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[quote]QUOTE: Originally posted by GP40-2 [quote]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] 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] Dear GP40-2, I presume this is what you're talking about: [url]http://en.wikipedia.org/wiki/Gaussian_function[/url]. 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
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