Wednesday, April 11, 2007

Concorde and Bernoulli's principle

There were people in Reading who said they got used to the sight and sound of Concorde flying over at about 11:10am each day. These people are the living dead.

Concorde didn't just fly over each day; it ripped a deep sonic wound through the morning sky. It was a living, surging, accelerating phoenix, desperate to reach the greatest speed possible, impatient at being held below Mach 1 until it reached Oceanic airspace.

There was also the evening flight to New York, where Concorde could take-off just after the Sun had set at Heathrow, and actually overtake the terminator on the Earth's surface, forcing the Sun to rise in the West, the passengers then alighting in daylight at JFK. On one of these evening flights, I was out in the garden when I saw Concorde go past at low speed and low altitude to the South, off its normal flightpath, and with its undercarriage still down. It disappeared from sight, but the sound continued to rumble away. Presently it appeared again, travelling in the opposite direction as it swept over the top of me. I later read that the undercarriage had failed to retract, and Concorde had been forced to return to Heathrow. A harbinger of more serious problems to come...

But did Concorde generate lift via Bernoulli's principle? Bernoulli's principle states that an increase in fluid velocity corresponds to a decrease in pressure, and a decrease in fluid velocity corresponds to an increase in pressure. Whilst Bernoulli's principle is often invoked to explain the phenomenon of aerodynamic lift generated by the air flow around an aircraft wing profile, there are alternative explanations which employ, in some combination: the 'Coanda effect', the notion of circulation, and Newton's third law. These alternative explanations are, at the very least, equally legitimate to the Bernoulli-principle explanation, and, amongst aerodynamicists, are considered to be superior to the Bernoulli-explanation. There is also a long-standing popular misconception associated with the Bernoulli-principle explanation, which has been widely disseminated, but which is completely false.

The Bernoulli-principle approach explains the lift generated by an aircraft wing as the consequence of lower pressure above the wing than below, resulting in a net upward force upon the wing. The lower pressure above the wing corresponds to faster air flow above the wing, in accordance with the Bernoulli principle. The Bernoulli principle itself merely states that lower pressure corresponds to faster airflow, and vice versa; it does not state that faster airflow causes lower pressure, any more than lower pressure causes faster airflow. Faster airflow does not have causal priority over lower pressure. However, at this point, the misconceived popular explanation implicitly assigns causal priority to faster airflow, explains the lower pressure as a consequence of the faster airflow, and explains the faster airflow above the wing as a consequence of the fact that wings have greater curvature above than below, and the air flowing over the top therefore follows a longer path than the air flowing below. Conjoined with this is a curious argument, which invokes the notion of a 'packet' of air, and claims that a packet of air which is divided at the leading edge of a wing must rejoin at the trailing edge, hence the air traversing the longer path over the top must travel faster to rejoin its counterpart at the trailing edge. This 'path-length' explanation of lift does not require the air at the trailing edge of the wing to be deflected downwards, despite the downdraught which can be experienced directly beneath a passing aircraft. If this explanation were true, and the cause of lift was merely the asymmetrical profiles of the upper and lower surfaces of a wing, then it would not be possible for an aeroplane to fly upside-down. In addition, experiment demonstrates that air passing over the upper surface of a wing travels at such speed that packets of air divided at the leading edge of the wing fail to rejoin at the trailing edge.

One alternative explanation argues that aircraft wings generate lift because they deflect air downwards, and, by Newton's third law, an action causes an equal and opposite reaction, hence the wing is forced upwards. According to this explanation, the trailing edge of a wing must point diagonally downwards to generate lift, and this is achieved either by tilting the wing downwards with respect to the flow of air, or by making the wing cambered, or both. Air is deflected downwards by both the lower and upper surfaces of the wing. The lower surface deflects air downwards in a straightforward fashion, given that the wing is either tilted with respect to the direction of airflow, or the lower surface is of a concave shape. However, the majority of the lift is generated by the downwards deflection of the air which flows above the wing. This explanation then depends upon the Coanda effect, the tendency of a stream of fluid to follow the contours of a convex surface rather than continue moving in a straight line. The flow over the surface of a wing is said to remain 'attached' to the wing surface. An aircraft wing is said to 'stall' when the boundary layer on the upper surface 'detaches' or 'separates', and is no longer guided downwards by the contours of the upper surface. In this circumstance, the lifting force generated by the upper surface of the wing suddenly becomes very small, and the lifting force that remains is generally insufficient to support the weight of the aircraft. To create lift at low speed, an aircraft must increase the angle of attack of the wing, and the upper surface is carefully contoured to prevent flow detachment under these conditions.

(See 'Explanation and discovery in aerodynamics' for further details)

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