Crazy as it might sounds, yours truly has a US Patent...well, I only have one so nothing to shout about. As engineers, one of our lifelong goals is to invent something new, and the patent truly is something I have always wanted. It's not so simple as going out there to buy something on the shelf of a supermarket. This was done back when I was a Product Engineer at Hewlett-Packard printing division.
We tried quite a number of solutions and finally found one that works. As the tray with the 500 sheets is being inserted into the printer, the wall will block the paper stack from moving and jamming the paper path. After a few seconds, the wall will come down and thus, the printer will act as per normal.
Oh yes, the wall is NOT straight wall...we found after several iterations that the top of the stack happen to have a greater momentum and will move more than the paper at the bottom. Despite looking weird, the paper stack will become straight after hitting the wall...yes, we tested this many times.