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Unread 06-11-2008, 20:16
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Re: Mentors, Be careful what you teach your Future Engineers

As long as were playing the "Is this even possible" game, here comes the math:

As long as v^2/r is greater than gravity, you can make the loop. The kicker on a passenger train is that r actually has to be pretty large (Trains are not terribly flexible in the vertical plane). Just to see the math, if r=100feet the loop would be at least 200 feet tall (That puts it up there with some of the tallest coasters). v^2/100>32.2 ft/s^2 therefore V^2 = 3220 and thus v would be about 57 ft/s which is about 40mph. Now that is the speed at the peak. Assuming that the train has low power to weight ratio you can figure the entrance speed required to do the loop. The looh height H times Gravity times the mass (mgH) will equal the change in kinetic energy between the top and the bottom (0.5*m*V1^2 - 0.5*m*V2^2). Mass cancels out so gH=0.5*(V1^2-V2^2) This means 12880=(V1^2-57^2) therefore V1^2=12880+3220... V1=126ft/s = about 87mph

So obviously this is nearly impossible because Back to the Future 3 showed us that if a train hits 88mph you will end up in the past or future, or some sort of alternate universe.
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