Is there a two way flying machine that is faster than minecarts?

I thought of building a sort of subway but I was kind of bored of the regular walking, minecarts, and boats on ice. So I remembered flying machines. Is there a two-way design that is actually faster than going by the ordinary minecart? If so please give me a link or picture or at least some form of instructions.

Solution 1:

A minecart's top speed is 8 blocks per second (along one axis) .

A piston powered flying machine would be bound to redstone ticks, there are 10 redstone ticks per second. In theory, if you manage to push the flying machine every single redstone tick, then you could go at up to 10 blocks per second.

This would require an extended piston to instantly be replaced, or pushed forward. You would need at least a second redstone tick, just to move the piston back into place, making the theoretical top speed of a flying machine 5 blocks per second¹, which is slower than a minecart.

_{1: 5 blocks average speed, it is however possible to go at up to 10 blocks per second in quick bursts.}