Air speed and blowing pressure in woodwind and brass instruments: how important are they?

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Air speed is a hot topic in wind and brass performance. So is the blowing pressure that maintains it. To help with these discussions, this page discusses the basic science involved and gives possible ranges of values.

Air speed and air flow — and some values for both

To begin, let's distinguish air flow rate, measured in litres per second and air speed, measured in metres per second. Let's start with some values. First, imagine taking a deep breath and exhaling five litres in five seconds; this gives a value of 1 litre per second (1 L/s equals 10−3 m3s−1), which is a very high value for playing. For a low value, take the same volume, but exhale slowly enough to last fifty seconds: one tenth of a litre per second (0.1 L/s equals 10−4 m3s−1) is a low value. Air is compressible, but blowing pressures are usually rather less than 10% of atmospheric pressure, so it doesn't compress much in playing. Consequently, to an approximation that's good enough for now, the average volume flow out of the lungs equals that passing through the mouth, which equals that between the lips, and this rate will usually always be in the range 0.1 to 1 L/s.

The flow through a pipe increases if you increase the speed at which the air flows, or the cross section of the pipe: the average air speed multiplied by the cross section gives the average air flow rate. So let's consider a place in our mouth or throat where the cross section is about ten square centimeters (= 10−3 m2). Divide this into our range of likely flows and we get a range of air speeds from 0.1 to 1 metre per second — at that point with the large cross section. Now consider a location with low cross section, say a tenth of a square centimeter (= 10−5 m2). Such a value is possible for the lip aperture of a flutist, between a trumpetter's lips, or between a clarinet reed and mouthpiece. (An oboe reed cross section is even smaller.) If the tongue is held near the hard palate (in an 'ee' configuration), the cross section would have an intermediate value, say roughly 1 square centimetre,but depeding on the tongue shape.

Combine our range of flows (0.1 to 1 litres per second) and apertures (0.1 to 10 square centimetres): this tells us that the air speed will usually be in the range 0.1 m/s (a wide area of the mouth or throat with soft playing) to 100 m/s (for loud playing and a narrow aperture). It's worth repeating that dependence on aperture cross section: the average flow rate could simultaneously be 1 m/s in a flutist's throat and 100 m/s where it leaves the lips. (I've been talking about average values here: that's because we have air motion due to the steady exhalation and also due to sound waves. So I'm thinking of an average taken over a time of about a few hundredths of a second or more.)

(Because of the small aperture, oboes require very small flow rates. However, the fact that an oboist can play very long soft passages without breathing doesn't mean that you should: if the conductor goes blurry, you are about to faint.)

Blowing pressure

The blowing pressure in the mouth is what accelerates the air to high speed between the lips, and the kinetic energy of the high speed air is roughly equal to the work done on it by the blowing pressure. So the blowing pressure is proportional to the square of the average speed between the lips or flowing past the reed (P ≈ ½ρv 2 where ρ is the density of air and v the speed). One kilopascal (1 kPa) produces roughly 40 metres per second, but for 80 metres per second, one requires about 4 kPa. Measured blowing pressures usually range between 1 to 10 kilopascals (kPa) or 1% to 10% of atmospheric pressure, though (potentially dangerous) higher pressures are sometimes recorded. This range is enough to accelerate air from rest up to speeds between roughly 1 and 100 metres per second, consistent with our simple estimations above.

Generating and controlling that pressure is tricky and various muscles in the torso must be coordinated to produce a smooth rise, a steady supply and a smooth fall, just for a simple note. When the lung volume is near maximum, the elasticity of the distended torso, which can be helped by the muscles used to contract the lung volume for exhalation, if needed. At low lung volume, however, the torso's elasticity produces a small suction, so extra muscular tension is required. Sometimes, the diaphragm (which is usually used for inhalation) can be used to reduce pressure, if very low pressure is required for soft playing at high lung volume.

A warning for high-range trumpeters and perhaps oboists: sustained very high pressures are reported to affect circulation in the head and neck, with reports of possible consequences including stroke and eye damage. Be careful, and try to achieve the high range with embouchure rather that pressure; oboists should avoid very hard reeds.

Input power

While we're here, we should calculate the power. Take the range above of 0.1 to 1 litre per second (10−4 to 10−3 m3s−1). Multiply this by the pressure (1 to 10 kPa) to give the range of power provided by the player's breath to the instrument: here that gives 0.1 to 10 watts. This overestimates the range in practice, however, because high notes, which require higher pressure on most instruments, are usually played with lower flow, so power over a watt is rare. Instruments have typical efficiences of only 1% or so, so the output sound power is usually measured in milliwatts. However, one milliwatt at one metre distance gives about 80 decibels (how to relate power to dB).

How important are air speed and power in performance?

Air speed at the lips or mouthpiece is often important in the operation of the instrument. For the flute, both the register and the intonation are dependent on the time that the air jet from the lips takes to reach the edge of the embouchure hole, and that time is the distance travelled divided by the air speed. For brass instruments, fast moving air between the player's lips produces a suction that acts to close the lips during their vibration. A similar effect acts on the reeds of woodwind instruments.

For the flute (or recorder), the jet leaving the lips has a reasonably steady flow. For other instruments, however, the flow varies strongly because the aperture between lips or between reed and mouthpiece varies in size. In a brass instrument, and sometimes in reed instruments, the aperture closes completely during the vibration cycle, so the flow rate and the air speed fall briefly to zero.

Air speed is difficult to sense, and what musicians mean by it is often unclear. While the blowing pressure and the air speed past the lips or reed have direct effect on the performance, the different air speeds in different parts of the mouth have less effect. Pressure and speed are correlated, so it is possible that when a teacher asks a student to 'maintain air speed', perhaps s/he means 'maintain blowing pressure'. Another possibility is that saying this has the effect of getting the student to adopt a vocal tract shape whose acoustic resonances have some particular values or some other subtle effect.

Controlling and varying the air pressure in the mouth is a fundamental skill in wind and brass instrument performance. Loud playing in general requires higher pressure and/or higher flow. High pressure also gives faster attacks. When starting a note, the blowing pressure is often increased and the tongue is released during that increase. The pressure usually falls during the end of the last note of a phrase. On many instruments (the clarinet is an exception), higher pitch requires higher pressure at the same loudness. For flutes, blowing pressure is roughly proportional to frequency, and a flute's loudness is largely determined by flow, which is controlled via the size of the lip aperture. Variations in pressure and other control parameters are are used to produce accents and to give musical ‘shape’ to a phrase. Variations in pressure can also be used in vibrato.

This page grew out of a question on our FAQ. Let me know if it's not clear.

For further reading:

Acknowledgment

Our research work on saxophones is supported by the Australian Research Council, by Yamaha Music Australia and by Legere reeds.

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