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# Re: TRAINS - Correction

So here is the actual statistic not confused by fading memory, I still think
it is impressive:

One can transport 1 ton of freight 100 km with 14 oz of diesel fuel, by
freight train.

Joel

That is a really interesting combination of units. But what does it mean?
Is it the marginal fuel used to move that much cargo, over and above that
used just to get the locomotive and the railroad car there? Does it depend
on the length of the train? If I am hauling a fully loaded 150 car train
and add 1 ton to one of the cars, do I use 14 oz. more fuel per 100 km? Or
is it the total fuel to move the train per ton of cargo carried? This sound
impressive but it may be considerably less so when put in the context in
which it was derived.

Speaking of units confusion, an interesting one occurs in rocketry. The
specific impulse of a rocket engine is a measure of the momentum change of
the rocket per unit mass of fuel carried. In metric (SI) units that would
be measured in newton seconds per kilogram of fuel. In the SI system that
is the end of the simplification, if you want the units to be descriptive
of what it represents. But dividing out the kilograms leaves meters per
second, or velocity. But since the velocity of the rocket is dependent on
lots of other things than the impulse delivered by the fuel, that isn't a
particularly useful unit to use. But in the "American" system, the units of
specific impulse work out to pound (force) seconds per pound (mass). Of
course no one puts in the force or mass modifiers and so the "obvious"
cancellation reduces the unit immediately to seconds. There is a unit
diabolically designed to confuse the uninitiated. Without knowing what was
improperly cancelled from the units, one would have a great deal of trouble
using the expression in any other equation. Or even making sense out of the
numbers given, except that as usual "bigger is better." But there it is.
Next time you or one of your students has occasion to purchase some model
rocket motors, check the specification sheet and see what units they
present specific impulse in. Right. Seconds.

Hugh

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