Hear my 'plane a comin'

This article came third in a popular science writing competition organized by the Times Higher Education Supplement and Oxford University Press

Aircraft make noise and that noise is instantly recognizable: Apocalypse Now would not have been the same with car horns backing the Wagner. Closer to home, the noise of civil aircraft near airports is annoying because of both its volume and its nature. The problem of understanding and controlling the noise made by propellers and fans is one which is becoming increasingly important as air traffic increases and people living near airports become less inclined to tolerate such noise.

The first thing to realize is that noise (or `sound', if you like it) is a tiny by-product of other physical processes. On a bus, you can often hear quite clearly the noise from the headphones of someone sitting three or four metres away. The headphones have little effect other than the noise they make: the wearer's head is not shaken by them yet they are audible at large distances. Given that a propeller is designed to exert large forces on the surrounding air, it would be surprising if it were not noisy. The engineering problem of reducing the noise, while retaining reasonable efficiency, is difficult precisely because the noise from propellers is such a small proportion of the total input energy. Acoustics is a science of extraordinary delicacy, as the headphones on the bus demonstrate. Even minuscule systems carrying tiny amounts of power can generate clearly audible noise. The challenge today is to understand the physics of noise generation by propellers and to use that understanding to reduce the noise reaching the ground and the passengers.

The process of noise generation by rotors (propellers and fans as well as helicopter rotors) relies on principles which may well be familiar, but with the complication that the source of the noise is moving in circles. Underlying all such prediction is the Doppler effect, familiar from school science lessons. The classic example is the sound made by a villain as he falls off a cliff after getting his just deserts. As he falls, the sound of his scream becomes quieter--he is moving further away--and drops in pitch. This drop in pitch is due to the Doppler effect. As the villain falls, he accelerates. As his speed increases, the pitch of his scream is shifted by an amount which depends on his speed: the sound is stretched by the movement of the source.

Think of the deranged pilot in Doctor Strangelove. At the end of the film, he rides a falling bomb into eternity. As a thought experiment, let us assume that in his eagerness to kill the pesky Reds, he throws hand grenades from the aeroplane, one per second. As long as he is in the aircraft, one grenade hits the ground every second. When he climbs aboard the bomb, he continues to throw hand grenades, still once per second. Now, each time he throws a grenade, he is a little closer to the ground than he was when he threw the previous one and the time between successive grenades is reduced slightly. The frequency of arrival of the grenades is increased because the source is approaching the arrival point--the stream of grenades has been Doppler shifted. If the pilot simply drops the grenades, so that they fall at the same speed as his bomb, the grenades all arrive at the same time (as does the bomb). This is equivalent to sonic boom: the source moves at the same speed as its sound and everything arrives at once.

The physics of sound radiation by rotors is analogous except that now the Doppler effect must be applied to sources moving in circles. To get an idea of how this changes things, transfer our pilot to a roundabout, still carrying his bag of hand grenades. As the roundabout turns, he throws grenades at some nest of sedition in the vicinity. During part of the rotation he is approaching his target and for part he is receding from it. The distance between the pilot and the target varies over one revolution, so the time of flight of the grenades varies correspondingly. The time between the arrival of two successive grenades varies over a revolution. If the speed of the roundabout is increased, then the difference between the flight times of two successive grenades can be equal to the interval between their departures. Then they arrive together in a brief sonic boom. If the roundabout is completely out of control, and speeds up even further, the target can be hit by more than two grenades simultaneously.

In order to predict the noise from a propeller, an essential stage in assessing a new design, the acoustician begins from a knowledge of the aerodynamics of the system to characterise the acoustic source (just how mad is the pilot? how big are his hand grenades?). The noise heard by people in the passenger cabin and on the ground then depends on the effect of motion on the sound from this source (how do the hand grenades fly?). This would be difficult enough were it not for the fact that aeroplanes do not fly in straight lines.

Noise from aeroplanes is usually only a problem near airports. At other stages of a flight, the ground is too far away for those on the ground to be affected. Passengers may not like the noise but at least they have the satisfaction of going somewhere. When an aeroplane is near an airport, it is usually taking off or landing, which means that it is not pointed in its direction of motion--very few aircraft land in a nose-first dive. This introduces a new complication in both the aerodynamics and the acoustics of the problem. The source is different and the sound radiates away differently. For high speed propellers, as used on modern commuter aircraft, the second effect is more important. Think of our pilot on a roundabout which is tilted, like one of the more thrilling funfair rides. As it turns, the pilot rises and falls during a revolution. Now the pilot's speed of approach depends on which side of the roundabout you are standing. If you stand on one side, he is rising as he approaches you. If you stand on the opposite side, he is sinking as he approaches. The effect of this vertical motion on the velocity of his hand grenades alters the Doppler effect and means that the exact rate of arrival of grenades depends on your position relative to the rotation of the roundabout. This is the so-called incidence problem (the aircraft is said to operate `at incidence' in this situation). This is important whenever the aircraft is changing its altitude, not just when it takes off or lands but at any time during a flight.

The first serious studies of propeller noise were carried out, naturally enough, by military research organisations. By 1919, the Royal Aeronautical Establishment was testing supersonic propellers. The noise is described as having ``peculiar and indescribably unpleasant physiological effects''. The research was motivated by considerations of what would now be called `stealth', the ``great importance of silencing aircraft for operations over enemy territory''. Since 1939, aircraft have been detected using electromagnetic rather than acoustic radiation and the military importance of noise from aircraft is of less relevance (although helicopter noise is still an important issue, and not just for film makers). If radar can see you coming from hundreds of miles away, the noise you make is not really an issue. For many years, civil aircraft noise was not a problem because there were very few civil aircraft. It is only since the beginning of mass tourism that large airports handling large numbers of aircraft have become widespread and that the issue of noise control has arisen.

One of the first large investigations into noise from civil aircraft which considered the effect of noise on the general population was carried out during the design of Concorde and its engines. Since then, noise has been an important factor in the design of all new aircraft and has led to a trade war between the European Union and the United States over the issue of `hushkits', devices fitted to old aircraft to make them comply with new noise regulations. The study of aircraft noise is of scientific interest (with links to other areas of science) but also of great commercial and environmental importance. The challenge is to develop an improved understanding of aircraft noise and to incorporate that knowledge into new designs.

What is to be done? ``The philosophers have only interpreted the world, in various ways; the point is to change it.'' The development of quieter aircraft is currently driven by the quite legitimate desire of people living near airports to get some sleep. If aircraft are not made quieter, they will not be allowed into airports. The other factor driving development of quieter aeroplanes is the desire of passengers, especially high-fare business-class passengers, for more comfortable flights. If aircraft are not made quieter, passengers will not want to fly in them. To some degree aircraft cabins can be made quieter by improving their acoustic insulation, but this only gets you so far and will never be a solution to the problem of exterior noise. Sooner or later, the powerplant has to be made quieter. Similarly, the one sure solution to the environmental noise problem--reducing the number of flights--is unacceptable. Even people who live near airports will not accept a reduction in noise if that reduction is at the price of a cheap summer holiday.

The methods currently being studied for reducing noise from propellers are all informed by a knowledge of the physics of the kind I sketched earlier. Returning to the bomb-flinging pilot, the obvious ways of reducing the noise are to give him smaller hand grenades which do less damage when they arrive; to have the grenades arrive at a lower rate; to catch the grenades before they land.

The first of these approaches means giving the propeller more blades. This may seem a perverse way of reducing the noise but there is method in it. A propeller is designed to give a certain amount of thrust. When an aircraft designer picks a propeller, she essentially looks in a catalogue and asks `What size of propeller do I need for this capacity of aircraft?'. The number of blades, from the aircraft design point of view, is irrelevant. But if you have more blades, the thrust is distributed over a larger area, so the load on each blade is lower. In effect, the pilot has more hand grenades but they are smaller. A second approach is to make the blades thinner. If you look at a modern aircraft, the propellers typically have six blades (rather than three or four) and they are thinner than the hefty wooden blades familiar from the movies. By reducing the blade thickness, the propeller can rotate at the high speeds needed for modern aircraft without disturbing the incoming flow any more than necessary. This allows reduces the generated noise. Finally, the same effect can be had by making the propeller bigger. Making the blades longer distributes the thrust over a larger area, in the same way as increasing the number of blades.

The second way of reducing the noise is to play around with the Doppler effect. The simplest thing to do is to have the propeller rotate more slowly. By cutting down the speed of the roundabout, the pilot's hand grenades arrive at a steadier rate and you never have to face two of them arriving at the same time, or very close together. Obviously, if the propeller has been made larger to distribute the load, this may have to happen anyway, which is one of the reasons why modern propellers have lots of blades, rather than a few big ones. A large number of shorter blades means that the aircraft can fly at high speed, without the propeller moving supersonically, whereas with a large propeller, you have to reduce the rotation speed if you don't want the propeller to move supersonically (which is why helicopters are limited in speed).

The last method of reducing the noise is analogous to catching the hand grenades in flight. The principle is that of cancelling noise with an inverted version of itself (if you wire one of the speakers on your stereo backwards, you can hear the effect). Such a method is already used to control the noise in some aircraft, by measuring the sound inside the cabin with microphones and playing a suitable signal through a set of loudspeakers to partially cancel the noise sensed by the measuring microphones. Such an approach is not possible for external noise (how would you generate a signal capable of cancelling noise over central London?) but a similar idea is useful. Conceptually, the simplest method on a twin-engine aircraft is to synchronize the propellers so that they partially cancel out each other's noise. This has some benefits for cabin noise but the external noise is not much reduced. The favoured method is to shape the propeller blade in such a way that one part of the propeller partially cancels the noise from another part.

If you take a look at a modern propeller aircraft, you will probably notice that the blades are not straight. Their leading edges are bent (`swept') for the same reason as the wings of Concorde are swept: to allow them to operate at high speed. The main reason for this shape is aerodynamic. Without such a profile, the propeller would simply be unable to operate efficiently at high flight speeds (remember, the propeller moves faster than the aeroplane). The detailed design of the sweep, however, depends in part on the acoustics. By shaping the blade appropriately, different parts of the blade throw their hand grenades at different times so that they collide in flight and cancel each other out.

The design of a modern propeller is a good example of the complexity of almost any piece of serious engineering. The physics are nominally well-understood, the requirements are clear and there is a well-established technological base for the design. Unfortunately, while the physics are well-understood, there are numerous competing influences which make it difficult to make predictions with confidence. Even the basic problem of predicting radiation from a rotating source cannot be considered definitively solved, in spite of its importance in acoustics, electromagnetism and astronomy.

The requirements for a given propeller are quite clear: ``X thrust at speed Y and no more than Z decibels''. These requirements are often contradictory, however, and the criteria for deciding priorities are ofen unclear. The problem today is that passengers want to spend less time in flight so aircraft have to be faster. This means that propellers are operating supersonically. At the same time, the people (literally) on the ground, want less noise in their houses. These two requirements are contradictory unless there is some radical improvement in the technology. The noise around an airport can be reduced by changing the way aircraft land and take off (a steep ascent means that a smaller area is affected by noise, for example) but as air traffic increases, this can only bring about short term improvements.

We have been building aircraft propellers for more than a century. The technology is established and the basic principles have been known for a long time. The reason for the difficulty is that we are working at the limits of what we know. Since 1919, we have been testing supersonic propellers and we have still to work out how to make them quiet. The aerodynamics of propellers are known: we now have to develop an equally good understanding, not of the physics of noise generation, but of the implication of the physics for the technology. The question is not one of predicting noise, but of understanding the effect of design parameters on the acoustics.

The importance of the problem is not confined to aeroplanes. One new development which will introduce new problems of noise prediction and control is the civil tiltrotor. This is an aircraft, under development in both Europe and the United States, which has helicopter-like rotors which tilt so that it can land and take off like a helicopter but cruise like an aeroplane. The advantage is that it will be able to fly right into city centres as helicopters can, but will be able to cruise at much higher speeds, comparable to those of a commuter aeroplane. This opens up the possibility of real city-centre-to-city-centre services at speeds which helicopters cannot hope to match. The aerodynamics of tiltrotors seem to be reasonably well-understood, although military versions have had a number of accidents recently, but it is noise control which will decide whether or not tiltrotors will be allowed to fly into densely populated areas. Like helicopters, tiltrotors experience an extreme version of the `incidence' problem described earlier, especially when they are in the process of switching from `helicopter mode' to `aeroplane mode', giving rise to new and unusual problems in noise prediction. Since this switch, by definition, will probably happen near city centres, its acoustics are of some interest.

The dialectic of demand for increased air traffic and reduced noise is leading to a synthesis of mathematical, physical and engineering ideas to produce new aircraft and new ways of operating them. The future looks hopeful, at least for those of us working on the problem.