Lateral Thoughts Physics World  February 2017
(Léon Benett 1886)

Vernian flying machines

In 1870 Jules Verne published The Clipper of the Clouds. The novel, also known as Robur the Conqueror, follows the exploits of a marvellous flying ship. But the Albatross, as the ship is named, is no mere gas-filled zeppelin – it is more an ocean-going schooner with a stout wooden hull, capable of carrying tonnes of stores for long voyages across the sky. To support all of this weight, Verne imagines the Albatross with several masts that, instead of sails, bear horizontal propellers that spin when the masts are revolved. In a further stretch of the imagination, the Albatross, with its large cargo, is described as being powered by electric batteries. At that time, the only batteries available were based on primitive zinc–carbon primary or lead–acid secondary cells, and electric motors were heavy for their power. Verne gets around this problem by telling us that they use a new kind of battery, able to provide extremely large amounts of power, almost indefinitely.

Verne imagines the Albatross with several masts that, instead of sails, bear propellers that spin when the masts are revolved

Meanwhile, back in the real world, practical men were focusing most of their efforts to achieve flight by building wings. In 1852 Sir George Cayley, after long studying of the potential of the fixed wing, produced the first heavier-than-air machine to carry a man. Others followed with increasingly better gliders, until by the end of the 19th century it only remained to add a light enough engine of sufficient power for sustained flight.

A long wing is particularly energy efficient at producing aerodynamic lift. As the wing moves forward, it covers a given area per second that is determined by the wingspan multiplied by the velocity. Due to the pressure difference between the upper and lower surfaces, the air above and below the wing is affected. Of this large volume of air, a good proportion is given downward momentum. Newton’s equations of motion show that the lift force must equal the downward momentum given to the air. The laws also show that the energy given to the air depends upon the square of the velocity imparted. It therefore follows that to reduce the energy required for a given lift force, the velocity given to the air must be minimized by acting upon as large a volume (and hence mass) of air as possible.

This is something a fixed wing does very well, especially if it is long, as the main source of wasted energy occurs at the wing tips where there is turbulence due to the mixing of air flows from above and below the wing. It is difficult to find any evidence that the pioneers of flight realized the relevance of Newton’s equations, despite them being formulated almost two centuries previously. At the very least, though, there was an appreciation that as the atmosphere is very tenuous, one would need to act on large volumes of it.

Verne, however, seems to have had even less of such an appreciation. Until recently, the flying machine described in his story seemed so bizarre, that it seemed impossible to think of it being in any way prophetic. Rather than an early example of science fiction, the story was better regarded as science fantasy. This has all changed in the last few years, however, as more and more “Vernian” flying machines or drones take to the skies. As to why these might be so-called, consider the following. Their lift is derived from four or eight propellers revolving around vertical axes; control is obtained by speed variation of all or some of the propellers; and the power source is an electric battery. And finally, almost all drones, like Verne’s ship, make no attempt to increase efficiency by either reducing air velocity or reducing losses from the propellers. In essence, the main differences appear to be in size and weight. Even then, so many such machines have been produced that their total weight must soon approach whatever the Albatross was supposed to weigh. Well over a million Vernian drones were sold last year alone, just for civilian use.

Why then, in seeming disregard of Newton’s equations, has efficiency been abandoned to follow the ideas of Verne? The reason seems to be that of easy and precise control. Many uses of drones require remote piloting. This is cheaply done electronically, without the need for mechanical actuators, by varying the speeds of the propellers. Being small, drone propellers have little inertia and so can rapidly respond to control commands. This is important, but it is still curious that no more attention seems to have been paid to flying efficiently than did Verne for his proposed flying ship. He at least could imagine batteries providing unlimited energy.

The lithium-ion polymer batteries used today store far more energy per kilogram than any batteries available in Verne’s day, but there is still no energy to waste if duration is an issue. While several small propellers are more efficient than one small, faster-turning propeller (since more air at lower velocity provides the lift), every propeller will waste a lot of energy in tip losses. It would seem obvious to design these instead as ducted fans to reduce this loss. It could also be worth looking to increase air flow at the expense of velocity, either by outer ducts as in a bypass jet engine or perhaps by using the Coanda effect. With modern ultra-lightweight materials, the extra weight of such additions should be a good deal less than the extra lift they could give. Given a large and increasing worldwide market, it is surprising that the design of drones still follows an inefficient idea that Verne first put forward so many years ago.