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I think it's pretty clear that you need to plan on at least three feet, and I'm tend to doubt even that will work!  You're looking at a 16 degree slope trying to do 6" in three feet, I suspect that's a tall order for most model trains.  I think they only way you'll really know is pick the locomotive and then do some experiments, you're in uncharted waters here.

I think the cog railway is sounding more like a good option...

The transitions from level to sloped should not be done with flat pieces of track but rather with tracks curved in the vertical direction - but probably difficult to make. GRJ's suggestion to use a 0-4-0 steam engine is a good one because all 4 wheels can remain in contact with the rails through the transition. If you use a typical O-gauge 0-6-0 steamer with the axles mounted rigidly (not independently sprung), an axle will lose contact during the vertical transitions.

MELGAR

If you're feeling so inclined, you could construct a manually or mechanically operated car elevator with either a short tail track at the top for a mule, or a winch system. That would maximize your horizontal space usage, but would complicate operations. 

Otherwise, you will need to curve your transition track piece as suggested above, or extend your grade. 

I had little difficulty bending Gargraves Flex track in the vertical to transition top & bottom on a short incline. I was only doing 8% but it worked fine with every loco (all fairly short diesel & steam; "O31 capable" is one of my loco & rolling-stock criteria). I did also try 12% but my strongest puller (an O27-capable F3 with Magnetraction) could only haul 2-3 cars up that roller coaster.

Ok, it sounds like I do not need the engine to be able make this climb.  I just need the cars to be able to be pushed and pulled up and down the decline.  If that is the case then the only real problem I see is keeping the couplers from disconnecting as they make the initial descent.  Putting the curve at the top and bottom of the track should solve your 'bottoming' problem.  If the engine is operating on a level surface size of engine is not a problem.

or I am totally missing something so it is back to the 'cog'.  And goodnight to all.

Would you consider using a pw Lionel 41 Army switcher ? They're geared low and won't start free wheeling down a steep grade.  

I have two 41's  pulling approx. 14 cars. At one point they go down a grade about 5" with in 2 1/2 ft, then start to climb back up the 5" within about 5 ft. The reason for the sudden down grade and climb back up on my layout, the whole train completely disappears in a 3' mountain, goes down under the platform and starts to make a climb back up to exit the other end of the mountain.  

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