Why do planes float?

A hot-air balloon or an airship genuinely floats: it contains a gas less dense than the surrounding air, so Archimedes' buoyant force exceeds its weight. An airplane is the opposite, a machine heavier than air. A single-aisle jet at takeoff weighs around 70-80 tonnes, while the air occupying its volume weighs only a few dozen kilos. Nothing holds it up through buoyancy. What happens is that it stays up through constant work: the engines push it forward and the wings convert that speed into a vertical force. As soon as the airspeed disappears, so does the lift, and the aircraft descends. The feeling that it is floating, in cruise, comes from the absence of nearby visual references at that altitude and from the stability of the flight, but the wing is working at every moment.

The wing is a curved airfoil that moves forward at a slight angle relative to the airflow. The air around it curves and flows downward off the trailing edge; according to Newton's third law, if the wing pushes air down, the air pushes the wing up. Seen from the pressure side, air accelerates over the upper surface and pressure drops, while beneath the lower surface it increases: the difference, integrated over the whole surface, is lift. Both descriptions are the same physics. What is not correct is the popular explanation that the air above must reach the trailing edge at the same time as the air below; in fact it arrives earlier. Lift grows with the square of speed, with air density, with wing area and with angle of attack, until the flow separates and the wing stalls.

In level flight, lift equals weight and thrust equals drag. If pilots want to climb, they increase power or angle of attack; if they want to descend, they reduce one or the other. An aircraft without engines does not fall like a stone either: it glides, trading altitude for speed, and an airliner can cover 15-20 km horizontally for every 1,000 m of altitude lost. That is why gliders fly for hours without an engine, seeking rising air. What an airplane does, in short, is fall very slowly forward while the engines compensate for the energy loss.

The other reading of the question also has an answer. Land aircraft are not designed to land on water, but the pressurized fuselage is an almost airtight tube, and the wings contain tanks that, empty or nearly so, add volume. Certification regulations require analyzing behavior in an emergency water landing and providing exits and rafts. In January 2009, a US Airways Airbus A320 with no thrust in either engine landed on the Hudson River and stayed afloat long enough to evacuate all its occupants. Seaplanes and amphibians, with floats or a boat-shaped hull, are indeed built to float and take off from water routinely.