Weight at the nose of a paper aeroplane

Where the centre of gravity has to sit before a glider will fly at all.

A paper aeroplane only glides properly if its centre of gravity sits ahead of the point where its wings' lift effectively acts, typically somewhere around a quarter to a third of the way back from the wing's leading edge.

The short version

Every glider, whether it is folded from a sheet of paper or built from balsa and covered in tissue, balances two things against each other: the pull of gravity acting through its centre of gravity, and the push of lift acting through a point on the wing called the centre of pressure. For steady, straight flight these two forces need to work together rather than fight each other, and the arrangement that does that reliably is a centre of gravity sitting a little ahead of the centre of pressure. Too far forward and the model dives, and can end up not flying at all since it noses straight into the ground. Too far back and the model can appear to fly beautifully for a moment before tipping into a slow, uncontrollable climb and then a stall, because there is nothing left to pull the nose back down once it starts to rise.

The physics of balance

The reason the forward position is needed has to do with which direction the two forces rotate the aircraft when they drift out of line. If the centre of gravity is ahead of the centre of pressure, any nose-up disturbance, a gust, a bump in the air, a slightly clumsy throw, increases the angle at which the wing meets the air. A wing meeting the air at a steeper angle produces more lift, further back along the fuselage than the centre of gravity, and that extra lift acting behind the pivot point pushes the nose back down. The aircraft corrects itself without any input at all. Moving the centre of gravity behind the centre of pressure produces the opposite effect from the same disturbance: the extra lift from the nose-up gust acts ahead of the pivot and pushes the nose up further, making the disturbance worse rather than correcting it, until the model runs out of speed and stalls.

The shuttlecock comparison

A badminton shuttlecock demonstrates the same self-correcting arrangement in an even simpler form. Its cork nose is heavy and its feathered skirt is light and draggy, so however it is struck and however it tumbles off the racket, it always ends up flying nose first, cork leading, feathers trailing. The heavy end sits ahead of where the air resistance acts on the skirt, exactly the relationship a stable glider needs between its centre of gravity and its centre of pressure, and the shuttlecock finds that orientation on its own within a fraction of a second of being hit. A paper aeroplane cannot rely on drag alone to sort itself out the way a shuttlecock does, since its wings are far more efficient at flying than a badminton skirt is at flying badly, but the underlying idea, weight leading and resistance trailing, is the same one folded into a flatter shape.

The one number worth remembering

For a typical simple glider, the centre of gravity wants to sit somewhere between about a quarter and a third of the way back from the wing's leading edge, measured along the average width of the wing. Nose weight, whether it is a paperclip pressed onto the front of a paper dart or a lump of clay in the nose of a balsa glider, is usually there to drag the centre of gravity forward into that band, because the raw materials of the airframe alone often balance too far back to fly well.

Where this stops being true

The quarter-to-a-third guideline assumes a fairly conventional layout, a single main wing carrying most of the lift with the fuselage and any tail surfaces contributing comparatively little. Tailless and delta-shaped aircraft, and unusual layouts with the horizontal surface ahead of the wing rather than behind it, shift the ideal balance point elsewhere, because the assumptions behind the rule, about where the various surfaces are and how much lift each contributes, no longer hold. The physics of leading weight and trailing resistance still applies, but the particular fraction that works for a simple dart does not transfer automatically to every shape.