Maths Museum Museum
    Bernoulli, 1995 Maths Museum
© Maths Museum
Bernoulli's 125cc motor drives two caged propellers of 270cm diameter, to provide a vertical lift the equivalent of 200kg. The apparatus is stabilised by a matching pair of control balloons, 3m in diameter and containing 8m3 of air or helium gas. It is intended to carry two people only; steering is achieved by 'body displacement', the coordinated movement of the pilot and passenger around the platform.

Daniel Bernoulli was the 17th century mathematician who first calculated the fluid dynamics of wings, and was born in Groningen, while his father Johann, held the chair of mathematics there. 'Bernoulli's Principle,' a fundamental law of all fluids in motion, states that when flow speed increases, pressure decreases and vice versa.

First called 'Paradox', this machine was intended to work with two parachutes. The propellers had to be caged to prevent the parachutes from landing on them and getting tangled up. The original idea was that once the propellers started turning they would blow the parachutes upwards and the air from inside the parachutes would be returned to earth. I tested it like this but the parachutes didn't behave nicely; they became deformed and the force of the air was lost. I discovered that you have to have a hard parachute; a half-sphere made of plastic rather than cloth works - more or less - but not perfectly.

Then it occurred to me that the best way to stabilise the machine was with two small balloons attached to the cages to keep the platform level. So that was that. The helium gas gives it direction and the balloons float upwards so that the direction of flight is guaranteed. I tested 'Bernoulli' in the Ardennes in 1995. The Honda motor was excellent but the cages around the propellers were to narrow. After that test run I decided that the cages, although they were beautiful, had to go.

I still have plans for an improved version with balloons but no cages. It would have two much larger propellers so that it would require very little energy to achieve lift-off. It would also have something like a ship's mast, 7 or 8 m long, to hoist the balloons. This would give much greater stability because of the leverage provided by the length of the pole. Of course you could use much bigger balloons, large enough to lift the entire thing.

It's hard to believe now but at the time that Bernoulli was alive the people in the Netherlands were the most advanced in the world: they had the best inventors, scientists - everything. But the most advanced people are always persecuted and Bernoulli had to flee from Antwerp to Groningen in Holland to escape from the Spanish. Perhaps a machine like this would have helped him escape more easily.

© Panamarenko

125cc Honda motor 35 PK, two propellers, PVC, wood and iron

Ronny Van de Velde Gallery, Antwerp

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