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WW2 German tanks and American tanks both share this trait.  What was the reasoning behind it?  Was it because the driver sat in the front and it would be easier to put the gearbox next to his shifters?

A rear mounted gear box driving rear sprockets could reduce vehicle's height and decrease vulnerability.  I believe the trade off would be worth it.

The earliest tanks had horrible drivetrains.  For example the British Mk IV during WWI had 5 men dedicated to the automotive systems of the tank.  1 - driver, 2 - mechanics (1 for each engine), 2 transmission men (one for each transmission.)  Later tanks had one driver only, because drivetrains were finally developed that were one-man operable.  Transmission technology adavanced rapidly during WWII.  Even being used in rear-engined, rear drive units, as evidenced by the powerful IS-3s that paraded thru Berlin in 1945.

basically the OP is right on.

blurr91, on Nov 17 2011 - 21:30, said:

It is to be noted that in some cases the driver sat astride the transmission. M3 Medium, for example.

In some cases, it was simply an inability to create a transmission/final drive combo which was small enough to fit into the same end. T-34 was notable because with the transverse engine, and a bit of judicious design (and a 2-pound sledge next to the driver), they managed it. However, if you're looking at some engine like the Chrysler multibank or the Wright Continental, the output shaft is a couple of feet above the hull floor. It's just as easy to tilt the propellor shaft at a slight angle so by the time it gets to the other end of the tank, it's at a reasonable height for the transmission. No reliability issues caused by cogs or other systems to do the same job in less space.

I wrote a giant post about this in some vehicles quite a while ago, I'll try and find it.

Several reasons. One being that the engine's drivetrain was used to traverse the turret. Secondly, it's easier to keep good tension on the tracks of the sprocket is pulling instead of pushing. Thirdly, it helps weight distribution, not having all the weight at the rear of the tank. Another reason is that it's easier to "pull" a heavy load then it is to "push" it. Front-drive effectively pulls the tank forward.

There were a lot of reasons, really. But eventually vehicles moved onto hydraulic or electric turret drives, "slack-tracks", etc, and the advantages of the front-drive platform no-longer outweighed the disadvantages--like having your transmission exposed by being in the front of the tank. Anyone who's ever had their engine KO'd from a frontal shot knows what I'm talking about.

Not a specialist but if the American had the transmission on the front, its pretty good because despite they were given much more height, the overall width x lenght was considerably much more smaller than the tanks of the same era/year. I THINK.