pressure allowed the boiler to create more steam at a lower pressure with the same heat. The boiler would therefore be able to create more steam for the cylinders to use, whereas the Big Boys would need a slightly shorter cutoff. Sincerely, Daniel Parks
QUOTE: Originally posted by trainjunky29 QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 True, but it's the pressure that causes the force on the piston, not the volume. The volume comes into play when trying to conserve steam--take away to much steam and the boiler pressure goes down. Sincerely, Daniel Parks No, the cylinder has a difinite volume that needs to be filled. If you limit the volume of steam entering the piston, regardless of the pressure, you limit the power. As the high pressue steam enters the cylinder, it expands and transfers its energy to the cylinder. Once a volume of steam is done expanding, no more power transfer. That's why the Allegheny was so powerful with just 260 lbs pressure. It was not the pressure producing the HP, it was the boilers ability to pruduce high volumes of steam to keep the cylinders filled at high speed. Dear GP40-2, The volume won't do you any good unless it's under pressure. The steam if it is under any decent amount of pressure whatsoever will expand to fill the full volume of the cylinder. The is then is what pressure it's under, and consequently, how much force it's exerting. Increasing pressure is probably the single most effective way to increase tractive effort and horsepower. Also, the steam does not expand in the admission phase, only cutoff and a little bit in compression (though by the time compression comes, it's pretty much done usefully expanding). In admission, the volume is being fully filled by steam straight fromt the boiler. Just clarifying. Sincerely, Daniel Parks
QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 True, but it's the pressure that causes the force on the piston, not the volume. The volume comes into play when trying to conserve steam--take away to much steam and the boiler pressure goes down. Sincerely, Daniel Parks No, the cylinder has a difinite volume that needs to be filled. If you limit the volume of steam entering the piston, regardless of the pressure, you limit the power. As the high pressue steam enters the cylinder, it expands and transfers its energy to the cylinder. Once a volume of steam is done expanding, no more power transfer. That's why the Allegheny was so powerful with just 260 lbs pressure. It was not the pressure producing the HP, it was the boilers ability to pruduce high volumes of steam to keep the cylinders filled at high speed.
QUOTE: Originally posted by trainjunky29 True, but it's the pressure that causes the force on the piston, not the volume. The volume comes into play when trying to conserve steam--take away to much steam and the boiler pressure goes down. Sincerely, Daniel Parks
QUOTE: Originally posted by tree68 I recall reading some time ago that steam engines came into their own at higher speeds, and that if it weren't for the physical problems of wheel balance and steam production, they would have no practical top end. It frankly surprises me that an FEF would take 10 miles to get to 110mph - I'd expect it sooner, but that's just my impression.
QUOTE: Originally posted by trainjunky29 QUOTE: Originally posted by timz QUOTE: Originally posted by tree68 I recall reading some time ago that steam engines came into their own at higher speeds, and that if it weren't for the physical problems of wheel balance and steam production, they would have no practical top end. It frankly surprises me that an FEF would take 10 miles to get to 110mph - I'd expect it sooner, but that's just my impression. When an 80-inch-driver engine is running 110 mph, each piston stroke takes 0.065 seconds, and the valve is open for maybe a third of that time. So the steam has maybe 1/40 of a second to get into the cylinder. It's a mystery that a steam locomotive can pull at all at that speed. The notion that steam has some sort of high-speed advantage is mostly wishful thinking; remember R. P. Johnson gave us an example of it in his book, in the chapter on high speed trains? Yes, but the steam's under a lot of pressure. Let's not get into a steam vs. diesel debate--we'll never get out of it.[:)][:D][8D]
QUOTE: Originally posted by timz QUOTE: Originally posted by tree68 I recall reading some time ago that steam engines came into their own at higher speeds, and that if it weren't for the physical problems of wheel balance and steam production, they would have no practical top end. It frankly surprises me that an FEF would take 10 miles to get to 110mph - I'd expect it sooner, but that's just my impression. When an 80-inch-driver engine is running 110 mph, each piston stroke takes 0.065 seconds, and the valve is open for maybe a third of that time. So the steam has maybe 1/40 of a second to get into the cylinder. It's a mystery that a steam locomotive can pull at all at that speed. The notion that steam has some sort of high-speed advantage is mostly wishful thinking; remember R. P. Johnson gave us an example of it in his book, in the chapter on high speed trains?
QUOTE: Originally posted by feltonhill GP40-2, I'm sure you know (and most everyone else here as well), that an N&W Class A could pull 160 cars between Williamson and Portsmouth, but on a very slight downgrade with many curves. They also could make at least 40-45 mph with this load. After the addition of a-tanks, they did the route non-stop with as many as 180 cars in about 3.5 to 4 hours. Every day, nothing special. OK, a single AC4400 could start considerably more than 160 cars, maybe as many as 320 as you claim. However, it couldn't make 40 mph with that load. I doubt that a single AC4400 could make 40-45 mph with 160 cars over that line. Trainjunky29's estimate of an FEF3 being able to make 100 mph in 10 miles is possible, but I doubt it would be more than an 800-900 ton train (about 12-13 cars). The AAR tests in 1938 set a goal of getting a 1000-ton 15-car train to 100 mph and an FEF-1 managed 102 mph on a slight downgrade (about -0.15% IIRC), not on level track. But how many cars could a single P42 get to 110 mph in 2 minutes? 12-13 sounds unlikely. It would further everyone's knowledge of trains if you would provide some additional context with your examples.
Quentin
Larry Resident Microferroequinologist (at least at my house) Everyone goes home; Safety begins with you My Opinion. Standard Disclaimers Apply. No Expiration Date Come ride the rails with me! There's one thing about humility - the moment you think you've got it, you've lost it...
QUOTE: Originally posted by GP40-2 A GE P42 can be crusing at 110mph in 2 minutes from a station stop not alone 10 miles.
QUOTE: Originally posted by GP40-2 Of course, I fully expect you to "respectfully disagree" with the above statement.
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