Two Engines Back Driving One Differential.
 

If I connected the drive shafts of one engine and five speed transmission to the left half-axle of a differential, and a second engine and five speed transmission to the right-half axle of the same differential, how many different ratios can I get at the center drive of the differential, and how would I calculate each?

I would include 1L/1R, !L/2R, 1L/3R, 1L/4R, 1L,5R, 2L/3R, 2L/4R, 2L/5R, 3L/4R, 3L/5R, 4L/5R, and 1L, 2L, 3L, 4L, and 5L, with the Right engine cut off.

I count 16 distinct gear ratios,(more, if I include independent throttle pedals) but I just don't know how to calculate backwards through a differential.

If I'm understanding right, you can have nearly infinite ratios, because of how a differential works. Varying the RPM of the two engines will affect the speed of the center drive too. I think?

Yeah, I think so, too, that is, IF, a differential can be driven backwards.

Sounds like the differential would become pointless in this case. If you'd want to couple two engines to a same final drive, it might be easier to consider the example of that GM Scenicruiser bus. Or something analogue to the power-split device fitted to the Prius.

It's probably more of an excess than useless. Who really needs a 16 speed tranny, or two engines? Just a mind exercise. If you remember my thinking on two CB900C engines, and how they might overpower a single CB900 transmission, this would allow a transmission for each. They could be shifted together, but if one was mis shifted, the Differential would protect from over- or under- revving the other.

Use the road as your limited-slip differential- each drivetrain gets it's own wheel.

Frank, if I shift one engine, and mis-shift the other, it will be like putting the brake on the mis-shifted side.

Use one shift linkage for both.

Maybe something similar to the clutch system used in those tiller-tractors still widely popular in Southeast Asia (one per wheel) which is able to compensate the lack of a differential while cornering on pavement is more likely to perform the way you want.

Or like ZIL 135, one engine transmission combo for each side, no interconnection between wheels, but road.