Guys,
I evidently assumed (mistakenly) that everybody would be able to understand that the Jim Fitch idea immediately implies exponentially increasing damage rates. To help clarify this, I'll state some basic principles the conditions under which this type of math is implicit. If this is not clear, please contact me.
Exponential functions apply mathematically when the rate of change of a variable (Y) is proportional to the current value of Y. If Y is the quantity whose rate of change is proportional the quantity of Y present, then Y will vary with time according to Y = C times e (the natural log) raised to the kt power or Y=CE(kt) where kt is an exponent. In this equation, T=time, C is the intitial value, and k is called the constant of proportionality.
Now does the Fitch example meet the criteria above? Yes, it defines that very criteria: If the rate of wear particle development is dependent on the concentration of wear particles (Y), then this perfectly meets the mathematical model/requirements for exponential growth.
Now remember that Stinky made an important point about exponential growth, it does not necessarily imply high values of anything (it just states that they get higher at an exponential rate). If C is low and k is low in the equation above, then you may never notice the growth especially if the sensitivity of your yardstick is not very good (This is called a UOA on BITOG)
Where does this equation apply in your everyday life....listen up now Jay!!!
1) BANK INTEREST --the amount of gain in capital per time period is proportional to the current amount there and the capital amount thus grows exponentially.
2)POPULATION GROWTH -- the rate of population increase is proportional to the current population and the population thus grows exponentially.
3) UNCONTROLLED NUCLEAR FISSION: the rate of population increase for fissuring neutrons is proportional to the amount already there and thus the population of free neutrons grows exponentially (at least until it gets a little too toasty if you smell what I'm cooking.)
4)PARTICLE INDUCED WEAR: The rate of wear particle increase is proportional to the current concentration of wear particles and thus the concentration of said particles must grow exponentially.
Now speaking with analogies here, controlled nuclear fission (as in a nuke power plant) would be analagous to having an excellent filter on your car thus stopping the consequences of unrestrained exponential growth. Perhaps current filters do remove many of the particles that would cause wear and perhaps this is one of the reasons that exponential growth rates are not generally observed. Now Jay, that is a theory and is thus sublect to debate and argument..........the mathematical invokation of the exponential growth rule is not
a theory but is implicit if you accept the Fitch premise. It can be no other way.
Now Jay, when I state theories, you can argue with me all day long and probably be right but you cannot ever be right arguing against the application of 10th grade mathematics to an obvious and clear-cut case where the math fits.
ALso, the last time I mentioned that the damage caused by particles may be dependent on lube film thickmesses, you accused me of making up that theory too. As you can see, it's a heavy theme in the Fitch article. I don't know if the general idea has ever been disputed. I don't know if 10th grade math has ever been disputed either. But if there's one here foolish enough to refer to facts as theories and to treat his own opinions as facts, it's you. You take the crown.
I evidently assumed (mistakenly) that everybody would be able to understand that the Jim Fitch idea immediately implies exponentially increasing damage rates. To help clarify this, I'll state some basic principles the conditions under which this type of math is implicit. If this is not clear, please contact me.
Exponential functions apply mathematically when the rate of change of a variable (Y) is proportional to the current value of Y. If Y is the quantity whose rate of change is proportional the quantity of Y present, then Y will vary with time according to Y = C times e (the natural log) raised to the kt power or Y=CE(kt) where kt is an exponent. In this equation, T=time, C is the intitial value, and k is called the constant of proportionality.
Now does the Fitch example meet the criteria above? Yes, it defines that very criteria: If the rate of wear particle development is dependent on the concentration of wear particles (Y), then this perfectly meets the mathematical model/requirements for exponential growth.
Now remember that Stinky made an important point about exponential growth, it does not necessarily imply high values of anything (it just states that they get higher at an exponential rate). If C is low and k is low in the equation above, then you may never notice the growth especially if the sensitivity of your yardstick is not very good (This is called a UOA on BITOG)
Where does this equation apply in your everyday life....listen up now Jay!!!
1) BANK INTEREST --the amount of gain in capital per time period is proportional to the current amount there and the capital amount thus grows exponentially.
2)POPULATION GROWTH -- the rate of population increase is proportional to the current population and the population thus grows exponentially.
3) UNCONTROLLED NUCLEAR FISSION: the rate of population increase for fissuring neutrons is proportional to the amount already there and thus the population of free neutrons grows exponentially (at least until it gets a little too toasty if you smell what I'm cooking.)
4)PARTICLE INDUCED WEAR: The rate of wear particle increase is proportional to the current concentration of wear particles and thus the concentration of said particles must grow exponentially.
Now speaking with analogies here, controlled nuclear fission (as in a nuke power plant) would be analagous to having an excellent filter on your car thus stopping the consequences of unrestrained exponential growth. Perhaps current filters do remove many of the particles that would cause wear and perhaps this is one of the reasons that exponential growth rates are not generally observed. Now Jay, that is a theory and is thus sublect to debate and argument..........the mathematical invokation of the exponential growth rule is not
a theory but is implicit if you accept the Fitch premise. It can be no other way.
Now Jay, when I state theories, you can argue with me all day long and probably be right but you cannot ever be right arguing against the application of 10th grade mathematics to an obvious and clear-cut case where the math fits.
ALso, the last time I mentioned that the damage caused by particles may be dependent on lube film thickmesses, you accused me of making up that theory too. As you can see, it's a heavy theme in the Fitch article. I don't know if the general idea has ever been disputed. I don't know if 10th grade math has ever been disputed either. But if there's one here foolish enough to refer to facts as theories and to treat his own opinions as facts, it's you. You take the crown.