The tray table that folds in half for stowage in the armrest of an airline seat is something I have long admired for its design ingenuity, but long cursed for its operational opaqueness and flimsiness. On domestic flights, tables of the kind I am describing are usually found in the first-class cabin and on seats facing a bulkhead. The more common rigid tray tables that swing down from the back of the seat in front of a passenger are obviously less costly to manufacture and install, and so are used wherever the seat pitch allows them.
But even before the more complex armrest table can be deployed into a (hopefully) flat and horizontal position, the airline passenger has to get the thing out of its underarm pocket. This can be more easily said than done, for there is no standard feature to grasp on the stowed table. Some models have a fabric loop, some a trigger-like hook, and some a corner hole. Since not all passengers are able to contort their bodies or squint their eyes sufficiently to see what aid might be lurking in the dark recess, they tend to feel around for a familiar shape and tug on it.
Once the table has been wrestled out of its hold, it can typically be rotated about an orthogonal axis to become a half table, often with a slight depression in its surface to keep drinks from walking off the edge during air turbulence or just under ambient vibration. It is in deploying this half table that passengers might first discover that the top can have a pronounced incline. On a recent flight from Chicago to Raleigh-Durham I found myself with such a table. As I waited for the flight attendant to bring me a drink, I almost put the table back into the armrest, since I would have had to hold the glass anyway.
The detailed design of the kinematically clever deployable armrest table understandably varies from airplane model to airplane model, but virtually all variations seem to depend for their operation on two primary mechanical principles: the hinge and the cantilever. Some also contain a slide or swivel feature, which enables the more corpulent user to push the tray forward or aside to gain some breathing room.
In one common form, the two halves of the table have their top edges connected through a pair of link hinges; the bottom edges of the two halves butt up against each other, providing reaction forces. Collectively, the forces maintain a cantilevered table top in a flat and horizontal position. One familiar form of tray table, when fully deployed, forms a bridge of sorts between a seat's armrests.
On my flight where the folded table sloped downward, the unfolded one would also have -- had it not been for the opposing armrest providing a support constraint. Thus, the fully opened table top formed not a flat plain but a shallow valley. The two halves inclined toward the center, creating a V into which everything from pencils to peanuts to plastic drink glasses would want to slide.