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 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 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 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 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 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 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 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
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QUOTE: Originally posted by GP40-2 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 Let's look at the data, and focus on speed vs. hp: Speed - Calc TE (lbs) - Actual DB Pull (lbs) - Actual DBHP 0 - 135,300 - 131,000 - 0 10 - 132,500 - 124,000 - 3,307 20 - 109,000 - 98,000 - 5,227 30 - 83,000 - 75,000 - 6,000 40 - 67,000 - 57,000 - 6,080 50 - 56,100 - 43,000 - 5,733 60 - 48,700 - 32,000 - 5,120 SPEED=X HP=Y X Y 0 0 10 3307 20 5527 30 6000 40 6080 50 5733 60 5120 70 4000 (extrapolated) 80 2800 (extrapolated) Plot those, and you will get a bell shaped curve. Maybe not a "pure Guassian", but a bell shaped curve none the less. I'm also curious why you think probability and statistics can not be used to describe how a steam locomotive works? After all, Monte Carlo routines are often used now in mechanical engineering design...
QUOTE: Originally posted by trainjunky29 QUOTE: Originally posted by GP40-2 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 Let's look at the data, and focus on speed vs. hp: Speed - Calc TE (lbs) - Actual DB Pull (lbs) - Actual DBHP 0 - 135,300 - 131,000 - 0 10 - 132,500 - 124,000 - 3,307 20 - 109,000 - 98,000 - 5,227 30 - 83,000 - 75,000 - 6,000 40 - 67,000 - 57,000 - 6,080 50 - 56,100 - 43,000 - 5,733 60 - 48,700 - 32,000 - 5,120 SPEED=X HP=Y X Y 0 0 10 3307 20 5527 30 6000 40 6080 50 5733 60 5120 70 4000 (extrapolated) 80 2800 (extrapolated) Plot those, and you will get a bell shaped curve. Maybe not a "pure Guassian", but a bell shaped curve none the less. I'm also curious why you think probability and statistics can not be used to describe how a steam locomotive works? After all, Monte Carlo routines are often used now in mechanical engineering design... Dear GP40-2, Due to the reasons I have sighted as points 1, 3, and 4 above, a horsepower curve looks little like a Bell-shaped curve. I presume by Monte Carlo Routine you mean what is described here: http://en.wikipedia.org/wiki/Monte_Carlo_method. You will notice that these have to do with random numbers. At the macroscopic locomotive level, as I'm sure you realize, random motions tend to cancel one another out. There's not much that's random on a Big Boy (other than which bolt will rust in place next [:)]). Sincerely, Daniel Parks
QUOTE: Originally posted by trainjunky29 Dear GP40-2, maybe you have established it, but wait one minute: If torque vs. rpm is Gaussian, wouldn't that mean that at 0 rpm's, you would have no torque? And if you have no torque when stopped, then how does a steam locomotive get things moving? Quite the contrary, a steamer's torque is at a maximum at speeds near 0, and only goes down from there. I admit that I may not have the benefit of college mechanical engineering classes, but I can still read a graph. Secondly, wikipedia is an open source document. That makes it MORE reliable--any malicious or ignorant falacies on the sight would soon be corrected by others either well-meaning or more knowledgeable. If you don't want to use wikipedia, then be my guest to pick some other reference. Without a reference, we could very easily end up arguing over two completely different subjects. Finally, why are we dealing with the largest of the large in terms of random numbers? You can model the Big Boy in Monte Carlo routines if you so desire. I personally prefer brass [:)]! And has anybody noticed that we are arguing about stuff completely different than what this topic started about [8D]? Sincerely, Daniel Parks
QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 Dear GP40-2, maybe you have established it, but wait one minute: If torque vs. rpm is Gaussian, wouldn't that mean that at 0 rpm's, you would have no torque? And if you have no torque when stopped, then how does a steam locomotive get things moving? Quite the contrary, a steamer's torque is at a maximum at speeds near 0, and only goes down from there. I admit that I may not have the benefit of college mechanical engineering classes, but I can still read a graph. Secondly, wikipedia is an open source document. That makes it MORE reliable--any malicious or ignorant falacies on the sight would soon be corrected by others either well-meaning or more knowledgeable. If you don't want to use wikipedia, then be my guest to pick some other reference. Without a reference, we could very easily end up arguing over two completely different subjects. Finally, why are we dealing with the largest of the large in terms of random numbers? You can model the Big Boy in Monte Carlo routines if you so desire. I personally prefer brass [:)]! And has anybody noticed that we are arguing about stuff completely different than what this topic started about [8D]? Sincerely, Daniel Parks Torque always has to start at zero. You just can't instantly have say 10,000 lbs ft torque out of no where-it has to start somewhere-and that starting point is zero. Now, we are getting into the idea of limits. If you graph the starting torque of any locomotive in small enough increments you will see a ramp up from a zero starting point, a maximum, and a fall back to zero. Second, as you are aware, power is torque X speed. It is possible to have a large torque reading while having zero power. Example: You are pressing hard on a wrench to remove a stuck bolt. When you first place the wrench on the bolt, you don't instantly have maximum force. Your force starts at zero, then your muscles apply all the force they have. If you are applying all your strength, and the bolt still is not turning, you have created maximum torque BUT zero power. Now, the bolt slowly starts to free itself and turn. The torque reading on the wrench will go down, but the power you have produced will go up. Anyway, we were talking about a locomotives power at certain speeds, not it's tractive effort.. I said to graph the Big Boy's Power vs. Speed. I never said for you to graph a locomotives tractive effort curve (which is nothing more than a linear reading of the torque produced by the locomotive's wheels). P.S. Here's a tip for the future: You can say what you want about the Wikipedia, but I guarantee you if you use that thing for a college level paper you will get a nice big fat F on it.
QUOTE: Originally posted by trainjunky29 QUOTE: Originally posted by GP40-2 QUOTE: Originally posted by trainjunky29 Dear GP40-2, maybe you have established it, but wait one minute: If torque vs. rpm is Gaussian, wouldn't that mean that at 0 rpm's, you would have no torque? And if you have no torque when stopped, then how does a steam locomotive get things moving? Quite the contrary, a steamer's torque is at a maximum at speeds near 0, and only goes down from there. I admit that I may not have the benefit of college mechanical engineering classes, but I can still read a graph. Secondly, wikipedia is an open source document. That makes it MORE reliable--any malicious or ignorant falacies on the sight would soon be corrected by others either well-meaning or more knowledgeable. If you don't want to use wikipedia, then be my guest to pick some other reference. Without a reference, we could very easily end up arguing over two completely different subjects. Finally, why are we dealing with the largest of the large in terms of random numbers? You can model the Big Boy in Monte Carlo routines if you so desire. I personally prefer brass [:)]! And has anybody noticed that we are arguing about stuff completely different than what this topic started about [8D]? Sincerely, Daniel Parks Torque always has to start at zero. You just can't instantly have say 10,000 lbs ft torque out of no where-it has to start somewhere-and that starting point is zero. Now, we are getting into the idea of limits. If you graph the starting torque of any locomotive in small enough increments you will see a ramp up from a zero starting point, a maximum, and a fall back to zero. Second, as you are aware, power is torque X speed. It is possible to have a large torque reading while having zero power. Example: You are pressing hard on a wrench to remove a stuck bolt. When you first place the wrench on the bolt, you don't instantly have maximum force. Your force starts at zero, then your muscles apply all the force they have. If you are applying all your strength, and the bolt still is not turning, you have created maximum torque BUT zero power. Now, the bolt slowly starts to free itself and turn. The torque reading on the wrench will go down, but the power you have produced will go up. Anyway, we were talking about a locomotives power at certain speeds, not it's tractive effort.. I said to graph the Big Boy's Power vs. Speed. I never said for you to graph a locomotives tractive effort curve (which is nothing more than a linear reading of the torque produced by the locomotive's wheels). P.S. Here's a tip for the future: You can say what you want about the Wikipedia, but I guarantee you if you use that thing for a college level paper you will get a nice big fat F on it. I agree with most of this post. I do not, however, agree with your earlier post. Here's why: You said that torque vs. rpm was Gaussian. Certainly torque cannot go from 0 to whatever instantaneously. However, using your bolt example, you could put on, say, 150 foot-pounds, and the bolt would still be stuck. You would have 0 rpm's, but plenty of torque (not Gaussian). Similarly, with a Big Boy, you could have full steam pressure in the cylinders, with full torque, but not be moving (say the train you're coupled to has the hand-brakes applied, and you are on a "cog Big Boy" so the wheel's won't slip) (not Gaussian). Additionally, you said, "Trainjunky, we already established that the locomotive's job is to apply torque to the rails, and torque curves are gaussian in nature. Therefore, it is impossible for a steam locomotives power curve NOT to be gaussian in nature." There are three things here I hold issue with: 1.) A locomotive's job is to apply a force through the coupler to the train. Torque really isn't the issue here, it's the mechanical advantage between the crankpin and the tire on the locomotive's driving wheels (wheel and axle, so to speak) (Galileo once described the wheel as the "perpetual lever"). Then of course you have to figure in the friction between the wheel and the rail. Basically, torque isn't as important as force--the piston puts a linear force on the main rod, which creates torque, which is made into a "rectified" linear force by the wheels. 2.) We've already gotten into torque vs. rpm (or speed) curves, but just to summarize my argument: At zero rpm's (or zero mph), torque can vary from zero to whatever maximum the locomotive can produce. A gaussian torque vs. rpm curve would mean no or practically now torque at 0 rpm's. 3.) You assert that since torque curves are Gaussian in nature, horsepower curves are by default. I deny that torque curves are Gaussian in nature, but let's do a little math: For the sake of arugment, let's ignore the force fluctuations throughout a locomotive wheel's revolution (so that a constant force acts on the wheel all the time). Torque equals the perpendicular force times the radius from which it acts. Therefore, the perpendicular force = torque/radius. The force exerted to the rail is the aforementioned "torquing force" times the crankpin radius devided by the wheel's radius, or F = f x r / R (r/R is a mechanical advantage less than one). Finally, Power = Force x velocity. Now let's do some substitution, and you'll end up with Power = torque x velocity / wheel radius (or because there are 550 foot-pounds in a horsepower, Horsepower = torque x velocity / 550 x wheel radius). But let's just stick with Power = torque x velocity / a constant. We are graphing power vs. speed. Obviously, velocity vs. speed will be a linear graph. Even if torque vs. rpm were Gaussian (which I deny), a Gaussian graph times a linear graph would not be Guassian any more than a sinusoidal graph times a parabolic graph would be sinusoidal. Sincerely, Daniel Parks
QUOTE: Originally posted by Old Timer Anybody know how to get this back on topic? All I see is a couple of guys trying to out-brain each other. I don't see either one making any particular points on it. Old Timer
QUOTE: Originally posted by GP40-2 Man, you just don't give up even when you are wrong! I bet you drive your parents crazy. If you deny that torque curves are gaussian in nature, then your don't fundamentally understand torque. Since you don't have a true fundamental understanding of this stuff, many of your assumptions are wrong from that point forward. The difference between an man and a kid is that a kid whines and cries even when he is wrong. A man, on the other hand, admits his mistakes, learns from the experience, and moves on. Trainjunky, stop being a whiny kid, and learn to be a man.
QUOTE: Originally posted by GP40-2 A steam locomotive's power curve is exponential in nature... I mean that a steam locomotive's power curve follows the classic Gaussian Distribution Curve (i.e "the Bell Shaped Curve").... ...torque curves are gaussian in nature. Therefore, it is impossible for a steam locomotives power curve NOT to be gaussian in nature.... If you deny that torque curves are gaussian in nature, then your don't fundamentally understand torque.
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