Leonardo’s aerial screw
The short answer
In the late 1480s Leonardo da Vinci drew an aerial screw: a spiral linen sail about 5 m in radius, meant to climb into the air the way a screw goes into wood. To lift a 75 kg person it must push 735.75 N of thrust, and momentum theory gives an ideal minimum power of about 1.45 kW; a real screw would need more. It stayed a drawing, but a modern helicopter rotor also lifts by pushing air down.
Chapters and transcript
- 0:00
In the late 1480s, Leonardo sketched an aerial screw: a screw that bites the air.
Leonardo da Vinci drew an “aerial screw” in the late 1480s: a spiral sail, meant to climb into the air the way a screw goes into wood.
- 0:11
Its spiral sail of linen, stiffened with starch, had a radius of about 5 m.
The sail was of linen stiffened with starch, on a frame with a radius of about 5 m.
- 0:29
A 75 kg person weighs 735.75 N: that is the thrust the sail must make.
For a 75 kg person, the weight is 75 × 9.81 = 735.75 N. Lifting the person needs a thrust of at least that much.
- 0:38
The sail sweeps about 78.5 m² and pushes the air down at about 2 m/s.
The sail sweeps a disk of about π × 5² = 78.5 m². Momentum theory gives the air speed through it as √(T ÷ 2ρA) = 1.98 m/s, with air density ρ = 1.2 kg/m³.
- 0:49
Momentum theory gives the ideal power: about 1.45 kW to lift 75 kg.
The ideal power is P = T × v = 735.75 × 1.98 ≈ 1.45 kW. This is the minimum for an ideal disk with no losses.
- 0:57
Leonardo wrote that it must turn quickly enough to lift the structure.
Leonardo's annotations say a linen screw, if turned quickly enough, would push against the air and lift the structure.
- 1:07
The ideal figure is a lower bound: a real screw needs more power.
The ideal figure assumes no losses, so a real screw needs more power than 1.45 kW.
- 1:16
It stayed a drawing. The idea of lift from a spinning surface came back centuries later.
The screw stayed a drawing. Its design is similar to a modern helicopter rotor, which also lifts by pushing air down.
Sources
Every figure in the film comes from these. The animation is illustrative.